Nanocrystalline Materials

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Progress in M aterials Science Vol. 33, pp. 223-315, 1989 0079-6425/89 0.00 + .50

Pr in ted in Gre a t Br it a in . Al l r ight s reserved © 1990 Perga mo n Press p ie

N N O C R Y S T L L I N E M T E R I L S

H G l e i ter

U n i v e r s i t / it d e s S a a r l a n d e s u n d I n s t i t u t f ii r N e u e M a t e r i a l ie n G e b / i u d e 4 3

D - 6 6 0 0 S a a rb r ii ck e n F . R . G .

C O N T E N T S

1. INTRODUCTION

1 1. Basic Ideas

2. SYNTrmSIS

2.1. Generat ion of Na nom eter-Sized Clusters

2.1.1. Vacuum synthesis

2.1 .2 .

Gas-phase synthesis

2 . 1 . 3 .

Condensed-phase synthesis

2.1.4. Capped clusters

2.1 .5 . Cluster arrays

2.2 .

Cluster Deposition

2.2 .1 . High speed deposition

2 . 2 . 2 .

Deposition by ionized cluster beams

2 . 2 . 3 .

Consolidation

2.3 .

Other Methods

2.3 1. High-energy milling

2 . 3 . 2 .

M ixal loy processing

2.3 .3 .

Deposition methods

2 . 3 . 4 .

Sol -ge l method

3. STRUCTURE

3.1 . Chemical Composi t ion

3.2 .

Density

3.3 .

Microstructure

3.3 .1 .

Nanocrystalline metals

3.3 .2 .

Nanocrystalline ceramics

3.4 .

Effect of Consolidation Pressure on Mierostructure

3.5 . Thermal Stabi l i ty

3.5.1. Nanocrystalline metals

3.6 . Atom ist ic Structure

3.6 .1 .

X-ray diffraction studies

3.6 .2 .

EXAFS s tud ies

3.7 . Spectroscopy

3.7 .1 .

Positron lifetime spectroscopy

3.7 .2 .

Muon spin rotation studies

3.7 .3 .

M6ssbauer spectroscopy

3.7 .4 .

Hydrogen absorption

3.7 .5 .

Ram an scattering

3.8 . Nanocrystalline Alloys

3.8 .1. Nanom eter-sized sandwich structures

4. PROPERTIES

4.1. Se lf Diffusion

4.2 .

Solute Diffusion

4 . 3 .

Enhanced Solute Solubility

4 . 4 . Speci f ic Heat

4.4 . I .

Low temperature measurements of the specific heat

4.5 .

Entropy

4.6 .

Thermal Expansion

4 . 7 .

Optical and Infra-Red Absorpt ion

4.8 .

Magnetic Properties

JrM S . / ~ - A 2 2 3

2 2 4

2 2 4

2 2 8

2 2 8

2 2 8

2 2 9

2 3 2

2 3 4

2 3 4

2 3 5

2 3 5

2 3 6

2 3 6

2 3 8

2 3 8

2 3 9

2 3 9

2 3 9

2 4 0

2 4 0

2 4 0

2 4 2

2 4 2

2 4 6

2 4 8

2 4 9

2 4 9

2 5 4

2 5 5

2 5 9

2 6 1

2 6 1

2 6 2

2 6 3

2 6 7

2 7 0

2 7 1

2 7 7

2 7 8

2 7 8

2 7 9

2 8 2

2 8 2

2 8 5

2 8 6

2 8 8

2 8 8

2 9 0



224 PROGRESS IN MATERIALS SCIENCE

4.9. E l e c t r i c a l R e s i s t i v i ty 292

4 .10. M echan ica l Prope r t ies 294

4 .10 . I . E la s t ic p roper t ies 294

4 .10.2 . ln tern a l f r ic t ion 296

4.10.3. H a r d n e s s a n d f r a c t u r e 297

4.10.4.

Low tem pera ture duc t i l i t y o f nanocrys ta l line ceram ics

298

4.10. 5 . Pla st ic deformation o f nanocrysta ll ine m eta ls 301

4 .1 I . K ine t ic E f fec t s 302

4.12. Recrys ta l l i za t ion 304

4.13. Rad ia t ion Damage 305

5. NANOGLASSES 305

ACKNOWLEDGEMENTS 307

REFERENCES 308

1. INTRODUCTION

In ma te r i a l s s c i ence and so l id s t a t e phys ic s p rogre s s ha s been made in many ca se s by one

o f t h e f o ll o w i n g tw o a p p r o a c h e s . E i t h e r b y d e v e l o p in g a n d a p p l y i n g n e w m e t h o d s o f

inves t iga tion o r by p repa r ing ma te r i a l s w i th nove l s truc tu ra l f e a tu re s and /o r p rope r t i es .

T r a n s m i s s i o n e l e c t r o n m i c r o s c o p y , M 6 s s b a u e r s p e c t r o s c o p y , a n d t u n n e l i n g m i c r o s c o p y a r e

exam ple s fo r the f i r st app roach . The d i s cove ry o f me ta l l ic g las ses , h igh t em pera tu re

supe rconduc to rs o r quas i -c rys ta l s r ep re sen t deve lopmen ts re su l t ing in ma te r i a l s w i th nove l

s t ruc tu ra l f e a tu re s an d /o r p rop e r t i e s . In the ca se o f nanoc rys ta l l ine ma te r i al s , t he gene ra t ion

of sol id s w i th new a tom ic s t ruc tu re s and p rope r t i e s w as a t t empted by u t il iz ing the a tom ic

a r rangem en ts in the co re s o f de fec t s such a s g ra in boun da r i e s , i n t e rphase b oun da r i e s o r

dis loca t ions .

1.1.

asic Ideas

The s t a t e o f lowes t free ene rgy o f a so l id a t low tem pera tu re i s the pe r fec t c rys ta l , i .e . a

th ree -d imens iona l pe r iod ic o r quas i -pe r iod ic a r ray o f a toms .* Ho we ve r , s ince the ea r ly pa r t

o f th is c en tu ry i t is kno wn tha t so l id s dev ia ting f rom th is pe r fec t ly o rde red s t ruc tu re m ay

exh ib i t a t t r a c tive fea tu re s . In fac t, nu m erous s t ruc tu ra l s tud ie s o f so lid s have revea led a w ide

va r i e ty o f dev ia tions . Th e va r iou s dev ia t ions m ay be d iv ided in the fo l lowing two c las se s . The

f i rs t c l a ss is ob ta ined by the rm a l ly d i so rde r ing the c rys tal l ine s t ruc tu re o f a ma te r i a l and by

f reez ing- in the d i so rde red s t a t e by means o f quench ing . G la s se s , e .g . v i t r eous qua rz o b ta ined

by rap id ly so l id i fy ing the me l t , t he pa r t i a l ly o r fu l ly d i so rde r s t a t e o f o rde red a l loys gene ra ted

by quench ing the d i so rde red ma te r i a l f rom h igh t empera tu re s o r the f rozen- in o r i en ta t iona l

d i so rde r in ce r t a in molecu la r compounds , a re s t ruc tu re s be long ing to th i s c a tegory . As an

example , a tw o-d im ens iona l h a rd sphe re mode l o f a g la s s is show n in F ig . 1 in comp ar i son

to a pe r fec t c rys ta l o f ha rd sphe re s F ig . 2 ). In m os t m a te r i a ls w i th g la s sy s t ruc tu re s , t he

dens i ty and the nea re s t ne ighbor coord ina t ion va r i e s typ ica l ly by a few pe rcen t r e l a t ive to

the perfec t c rys ta l .

In the s econd c la s s o f d i so rde red ma te r i a ls , t he dev ia t ion f ro m the pe r fec t c rys ta l i s induced

by inco rpora t ing de fec t s such a s vacanc ie s , d i s loca t ions , g ra in o r in t e rphase bounda r i e s . As

m ay b e seen f rom F igs 3 , 4 and 5 , the a tomic d i sp lacemen ts a s soc ia t ed wi th the inco rpo ra t ion

of de fec t s s igni f ic an tly a l t e rs the a tom ic dens i ty and coord ina t ion in the de fec t co re reg ion .

Fo r exam ple , the a tomic den s i ty in the co re reg ion o f g ra in bo unda r i e s i s r educed typ ica l ly

In the case of certain polymeric solids, steric reasons prevent the formation of perfect crystals, e.g. due to bulky

atactic side groups.



N A N O C R Y S T A L L I N E M A T E R I A L S

5

Fl6. 1. H ard sphere mode o f a two-dimensional glassy

structure. The atomic density and nearest neighbor

coordination is slightly changed relative to the perfect

crystal lattice (Fig. 2).

FIG. 2. Ha rd sph ere model of the two-dimensional

structure of a perfect crystal (hexagonal array of atoms).

b y a b o u t 15 t o 3 0 ( cf . F i g s 4 a n d 5 o r R e f . 1 4) w h i c h is a l m o s t a n o r d e r o f m a g n i -

t u d e m o r e t h a n t h e d e n s i ty d i f f er e n c e b e t w e e n t h e g la s s y a n d c r y s t a l li n e s ta t e in m o s t

m a t e r i a ls . T h e s t r u c t u r a l c h a n g e s , c a u s e d b y th e i n c o r p o r a t i o n o f d ef e c ts , d i ff e r f r o m

t h e s t r u c t u r a l c h a n g e s o b t a i n e d b y f re e z in g - in t h e h i g h t e m p e r a t u r e a t o m i c a r r a n g e m e n t

o f th e s a m e m a t e r i a l b e c a u s e b o t h s t r u c t u r e s h a v e d i f fe r e n t p h y s i c a l o r ig i n . T h e h i g h -

t e m p e r a t u r e s t r u c t u r e i s d u e t o t h e t h e r m a l e n e r g y s t o r e d i n th e m a t e r i a l w h e r e a s t h e

d e f e c t c o r e s t r u c t u r e i s c a u s e d b y t h e i n c o m p a t i b i l i t y i n t r o d u c e d i n t o t h e l at ti c e in t h e

f o r m o f a d e f e c t a n d d o e s n o t r e q u i r e a n y t h e r m a l e n e r g y . I n f a ct , in t h e s pe c if ic c a s e o f

g r a i n b o u n d a r i e s , t h e r e i s a m p l e e x p e r i m e n t a l a n d t h e o r e t i c a l e v i d e n c e ~5) t h a t t h e a t o m i c

s t ru c t u r e o f t h e b o u n d a r y c o r e is a t w o - d i m e n s i o n a l p e r i o d i c a r r a n g e m e n t o f a to m s ( cf .

F i g s 4 a n d 5 ). I t c a n n o t b e d e s c r i b e d i n t h e f o r m o f a t h in d i s o r d e r e d o r l iq u i d - li k e g l a s sy

FIG. 3. Edg e dislocation in a simple cubic crystal. In the

dislocation core, the atomic density and coordination is

changed in comparison to the perfect cubic lattice,

FIG. 4. Atomic structure of a Z = 5, 310 grain b oun dary

in N iO deduced fro m the high resolution electron m icro-

graph show n in Fig. 5, section A. ~4)



226 P R O G R E S S I N M A T E R I A L S S C I E N C E

P IG . 5 . E l e c t r o n m i c r o g r a p , o f a s y m m e t r i c Z = 5 , 3 1 0 g r a i n b o u n d a r y i n N i O . ~ 4) T h e b l a c k r e g i o n s

r e p r e s en t t h e a t o m i c p o s i t io n s . I n t h e b o u n d a r y c o r e t h e a t o m i c d e n s i t y a n d c o o r d i n a t i o n i s c h a n g e d

i n c o m p a r i s o n t o t h e p e r f e c t l a tt i c e T h e b o u n d a r y s t r u c t u r e s i n t h e f a c e ts A a n d B a r e d i f f er e n t d u e

t o t h e v e r t ic a l d i s p l a c e m e n t o f t h e b o u n d a r y p l a n e r e l a ti v e t o t h e t w o c r y s t a l s. ~ 4)

layer which indicates in another way the difference between thermally induced disorder and

the structural changes induced by incorporating defect cores. As a matter of fact, the

boundary core structure is the atomic arrangement of minimum energy in the potential

field of the adjacent crystals. As a consequence, the boundary core structure depends on

the interatomic bonding forces and the boundary crystallography (i.e. the misorientation

between both crystals, the boundary inclination and the translational position of both crystals

relative to one another). Hence in any given material (e.g. NiO) a very large variety of

grain boundary core structures exist. One example is shown in Fig. 5. The small vertical

displacement of the boundary plane in the section A relative to the section B results in two

different core structures although all other parameters (crystal misorientation, boundary

inclination, etc.) are unaltered. In conventional polycrystals (grain size typically /> 1 #m) the

atomic structures of the boundary cores are not noticed in most structural investigations such

as X-ray diffraction, EXAFS, spectroscopic studies, because the fraction of atoms located

in the core o f the boundaries is 10 -4 or less. However, i f one generates a mater ial which

contains such a high density of defects that 50% or more of the atoms are situated in the

cores of defects, then the atomic structure o f the entire material depends on the core structures

of the defects.

It is the basic idea°) of nanocrystalline materials to generate a new class of disordered

solids by introducing such a high density of defect cores that 50% or more of the atoms

(molecules) are situated in the cores of these defects. Depending on the type of defects utilized

(grain boundaries, interphase boundaries, dislocations, etc.) nanocrystal ine materials with

different structures may be generated. Nevertheless, all of these materials have the following

microstructural feature in common. (1'2,*~) They consist of a large volume fraction of defect

cores and (strained) crystal lattice regions? As an example, Fig. 6 shows the structure of a

two-dimensional nanocrystalline material. The crystals are represented by hexagonal arrays

of atoms with different crystallographic orientations. Hence the atomic structures of the

core regions of the various boundaries between the crystals are different because their

structure depends on the crystal misorientations and boundary inclinations. The boundary

core regions (open circles, Fig. 6) are characterized by a reduced atomic density and

interatomic spacings deviating from the ones in the perfect lattice. The physical reason

for the reduced density and the non-lattice spacings between the atoms in the boundary cores



N A N O C R Y S T A L L I N E M A T E R IA L S 2 2 7

FIG. 6. A tomic structure o f a two-dimen sional nanocrystalline material. The structure w as com puted

by following the proc edure given in Re f. 13. The interaction between the atoms w as represented by

a M orse potential fitted to gold (cf. Re f. 13). The atoms in the centers of the crystals are indicated

in black. The o nes in the bound ary c ore regions are represen ted by o pen circles.

i s t h e m i s f it b e t w e e n t h e c r y s t a l l a tt ic e s o f d i f fe r e n t o r i e n t a t i o n j o i n e d a l o n g c o m m o n

i n t e rf a c e s . * I n o t h e r w o r d s , t h e n a n o c r y s t a l l i n e s y s t e m p r e s e r v e s in t h e c r y s ta l s , a s tr u c t u r e

o f lo w e n e r g y a t t h e e x p e n s e o f t h e b o u n d a r y r e g i o n s w h i c h a r e r e g i o n s a t w h i c h a l l t h e

m i s f it is c o n c e n t r a t e d s o t h a t a s tr u c t u r e f a r a w a y f r o m e q u i l i b r i u m i s f o r m e d . A s t r u c t u r e

o f s i m i l a r h e t e r o g e n i t y i s n o t f o r m e d i n t h e r m a l l y i n d u c e d d i s o r d e r e d s o l id s s u c h a s g la s s es .

T h e m i s f it b e t w e e n t h e c r y s t a l s n o t o n l y r e d u c e s t h e a t o m i c d e n s i t y in t h e i n t e r fa c i a l r e g i o n

i n c o m p a r i s o n t o t h e p e r f e c t la t ti c e b u t a l s o c a u s e s s t r a in f ie ld s t o e x t e n d f r o m t h e b o u n d a r y

c o r e r e g i o n s i n t o t h e c r y s t a l l i t e s . T h e s e s t r a i n f i e l d s r e m o v e t h e a t o m s f r o m t h e i r i d e a l

l a tt ic e s it es . T h e a m o u n t o f a t o m i c d i s p l a c e m e n t d e p e n d s p r i m a r i l y o n t h e i n t e r a t o m i c

p o t e n t i a l . H e n c e d i f fe r e n t m a t e r i a l s a r e e x p e c t e d t o e x h i b i t d if f e r e n t a t o m i c s t r u c t u r e s i n t h e

n a n o c r y s t a l l i n e s t a t e .

S o f a r , al l p u b l i s h e d s t u d ie s o f n a n o c r y s t a l l i n e m a t e r i a l s h a v e f o c u s e d a t t e n t i o n o n

n a n o c r y s t a l l i n e m a t e r i a l s o b t a i n e d b y i n t r o d u c i n g a h i g h d e n s i t y ( t y p i c a l l y

1 19

p e r c m 3 ) o f

g r a i n ( o r i n t e r p h a s e ) b o u n d a r i e s . I n o r d e r t o a c h i e v e s u c h a h i g h b o u n d a r y d e n s i t y , a c r y s t a l

s iz e o f a f e w n a n o m e t e r s ( 1 0 n m o r l e ss ) is r e q u i r e d . N a n o c r y s t a l l i n e m a t e r i a l s h a v e a l s o b e e n

c a l l e d u l t r a - f i n e g r a i n e d m a t e r i a l s , (1) n a n o p h a s e m a t e r i a l s (5) o r n a n o m e t e r - s i z e d c r y s t a l l i n e

m ate r i a l s . (3)

I n o r d e r t o l i m i t t h e l e n g t h o f th i s re v i e w , w e s h a l l f o c u s a t t e n t i o n p r i m a r i l y o n e q u i a x e d

n a n o c r y s t a ll in e , b u l k m a t e r i a l s a n d t h u s e x c l u d e m u l t i la y e r a n d f i la m e n t r y n a n o m e t e r - s i z e d

s t r u c t u r e s a s w e l l a s t h i n f i lm s , A t t h e e n d o f t h is r e v i e w a b r i e f s e c t i o n w i ll b e a d d e d o n a n

a p p a r e n t l y n e w l y e m e r g i n g f i e ld o f n a n o m e t e r - s i z e d s t r u c t u r e s c a l l e d n a n o g l a s s e s . (t°-12) T h e

d e v e l o p m e n t o f o u r u n d e r s t a n d i n g o f n a n o c r y s t a l l in e m a t e r i a l h a s b e e n d o c u m e n t e d i n

sev e ra l r ev i ew s . (2'¢-~°'~6) T h ese r ev i ew s c l ea r l y i n d i ca t e t h a t m an y o f t h e s t u d i e s p e r f o r m ed so

f a r a r e h a m p e r e d b y d i ff ic u lt ie s t y p i c a l to n e w l y d e v e l o p i n g a r e a s ; f o r e x a m p l e , b y d i f fi cu l ti es

*The atomic density in the boun daries of a nanocrystalline material is probably lower than in bicrystals or polycrysals

with large crystal sizes due to the limited rigid body translationsm3 n nanocrystalline materials. The b oundaries

of different atomic structure formed on opposite sides of a nanom eter-sized crystal in a nanocrystalline material,

require different rigid body translations to max imize the atom ic density in both interfaces. If the crystal size is

a few nanom eters, the different rigid body translations w ould req uire unrealistic elastic distortions of the small

crystal. This is not the c ase in bicrystals or coarse-grained polycrystals.



8

PRO G RESS I N M TERI LS SCI EN CE

i n spec imen p repa ra t ion , by a la ck o f r e l iab le me thod s fo r spec imen cha rac te r iza t ion and by

the p re sen t l imi t a t ions in mode l ing such sys t ems theo re t i c a l ly .

The pape r i s o rgan ized a s fo l lows . Sec t ion 2 dea l s w i th the me thods ava i l ab le to gene ra t e

nanoc rys ta l l ine ma te r i a l s . In the subsequen t sec t ions the s t ruc tu re (mic ros t ruc tu re , a tomic

a r rangem en t , Sec t ion 3 ) and the p rope r t i e s o f nanoc rys t a l l ine m a te r ia l s (Sec t ion 4) w ill be

cons ide red .

2. SYNTHESIS

So fa r , the syn thes i s o f nanoc rys t a l l ine ma te r i a l s ha s been ca r r i ed ou t m os t f r equen t ly by

assembl ing p re -gene ra ted sma l l c lu s t e rs by means o f in s i tu con sol id a t ion and s in te ring . Thu s,

we sha l l f i r s t r ev iew the va r ious t e chn iques be long ing to th i s c a t egory . Subsequen t sec t ions

wi l l be devo ted to the p rocedure s wh ich do no t r equ i re p re -gene ra ted c lus t e r s . Fo r r ev iews

of the syn thes i s o f sma l l c rys t a l s we re fe r to Re fs 17 -24 .

2 .1 . G e n e r a ti o n o f N a n o m e t e r S i z e d C l u s te r s

The t echn iques fo r the gene ra t ion o f nanome te r - s i zed c lus t e r s m ay be d iv ided in to th ree

b ro ad ca tegori e s : °7> vacuum , ga s -phase and conde nsed-p hase syn thes i s.

2 .1 .1 . V acuu m syn thes i s

2 . I . 1 .1 . Spu t ter ing . W h e n i o n s o f a s u i t a b le s u b s t a n c e ( f o r e x a m p l e, t h o s e o f A r o r K r ) ,

a cce le ra t ed to h igh ene rg ie s , a re d i rec t ed toward a su r face , a toms and c lus t e r s , bo th neu t ra l

and ion ic , a re e jec t ed . Th i s me th od o f vapor i z ing ma te r i a l s i s c a l led spu t t er ing . T he ra t io o f

a t o m s t o c l us t er s a n d i o n s t o n e u t ra l s p r o d u c e d d e p e n d s o n t h e m a s s a n d e n e r g y o f t h e

p ro jec t il e ion and a va r i e ty o f o the r expe r im en ta l pa rame te r s . To day , p r im ar i ly two types o f

spu t t e r ing sou rce s a re in use . Ene rge t i c ions a re p roduced in an ion gun and acce le ra t ed

tow ard the su rface o f the ta rg e t mater ia l/25> Cluste rs a re e jec ted d i rec t ly f rom the surface as

a sma l l f r ac tion o f the ove ra ll ma te r i a l spu t t e red . The f rac t ion o f a tom s inco rpo ra ted in the

la rge-s ized c luste rs pr od uc ed wi th th is source i s ra ther low, typica l ly 10 -4 or less of the to ta l

n u m b e r o f a t o m s s p u t te r e d .

A l t e rna t ive ly , ho l low ca tho de spu t t e r ing m ay be u t ili zed326~ The ma te r i a l t o be

vapor i zed i s f ab r i ca t ed in to a cy l ind r i ca l cup pe r fo ra t ed a t one end . A coax ia l e l ec t rode

i s p l aced wi th in the cup and a h igh vo l t age i s imposed be tween the cy l inde r and the

in te rna l e l ec t rode so a s to make the fo rmer the ca thode . When gas i s pa ssed th rough the

sys tem, a d i scha rge i s s truck and the ion ized gas ( l a rge ly in the fo rm o f ca t ions) i s a cce le rat ed

tow ard the inne r su r face o f the cy linde r, vapor i z ing a po r t ion o f it . The va por i s con f ined

fo r a pe r iod o f time wi th in the ho l low ca thode , and i f i t beco mes supe rsa tu ra t ed , c lus t e r

g r o w t h c a n o c c u r . L i n e b e r g e r e t al. ~27~have used such a sou rce e f fec tive ly to ma ke and s tudy

clusters.

A d ra wb ack to spu t t e r ing i s t ha t i t u sua l ly p rodu ces sma l l amou n t s o f c lus te r s and c lus t e r

in t ens i ty d i s t r ibu t ions tha t dec rea se exponen t i a l ly w i th inc rea s ing c lus t e r s i z e . Mos t app l i -

ca t ions o f th i s t e chn ique a re fo r c lus t e r i on fo rma t ion in s ide o r in p rox imi ty to a mass

spec t rome te r . In a f ew ca ses , no tab ly c a rbo n an d s il icon , spu t t e r ing y ie lds b road e r d i s t r i-

bu t ions o f c lus t e r i ons .

2 .1 .1 .2 . Lase r ab la t i on . This t e chn ique use s h igh -power p u l sed l a se r s to vapor i ze c lus t e r i ons

f rom so l id su r face s. The wave leng th o f the l a ser l igh t ha s to be ad jus t ed to the ma te r i a l .




229

Fo r t he ab l a t i on o f m e t a l s , U V - l a se r s ( e .g . exc i m er la s e r s ) a r e r eq u i r ed a s t he r e f l e c t iv i t y o f

m an y l i qu i d m e t a l su r f ace s i n t he I R o r v i s ib l e r eg i m e i s c l o se t o 100% . I n one app l i ca t i on , ~2s)

l a se r a b l a t i o n w a s u t i l i ze d d i re c t l y i n s id e a F o u r i e r - t r a n s f o r m i o n - c y c l o t r o n - r e s o n a n c e m a s s

s p e c t r o m e t e r , a l l o w i n g m o n i t o r i n g o f th e c l u s t e r i o n s a n d t h e i r r e a c t i o n p r o d u c t s w i t h a n

i n t r o d u c e d r e a g e n t g a s .

2.1.1.3.

Liq u id m e ta l i on sources.

L i q u i d - m e t a l io n s o u r c e s a r e t y p i c a l l y f o r m e d b y a

s m a l l t u n g s t e n w i r e w i t h i ts t ip s h a p e d t o a r a d i u s o f a f e w m i c r o n s a n d w e t t e d w i t h a

m e t a l a b o v e i t s m e l t i n g p o i n t . W h e n t h i s t i p i s b r o u g h t t o a f e w k i l o v o l t s p o t e n t i a l

w i t h r e s p e c t t o a g r o u n d e d a p e r t u r e , t h e l i q u i d i s p u l l e d u p i n t o a c o n e a s t h e e l e c t r o s t a t i c

f o r ce s exceed t he su r f ace t ens i on f o r ce s o f t he l i qu i d . Wi t h t he ve r y h i gh e l ec t r i c f i e l d a t

t h e e n d o f t h e c o n e , io n s a r e e m i t t e d b y f ie ld e v a p o r a t i o n . A t o m i c i o n s a r e t h e p r i m a r y

em i t t ed spec ie s , bu t t he r e i s a l so s i gn i f i c an t em i s s i on o f ion i zed c l u s t e r s and even i on i zed

d r o p l e t s . T h e s e s o u r c e s w o r k f o r t h o s e m e t a l s w h o s e v a p o r p r e s s u re s a r e s u f f ic i e n tl y l o w

a t t h e i r m e l t i n g p o i n t s n o t t o i n t e r f e r e w i t h m a i n t a i n i n g t h e e x t r a c t i o n v o l t a g e , e . g . A u ,

G a a n d I n .

T h e p r o d u c t i o n o f i o n i z e d c l u s te r s ( d r o p le t s ) f r o m l i q u i d - m e t a l io n s o u r c e s i s r a t h e r l i k e

a n i n k - d r o p p r i n t e r w i th a m e t a l i n k . A m i c r o n d i a m e t e r b e a m o f fo c u s e d c h a r g e d g o l d

d r op l e t s h a s b een r ea l iz ed i n F r an ce (29) an d t he w r i t i ng o f m e t a l l i c l ine s w i t h suc h a be am has

b e e n s u g g e s t e d , t~7) B e c a u s e t h e d r o p l e t s c o n t a i n m i l l i o n s o f a t o m s e a c h , t h e d e p o s i t i o n r a t e

m i g h t b e a t t r a c ti v e , e v e n in t h i s s e ri a l p i x el m o d e o f p a t t e r n f o r m a t i o n . N o t m u c h h a s y e t

b e e n d o n e t o c h a r a c t e r i z e th e m a t e r i a l p r o d u c e d w i t h th i s k i n d o f b e a m .

2 .1 .2 . Gas phase s yn the s i s

2.1.2.1.

Ine r t gas condensa t ion .

I n t h e c a s e o f i n e r t g a s c o n d e n s a t i o n t h e a g g r e g a t i o n o f

v o l a t il i z e d m o n o m e r s i n t o c l u s t e rs is a c h i e v e d b y (1 ) e s ta b l i s h in g a m o n o m e r p o p u l a t i o n , (2 )

c o o l i n g t h e m o n o m e r s b y co l li si o ns w i t h c o l d i n e rt g a s a t o m s , a n d (3 ) g r o w t h o f c lu s te r s

b o t h b y a d d i t i o n o f m o n o m e r t o i n d i v id u a l cl u st e rs a n d b y a g g r e g a t i o n d u e t o c o ll is io n s

b e t w e e n c l u s t e r s . S o f a r , o v e n s o u r c e s , s p u t t e r i n g s o u r c e s , e l e c t r o n g u n e v a p o r a t i o n , l a s e r

e v a p o r a t i o n , p y r o l y s i s , h y d r o l y s i s o r s u p e r s o n i c e x p a n s i o n h a v e b e e n u t i l iz e d .

2.1.2.2.

Oven sources.

T h e s i m p l e s t t e c h n i q u e f o r e s t a b l i s h i n g a m o n o m e r p o p u l a t i o n i s b y

m e a n s o f a h e a t e d c r u c ib l e o r o v e n . A w i d e v a r ie t y o f o v e n - b a s e d s o u r c e s h a s b e e n d e v e l o p e d .

D i r e c t e v a p o r a t i o n i n t o a g a s t o p r o d u c e a n a e r o s o l o r s m o k e o f c l u s te r s h a s b e e n e x t e n s iv e l y

s t ud i ed by s eve r a l g r oups . ¢3°'3~) N ea r t he sou r ce , sm a l l c l u s t e r s o f f a i r l y un i f o r m s ize a r e

o b s e r v e d . F a r t h e r f r o m t h e s o u r c e t h e c lu s t e rs b e c o m e l a r g e r w i t h a b r o a d e r s iz e d i s t r ib u t i o n .

F i n a l l y , a t s o m e l i m i t i n g d i s t a n c e f r o m t h e o v e n , w h i c h d e p e n d s o n i n e r t g a s p r es s u r e a n d

e v a p o r a t i o n r a t e , t h e c l u s te r s r e a c h a l i m i t i n g si ze w h i c h i n c r e a se s w i t h i n c r e a s in g e v a p o r a t i o n

r a t e a n d w i t h t h e a t o m i c w e i g h t o f t h e i n e r t g as .

T h e m e a n c l u s t e r siz e i n s u c h a s o u r c e c a n b e c o n t r o l l e d b y v a r y i n g t h e e v a p o r a t i o n r a t e

f r o m t h e o v e n a n d t h e p r e s su r e o f th e i n e r t g a s in th e e v a p o r a t i o n c h a m b e r . C l u s t e rs w i t h

m e a n d i a m e t e r s a s sm a l l a s 3 - 4 n m h a v e b e e n g e n e r a t e d b y t h i s p ro c e s s. T h e c l u s t er s e x h i b it

a l og - no r m a l s iz e d i s t r i bu t i on . Su ch a d i s t r i bu t i on i s cha r ac t e r i s t i c o f c l u s t e r - c l u s t e r

a g g r e g a t i o n w h i c h i s a l s o s u g g e s t e d b y t h e d i f f e r e n t m o r p h o l o g y o f s m a l l a n d l a rg e c l u st e rs .

T h e m e a n c l u s t e r si ze c a n b e r e d u c e d a n d t h e s iz e d i s t r i b u t i o n s h a r p e n e d b y i m p o s i n g a f o r c e d

c o n v e c t i v e f l o w o n t h e i n e r t g a s . S e v e r a l s o u r c e s b a s e d o n t h i s c o n c e p t h a v e b e e n d e v e l -

o p e d . 32-34) Th e s ho r t r e s i dence t i m e o f t he c l u s t e r s c l o se t o t h i s sou r ce r educes c l u s t e r - c l u s t e r

a g g r e g a t i o n r e s u l t in g i n s m a l l e r c l u s te r s a n d a n a r r o w e r s iz e d i s t r ib u t i o n . F o r e x a m p l e , a

m ul t i p l e - e xpa ns i o n c l u s t e r sou r ce ~35) p r o duc es a s iz e d i s t r i bu t i on w i t h a c on s t an t f u l l w i d t h



23 PRO G RESS I N M TERI LS SCI EN CE

a t ha l f max imu m of le s s than 0 .5 nm and a con t ro l l ab le m ean s i ze rang ing f ro m le ss than 1 nm

t o a p p r o x i m a t e l y 5 n m .

Na tu ra l ly , sub l ima t ion m ay a l so be u ti l iz ed in s tead o f evap ora t ion fo r so l id s w i th h igh

v a p o r p r e s su r e s. T h i s a p p l ie s , f o r e x a m p l e , t o M g O w h i c h h a s b e e n h e a t e d i n 2 00 P a o f H e

to tem per a tur es o f a ro un d 1 ,600°C M gO m el ts a t 2 ,852°C). 36) The m ater ia l which subl imes

w a s f o u n d t o b e o x y g e n d e f ic ie n t, b u t i s f u ll y c o n v e r t e d t o s t o i c h io m e t r ic M g O b y s u b s e q u e n t

e x p o s u r e t o o x y g e n in t r o d u c e d i n t o t h e v a c u u m c h a m b e r .

Oven-based source s su f fe r f rom the fo l lowing d rawbacks . The t empera tu re l imi ta t ions

i m p o s e d b y t h e o v e n o r c r u c i b l e m a t e r i a l ; c h e m i c a l r e a c t i o n s o c c u r b e t w e e n m a n y m e t a l s

and the f requen t ly used re f rac to ry me ta l c ruc ib le s ; inhomogeneous t empera tu re d i s t r ibu t ions

ex i st i n the mol ten m e ta l l e ad ing to unsa t i s fac to ry co n t ro l an d rep roduc ib i l ity ; the p roduc t ion

of a l loy c lus ter s i s r e s t r ic t ed b y the d i f fe ren t a c tiv i ti e s o f the cons t i tuen t s ; eva pora t ion o f

t echno log ica l ly in te re s ting ce ramics such a s A1203 i s l imi ted by the ox id a t ion o f r e f rac to ry

boa t s .

T h e p r e p a r a t i o n o f o x i d e c er a m i c s b y o v e n - b a s e d s o u r c e s h a s b e e n a c h i ev e d b y e v a p o r a t i n g

t h e m e ta l li c c o m p o n e n t T i , F e ) i n H e s o t h a t a n a n o m e t e r - si z e d m e t al p o w d e r w a s o b t ai n e d .

The loo se me ta l l ic pow der was subseque n t ly ox id ized by in t roduc ing o xygen typ ica l p re s su re

2 kPa ) in to the cham ber . °7~) X- ra y d i f f rac tion o f the a s -p repa red TiO 2 s ample s show ed ~°)

tha t the s t ab le ru t i l e phase was the on ly phase p re sen t , w i th no ev idence fo r un reac ted T i o r

o t h e r T i - o x i d e ph a s es . T h e c o m p o s i t i o n o f t h e s am p l e w a s d e t e rm i n e d b y R u t h e r f o r d

backsca t t e r ing ana lys i s to be oxygen de f i c i en t in the a s -p repa red s t a t e , T iOi .7 , bu t a f t e r

s in te r ing a t 300°C i t becam e nea r ly s to ich iome t r i c , T iOL95. A t the s ame t ime , the c o lo r o f the

sample ch anged f rom b lack to wh i t e , t he no rm a l c o lo r o f bu lk ru t il e . 4°)

Na tu ra l ly , po s t ox ida t ion i s no t l imi ted to fu l ly ox id ized pa r t ic l e s. F o r example , ox ida t ion

of sma l l A1, Zn o r M g c rys ta l s ha s been u t il i zed to gen e ra te nanom e te r - s ized pa r t ic l e s w i th

me ta l l ic co re s and ox id ized su r face s . The m e tho d o f reac t ing sma l l me ta ll i c pa rt i c le s w i th

a ga seous phase ha s been app l i ed to gene ra te nanome te r - s i zed hyd r ide pa rt i c le s e .g . T i l l2 )

by evap ora t ing the m e ta ll i c com po nen t in an H2 a tm osph e re o f 50 kPa . 41) Subse quen t

hea t ing o f the T il l2 pa r ti c le s 400°C , 1 min , vacu um ) conve r t ed them in to T i w i th hcp -

s t ruc tu re . Re -hydrogena t ion in to T i l l2 was ach ieved by annea l ing the pa r t i c l e s a t 250°C fo r

5 min a t l0 kPa H2 p re s su re . Iw am a and cow orke r s 42) have succeeded in p rod uc ing a va r i e ty

o f t r ans i t ion -me ta l n i t r ide s in u l t ra f ine po wd er fo rm by evapo ra t ing me ta l s in e i the r N 2

o r N H 3 g a s.

Rece n t expe r im en t s revea led tha t , a t l e a st in one ca se , con t ro l o f the ine rt ga s p re s su re

a f fect s no t on ly pa r t i c l e s iz e, b u t a l so the phase o f the re su lt ing m a te r i a l f l 3) U l t ra f ine po wd ers

o f T i we re found to reac t w i th oxygen to fo rm fu t i le T iO2) pa r t ic l e s o f ave rage d iame te r

12 nm, i f H e p re s su re s o f g rea te r than 500 Pa we re p re sen t du r ing evapora t ion . Ho wev e r , i f

the He p re s su re used w as le ss than 500 Pa a nd g rea te r than ab ou t 10 Pa , sma l l T i pa r ti c l es

were s t i l l fo rmed , bu t the se pa r t i c l e s d id no t fo rm ru t i l e when exposed to oxygen . In s t ead ,

in th i s c a se , an unexpec ted amorphous phase was fo rmed . Whi le the rea son fo r th i s unusua l

behav iour in T i i s no t ye t unde rs tood , wha t i s c l ea r i s tha t th i s demons t ra t e s tha t phase

con t ro l u s ing nanoc rys ta l l ine p roces s ing i s a po ten t i a l fu tu re ma te r i a l s eng inee r ing app l i -

c a t io n . U n e x p e c t e d n e w p h a s e s o f e r b i u m o x i d e s h a v e a l s o b e e n p r o d u c e d v i a th e n a n o -

c rys ta ll ine p roces s ing rou te . 44) In fac t , com pac ted nanoc rys ta l l ine e rb iu m ox ide 10 nm g ra in

s iz e) w a s f o u n d t o b e c o m p o s e d o f t w o f c c f o r m s o f e r b i u m o x id e s, o n e o f w h i c h i s a n e w

f c c e r b i u m s e sq u i o x id e w i th a = 0 . 3 7 4 n m , a n d a n e w E r 2 0 3 p h a s e w i th a m o n o c l i n ic

s t ruc tu re . T h i s l a tt e r phase can be rega rded a s a d i s to r t ed hexago na l s t ruc tu re caused by

abso rb ing o xygen in to the l a tt i c e o f e rb ium dur ing ox ida t ion .



N N O C R Y S T L L I N E M T E R I L S

231

2.1.2.3.

S p u t t e r i n g

D C a n d R F m a g n e t r o n s p u tt e ri n g h a ve b e c o m e st a n d a rd p r o c e d u re s

in th in f i lm p repa ra t ion . In fac t , t hey can be app l i ed equa l ly we ll fo r the depos i t ion o f me ta l s ,

me ta l l i c a l loys , s emiconduc to rs and ce ramics . The re fo re , spu t t e r ing s eems su i t ab le fo r the

p r o d u c t i o n o f n a n o c r y st a ll i n e m a t e r ia l s. T h e n o r m a l o p e r a t in g p r e s su r e o f s p u t te r s o u r c e s

(10 - I to 10 -2 Pa ) , how eve r , i s s eve ra l o rde rs o f magn i tude lower than the p re s su re range

requ i red fo r pa r t i c l e fo rma t ion du r ing ine r t ga s condensa t ion in l abora to ry s i ze evapora to rs

(102 to 103 Pa) . R ela t ive ly few da t a a re av a i lable on sput te r in g y ie lds in the pressure ra nge

of in t ere s t, a l th ough som e p ionee r ing wo rk 45) ha s sh ow n tha t s imple d iode spu t t e r ing cou ld

be used to p roduce u l t r a f ine pa r t i c l e s in the de s i red s i ze range . Spu t t e r ing a t such h igh

pre s su re s is pos s ib le s ince the w id th o f the da rk space in the p la sm a i s inve rse ly p ropor t io na l

to the ga s p re s su re so tha t the num ber o f co l l is ions be twe en acce le ra t ing ions and gas a toms

in the da rk space is indepen den t o f ga s p re s su re . In add i t ion to i t s w ide app l i cab il i ty ,

s p u t t e r i n g h a s o t h e r a d v a n t a g e s o v e r m o s t t h e r m a l e v a p o r a t i o n t e c h n i q u e s :

( i ) The com pos i t ion o f the spu t t e red m a te r i a l i s the s ame a s tha t o f the t a rge t , mak ing a l loy

synthes is poss ib le .

( i i) The spu t t e r ing cond i t ions a re s t ab le and read i ly con t ro l l ab le by mea ns o f the p la sma

current .

( i i i ) The hea t load on the chamber wa l l s i s f a r sma l l e r than du r ing the rma l evapora t ion ,

reduc ing ou tgas ing and subsequen t impur i ty inco rpora t ion by the sma l l pa r t i c l e s .

The app l i ca t ion o f a com merc ia l ly ava i l ab le magne t ron spu t t e r ing dev ice fo r p rep a ra t ion

of m e ta ll i c and ce ramic c lus te r s (A1 , M o, W , Cug~M n 9, A152Ti4s, TiO2, N iO and ZrO 2) wi th

dia m eter s o f 7 to 50 nm ha s be en s tu die d recently346'47)

2.1.2.4.

L a s e r a b l a t i o n

In the ca se o f l a s er ab la t ion , a h igh -pow er l a s e r bea m ab la te s a

s amp le t a rge t loca ted in an ine r t ga s chamb er . T he re su l t ing p lum e o f me ta l , be l ieved to be

mos t ly neu t ra l a toms , i s en t ra ined and coo led by the ca r r i e r ga s , r e su l t ing in the requ i red

supe rs a tu ra t ion and c lus te r g rowth . M e ta l dens it ie s a re usua l ly low enough tha t g row th

i s dom ina ted by success ive m on om er a dd i t ion . Resu l t ing c lus te r siz e d i s t r ibu t ions a re

b r o a d .

The l a s e r vapor iza t ion t e chn ique i s gene ra l and ve rs a t i l e . V i r tua l ly any ma te r i a l tha t c an

be fab r i ca ted in to an appr opr ia t e t a rge t m ay be used . C lus te r s o f s emico nduc to rs , ~4s)

t rans i t ion m eta ls (49) and m ain gro up m eta ls (5°) have a l l been gene ra ted in th is w ay. Al lo y

ta rge t s have been u sed , and in gene ra l the c lus te r s show the expec ted s t a t is t ic a l d i s t r ibu t ion

of a tom s . (51~ An o the r p roc edure com bines l a s e r vap or iza t ion o f one me ta l w i th s imul t aneou s

la se r py ro lys i s o f a ga seous p recu rso r o f ano th e r me ta l3 s2~ Th i s p recu rso r i s mixed wi th the

ca r r i e r ga s so tha t b o th types o f m ono m ers a re p re sen t in the c lus te r ing reg ion . In th is way ,

mixed c lus te rs o f e lemen t s tha t do n o t no rm a l ly a l loy can be p repa red . Such c lus te r s , a s we l l

a s m a c r o s c o p i c m a t e r i a l s m a d e f r o m t h e m , m a y b e f o u n d t o h a v e n o v e l p r o p e r t i e s .

A mo dif ied , nove l ve rs ion o f the laser a bla t ion app roa ch wa s recent ly u t i l ized C53) to

syn thesize nanoc rys ta l line c om pos i t e s o f me ta l l ic and non-m e ta l l ic spec ie s . A he a ted tungs ten

f il a m e n t w a s s im u l t a n e o u s l y e m p l o y e d f o r e v a p o r a t i o n a n d c o d e p o s i t i o n o f W v i a ch e m i c a l

t ransp or t mechan i sms . Th i s p roces s occurs in a reduc ing env i ronm en t o f hydro gen gas ,

w h e r e t h e e v a p o r a t e d s p e c i e s w e r e p r o d u c e d b y a l a s e r - i n d u c e d p l u m e . C o m p o s i t e l a y e r s

w e r e f o r m e d o n a N i a l lo y su b s t r a t e s ur f ac e , a t a r a te o f a b o u t 1 m / s e e . T h e m a t ri x o f

the com pos i t e f i lms was e ithe r AI o r W, a nd the d i spe rs ed phase w as am orp hou s s i l ic a fiber s.

The d iam e te r o f the f ibe r s was be tw een 25 nm and 120 nm, depen d ing on the in te rac t ion

times.



3

P R O G R E S S I N M A T E R I A L S S C I E N C E

2.1.2.5. Pyrolysis. La ser pyroly sis i s a techniq ue designed to sy nthesize u l t ra f ine re frac tor ies

by rap id ly h ea t ing w i th a l a se r a flowing reac tan t ga s m ixed wi th an ine r t c a r ri e r. Th i s l e ads

t o r a p i d g a s - p h a s e d e c o m p o s i t i o n o f t h e r e a c t an t s a n d p r o d u c e s a s a t u r a t e d v a p o r o f t h e

d e s i re d c o n s t i t u e n t a t o m s . N u c l e a t i o n a n d g r o w t h o f c lu s te r s th e n o c c u r a s t h e d e c o m p o s i t i o n

pro du c t s a re quen ched b y co l l is ions w i th the a toms molecu le s ) o f the car r i e r ga s . The

techn ique has been used c~) to sy nthesize u l t ra f ine p ow der s o f Si, Si3N4, and SiC. ZrB2, FeSi2

134C, T iB2 TiO2, AI2 03 and TiO2 have been ob ta in ed by a s im i la r approach355-57) The synthesis

o f n o n - m e t a l s u s e s v o l at il e h y d r id e s , w i t h H 2 a s t h e b y - p r o d u c t . C o m p o u n d s o f n o n - m e t a l s

a re p roduced by add ing to the ga s mix tu re e thy lene to y i e ld the ca rb ide , ammonia to y i e ld

the nitride, e tc .

M e t a ls a n d c o m p o u n d s o f m e ta l s , a s w e ll a s c o m p l e x c o m p o u n d s o f n o n - m e t al s , r e q u i re

a d i f fe r e n t a p p r o a c h . T h e m e t a ls a r e i n c o r p o r a t e d i n t o c o m p o u n d s w h i c h a r e v ol a ti le u n d e r

the expe r imen ta l cond i t ions . Th i s i s u sua l ly done w i th o rganome ta l l i c compounds , o r w i th

m e t a l c a r b o n y l s . R i c e a n d W o o d i e ~Ss) have synthesized Si /N /C po w de r o f 100 nm diam eter

s p h e r e s f r o m t h e p y r o l y s i s o f M e 3 S i N H S i M e a . W C a n d W / C / O , a s w e l l a s M o S 2 a n d

MoS2Cx, have a l l been syn thes i zed by th i s approach ; dop ing the se ma te r i a l s w i th Co o r Zn

was a l so ach ieved . Un ique Fe C ca ta lys t s have a l so been syn thes i zed b y th i s p rocedu re , t59)

Lase r py ro lys i s ha s the adv an tage o f be ing a con t in uou s p rocess , wh ich is sca lab le w i th

l a se r p o w e r a n d r e a c t a n t f l o w ra t e. T h e c o s t o f m a t e r ia l s p r o d u c e d b y t hi s a p p r o a c h is

p r imar i ly de te rmined by the cos t o f the chemica l s .

T h e a p p r o a c h c o u l d b e e x te n d e d b y t h e u s e o f U V l as e rs , w h e r e p h o t o c h e m i c a l d e c o m p o -

s i t ion may be u t i l i z ed to p roduce the in t e rmed ia t e s . Th i s wou ld l e ad to a low- tempera tu re ,

supe rsa tu ra t ed vapor whe re i t i s more l ike ly tha t me ta s t ab le phase s w i l l agg rega te and be

stabil ized.

2.1.2.6. Flame hydrolysis. Flam e hydro lys i s is t he reac t ion o f vo la t i le comp oun ds , e .g . T iCI4

or S iCI4 , i n an oxygen-hydrogen f l ame . I t l e ads to h igh ly d i spe r sed ox ide c lus t e r s and has

bee n app lied to a w ide va riety o f co m po un ds ~6°-63) such as SiO2, A1203, TiO2 , Z rO2 , Bi2 03 ,

Cr2 03 , Fe2 03 , N iO , G eO2, V2 05 , e t c. The m a jo r advan tages o f th is t e chn ique a re h igh pu r i ty ,

chemica l f l ex ib i li ty , and the poss ib i l i t y to syn thes i ze mixed ox ides . Depend ing on the p rocess

cond i t ion , c lus t e r si ze s be tween 5 and 50 nm a re ob ta ined .

2.1.3. C ondensed phase synthesis

2.1.3.1. Metals. I f a r educ ing ag en t i s adde d to an ac id ic aque ous so lu t ion o f me ta l i ons ,

then sma l l neu t ra l me ta l c lu s t e r s w i l l fo rm. D ia lys i s c an be used to r emove rema in ing ions

and a th i ckene r , such a s ge la tine , c an be added to p reven t agg rega t ion o f the pa r ti c le s .

Rela t iv e ly narro w size d is t r ib ut ion s have been ac hieved w i th th is techniqu e e .g . Ag, ~64)A u , 65)

Pt t66)) wi th rou gh con tro l of the m ean c luste r s ize s imi la r to thos e achieve d w i th iner t -gas

c o n d e n s a t i o n .

T h e m e t h o d o f t h e g r o w i n g s m a ll m e t a l c lu s te r s b y m e a n s o f th e m i c r o e le c t ro d e m e t h o d

has been u t i l ized in recent years to gen era te smal l A g c lu ste r s : 2xt3°~ A solu t io n c onta in ing

a few 1 0 - 4 M A g + io n s w a s e x p o s e d t o a s h o r t p u l s e o f r a d i a ti o n p r o d u c i n g a k n o w n

am ou n t o f hyd ra ted e l ec t rons in the 10 -6 M range . T he l a t t e r r ap id ly reac t w i th s i lve r ions

to fo rm a toms , A g + + e~-- -, Ag ° , wh ich subs equen t ly agg lomera te to l a rge r pa r t ic l e s. A t

a cer ta in p ar t ic le s ize , i.e. a f te r a cer ta in t ime o f agglom era t ion , meta l l ic s i lver col lo id

was p re sen t , r e cogn izab le by the appea ra nce o f the 380 nm p la sm on abso rp t ion . In a

second s tud y , °31) su l fon a top ro py lv io logen SPV) was used . T he pu l se o f r ad ia t ion p rodu ces

k n o w n a m o u n t s o f th e ra d ic al a n i o n S P V - a n d o f A go a t o m s . T h e A g a t o m s a g g l o m e r a t e




233

i n to s i lv e r p a r ti c le s a n d g r o w f u r t h er b y t h e r e a c t io n S P V - + A g + + A g n ~ S P V + A g , + t .

Sma l l go ld c lus ter s hav e been g row n by a c losely re l a ted m e thod . °32~ A so lu t ion con ta in ing

1 .7 × 10 -4M N aA u(C N)2 was expo sed fo r 0 .5 s to h igh -ene rgy e l ec trons . U nd e r the se

c i rcums tances a l l the go ld complexes we re reduced b y hydra ted e l ec t rons to y ie ld go ld a tom s ,

e~q + Au (CN )~- -~ A u ° + 2C N - . On e s econd a f t e r the e l ec t ron i r rad ia t ion occur red , the

p la sm on ban d typ ica l o f A u c lus te rs was p re sen t . A bo u t 2 s la t e r , ind ica t ions o f l a rge r go ld

pa r t i c l e s we re no t i ced sugges t ing rap id pa r t i c l e g rowth . Me ta l c lus t e r s a re gene ra l ly sho r t -

l ived in aqu eou s so lu t ion a s they rap id ly agg lom era te . H ence , s t ab i l iz a t ion o f in t e rmed ia te

c lus te r si ze s wou ld be o f in t e re s t fo r the co n t ro l l ed g row th o f me ta l c lus t e rs o f a p re -de ter -

m ined s ize. Su ch a s tabi l iza t ion has recen t ly been achieved in the case of s ilver c lus te rs form ed

in the rad io ly t i c r educ t ion o f A g ÷ ions in the p re sence o f sod ium po lyp hosp ha te . °33~ The l a t t e r

i s known to be an exce l l en t s t ab i l i z e r fo r many ino rgan ic co l lo ids . In th i s expe r imen t , a

so lu t ion con ta in ing 2

x 1 0 - 4 M

Ag ÷ ions , 2 x 10 -4M p o lyph osph a te , and 0 .1 M 2 -p rop ano l

was v - i r rad ia t ed . Unde r the se cond i t ions , r educ ing rad ica l s , i . e . hydra ted e l ec t rons and

1-hydroxyme thy le thy l r ad ica l s , we re gene ra ted wh ich reduce the s i lve r ions .

Co l lo ida l suspens ions o f me ta l c lus t e r s in o rgan ic so lven t s have a l so been gene ra ted by

depos i t ing me ta l a tom s in to low- tem pera tu re o rgan ic so lven t s . (67) C lus te r g row th i s even tua l ly

inh ib i t ed by s t rong ly bound so lven t molecu le s .

F u r t h e r m o r e , s p a r k e r o s i o n h a s b e e n u t il iz e d a s a m e t h o d f o r p r o d u c i n g f in e p o w d e r s o f

me ta l s , a l loys , s emiconduc to rs , and compounds36s ) The t echn ique invo lves ma in ta in ing

repe t i tive spa rk d i s cha rges am ong chun ks o f ma te r i a l im mersed in a d ie l ect r ic liqu id . As a

re su lt o f the sp a rk d i s cha rge the re i s h igh ly loca l ized me l t ing o r vap or iza t ion o f the m a te r ia l .

T h e p o w d e r s a r e p r o d u c e d b y t h e f r e e z i n g o f t h e m o l t e n d r o p l e t s o r t h e c o n d e n s a t i o n a n d

f reez ing o f the vap or in the d ie l ec tr i c l iqu id . The pow ders a re q uenche d i n s i tu t o the

tem pera tu re o f the l iqu id . Pa r t i c le s can be p r odu ced in s izes rang ing f ro m 5 nm to 75 /~m.

T h e a v e r a g e p o w d e r s iz e a n d p r o d u c t i o n r a te d e p e n d o n t h e p o w e r p a r a m e t e r s, t h e m a t e r i al

used , and the d ie lec t r ic l iquid .

The gene ra t ion o f me ta l li c c lust e r s by p rec ip i t a t ion f ro m a so l id c rys ta l l ine o r g la s sy ma t r ix

has been used fo r numerous s tud ie s on i so la t ed

c l u s t e r s . 0 3 9 t 51 ,t 52 )

In a few cases i t has been

poss ib le to d issolve the m atr ix se lec tive ly w i tho ut d issolv ing the c lus te rs resul ting in a

co l lo ida l suspens ion o f c lus te r s in the so lven t.

2.1.3.2. S e m i c o n d u c t o r s B y c o n t r o l o f t e m p e r a t u r e , c o n c e n t r a t io n , a n d s o l v e nt d u ri n g

l iq u id p h a s e p r e c ip i t a ti o n o f c o m p o u n d s e m i c o n d u c t o r s i t h a s b e c o m e p o ss i b le to m a k e a n d

s tabi lize c rys ta l l ites w i th d iam eters < 5 nm. (69) Bet te r s ize con tro l and col lo id s tabi l i ty c an

be ach ieved th rou gh the use o f mic roscop ica l ly s t ruc tu red l iqu id mix tu re s, such a s wa te r -

soa p- he pta ne , in which th e c rys ta l l ites a re s tabi l ized in smal l (2-10 nm ) w ater po ols (7°) te rm ed

inverse mice l les .

Sma l l s emiconduc to r c lus t e r s c an a l so be p repa red in s ide ionomers . Ionomers a re a c l a s s

o f c o p o l y m e r s c o n t a in i n g i o n ic s i d e- c h ai n g r o u p s s u c h a s C O O - a n d S O ~ - . T h e s e i o n ic g r o u p s

t e n d t o a g g r eg a t e t o g e t h e r f o r m i n g d o m a i n s , a n a l o g o u s t o t h e f o r m a t i o n o f io n i c p o o l s i n

micel les. M eta l ions , such as C d 2+ and Pb 2+, can be ea s i ly exchanged in to the se ion ic do ma ins

whe re syn thes i s o f de s ired s em icondu c to r c lus te r s c an b e cond uc ted . Fo r exam ple , s t ab le PbS

c lus te r s , r ang ing in s i ze s f rom mono-molecu la r to bu lk , have been syn thes ized in e thy lene -

15% me thac ry l i c a c id co po lym er f l t~

S i li c ate g la s ses have been used a s hos t s fo r the h igh - t empe ra tu re syn thes is o f s em icond uc to r

c lus ter s such a s CdS xSi l -x and CuC1. In the ca se o f CdS xSe t -x d op ed g las se s , wh ich a re

ava i lable as commerc ia l color f i l te rs , e lementary Cd, S and Se a re f i rs t d issolved in the g lass




mel t i n the p re sence o f excess am oun t s o f Zn . A f te r the g l a ss i s fo rm ed up on coo l ing ,

CdSx Se -x c rys t a ll i te s o f va r ious s izes can then be p ro duc ed by con t ro l l ed annea l ing f l 2)

2.1.3.3. Ceramics Decompos i t ion and p rec ip i t a t ion reac t ions in ion ic ma te r i a l s have been

u t il iz ed to gene ra t e nanome te r - s i zed c lus t e rs . Fo r example , decom pos i t ion o f M e(OH )2 and

MgC O3 y ie lded M gO c lus t e rs w i th ab ou t 2 m m d iam e te r f l 3-75) The so lu t ion so l -ge l m e tho d

has b een u t i l ized in a va r ie ty o f systems to g enera te sm al l (< 10 nm ) c luste rs o f SiO2, A120 3 ,

TiO2.

H y d r o t h e r m a l r e a c ti o n s ( r e ac t io n s o f th e w a t e r a b o v e i ts b o i li n g p o in t ) h a v e b e e n p r o p o s e d

to be a pp lied to syn thesiz e sm all c luster s. ~6°)T h e t w o r e a c t i o n s a p p li e d s o f a r a r e h y d r o t h e r m a l

p rec ip i t a t ion and hyd ro the rm a l ox ida t ion , tTs) Bo th reac t ions y i e ld suspen s ions o f c rys t a l li ne

me ta l ox ides in w a te r . S im ple ox ides (ZrO2 , S iO2 , A l2 03 , T iO2 , M gO , CaO ) , a s we l l a s mixed

o x i d e s ( Z r O 2 - Y 20 3 , Z r O 2 - Y 2O3-M gO , Z rO2 -M gO , ZrO2 , ZrO2-A12 0 3 BaFe l2 O i9 , BaTiO3) ,

have been p repa red in the s ize ranges be twee n 10 nm and 100 nm.

2.1.4.

Capped c lus ters

In o rde r to i so la t e m ac rosc op ic am oun t s o f c lus t e rs f rom the l iqu id -phase reac t ion m ed ia ,

i t is necessa ry to mo d i fy chemica l ly the ba re su r face to p reven t c lus t e r fu s ion . Po lymer ic ,

h igh ly ion ic , i no rgan ic pho sph a te s have been used 79) to p ro tec t pow ders o f Cd3 P2 , CdS , e t c . ,

wh ich cou ld then be re -d i spe r sed in wa te r . A d i rec t o rganome ta l l i c syn the t i c me thod fo r

su r face reac t ions on c lus t e r s ha s r ecen t ly been ach ieved in inve rse mice l l e co l lo ida l p rep -

a ra t ions , t~s°) Th i s m e th od chemica l ly bon ds o rgan ic g roup s to cha lcogen ide a tom s on the

c lus t e r su r face . The su r face changes f rom hydroph i l i c to hydrophob ic , and a s a r e su l t t he

c lus t e r s p rec ip i t a t e a s a pu re , c apped , c lus t e r powder . They re -d i sso lve in typ ica l o rgan ic

so lven ts , c an b e d i spe r sed in po lym er fi lms , and in gene ra l cou ld be used in the syn thes i s o f

c lus t e r -conso l ida ted ma te r i a l . Fo r example , t he powder can be p re ssed in to pe l l e t s w i thou t

fus ion o f the c lus t e r s .

Ex t rem e ly sma ll mon od i sp e rse m e ta l and s em icondu c to r c lus t e r mo lecu le s , cons i s t ing o f 30

a tom s o r le ss , c an b e p repa red and c rys t a ll i z ed v ia d i rec t chemica l syn thes i s. M any example s ,

such as i ron su l fur c luste rs ~sl) and gold -s i lve r c luste rs , ts2) have been rep or ted in the l i te ra ture .

N o a t t em pt i s m ade he re to r ev iew th is a rea o f cl a ssi cal chemica l syn thes is .

2 1 5 Clus ter arrays

The goa l o f th is ap pro ach i s t o a ssem ble c lus t e r s in we l l -de f ined th ree -d imens iona l a r rays

to fo rm new type s o f so l id s . The p r inc ip le o f th is idea ha s been dem ons t ra t ed recen t ly w i th

the sy nthesis o f CdS superc luste rs inside zeol i tes . In zeol i te y~s3) d iscre te (CdS)4 cubes

wi th a CdS bo nd l eng th o f 0 .247 nm have been syn thes i zed w i th in the 0 .5 nm soda l i t e cages .

T h e y a r e s t ab i li z ed b y t h e i n t er a c ti o n b e t w e e n C d a t o m s a n d f r a m e w o r k O a t o m s . C u b e s i n

the ad jacen t soda l i t e un i t s fu r the r in t e rac t w i th each o the r , v i a supe r -exchange th rough the

hos t l a t t i c e , t o fo rm an in t e r lock ing th ree -d imens iona l " supe rc lus t e r " s t ruc tu re . The op t i ca l

abs o rp t ion spec t rum o f the se supe rc lus t e r s lie s be tween those o f c lus te r s and bu lk . A nov e l

o r i en ta t iona l e f fect ha s a l so been obse rved . By chang ing the ho s t f rom zeo l it e Y to A , the

re l a tive o r i en ta t ion o f the cub es i s change d f rom ve r t ex - to -ve r tex to f ace - to - face. Th i s r e su l ts

in a 0 .3 eV b lue - sh i f t in the supe rc lus t e r abs o rp t io n spec t rum, re fl ect ing the change in the

geom e t r i ca l and e l ec t ron ic s t ruc tu re s o f the supe rc lus t e r s a s imposed by the zeo l it e hos t.

Using d i f fe rent zeol i tes as the templa te , superc luste rs wi th d i f fe rent s t ruc tures and e lec t ronic

p rope r t i e s c an be bu i l t .

A t p re sen t , becau se o f the p re sence o f de fec t s in bo th the zeo l it e hos t s and the

semiconduc to r c lus t e r s , CdS supe rc lus t e r s in zeo l i t e s a re b roken in to sma l l doma ins . To



N A N O C R Y S T A L L I N E M A T E R I A L S 235

remove th i s p rob lem, be t t e r qua l i ty zeo l i t e c rys t a l s and improved syn the t i c p rocedure s a re

needed .

A n o t h e r a p p r o a c h t o w a r d t h e s a m e g o a l w a s p r o p o s e d b y U m e m u r a . (~ ) I n o r d e r

to gene ra t e a r egu la r a r ray o f sma l l pa r ti c l es o n a s i l icon subs t ra t e f o r mic roe lec t ron ic

app l i ca t ions such a s memor ie s , a two s t ep p rocess ha s been made . In the f i r s t s t ep , a squa re

l a tt ic e o f c a r b o n w a s d e p o s i t e d o n t h e S i b y m e a n s o f a n a r r o w e l e ct r o n b e a m . B y d e p o s i t in g

subsequen t ly a Au o r KC1 pa r t i c l e in to eve ry squa re , a r egu la r a r ray was ob ta ined . The

accuracy o f the l a t t i c e i s s t i l l i n fe r io r in compar i son to the qua l i ty ach ieved by mode rn

m i c r o f a b r i c a t io n m e t h o d s . I f t h e a c c u r a c y c a n b e i m p r o v e d , t h is a p p r o a c h w o u l d o p e n t h e

w ay to de s ign quan tum -we l l dev ice s . A so me wh a t r e l a ted app roac h i s t he gene ra t ion o f sma l l

pa r t i c le dev ice s ca l led sup e ra to m s . (ss-sT) These pa r t i c l e s a re com pos ed o f two sem icondu c to r

subs tances a r ranged regu la r ly a s a co re and a she l l wh ich re semble s func t iona l ly the co re

and e l ec t ron she ll o f an a tom , re spec t ive ly . The app l i ca t ion o f such s t ruc tu re s r equ i re s the

ava i l ab i l i t y o f monod i spe rse sma l l pa r t i c l e s .

2.2. Cluster Deposition

On e app roac h to f ab r i ca t e a bu lk p iece o f a nanoc rys t a l l ine m a te r i a l is t o depos i t t he sma l l

c lus t er s gene ra t ed by one o f the me th ods d i scussed in the p rev ious sec t ion on a so l id subs t ra t e .

The fo l lowing th ree m e thod s o f c lus t e r depos i t ions have been s tud ied so fa r .

2.2.1.

High speed deposi t ion

K a s h u

et al. ss)

have depo s i t ed nanom e te r - s i zed c lus t e rs o f Ag , Fe , N i , Cu , Au , T i , Pb , Zn ,

T iN and RuO 2 by us ing c lus t e r s en t ra ined in a ga s j e t (F ig . 7 ). A g la ss, me ta l , o r p l a s t i c

subs t ra t e su r face loca ted c lose and n o rm a l to the j e t is exposed fo r co l l id ing w i th the c lus t er s .

W i th a su f f i c ien t ly h igh ve loc i ty (> 100 m/s ) o f j e t f low aga ins t t he subs t ra t e , t he c lus t e rs h ad

su f fi c ien t ene rgy wh ich w as re l ea sed du r ing the co l l i s ion to ma ke them s t ick to the subs t ra t e

a n d t o o n e a n o t h e r . W i t h a t in y n o z zl e ( ~ 0 . 3 m m d i a m e t er ) , a li ne p a t te r n o f a s -d e p o s i t e d

c lus t e rs 0 .3 m m wide was gene ra ted . F o r the depos i t , a g reen dens i ty o f ove r 55% fo r As ,

C u , N i , e t c . , w h i c h c o r r e s p o n d s t o a c o n v e n t i o n a l p o w d e r c o m p a c t m a d e b y u s i n g h i g h

pre ssu re conso l ida t ion w as ob ta ined . I f a conven t iona l mi l l ime te r - si zed fine pow der was used

ins t ead o f the nanom e te r - s i zed c lus te r s , no so lid depos i t was fo rmed . Co dep os i t ion o f

d i f feren t ma te r i a l s , e .g . A g-F e , Pb -Z n , f rom a s ing le nozz le i s poss ib le , r ega rd less o f the

speci fi c dens i ty o f e ach comp one n t . T he m ic roana lys i s r eco rds ind ica te un i fo rm d i s t r ibu t ion

g s

F i ~ . 7 . A r r a n g e m e n t o f t h e s p r a y d e p o s i t i o n m e t h o d f o r s m a l l a s g r o w n pa rt ic le s3 8 8)



36

P R O G R E S S I N M T E R I L S S C I E N C E

of the comp onen t s . The e l ect r ic a l r es i s tiv ity o f a ga s - je t depos i t ed N i pa t t e rn was h ighe r than

the on e o f conven t ion a l s i lve r pa s t e . Th e re s i s t iv i ty o f a RuO 2 depos i t cou ld be m an ipu la t ed

b y v ar y in g t h e d e p o s it io n p a r a m e t er s b e t w e en 1 0 - ' f l c m a n d , ~ 4 x 1 0 - 4 f l c m , w h i ch is

app l i cab le to co mm erc ia l ap p l i ca tions . (ss) The depo s i t ion p rocess m ay be p e r fo rm ed a t

am bien t t em pe ra tu re , bu t a lower t empe ra tu re ca r r i e r ga s m ay a l so be used i f a h ighe r ga s

f low i s employed . In c l a ss i ca l me ta l lu rg ica l t e rms th i s p rocess seems to be ba sed on

low - tem pera tu re ba l li s ti c conso l ida t ion . An in t ere s ting , s l igh t ly d i f feren t app l i ca t ion o f th is

m eth od is a gas je t con ta in ing f rozen CO2 fine par tic les . (ss) Th e co l l id ing CO2 par t ic les r em ove

organic f i lms on g lass , ceramics , or meta l subst ra tes . Sol id CO2 par t ic les have a hardness

su f fi c ien t t o s t r ip -o f f l aye r s o f a pho to re s i s t on ch rom ium ox ide coa ted g lass , w i th ou t c au s ing

any damage to the ch romium ox ide coa t ing . So l id CO2 pa r t i c l e s a l so seem app l i cab le fo r

remova l o f a c ry l i c o r s ty rene p la s t i c s .

2.2.2. Deposition by ionized cluster beams

Tak ag i and Y am ad a (89'9°) have p ionee red th in f i lm depo s i t ion by ion ized c lus t e r be am s .

T h e s e b e a m s a r e g e n e r a t e d b y e x p a n d i n g a v a p o r b e a m a d i a b a ti c a ll y t h r o u g h a n o z zl e.

Du r ing expans ion , a f r ac t ion o f the a tom s conden ses in the fo rm o f sma l l c lu s te r s con ta in ing

typ ica l ly 1 ,000 a toms . An e l ec t ron beam pos t - ion ize s a sma l l f r ac t ion o f the c lus t e rs , wh ich

can then be acce le ra t ed to a depos i t ion subs t ra t e w i th any des i red impac t ene rgy , t yp ica l ly

ab ou t 1 eV pe r a tom o f the c lust e r . The re i s no m ass se l ec tion ; a tom s , sma l l c lu s te r s , and

neutra l la rge c luste rs as wel l as the ionized la rge c luste rs s t r ike the subst ra te . The ionized and

acce le ra t ed c lus t e rs a re p i c tu red a s d i ssoc ia t ing a t t he mom ent o f impac t on the sub s t ra t e ,

d e s o r b i n g l o o s e l y b o n d e d a t o m s a n d i m p u r i ti e s a n d g iv in g m o b i l it y t o a t o m s t h a t h a v e

a l ready l anded a t t he su r face a s we l l a s those o f the d i ssoc ia t ed c lus t e r s . In one sense , t he

ion ized c lus t e r beam s a re an ion a ss i s t ed p rocess , s ince a t mos t on ly a few pe rcen t o f the

to ta l am ou n t o f ma te r i a l be ing depo s i t ed i s be l i eved to cons i s t o f ion ized c lus te r s . M os t o f

t h e d e p o s i t is p r o b a b l y m a d e u p o f n e u t r al a t o m s o r p e r h a p s s m a ll c lu s te r s. S u c h s o u r c e s h a v e

been u t i l ized to gene ra te th in f ilms, e .g . ep i taxia l a lum inum on s i l icon, (9°) and i t i s be ing used

com me rc ia l ly for gold m irror coa t ings. (9~)

2.2.3. onsolidation

The f i r s t a t t empt to gene ra t e and s tudy bu lk nanoc rys ta l l ine ma te r i a l s was ba sed on the

co l l ec tion and conso l ida t ion o f sma l l c lu s t e rs .

A s c h e m a t ic p i c t u re o f a n u l tr a -h i g h v a c u u m a p p a r a t u s d e v e l o p e d f o r th i s p u r p o s e is

i l lust ra ted in Fig . 8 . (92-94) A t th is t ime, o nly the iner t gas co nde ns a t ion m eth od for pro duc ing

the pa r t ic l e s ha s been em ploy ed fo r the syn thes is o f nanoc rys t a l line ma te r i a l s. As sho wn in

F ig . 8 , t he pa r t ic l e s a re p rod uce d b y a two s t ep p rocess . The sub s tance (e.g . Cu) i s evap ora ted

by re s i s t iv i ty hea t ing f rom a re f rac to ry me ta l boa t . The evapora ted a toms t r ans fe r the i r

the rma l ene rgy to the ine r t ga s and cond ense in the fo rm o f sma l l c rys t al s . The c rys t a ls

a re ca r r i ed b y a convec t ive cu r ren t o f ine r t ga s to a l i qu id -n i t rogen coo led co ld f inge r .

Subsequen t ly , t he ine r t ga s i s r emoved and the pa r t i c l e s a re sc raped f rom the co ld f inge r and

funne led in to a p i s ton a nd anv i l- l ike dev ice whe re they a re com pac te d us ing p re ssu re s o f

ab ou t 1 -5 GP a . Coo l ing o r hea t ing o f the spec imen dur ing com pac t ion i s e a s ily poss ib le.

As a consequ ence o f the c l ean hand l ing con d i t ions , t he pow ders bec om e pa r t i a lly s in t e red

d u r i n g c o m p a c t i o n a n d h a v e d e n si ti es o f a b o u t 7 0 - 9 0 % o f t h e b u lk . C l e a rl y , th e p r o c es s i n g

techn ique a l lows fo r g rea t ve r sa t i l i t y : compos i t e ma te r i a l s c an be p roduced by us ing two o r

m o r e e v a p o r a t o n s o u r c e s ; o x i d e o r o t h e r c e r a m i c m a t e r i a l s c a n b e p r o d u c e d b y m i x i n g o r




37

~ I I I Ih

ROTATING CO LD FINGER

(

i q u i d n i t r o g e n

)

d B n ~ S C R P E R

NERT GAS

{e,g. He)

EVAPORATION

VALVE

VACUUMPUMPS- -----_~

FIXED PISTON.

l ~ l

SLI E ~ ]

FUNNEL

BELLOWS

UHV VACUUM

CHAMBER

LOW PRESSURE

-ANVIL COMPACTIONUNIT

S L E E V E HIGH PRESSURE

PISTON - - - ~ v ~ ' r / / l~-~ --~/ / /A -~ PISTON COMPACTION NIT

P ~ X \ \ \ \ \ \ \ \ \ ~ J

FIG, 8. S c h e m a t i c d r a w i n g o f a g a s - c o n d e n s a t i o n c h a m b e r f o r th e s y n t h e s is o f n a n o c r y s t a l li n e

m a t e r i a l s. 92-94) T h e m a t e r i a l e v a p o r a t e d c o n d e n s e s i n t h e i n e r t g a s i n t h e f o r m o f s m a l l c r y s t a l l it e s a n d

i s t r a n s p o r t e d v i a c o n v e c t i o n t o t h e l i q u i d - n i t r o g e n f i l l e d c o l d f i n g e r . T h e p o w d e r i s s u b s e q u e n t l y

s c r a p e d f r o m t h e c o l d f i n g e r , c o l l e c t e d v i a t h e f u n n e l a n d c o n s o l i d a t e d f i rs t i n t h e lo w - p r e s s u r e

c o m p a c t i o n d e v i c e a n d t h e n i n t h e h i g h - p r e s s u r e c o m p a c t i o n u n i t . B o t h u n i t s a r e k e p t u n d e r U H V

c o n d i t i o n s . I f t h e i n e r t g a s i s i n t h e c h a m b e r , i t is se p a r a t e d b y a v a l v e f r o m t h e p u m p s . I n s t e a d o f

a n e v a p o r a t i o n d e v i c e , a s p u t t e r i n g s o u r c e h a s b e e n u t i l i z e d suc ces sfu l ly . ~ 47)

r e p la c in g t h e in e r t g a s w i t h a r e a c t iv e g a s ; p a r t i c l e s i z e c a n b e c o n t r o l l e d b y t h e e v a p o r a t io n

rate an d the co nd en sat ion gas pressure , t92-94)

A l t h o u g h t h e g e n e r a l f e a t u r e s o f s y n t h e s i s s e e m t o b e c l e a r , t h e d e t a i l e d p r o c e s s e s w h i c h

t a k e p l a c e d u r i n g c o m p a c t i o n a n d t h e r e s u lt in g s t r u c t u re o f t h e m a t e r i a l a re n o t y e t w e l l

c h a r a c t e r i z e d . D u r i n g t h e c o l l e c t i o n o f t h e p o w d e r o n t h e c o l d f i n g e r , s o m e p a r t i c l e s

a g g l o m e r a t e a n d f o r m g r a i n b o u n d a r i e s ; i n c o m p o u n d p o w d e r s , b o t h g r a i n b o u n d a r i e s

a n d h e t e r o g e n e o u s i n t e r f a c e s m a y f o r m . M o s t i n t e r f a c e s , h o w e v e r , a r e f o r m e d d u r i n g t h e

c o m p a c t i o n p r o c e s s. B e f o r e t w o p a r t ic l es ( n a n o m e t e r - s iz e d c r y s t a ls ) a re b r o u g h t i n t o c o n t a c t ,

t h e i r a t o m s l ie o n r e g u la r la t t ic e s i t e s , w i t h p o s s ib l e r e la x a t io n s a t t h e f re e s u r f a c e s. A s c o n t a c t

i s m a d e b e t w e e n t h e t w o c r y s t a l s , a n i n t e r f a c e i s f o r m e d w i t h a n a t o m i c s t r u c t u r e c o n t r o l l e d

b y t h e p a r a m e t e r s d i s c u s s e d in t h e f i r s t s e c t i o n .

F u r t h e r i m p r o v e m e n t s i n p o w d e r c o n s o l i d a t i o n s e e m t o b e p o s s i b l e b y u t i li z in g t h e c o r e

e x t r u s i o n p r o c e s s w h i c h h a s b e e n s u c c e ss f u l ly a p p l ie d t o th e c o n s o l i d a t i o n o f m e t a l l ic

g la s s e s . (95) W h e n a b i l l e t o f p o w d e r , p a c k e d in t o a c y l in d r i c a l c o n t a in e r , i s e x t r u d e d , a n




i n h o m o g e n e o u s , p o r o u s b u l k g l as s y m a t e r ia l w a s f o u n d t o r es u lt . T h e h o m o g e n e i t y o f t h e

ex t ruded ma te r i a l m ay be imp roved by p lac ing a co re o f a su it ab le ma te r ia l i n the cen t ra l

ax i s o f the con ta ine r to be ex truded . T he pub l i shed obse rva t ion s(95) dem ons t ra te tha t the

c o e x t r u s i o n o f th e c o r e a n d t h e c o n t a i n e r r e s u lt s in a h o m o g e n e o u s g l a s sy b o d y w i th a

re s idua l po ro s i ty o f le ss than 0 .1%. The same t echn ique seems app l i cab le to the p rocess ing

of nanoc rys t a l l ine ma te r i a l s .

2.3.

Other Methods

2.3.1. High energy mil l ing

The red uc t ion o f g ra in s ize in pow der sample s to a f ew nanom e te r s du r ing heavy

me chanica l de for m at io n wa s invest iga ted b y severa l authors396-1°°) By high-energy ba l l

mi l ling, t he g ra in s i ze o f pu re bcc me ta l s (C r , Nb , W ) , me ta l s w i th hcp s t ruc tu re (Zr , H f , Co ,

R u ) a n d i n t e r m e t a l l i c c o m p o u n d s w i t h C s C I s t r u c t u r e ( C u E r , N i T i , A I R u , S i R u ) a n d

immisc ib le sys t ems (FeAI) can be reduced to nanome te r sca le s . The de fo rma t ion i s l oca l i z ed

a t the ea r ly s t age in shea r b ands w i th a th i ckness o f abo u t 1 /~ m. Na nom e te r - s i zed g ra ins a re

nuc lea ted w i th in the se shea r bands . Fo r longe r d u ra t ions o f ba l l mi l ling th i s r esu l t s i n an

ex t reme ly f ine -g ra ined m ic ros t ruc tu re w i th rand om ly o r i en ted g ra ins (5 -13 nm in d iame te r )

sepa ra t ed by h igh ang le g ra in bound a r i e s . T he rm a l ana lys i s o f the se sample s a llowed fo r a

quan t i t a t ive de te rm ina t ion o f the en tha lpy s to red in the se ma te r i a l s and an e s t ima t ion o f

the re l a ted g ra in b ou nd a ry ene rg ie s. Excess en tha lp ie s o f up to 40% of the hea t o f fu s ion

a n d e x c e s s h e a t c a pa c i ti e s o f u p t o 2 0 0 i n c o m p a r i s o n t o t h e u n d e r f o r m e d s t a t e h a v e

been ach ieved , exceed ing by fa r any va lues de te rmined fo r conven t iona l de fo rma t ion

processe s . These va lues a l so exceed the ene rgy o f g ra in bou nda r i e s in fu l ly equ i l ib ra t ed

po lyc rys t a l s . The va lues a re com parab le , how eve r , t o the excess en tha lp ie s and the excess hea t

capac i t ie s r epor t ed (cf . Sec t ion 4 .4 ) fo r nanoc rys t a l l ine m a te r i a ls p re pa red by conso l ida t ion

o f n a n o m e t e r - s iz e d c l us t er s a c c o r d i n g t o t h e m e t h o d d i s cu s s e d in t h e p r e v i o u s p a r a g r a p h

(Section 2.2.3).

The ba l l mi l l ing me thod does no t seem app l i cab le to me ta l s w i th fcc s t ruc tu re . I f me ta l s

wi th fcc l a t t i c e s t ruc tu re a re sub jec ted to h igh -ene rgy ba l l mi l l ing they a re found to s in t e r

to l a rge r pa r t i c l e s up to one mi l l ime te r in s i z e . Fcc me ta l s appea r to be too so f t fo r

e f fec t ive ene rgy s to rage . H igh-en e rgy ba l l mi ll ing seems a l so su i t ab le fo r gene ra t ing nano-

c rys t a l l ine a l loys . Fo r example , u s ing a p l ane ta ry -ba l l mi l l o r an a t t r i t o r a l lowed Sch lump

a n d G r e w e ~98) to pro du ce an equ iaxed c rysta l l ine s t ru c ture wi th a gra in s ize of < 10 nm in

a n F e - T a - W a ll o y, G e n e r a l l y t h e y f o u n d t h a t s y s t e m s o u t s i d e th e m e t a s t a b l e s ol id s o l u t io n

f i e ld o r in the two-phase amorphous /c rys t a l l ine reg ion cou ld l e ad to a nanoc rys t a l l ine

s t ruc tu re . Nanoc rys ta l l ine ce rme t s , such a s f rom Ti -Ni - -C , cou ld be p roduced by the same

m e t h o d . S i m i l a r r e s u l t s w e r e o b t a i n e d b y S h i n g u a n d c o w o r k e r s <97) w ho gen era ted na no -

s t r u c tu r e s i n b o t h A I - F e a n d A g - F e . H e r e , c o m p e t i t i o n t o o k p l a c e b e t w e e n t h e f o r m a t i o n

o f a n a n o c ry s t a ll i n e a n d a n a m o r p h o u s s t ru c t u re . A s a m a t t e r o f fa c t, it t u r n e d o u t t h a t

the chemica l compos i t ion s t rong ly in f luenced the amorph iza t ion . Fo r example , a sma l l

a m o u n t o f T i in t h e A I - F e s y s t em f a v o r e d th e f o r m a t i o n o f th e a m o r p h o u s p h a se .

Cryom i l ling ( i. e . h igh -ene rgy ba l l mi l ling in l iqu id n i t rogen) l e ads to a ma t r ix o f a lumin um

(for exam ple) wi th a f ine gra in s ize ( < 5 0 nm ) of d isp ersed AI N par t ic les . ~99) A m ajo r

advan tage o f the mechan ica l a l loy ing app roac h to p ro duc t ion o f nanoc rys t a l l ine ma te r i a l s is

tha t i t i s a qu an t i ty p rocess pe rmi t t ing seve ral k i log rams o f ma te r i a l t o be p rod uce d in t imes

o f u p to 100 hr . ~98)



N N O CRY ST LLI N E M TERI LS

239

2.3.2. M ixalloy processing

Th e m ixa l loy p rocess ing u t il iz e s the tu rbu len t m ix ing o f imp ing ing a l loy s t r eams an d

in situ chemica l reac tions31°1-1°3 ) Tw o o r m ore tu rbu len t s t r eams o f m ol t en me ta l a l loys

a re d i rec t ed in to a mix ing chamber . The re the s t r eams impinge a t h igh ve loc i t i e s . Due to

the h igh ly tu rbu len t f low , sma l l sca le edd ie s p rov ide rap id and e f fec t ive mix ing an d pe rm i t

c h e m i c a l re a c t io n s o n a n a n o m e t e r s ca le . F o r e x a m p l e , if o n e o f t h e m o l t e n s t r e a m s i s a C u - B

a l loy and the o the r s t r eam i s a coppe r a l loy con ta in ing a s t rong bo r ide - fo rming e l emen t such

as T i , nanome te r - s i zed T iB2 c rys t a l s a re fo rme d in the zone o f mixing . Sub seque n t r ap id

so l id i f i c a t ion re su l t s i n f ine -g ra ined ma te r i a l con ta in ing nanome te r - s i zed the rma l ly s t ab le

dispersions.

2.3.3. Deposition methods

Du r ing th in f i lm gene ra t ion , t he fo rm a t ion o f nanoc rys t a l l ine s t ruc tu re s ha s been repor t ed

by nu m erou s au tho rs . Fo r exam ple , t h in f ilms o f Fe60Co40 p roduc~x l by

electron beam

evaporation and u l t r a -h igh vacu um cond i t ions l ed to c rys t a l s iz es o f abo u t 8 r am. °°4) The f i lms

w e r e s h o w n t o c o n s i st o f t h e s m a l l c ry s ta l li te s a n d ( a b o u t 3 0 v o l % ) g r a i n b o u n d a r i e s . T h i n

f il m s p r o d u c e d

by laser breakdown

c h e m i c a l v a p o r d e p o s i t i o n f r o m n i ck e l a n d i r o n c a r b o n y l s

led to gra in s izes sm al le r th an 10 nm396) Ra pid

solidification

h a s b e e n d e m o n s t r a t e d f o r

severa l p ure m eta ls as w el l as a l loys to resul t in nan ocrystaU ine s t ruc tures . °°6-1°s) Fu r ther -

m o r e ,

electrodeposition

o f N i - P a l lo y s u n d e r s u i ta b l e c o n d i t io n s l e a d s t o n a n o c r y s ta l li n e

structures.009-~12)

In the case of s i l icon,

chemical transport

i n a l o w - p r e s s u r e h y d r o g e n p l a s m a h a s b e e n

u t i li z ed .° 13) The c rys t a l s iz e ( and hyd roge n co n ten t ) va r i ed f ro m 5 nm (12% ) to 15 nm (1% )

a s t h e d e p o s i t io n t e m p e r a t u r e w a s i n cr e a s ed f r o m 1 1 0 -4 0 0 ° C . A c h e m i c al t r a n s p o r t p r o c e s s

fo r gene ra t ing nanoc rys ta l l ine , h igh -s t reng th i ron w h i ske rs ( c rys ta l s iz e be tw een 5 and 30 nm)

w as d ev e lo p ed . (114,115)

Chem ica l vap or depos i t ion (CV D) has been u t i li z ed to syn thes ize nanoc rys t a l l ine ma te r i a l s

based on the n i t r ide s and ca rb ides o f t i t an ium and s i li con . °16) The CV D reac to r u sed w as

a c o m p u t e r c o n t r o l l e d h o t - w a l l r e a c t o r . L a y e r e d d e p o s i t s w e r e p r o d u c e d b y p u l s i n g t h e

r e a c t a n t g a s e s j u d i c i o u s ly u n d e r s o f t w a r e c o n tr o l . T h e d e v e l o p m e n t o f a c o l u m n a r s t r u c tu r e

w h i c h is en d e m i c t o m o s t C V D m a t e r ia l s w a s s u p p r e s s e d b y th e a b o v e p r o c e d u r e . T h e s a m e

p r o c e d u r e w a s a p p l i e d t o g r o w n a n o c r y s t a l l i n e c a r b o n f i l m s a n d f i l a m e n t s f r o m m e t h a n e -

h y d r o g e n m i x tu r e s b y R F - p l a s m a a s s is t ed C V D . C r y s t a l siz es a s s m a ll a s 2 t o 3 n m w e r e

o b t a i n e d .

2.3.4. Sol ge l method

N a n o m e t e r - s iz e d c e r a m i c s t r u c tu r e s h a v e b e e n g e n e r a te d b y m e a n s o f a s o l - g e l te c h n iq u e .

B o t h s tr u c t u r a l a n d c o m p o s i t i o n a l n a n o m e t e r s tr u c t u r es a re o b t a i n e d b y s e e d i n g o f a

ce ramic p recu rso r w i th c rys t a ll ine so l s o f the f ina l equ i lib r ium phase to ca t a lyse nuc le -

ation3~17-127) Th is pro ces s, wh ich co nsis ts o f intr od uc ing crys tal l ine n uclei in a ma trix in or de r

to lower the nuc lea t ion ene rgy requ i red to fo rm the expec ted phase , ha s been known fo r a

long t ime in th e case o f l iquids a nd g lasses .

A s ign if i can t advan tag e o f the so l -ge l t e chn ique in com par i so n to m e thod s invo lv ing

h igh t emp era tu re s ( e.g . c a l c ina t ion , eva pora t ion ) i s t he low t empera tu re o f the me th od .

T h e p r e p a r a t i o n o f s t o ic h i o m e t r ic c o m p o u n d s c o n t a i n i n g o n e o r m o r e c o m p o n e n t s

wi th a h igh v apo r p re ssu re , e .g . Pb in (BaPb)TiO3 fe rroe lec t r ic s , pose s se r ious p rob le m s due to

the P b lo ss . Th i s d i f f icu l ty can be avo ided by the so l -ge l app roach . In f ac t , t he spec if ic su r face

JPMS 33/4. B



24 P R O G R E S S I N M A T E R I A L S S C IE N C E

area o f (BaPb)TiO3 so l -ge l der ived powde rs have been fou nd to be ab ou t 50 m2/g in

com par i son to 4 m2/g fo r po wd ers p repare d by ca l c ined m ixed ox ides . 0~)

3. STRUCTURE

M ost o f t he s tud ies pub l ished so f a r on the s t ruc tu re o f nanocrys t a l l i ne ma ter i a l s have been

car r i ed ou t by us ing nanocrys t a l l i ne so l ids genera t ed by conso l ida t ion o f smal l c lus t e r s

p r o d u ced b y i n e r t g a s co n d en s a t i o n .

3.1.

hemical omposition

S y s t ema t ic s tu d i e s o f t h e i m p u r i t y co n t en t o f s o me n an o c r y s t a ll in e me t a ls ( C u , P d , F e ) h av e

b een p e r f o r me d u t il iz in g m as s s p ec t r o me t r y , ga s ch r o m a t o g r ap h y , X - r ay f lu o r es cence , a t o mi c

ab s o r p t i o n s p ec t ro s co p y , X - r ay p h o t o e l ec t r o n s p ec t r o s co p y , A u g e r e l ec t ro n s p ec t r o sco p y an d

PI X E analysis . Th e s tudies revea led the fo l lowing im puri t ies . °34-1~s) M etal l ic im puri t ies o wing

t o t h e ev ap o r a t i o n p r o ces s an d t h e co mp ac t i o n p r o ced u r e lie in t h e o r d e r o f 10 - 4 a t u p t o

5 . I n co n v en t i o n a l ev ap o r a t o r s ( n o b ak i n g ) t h e o x y g en co n t en t o f me t a l li c s amp l e s w i t h

l o w o x y g en a f fi n it y ( P d , C u ) is o f th e o r d e r o f ab o u t l a t . F o r me t a l s w i t h a h i g h e r o x y g en

af f in i ty (Fe) abou t 4 a t oxyg en was no t i ced . Bak ing o f the evap ora to r wall s r educes i t t o

ab ou t I0 -2 a t so t ha t even reac t ive ma ter i a l s can be p repa red in t he nanoc rys t a l l i ne fo rm.

I n a ll c a se s t h e co n cen t r a t i o n o f h e l iu m w as < 50 p p m.

M ost o f t he meta l l i c impur i t i es resu l t f rom the p i s tons o f t he conso l ida t ion un i t , f rom the

eva pora to r m ater i a l ( e.g. t he W boat ) , o r i s sc raped o f f f rom the co ld - finger su r face . Hence

t h e co n cen t r a t i o n o f me t a l li c i mp u r it ie s ma y b e r ed u ced b y ab o u t o n e o r d e r o f mag n i t u d e

i f th e s ma l l c r y s ta l s a r e p r o d u ced b y s p u t te r i n g ( in s t ead o f ev ap o r a t i o n ) an d b y co a t i n g t h e

su r faces o f t he co ld f i nger and the p i s tons wi th t he same mater i a l as t he nanocrys t a l l i ne

subs t ance to be genera t ed .

In n anoc rys t a l l i ne ox ides genera t ed by pos t -ox ida t ion o f nan ocrys t a l l i ne meta l l ic powders ,

non-s to i ch iome t r i c com pos i t i ons h ave been no t i ced . (m) Fo r exam ple , X- ray d i f f r ac t ion o f a

TiO2 sample p rep ared by ox id i z ing nanocrys t a l l i ne Ti pow der show ed tha t t he s t ab le ru t i le

phase was the on ly phase p resen t , wi th no ev idence fo r un re ac t ed Ti o r o th er Ti -ox ide phases .

Th e c o m p o s i t i o n o f t h e s amp l e w as d e t e r m i n e b y R u t h e r f o r d b ack s ca t te r i n g an a ly s is t o b e

oxyge n def ic i en t i n t he as -p repa red s t a te ,

TiO~.7,

bu t a f t e r s in te r ing a t 300°C, i t becam e near ly

s toich iom etr ic , T iOi .95.

A t t h e s ame t ime , t h e co l o r o f t h e s am p l e ch an g ed f r o m b l ack t o w h it e ,

t he n orm al co lo r o f bu lk fu ti le . S imi l a r ly , nanocrys t a l l i ne ZrO2 spec imens p repare d by

p o s t - o x i d a ti o n o f th e me t a l p a r t ic l e s o b ta i n ed b y D C - s p u t t e r in g o f Z r i n an A r - a t m o s p h e r e

o r b y r eac ti v e R F - s p u t t e r in g o f Z r i n an A r /O 2 a t mo s p h e r e h ad a ch emi ca l co m p o s i t io n o f

ZrO2±0 .2 . X- ray d i f f r ac t ion exper imen t s i nd i ca t ed the p resence o f bo th monocl in i c and

te t r agonal phases i n nanocrys t a l l i ne

ZrO 2. 037

Th e p r ep a r a t i o n o f a ll oy s mad e u p o f

com pon en t s w i th d i f f e ren t vap or p ressu res seems to be poss ib l e by mea ns o f spu t t e r ing an d

ha s be en succ essfu l ly teste d f or Ti4sA152 an d Cug~

M n 9 . 137)

3.2. Density

Th e d en s i t y o f me t a ll ic n an o c r y s t a l li n e ma t e r i a ls v ar ie s b e t w een 7 5 an d m o r e t h an 9 0

of t he c rys t a l li ne dens i ty (depen d ing on the mater i a l ) , appro ach in g 100 af t e r g ra in g rowth .

Th e in i ti a l dens i ty o f nanoc rys t a l l i ne spec imens ob ta ined by co nso l ida t ion o f smal l par ti c l es

s eems to d ep en d o n t h e s p ec i men t h ick n es s an d t h e ch emi ca l co mp o s i t io n . N an o c r y s t a ll in e

Fe an d W (7 nm gra in s ize , abo u t 0 .1 m m th i ckness ) exh ib i t a dens i ty o f abo u t 70 o f a




24

s i n g le c r y st a l. U n d e r s im i l a r c o n d i t i o n s d e n si t ie s o f a b o u t 9 0 o r m o r e a re a c h i e v e d f o r

C u a n d P d . L o w e r d e n s i t i e s a r e n o t i c e d f o r t h e s a m e m a t e r i a l i f t h e s p e c i m e n t h i c k n e s s

in c r e a s e s . I n t h e c a s e o f t h in s p e c im e n s , a l a r g e f r a c t io n o f t h e d e n s i t y d e f i c it s e e m s t o r e s u l t

f r o m t h e r e d u c e d a t o m i c d e n s i ty i n th e b o u n d a r i e s . F o r e x a m p l e , t h e d e n s i t y o f n a n o -

c r y s ta l li n e s p e c i m e n s o f F e ( 7 r im ) o r P d ( 1 0 r im ) w a s o b s e r v e d t o i n c r ea s e f r o m a b o u t 7 5

a n d a b o u t 9 0 , r e s p e c t iv e ly , in t h e a s - c o m p a c t e d s t a t e , t o n e a r ly 10 0 a f t e r a n n e a l in g a t

70 0°C an d 30 0°C . 035A38)N o o p e n p o r o s i t y w a s d e t ec t ed ( g a s p e rm e a t i o n , B E T m e a s u r e m e n t s )

f o r a s - c o m p a c t e d n a n o c r y s t a U i n e f c c m e t a l s ( P d , C u ) . M e t a l l o g r a p h i c i n v e s t i g a t i o n s o f

a s - c o m p a c t e d n a n o c r y s ta U i n e C u a n d P d re v e a le d b e t w e e n 1 a n d 8 v o l c l o s e d p o r o s i t y

i n C u a n d p r a c t i c a l l y n o p o r e s i n P d f o r s i m i l a r c o n s o l i d a t i o n c o n d i t i o n s a n d g r a i n s i z e s .

N a n o c r y s t a l l i n e r e f r a c to r y m e t a l s (e . g. W ) s e e m t o e x h i b i t o p e n p o r o s i t y i n t h e a s - c o m p a c t e d

s t at e . T h e r e s id u a l p o r o s i t y m a y b e r e d u c e d t o v i r tu a l ly z e r o b e x t r u d i n g t h e a s - c o n s o l i d a t e d

mater ia l .

T h e d e n s i t y o f s e ve r a l n a n o c r y s t a l l in e S i fi lm s d e p o s i t e d b y m e a n s o f c h e m i c a l t r a n s p o r t

i n a l o w p r e s s u re p l a s m a h a s b e e n m e a s u r e d . (H g) T h e t e m p e r a t u r e o f d e p o s i t i o n w a s v a r i e d

b e t w e e n 1 8 0 °C a n d 2 6 0 ° C . T h e m e a s u r e m e n t s w e r e p e r f or m e d o n s a m p l e s w h i c h w e r e

p e e l ed o f f t h e s u b s t ra t e s ( m o l y b d e n u m , g l a s s ) u s i n g t h e f l o t a t io n t e c h n i q u e i n a s o l u t i o n o f

t h a l l i u m - f o r m a t e / m a l o n a t e w i t h w a t e r . A f a ir ly r e p r o d u c i b l e d e n s i t y o f 2 . 3 3 g c m - 3 + 2 w a s

f o u n d f o r t h e f o u r s a m p l e s m e a s u r e d . T h i s v a l u e a g r e e s w e l l w i t h t h e d e n s i t y o f c r y s t a l l i n e

s i l i c o n . T h e d e n s i t y o f a m o r p h o u s h y d r o g e n a t e d s i l i c o n w i t h a h y d r o g e n c o n t e n t l a r g e r t h a n

10 at is gen era lly low er. 04°)

T h e d e n s i t y o f c e r a m i c n a n o c r y s ta U i n e s p e c i m e n s i n th e a s - c o m p a c t e d s t a te s e e m s t o b e

c o n t r o l l e d t o a l a r g e e x t e n t b y o p e n p o r o s i t y . A d e t a i l e d s t u d y o n t h i s q u e s t i o n h a s b e e n

p e r f o r m e d b y H a h n

t

a l . 04t'142) for n ano crys ta l l ine TiO 2. T he den s i ty w as m eas ure d w hi le the

s a m p l e s h a d o p e n p o r o s i t y b y t h e n i t r o g e n a d s o r p t i o n m e t h o d ( B E T ) , a n d b y g r a v i m e t r y

o t h e r w i s e . S i m u l t a n e o u s l y t h e g r ai n si z e w a s m o n i t o r e d b y X - r a y d i f fr a c t io n a n d t r a n s m i s s i o n

a n d / o r s c a n n i n g e l e c t r o n m i c r o s c o p y . P l o t t e d i n F i g . 9 a r e t h e g r a i n s i z e s a n d d e n s i t i e s o f

n a n o c r y s t a l l in e T iO 2 a s a f u n c t io n o f t h e s in t e r in g t e m p e r a t u r e . T h e in i t ia l d e n s i t y a f te r

c o m p a c t i o n a t 1 5 0 °C w a s a b o u t 7 5 o f p u r e b u l k ru t il e ( 4 .2 5 g /c m 3 ) . T h i s g r e e n b o d y d e n s it y

e -

Z

L

W

hl

ISC IFrn ot

o • p = O IO O O * C

~ • p = I G P o r

o • p = ° rT igs,V.8)°z 2 l ii

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i 0 0 - -

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o 5 i o o o

S I N T E R I N G T E M P E R A T U R E ( * C )

F IG . 9 . D e n s i t y ( o p e n

s y m b o l s ) a n d g r a i n s i z e c l o s e d s y m b o l s ) o f n a n o c r y st a ll in e T i O 2 a s a f u n c t i o n

o f s i n t e ri n g t e m p e r a tu r e ; i n c l u d e d a r e d a t a f o r p r e s s u re - a s s is t e d s i n te r in g a n d Y - d o p e d n a n o c ~ s t a l f i n e

T i O 2 . T h e s i n t e r i n g t i m e s i n a l l c a s e s w e r e 1 5 h r . 4 2 )



242

P R O G R E S S I N M T E R I L S S C I E N C E

i s r emarkab ly h igh in v i ew o f t he f ac t t ha t i dea l pack ing o f a monod i sper sed d i s t r i bu t ion

o f s p h e r es y ie ld s a d en s i ty o f 7 8 % . Th e h i g h d en s i ty w as a t tr i b u t ed t o a co mb i n a t i o n o f

p rocess ing fac to r s . D ur ing the i n it ia l ox ida t ion o f t he Ti p owd er , t em pera tu re s ri se wel l over

600°C so tha t par t i c l es i n c lose p rox imi ty a re ab l e t o s in t e r and fo rm dense agg lomera t es .

Th e c o m p ac t ed p o w d er is t h u s co m p r i s ed o f a b i mo d a l d i s t ri b u ti o n o f d en s e ag g lo mer a t e s

and smal l par t i c l es fo r wh ich h igh dens i t i es a re eas i e r t o ach ieve . Dens i f i ca t ion dur ing the

co n s o l i d a t io n p r o ces s w as t h u s s u g g est ed to o ccu r b y a co m b i n a t i o n o f g r a in b o u n d a r y s li di ng

an d f r ac t u r e o f ag g lo mer a t e s a s t h e g r een b o d y d en s i t y is f o u n d t o b e a s t r o n g f u n c t i o n o f

com pac t ion p ressu re . L i t t le dens i f i ca tion was foun d to occ ur du r ing p ressu re less s in t e r ing a t

t em pera tu res be low ~ 550°C (F ig . 9 ). Abo ve 600°C, how ever , t he dens i ty i ncreased wi th

t em pera tu re , r each ing a va lue o f 96 -99% bu lk dens i ty a t 900°C. These s in t e ring t em pera tu res

a r e f a r l o w er t h an t h o s e r eq u i r ed fo r s t an d a r d t it an i a p o w d er s . F o r ex amp l e , i t w as o b s e r v ed

tha t d ens i f i ca t ion o f TiO2 wi th an in it ia l par t ic l e s ize o f 1 .3 m requ i red t em pera tu re s in excess

o f 1 ,100°C fo r comple t e dens i f i ca t ion .(142) Th e red uc ed s in ter ing te m per atur e in na no-

crystal l ine TiO 2 i s read i ly exp lained by the sma l l crysta l s ize. (143) W hi le dens i f icat ion beg ins

at 600°C, Fig . 9 il lust rates that th e grain s ize rema ins s table unt i l the s in ter ing at tem pera tures

o f 1 ,000°C o r more . Al though var ious micros t ruc tu ra l f ea tu res can suppress g ra in g rowth ,

pore d rag w as suspec t ed to be t he s t abi li z ing fo rce be low 800°C. T o increase t he d r iv ing fo rce

fo r den s i f ica t ion bu t no t fo r g ra in g row th , nan ocrys t a l l i ne TiO2 was s in t e red by h o t i sos t a ti c

p ress ing us ing abou t 1GP a a t 450 and 550°C. As m ay be seen f rom Fig . 9, t he dens if i ca tion

i s s ign i f ican t ly enh anc ed by th is p rocedu re , a t t a in ing dens i ti es in excess o f 95% a t 550°C,

whi l e g ra in g ro wth i s suppressed . D op ing t r ea tm en t s can a l so in f luence g ra in g row th as

ind ica t ed in F ig . 9 fo r add i t i ons o f 1 .8 and 7 .7 a t% Y to TiO2 . In b o th cases , g ra in g row th

i s no tab ly r educed whi l e dens i f i ca t ion i s enhanced .

Compara t ive pos i t ron ann ih i l a t i on s tud ies o f t he dens i f i ca t ion p rocess o f nanocrys t a l l i ne

and conv en t iona l ceramics du r ing annea l ing l ead to a s imi la r p i c tu re . °44) The s imple two-

s t a t e pos i t ron ann ih i l a t i on behav io r observed in TiO 2 samples w i th g ra in s izes o f 12 nm and

13 m (bo th conso l ida t ed a t 1 .4 GP a) i nd i ca t es t ha t bo th ma ter i a l s began to dens i fy r ap id ly

abov e 500°C. H owe ver , t he nanocry s t a l l i ne m ater i a l d id so mo re r ap id ly wi th i ncreas ing

tempera tu re t han the coar ser -g ra ined sample , r esu l t i ng in a smal l e r vo id o r po re dens i ty a t

900°C. Th e in ten si ty 12 (Fig . 10) o f the l i fet ime s ignal co rres pon ding to p osi t ro n an nihi lat ion

f r o m v o i d - t r ap p ed s ta t e s d ec r ea s e s m o r e r ap i d ly w i th t emp e r a t u r e i n t h e n an o c r y s t a l li n e

s amp l e t h an i n t h e co a r s e r - g r a i n ed o n e , i n d ica t in g a m o r e r ap i d d ec r ea s e o f v o id d en s i ty . Th e

pos i t ron l i f e t ime measuremen t s , wh ich a re sens i t i ve t o vary ing pore s i zes when they a re

smal l , a l so i nd i ca t e smal l e r po re o r vo id s i zes i n t he nanocrys t a l l i ne sample r e l a t i ve t o t he

coar ser -g ra ined mater i a l t h rough the smal l e r va lues o f t he vo id - t r apped pos i t ron l i f e t ime z 2

at al l the s in ter ing temperatures invest igated (Fig . 10) .

3.3. Microstructure

3.3.1. Nanocrystalline metals

The micros t ruc tu re o f nanocrys t a l l i ne meta l s was inves t iga t ed by t r ansmiss ion and

s can n i n g e l ec t ro n m i c r o s co p y , tu n n e l i n g mi c r o s co p y , sma l l an g l e X - r ay an d n eu t r o n d i ff rac -

t i on and X- ray t ex tu re ana lys i s .

3.3.1.1.

Electron microscopy

Stud ies by conven t iona l and h igh reso lu t ion t r ansmiss ion

e l ec t ron m icroscop y (TEM ) ind ica t e t ha t nanoc rys t a l l ine me ta l s cons i st o f smal l c rys t a ll it es

o f d i f f e ren t c rys t a l l og raph ic o r i en t a t ions sep ara t ed by g ra in bo unda r i es (F ig. 11 ) . The

d i s t r i bu t ion o f g ra in s izes mea sure d by T E M is shown in F ig . 12 and seems to ag ree rough ly




43

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~ 400

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I I I I

200 4(30 600 800

TEMPERATURE (°C )

I

I I I 1

1000

F I o . 1 0 . R e s u l t s o f a t w o - c o m p o n e n t l i fe t i m e f i t t o p o s i t r o n a n n i h i l a t i o n l if e t im e d a t a f r o m t h e 1 2 n m ,

1 .4 G P a n a n o c r y s t a l l i n e s a m p l e s ( fi ll e d c i rc l es ) a r e c o m p a r e d t o t h o s e f r o m 1 .3 m , 1 .4 G P a ( o p e n

c i rc l es ) a n d 1 . 3 /~ m , 0 . 3 2 G P a ( t r ia n g l e s ) s a m p l e s c o m p a c t e d f r o m c o m m e r c i a l p o w d e r a s a f u n c t i o n

o f s i n t e ri n g te m p e r a t u r e . T h e p o s i t r o n a n n i h i l a t i o n d a t a w e r e m e a s u r e d a t r o o m t e m p e r a tu r e ; n o

s in t e r i n g a ids we re used . (=~)

w i t h t h e r e su l t s o b t a i n e d b y s m a l l a n g le X - r a y o r n e u t r o n s c a t te r i n g F i g . 1 3 ). In a s -p r e p a r e d

s p e c i m e n s o f P d , C u a n d F e t h e m i c r o g r a p h s g a v e l i t t l e e v i d e n c e f o r a l a r g e v o l u m e f r a c t i o n

o f m a c r o s c o p i c p o r e s . ~145) A s t u d y ° ~ ) o f t h e a t o m i s t ic s t ru c t u r e o f t h e g r a in b o u n d a r i e s b y

h i g h r e s o l u t i o n T E M s u g g e s t e d a s i m i l a r b o u n d a r y s t r u c t u r e a n d w i d t h a s i n c o n v e n t i o n a l

p o l y c r y s t a l s . H o w e v e r , t h e s e r e s u l t s m a y h a v e t o b e c o n s i d e r e d w i t h c a r e . T h e p r e p a r a t i o n

o f t h i n s p e c i m e n s t h e s p e c im e n t h i c k n e s s f o r h i g h r e s o l u t i o n T E M h a s t o b e l e ss t h a n t h e

F I G . 1 1. M i c r o s t r u c t u r e o f a n a n o c r y s a U i n e m a t e r i a l

d e d u c e d f r o m t h e m e t h o d s m e n t i o n e d i n S e c t i o n 3 .3 . T h e

c r o s s - h a t c h e d a r e a s r e p r e s e n t t h e c r y s t a l s o f d i f f e r e n t

c r y s t a l l o g r a p h i c o r i e n t a t i o n s . T h e g r e y r e g i o n s s e p a r a t -

i n g t h e c r y s t a l s a r e t h e g r a i n b o u n d a r i e s .

70 ~

60

5 0

O3

>

n e

LL

O

3 0

W

X

20

Z

10

6 8 10 12 14 16 18 20

CRYSTAL DIAMETER [nm]

F I o . 1 2 . C r y s t a l s i z e d i s t r i b u t i o n i n n a n o c r y s t a l l i n e F e

m e a s u r e d b y t r a n s m i s s i o n e l e c t r o n m i c r o s co p y . °38)




)¢

~ 2

u ' )

0 i~ i~

~ 6 8 l b

CRYSTAL SIZE [nm]

C )

I - -

E

l - -

u ~

u ~

U.I

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. - I

n .

O

Z

F]o . 13 . No rm al ized s i ze d i s t r ibu t ion o f nanocrys taUine Pd ob ta ined f ro m the smal l ang le neu t ron

sca t t e r ing m easu rem en ts by f it ting the exper imen ta l da ta F ig . 14 ) by means o f the p roced ure d i scussed

in R efs 147 and 148 . Th e b rok en l ine rep resen ts the lo g -no rm al d i s t r ibu t ion . °47 ,t~ )

c rys ta l d i ame te r ) t r ans fo rms the th ree -d imens iona l c rys ta l a r rangem en t o f a bu lk nano-

c rys ta l l ine spec imen in to a two-d imens iona l a r rangemen t . Th i s p roces s may change the

bo un da ry s t ruc tu re a s i t a l t e rs the fo rce s be tw een ne ighbor ing c rys ta l s and induces new fo rce s

due to the ene rgy o f the f ree su r face o f the th in spec imen . Fur th e rm ore , due to the h igh

d i f fusiv i ty in nano c rys ta l l ine ma te r i a l s ( c f. Sec t ions 4 .2 and 4 .3 ) a tom s m ay d i f fuse f rom the

f ree su r face o f a th in spec imen in to the g ra in b oun da r i e s a t am bien t t em pe ra tu re s w i th in a

t ime much shor t e r than the t ime o f spec imen p repa ra t ion . Th i s p roces s may a l t e r the

bounda ry s t ruc tu re a s we l l .

3.3.1.2.

Small angle X-ray and neutron dif fraction.

In o rde r to cha rac te r i ze the mic ro -

s t ruc tu re o f nanoc rys ta l l ine P d (g ra in s ize d i s t r ibu t ion , ave rage a tom ic dens i ty in the g ra in

boun da r i e s ) , s tud ie s by means o f sma l l ang le X- ra y and n eu t ron s ca t te r ing had b een

pe rfo rm ed . 047'148) Sm all a ngle scatterin g is diffuse scatte ring at small valu es o f the s catterin g

v e c t o r

q I q l

=

q

= 41r s in 0 /2 ) . I t i s c aused by co r re l a t ions in the a r rangem en t o f s ca t t e ring

cen te r s ex tend ing ove r d i s t ances la rge r than the in te ra tomic spac ing . I f s ca tt e r ing f ro m a

pa r t i c l e o f ave rage s ca t t e r ing l eng th de ns i ty pp em bed ded in a m a t r ix o f ave rage s cat t e ring

length dens i ty Pm is cons id ered , the sca t te r ing c ross -sec t ion (SC S) is g iven by:

I ~ _ ° ° e iq d r 2

dd_~ (q) = A p F (r )

< O

wh ere Ap is (Pro - - Pp), and F( r) i s the fo rm fun c t ion of the par t ic le : F (r) = 1 ins ide, F(r ) = 0

ou t s ide the pa r t i c l e .

I f N pa r t i c le s a re d i s t r ibu ted in the s ample in an unco r re la t ed way , the SCS i s enhanced

by a fac to r N . I f co r re l a t ions in the a r rangem en t o f d if fe ren t pa r t ic l e s a re im por tan t , t he

SCS i s changed in a w ay cha rac te r i s t i c o f the spec i fi c co r re l a t ion . Fo l low ing P oro d °49) one

m ay qua l i t a t ive ly d is t ingu i sh two types o f co r re l a tion : l iqu id - typ e co r re l a t ions causing a

dec rea se o f the SCS a t sma l l q. Th i s k ind o f co r re l a t ion a r i s e s, fo r example , f rom dense

pack ing o f sphe r i ca l pa r t ic l e s. G as - ty pe co r re l a t ion causes an inc rea se o f the SCS a t sma l l

q and m ay a r i se f rom dense pack ing o f non-sphe r i ca l pa r t ic l e s tha t to uch on e ano the r in m any

places.

F igu re 14 show s the SCS o f neu t ron s fo r a nanoc rys ta l line P d s ample . The so l id line was

computed f rom the s i ze d i s t r ibu t ion

S R )

show n in F ig . 13 o f s ca tt e r ing un i t s ob ta ined f rom



N A N O C R Y S T A L L I N E M A T E R I A L S 2 4 5

E

o

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L

u 0

e

Z

k

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(.3

1 0 s .

x

x x

1 0 4

1 0 3

1 0 2

1 0 o

1 0 1

0 .1 1

S C A T T E R I N G V E C T O R q [n rn 1 ]

F I G . 1 4 . S m a l l a n g l e n e u t r o n s c a t t e r i n g c r o s s s e c t i o n o f n a n o c r y s t a l f i n e P d . T h e s o l i d l i n e c o r r e s p o n d s

t o t h e c a l c u l a t e d s c a t t e r i n g c r o s s s e c t i o n o b t a i n e d f r o m t h e s i z e d i s t r i b u t i o n o f F i g . 1 3 i n t h e e n t i r e

R r a n g e a d m i t t e d P , ~ = 2 0 0 n m ) . T h e d a s h - d o t t e d l i n e c o r r e s p o n d s t o t h e s i z e d i s t r ib u t i o n o f F i g .

1 3 , t r u n c a t e d a t R = 1 5 r im ; t h e b r o k e n l i n e g i v e s t h e l o g - n o r m a l d i s t r i b u t i o n a p p r o x i m a t e d t o t h e

s e c t i o n o f t h e s i z e d i s t r i b u t i o n s h o w n i n F i g . 1 3 a t s m a l l c r y s t a l s i z e s . t 7 )

e x p e r i m e n t a l d a t a b y t h e m e t h o d g i v e n b y G l a t t er . ° 5°) T h e s iz e d i s t r ib u t i o n s h o w n i n F i g . 1 3

m a y b e d i v i d e d i n t o t w o r e g io n s : t h e r e g i o n o f s m a l l r ad i i ( R ~< 1 5 n m ) - - c o n t a i n i n g t h e

a s y m m e t r i c p e a k a t 2 n m - - r e f l e c t s t h e s i ze d i s tr i b u t i o n o f P d c r y st a ll it e s. T h e c o n t r i b u t i o n

a t R > 1 5 n m i s d u e t o c o r r e la t i o n s in t h e a r r a n g e m e n t o f t h e c r y st a l li t e s.

Th e c r y s t a ll i te s i z e d i s t r ib u t io n c e n t e r e d a t R ,~ 2 n m i s s im i la r t o t h e l o g - n o r m d i s t r ib u t io n

f o u n d f o r i s o la t e d c r y s t a ll i te s . ° 1) Th e m e a s u r e d s i z e d i s t r ib u t io n a g r e e s r e a s o n a b ly w e l l w i t h

d ir e c t m e a s u r e m e n t s b y t r a n s m is s io n e l e c t r o n m ic r o s c o p y . (t38) Th e m e a s u r e d s i z e d i s t r ib u t io n

d o m i n a t e s t h e b e h a v i o r o f t h e S C S a t l ar g e q . I n t h i s ra n g e t h e S C S c a l c u l a t e d f r o m t h e s iz e

d i s t r ib u t i o n o f F i g . 1 3, t r u n c a te d a t 1 5 n m , c o i n c i d e s w i t h t h e e x p e r i m e n t a l c u r v e ( c o m p a r e

t h e d a s h - d o t t e d l in e in F i g . 1 4) . A t s m a l l q - v a l u e s t h e S C S i s e n h a n c e d a b o v e t h e o n e e x p e c t e d

f o r t h e c r y s t a l l i t e s d u e t o s p e c ia l c o r r e la t i o n s b e t we e n t h e c r y s t a l s . Ev id e n t ly t h i s c o r r e la t i o n

i s o f g a s - t y p e . I n o t h e r w o r d s , t h e c r y s ta l li te s a re n o t s p h e ri c a l a n d m a y t o u c h in m a n y

p l a c es . A t t h e s m a l l e st q - v a l u e s c o n t r i b u t i o n s f r o m v e r y l ar g e s c a tt e r in g u n i t s , p o s s i b l y v o i d s

o f s o m e # m s iz e a re o b s e rv e d . A d d i t i o n a l i n f o r m a t i o n a b o u t t h e m i cr o s tr u c tu r e m a y b e

o b t a i n e d f r o m t h e e v a l u a t i o n o f t h e S C S i n a b s o l u t e u n i t s . F o r t h i s p u r p o s e t h e n a n o c r y s -

t a l lin e m a t e r ia l wa s a s s u m e d t o c o n s i s t ( F ig . 1 1 ) o f c r y s t a ll i te s w i t h a n a v e r a g e d e n s i t y ~ c

( e q u a l t o t h e d e n s i t y o f s i n g le c r y s ta l li n e P d ) . A v o l u m e f r a c ti o n , v c, o f th e t o t a l v o l u m e o f

t h e m a t e r ia l i s f i l l e d w i t h c r y s t a l l i t e s . Th e b o u n d a r i e s o c c u p y a f r a c t io n o f 1 - r e . Th e

c r y s t a U i t e s a r e a s s u m e d t o b e e m b e d d e d i n a u n i f o r m m a t r i x o f g r a i n b o u n d a r i e s w i t h a

u n i f o r m d e n s i t y . O n t h e b a s i s o f t h i s m o d e l , t h e b o u n d a r y d e n s i t y m a y b e c o m p u t e d f r o m

t h e m e a s u r e d S C S i n a b s o l u t e u n i t s a n d t h e m a c r o s c o p i c s a m p l e d e n si ty . T h e m e a s u r e m e n t s

p e r f o r m e d °4 7) y i e ld a b o u n d a r y d e n s i t y o f a b o u t 6 0 % o f t h e l a t ti c e d e n s i t y . T h i s i s a




r emarkab ly l ow dens i t y fo r a so l i d s t a t e s t ruc tu re . In f ac t i t i s much lower t han the dens i t y

o f g lasses wh ich usua l ly dev i a t e by a f ew percen t f rom the c rys t a ll i ne dens i t y . On the o ther

hand , such a r educ ed den s i t y i n t he i n t e r f ac i a l r eg ions seems cons i s t en t wi th t he dens i ti es o f

c o m p u t e d g r a i n b o u n d a r y s t ru c tu r e s(15) as wel l as w i th th e red uce d de nsi ty obs erve d in th e

co re o f gra in bo un dar ies 2°~) an d dis locat ions . ~53) In fact , i t has been po inted ou t in the f i rs t

sect ion tha t the sm al l s ize of the crystal l i t es in na noc rysta l l ine m ater ial s i s likely to resul t in

a r ed u ced b o u n d a r y d en s i t y d u e t o t h e v e r y li m i ted r ig id b o d y r e l ax a ti o n .

C l ea r l y , t h e meas u r ed b o u n d a r y d en s i t y i s co r r ec t o n l y i f a s s u mp t i o n ap p l i e s t h a t t h e

SCS d ue t o t h e r es idua l po ros i t y o f a nan ocrys t a l l i ne sam ple is neg lig ib l e i n com par i son

to t he sca t t e r ing o r ig ina t i ng f rom the den s i t y d i f fe rence be twe en crys t a l s and the su r -

r o u n d i n g g r a i n b o u n d a r i e s . Th e s i mi la r it y o f t h e g r a i n s ize d is t r ib u t io n b y m ean s o f TEM

(Figs 12 an d 15) and SCS (F igs 13 and 16) seems to su ppor t t h i s assump t ion . M easure-

men t s o f t h e r e s i d u a l p o r o s i t y b y mean s o f co n v en t i o n a l me t a l l o g r ap h y u s i n g s can n i n g

e l ec t ro n mi c r o s co p y (S ec t io n 3 .2 ) s ug g es t a m ax i m u m e r r o r o f 3 0 % f o r t h e mea s u r ed

b o u n d a r y d en s i t y i n n an o c r y s t a ll i n e P d . I n o t h e r w o r d s , t h e av e r ag e b o u n d a r y d en s i t y i n

n an o c r y s t a l li n e P d s eems to b e b e t w een ab o u t 6 0 % an d 7 0 % o f t h e cr y s ta l d en s it y . A n

i n te r r aci a l d en s i t y o f ab o u t 6 0 % t o 7 0 % o f t h e la t ti c e d en s i ty w o u l d in d i ca te a r a t h e r o p e n

atom ic s t ruc tu re wi th a mu ch b ro ade r d i s t r ibu t ion o f i n t e ra tom ic spac ings t han in a l i qu id

or g lass , t he dens i t y o f w h ich d i ff e r s f rom the c rys t a l l ine dens i t y by a f ew percen t . The l ow

in t er fac i a l dens i t y ag rees wi th t he enh anc ed hyd rog en so lub i li ty , specif ic hea t , d i ffus iv i ty , the

r ed u ced e l a s t i c co n s t an t s o f n an o c r y s t a l l i n e s p ec i men s a s w e l l a s w i t h t h e a r g u men t s p u t

fo rw ard i n Sec t ion 1. I t is p resen t ly no t kn ow n ho w the f r ee vo lum e is d i s tr i bu t ed be twe en

t h e g r a i n b o u n d a r i e s a n d t h e t r ip l e j u n c t i o n s f o r m ed a t t h e i n te r s ec ti o n b e tw een t h r ee

boundar i es .

Measuremen t s o f t he [111] and [200] po l e f i gu res o f as -p repared nanocrys t a l l i ne Pd and

Cu revea l ed no p refered o r i en t a t i on o f t he c rys t a l l i t es . Hence i sos t a t i ca l l y conso l ida t ed

nanocrys t a l l i ne mater i a l s seem to be f r ee o f any s t rong t ex tu re .

2 0 0

1 5 0

u }

< ~ z

n,.,

u . 1 0 0

o

n , .

L U

m

z 5 0

I I I i I i

I

5 1 0

l T i 0 2

1 5 2 0 2 5 :~ 0

GRAIN DIAMETER nm)

FIG. 15. Grain-size distribution fo r an as-com pacted TiO2 rutile) sample determined using TEM. ~54)




q

_o

g g

Q c~

~ ~.

Z

rl

0

0

o

o

o

o

0

v - a s r e c e i v e d

; o

8 . 0 1 ~ . o

RADIUS nm)

(a)

1 6 0

2 0 . 0

o.

U 3

. .U 1 3

I o

m e ~-

~ O N

n

O L

m

IE z

z ~_

£

o

o - 4 hr s @ 5 5 0 C

f ~

O o

O o

i

4.0 8 0 12.0 16.0 20 0

RADIUS nm)

b )

F IG . 1 6 . S i z e d is t r ib u t i o n s d e t er m i n e d b y t h e m a x i m u m e n t r o p y m e t h o d f o r: a ) th e a s - c o m p a c t e d

n a n o c r y s t a l l i n e T i O 2 s a m p l e a n d b ) t h e s a m e s a m p l e a f t e r i s o t h e r m a l s i n t e r i n g f o r 4 h r a t 5 5 0 ° C . ° 5s )

3 . 3 . 2 .

N anocr ysta l l in e ceram ics

3 . 3 . 2 . 1 . G r a i n si ze d ist r i bu t i on an d boundary dens i ty T h e g r a i n s i z e d i s t r i b u t i o n a n d

b o u n d a r y d e n s i ty o f n a n o c r y s t a l li n e c e r am i c s h a s b e e n s t u d i ed s o f ar fo r T iO 2 m o s t

e x t e n s i v e l y . F i g u r e s 1 5 a n d 1 6 s h o w t h e g r a i n s iz e d i s t r i b u t i o n m e a s u r e d b y s c a n n i n g

t r a n s m i s s i o n e l e c t r o n m i c r o s c o p y ttg l ls 4) a n d s m a l l a n g l e n e u t r o n s c a t t e r i n g . °47 148 t55)

F i g u r e 1 7 s h o w s a s c a n n i n g e l e c t ro n m i c r o g r a p h o f t h e fr a ct u re s u r fa c e o f a s - c o m p a c t e d

a n d a n n e a l e d n a n o c r y s t a l l i n e T iO 2 . 0a l) T h e i n d i v i d u a l g r a in s o f t h e a s -p r e p a r e d s a m p l e

( F i g . 1 7 a ) h a v e a n a v e r a g e s i ze o f 3 0 n m . A s t h i s i s a b o u t t w i c e t h e s i z e m e a s u r e d

b y t r a n s m i s s i o n e l e c t r o n m i c r o s c o p y a n d X - r a y d i f f r a c ti o n , m o s t o f t h e p a r ti c le s v is i b le

JPMS 33/~4~




a ) b )

FI~. 17. High resolution scanning electron micrographs of nanocrystallineTiO~. Left side (a): as

prepared; right side (b): annealed for 14 hr at 1,173 K in an oxygen atmosphere.~4~)

in Fig. 17 are suspected to consist of several crystals. After sintering at 1,173 K for

14 hr a much denser structure than in Fig. 17a with more facetted grains was observed.

No porosity was detected after annealing. In fact, the density was more than 90 of the

crystalline value.

Small angle neutron scattering studies have been performed in the as-consolidated

condition and after isothermal sintering anneals up to 23 hr a t 550°CY 5) The data obtained

was analyzed by the maximum entropy method. This method devises a way to estimate the

power spectrum of a given real function by mapping it onto the unit circle of the complex

z-plane. The power spectrum of the given function is then completed by fitting the function

in the z-plane by a suitable polynomial of the form of a finite Laurent series. For the

as-consolidated material a boundary density of about 60 to 70 of the crystal density was

found, assuming the crystals to be ideal. The average boundary width was about 0.5 nm.

3.4.

Effec t o f onsol idation Pressure on M icros truc ture

The effect of the consolidation pressure on the structure of nanocrystalline metals was

studied by means of M6ssbauer spectroscopy and positron annihilation for Fe (7 nm crystal

size) and Ni (70 nm crystal size), respectively. The M6ssbauer spectra (Fig. 18) observed°56)

suggest the formation of a growing volume fraction of grain boundaries with increasing

pressure approaching a constant value beyond about 3 GPa. Studies by electron microscopy

support this result. Increasing pressure reduces the pore density and replaces free surfaces (e.g.

pore surfaces) by grain boundaries.

Figure 19 summarizes the positron lifetime and the lattice constant of the nanocrystalline

Ni as a function of consolidation pressure. In fact, the positron lifetime spectrum057'lss)

consisted of a short and a long component. The short one corresponded to single vacancies

whereas the long one indicates clusters of about 8 vacancies (cf. Section 3.7.1), The vacancies



N N O CRY ST LLI N E M TERI LS 49

a n d v a c a n c y c lu s t er s , th e c o n c e n t r a t i o n o f w h i c h is f o u n d t o b e a b o u t 1 0 - 4 a r e p r o p o s e d t o

o r i g in a t e f r o m t h e m i g r a t io n o f g r ai n b o u n d a r y d i s lo c a t io n s d u r i n g c o n s o l i d a t io n . T h e h i g h

vacan cy concen t ra t ion m ay enhance the d i f fus iv i ty in the se ma te r i a l s a nd thus re su l t in r ap id

densi f ica t ion .

3.5.

Therm al S t ab i l i t y

3 5 1 Nano crys t a l li ne m e t a l s

The the rma l s t ab i l it y o f nanoc rys t a l l ine m e ta l s was s tud ied by t r ansmiss ion e l ec t ron

m i c r o s c o p y , M r s s b a u e r s p e c t r o s c o p y , s m a ll a n d w i d e a n g le X - r a y d i f fr a c ti o n a n d p o s i t r o n

ann ih i l a tion . Nan oc rys ta l l ine m e ta l s exh ib i t c rys t a l g row th a t e l eva ted t empe ra tu re s . Ro ug h ly

speak ing , i n me ta l s w i th a c rys t a l s iz e o f abou t 10 nm, s ign if i can t c rys t a l g rowth (doub l ing

of the c rys t a l si ze in abou t 24 h r ) was no t i ced a t am bien t t emp e ra tu re o r be low i f t he

equ i l ib r ium me l t ing t emp e ra tu re , T in , was low er than ab ou t 600°C (e.g . in nanoc rys t a l l ine t i n

o r l e ad ) . Ho we ve r , i f Tm was h ighe r , t he s t ab i l i t y aga ins t g ra in g row th seems to b e enhanced ;

for exam ple , fo r F e to ~<200°C, for P d to ~< 150°C a nd for C u t o ~< 100°C. An exam ple °3s)

is s h o w n i n F i g . 2 0. T h e s a m e p i c tu r e e m e r g e s f ro m s t ud i e s b y m e a n s o f M r s s b a u e r

spec t roscopy and X- ray d i f f rac t ion .

F i g u r e 2 1 s h o w s a c o m p a r i s o n o f th e M r s s b a u e r s p e c t r a o f t h e s am e s p e c i m e n b e f o re a n d

a f t e r annea l ing a t 500°C in v acuum , o38) The second spec t rum (F ig . 21b) co inc ides w i th the

o n e o f c o n v e n t i o n a l F e w h e r e a s t h e f ir st o n e c o n s is t s o f a c o m p o n e n t w h i c h c o r r e s p o n d s t o

the ~ t -Fe spec t rum and a b road componen t due to the g ra in bounda r i e s ( c f . Sec t ion 3 .7 .3 ) .

N o c h a n g e o f th e M r s s b a u e r s p e c t r u m w a s n o ti c e d if t h e s a m e s p ec i m e n w a s a n n e a l ed i n

vacu um fo r 10 h r a t 100°C . In o rde r to av o id ox id a t ion e f fec ts a ll spec imens we re neve r

exp ose d to a i r b efor e an d a f te r annea l ing , o38)

X- ray d i f f rac t ion s tudies (cf . Sec t ion 3 .6 .1) o f nano crysta l l ine Fe wi th an in i t ia l gra in s ize of

6 nm ind ica te the fo l lowing e f fec ts . Annea l ing (1 h r a t 500°C) reduces the peak wid th and the

background in t ens i ty to the va lue s cha rac te r i s t i c fo r a conven t iona l po lyc rys t a l°56) su gg esti ng

t h a t t h e m a j o r i t y o f t h e g ra i ns h a v e g r o w n t o a s iz e b e y o n d a b o u t 3 0 n m . A s y s t e m a t i c s t u d y

of the annea l ing beh av io r o f nanoc rys t a l l ine P d by means o f pos i t ron ann ih i l a t ion (cf . Sec t ion

3 .7 .1 ) was pe r fo rmed by Schae fe r

e t

a l. 059) and led to the fo l low ing resul ts . In as-p repar ed

spec im ens, th e sp ect ra su gge st pr ed om ina ntl y tw o l ifet imes, z~ = 183 +__ ps an d z2 = 391 + 2 ps.

These tw o l i fe t imes we re in t e rp re t ed in t e rms o f pos i t ron ann ih i l a t ion a t s i te s in the

b o u n d a r i e s a s s o c i a te d w i t h a f r e e v o l u m e o f a b o u t o n e v a c a n c y a n d s p h e ri c al c lu s t er s o f a b o u t

e igh t vacanc ie s . Th i s r e su lt seems cons i s t en t w i th the expec ted op en s t ruc tu re o f the

bou nda r i e s (F igs 4 , 5 and 6 ) and the rema rkab ly low dens i ty in the boun da r i e s (Sec t ions 3 .3 .1

and 3.3.2).

In the pos i t ron l i f e t ime measu remen t s a f t e r i soch rona l annea l ing , t he fo l lowing fou r

tempera ture regimes were not iced (c f . Fig . 22) .

( I ) 20°C-350°C: The inc rea se o f me an po s i t ron l if e time was a t t r ibu ted to a r e -o rde r ing and

grow th o f in t e rfac ia l f r ee vo lum es . The num er ica l ana ly s i s o f the spec t ra show s tha t t he

l i fe t ime increase (Fig . 22) i s in i t ia l ly due to an increase of ra t io I 2 / I of the two l i f e t imes

obs erv ed in these m ater ia ls a t 150°C w i tho ut s igni f icant changes o f ~ or ~2 (Fig . 23). This

ind ica te s a r e l a t ive inc rea se o f the number o f s i t e s w i th l a rge r f r ee vo lume a t t he expense o f

vacancy-s i zed free vo lum es in the bounda r i e s . The co ncen t ra t ion dec rea se o f vacancy-s i zed

f ree vo lum es is un l ike ly to o ccu r in the c rys t a ll i te s becaus e h igh - t empera tu re s tud ie s o f bu lk

Pd c rys t a l s i nd ica te tha t mo nova canc ie s a re f rozen- in be lo w 120°C . ttr° ) The inc rea se o f ~ and

z2 abo ve 180°C is a t t r ibu ted to an agg lom era t ion o f vacancy-s ized f ree vo lum es and v acancy



25

o 1.0e

H

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VELOCIIY [mm/s]

PRESSURE 27.5MPo T=77K

a )

VV

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VELOCITY [mmls]

PRESSURE 32 .5 MPo T=77K

c )

K/I;

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4 6

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VELOCIIY [R~.]

PRESSURE 30MPa T=77K

b)

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-6 -4 -2 8 2 4 6

VELOCIIY En,'s]

PRESSURE 75MPo T=77K.

d)

I I I I

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VELOCETy Emm/s3

PRESSURE 85 MPa T: 77K

e )

FIG. 18 a - -e )

- \ / '

:




25

7.

o 1.00

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tO

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to

z

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W

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k ;

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6 3 3 6

VELO ITY

[mmls]

PRESSU RE 5 GPQ T= 77K

r )

F I G . 1 8 . M6 s s bauer s pec tra o f nanocrys ta l l ine F e as a fun c t ion , o f cons o l id at ion press ure . The n arrow

s ix - line com p one nt re s u lt s from F e a to m s s i tuated in the ~ -F e crys ta l lat ti ce . T he re s idua l broad

com pon ent i s due to the gra in boun dar ie s . ¢ tm

a g g r e g a t e s . T h e p h e n o m e n a o b s e r v e d i n t h i s t e m p e r a t u r e r a n g e a r e p r o p o s e d t o o c c u r i n t h e

b o u n d a r i e s w i t h o u t a n y d i s p l a c e m e n t o f t h e s e in t e r fa c e s b y c r ys t a l g r o w t h w h i c h a p p e a r s t o

be ne glig ibl e. ¢16t)

I r r e v e r s i b l e r e - o r d e r i n g p h e n o m e n a i n t h e i n t e r f a c e s a p p a r e n t l y o c c u r e v e n b e l o w t h e

a n n e a l i n g t e m p e r a t u r e s w h e r e c h a n g e s i n f a r e o b s e r v e d .

I I ) 3 5 0 ° C - 5 0 0 ° C : T h e d e c r e a se o f f i n F i g . 2 2 a r i s es f r o m a d e c r e a s i n g r a t io I 2 / I t T h i s

c h a n g e w a s i n te r p r et e d i n t e r m s o f t h e a n n e a l i n g - o u t o f v a c a n c y a g g r e g a t e s.

I I I ) 5 0 0 ° C - 9 0 0 ° C : m e a n p o s i t r o n l i fe t im e ~ r e m a i n s u n a l t e r ed a l t h o u g h s u b s t a n t i a l

c r y s t a l li t e g r o w t h i s o b s e r v e d . 0 61 T h i s o b s e r v a t i o n m a y b e u n d e r s t o o d i n t e r m s o f t h e p o s i t ro n

d i f f u s io n l e n g t h L + ~ 1 0 0 n m ° 62 ) in t h e c r y s t a l l it e s . L + s t il l b y f a r e x c e e d s t h e c r y s t a l li t e

d ia m e t e r d a n d t h e r e f o r e t h e p o s i t r o n s c a n a r r iv e q u a n t i t a t i v e ly a t t h e in t e r f a c ia l t r a p s , t h e

a t o m i c s t r u c tu r e o f w h i c h a p p e a r s t o b e u n c h a n g e d d u r i n g c r y st a l g r o w t h a c c o r d i n g t o t h e

o b s e r v e d u n a l t e r e d l i f e t im e s z ~ a n d T2 .

t ~

c

P

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PRESSURE GPo)

FIG. 1 9 . P o s i t r o n l i f e t i m e 3 2 ) a n d in t e n s i t y / 2 ) o f

n a n o c r y s t a l l i n e N i a s a f u n c t i o n o f t h e c o n s o l i d a t i o n

pres sure .O 57)

180

n ~

16o

u J

140

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120

v- 100

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>-

o~ 80

c .

40 >-

~- ,,, 60

2 5 4

~ J

~ 2

Z

i _ . . l

100 200 300 400 500

ANNEAUNG TEMPERATURE °C)

6 0

FXG. 20 . Average crys ta l d iam eter o f nanocrystaUine F e

as a func t ion o f the annea l ing tam perature anne a l ing

t im e w as 10 hr a t any on e o f the tem peratures g iven in

th i s

f ig ur e ) , ( t3s )



5


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V E L O C T T Y

Emm =]

F IG . 2 1 . C o m p a r i s o n o f t h e M 6 s s b a u e r s p e c tr a o f t h e s a m e n a n o c r y s ta i l in e F e s p e c i m e n b e f o r e a ) a n d

a f t e r C o) a n n e a l i n g 1 0 h r a t 5 0 0 ° C ) . l ~ )

. . . . 1 . . . . T . . . .

35O

: Ew 30 0 ~ ^

~-- 2 5 0

I L l

L L t o

Z

I I " 2 0 0

0

z

t -

o t 5 0

o .

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. . . . . . . ' . . . . .

5 0 0

1 0 o o i 5 o 0

T a { o C }

A N N E A L I N G T E M P E R A T U R E

F IG . 2 2 . V a r i a t i o n o f t h e m e a n p o s i t r o n l i f e ti m e a f t e r

i s o e h r o n a l a n n e a l i n g t , = 3 0 r a i n ) o f n a n o c r y s t a l l i n e P d

i n h i g h v a c u u m . ° sg )

4 3 O

4 t 0

~ 39

7 -- ~ 3 7 0

' , ' i -, 3 5 0

I J .

_.1

z 2 0 0

o ~ ~ 1 8 0

CL

. . . . i . . . . I , , , , i , ,

I ¢ ~ 0 , , , . o ~

| . . . . i . . . . i . . . . J • .

. . . . w . . . . I . . . . i - -

60

o r f U n g o

U J r ~ l

z . . .- 4 o

3 0 . . . . . . . . . . . , , , I , ,

1 0 0 2 0 0 3 0 0

T a [ ° C J

A N N E A L I N G T E M P E R A T U R E

F I G . 2 3 . P o s i t r o n l i f e t i m e s ~ l a n d 3 2 a s w e l l a s t h e

c o r r e s p o n d i n g r e l a t i v e i n t e n s i t i e s I I < > < ~ ) a n d 12 [ : ] E l )

a f t e r i s o c h r o n a l a n n e a l i n g G = 6 0 r a i n) n a n o c r y s t a l l in ¢

P d i n h i g h v a c u u m . ~59)




( IV) Annea l ing abo ve 900°C: A bov e 900°C the m ean l if e time ~ dec rea se s because d > L +

so tha t a m easu rab le f rac t ion o f pos i t rons i s ann ih i la t ed in the f ree de loca l ized s t a t e in

und i s tu rbed l a rge r c rys ta ll it e s . F ro m the mean pos i t ro n l i f e time longe r than Zr, pos i t ron

l i fe time in the f ree de lo ca l ize d s ta te , a t Ta = 1 ,280°C one is led to conc lude , tha t ev en a t

t h e se h i gh a n n e a li n g t e m p e r a t u r e s a m e a s u r a b l e n u m b e r o f in t e rf a ce s w i t h p o s i t r o n t r a p s

i s p re sen t in the spec imens . In fac t , i t appea rs tha t the nanoc rys ta l l ine s t ruc tu re i s pa r t ly

s t ab le up to annea l ing t empera tu re s c lose to the me l t ing po in t . Th i s i s conf i rmed by

t ransmis s ion e l ec t ron mic roscopy (TEM) s tud ie s a f t e r p ro longed ( s eve ra l hours ) annea l ing a t

1 , 2 8 0 ° C 1 6 3 ) showing nanoc rys ta l l ine reg ions w i th c rys taUi te s i ze s sma l l e r than 100nm

coexis t ing wi th la rge recrys taUized gra ins .

Simila r resul ts w ere ob ta in ed f ro m smal l angle X- ray sca t te r ing exper im ents (147'1~) per-

fo rm ed d ur ing annea l ing o f nanoc ry s ta l line Pd s ample s ( in it ia l g ra in s ize 8 nm, annea l ing

t ime 1 ,800 s a t 520 K and 1 ,023 K, respec t ive ly) . Th e resul ts of these me asure m ents a re

com pare d in F ig . 24 wi th the da ta o f the a s -p repa red spec imen (300 K) . Tw o reg ions

may be d i s ce rned , wh ich behave d i f fe ren t ly on recove ry : a t l a rge q -va lues the func t iona l

depend ence o f the s ca t t e ring c ros s s ec t ion on the d i f f rac t ion vec to r (q ) r ema ins nea r ly

unchan ged , bu t the s ca t t e red in tens ity dec rea se s by ab ou t a f ac to r o f 2 a t 1 ,023 K . A t sma l l

va lues o f q , t he dec rea se o f the s ca t t e r ing c ros s s ec t ion wi th q ge t s s t e epe r a f t e r annea l ing ,

so tha t the in tens i ty rema ins nea r ly unchanged a t the sma l l e s t q -va lues measu red . These

obse rv a t ions a re com pa t ib le w i th the t r ans fo rm a t ion o f a pa r t o f the c rysta ll i te s e i ther

in to som e la rge c rys ta l s , o r in to a sys tem o f c rysta ll i te s w i th h igh gas - ty pe co r re l a t ion .

A f rac t ion o f the c rys ta l li t es r ema ins ra the r u na f fec ted by the annea l ing up to 1 ,000 K , and

causes the unchanged s ca t t e r ing s igna l a t l a rge q . One rea son fo r the appa ren t s t ab i l i ty o f

som e reg ions o f a nanoc rys ta l l ine ma te r i a l m ay b e the h igh exces s en t rop y (c f. Sec t ions 4 .4

and 4.5).

G r y a z n o v e t a l . ~ 64 ) s tud ied the p roces se s occur r ing du r ing annea l ing o f nanoc rys ta l l ine

Cu and Ni spec imens (g ra in s ize 50 to 70 nm ) by m easu r ing the sh r inkage o f po ro us

spec imens . Th e h igh ra t e s o f sh r inkage obse rv ed du r ing the in it ia l s t age o f s in te ring w ere

in te rp re ted in t e rms o f a d i f fus iona l mo t ion o f ind iv idua l c rys ta ll i te s a s we l l a s by a bou nd a ry

ene rgy induced ro ta t ion . These p roces se s we re sugges ted because the sh r inkage ra t e obse rved

e x c e e d ed th e o n e e x p e c t e d o n t h e b a s is o f v o l u m e a n d b o u n d a r y d i ff u si v it y b y a b o u t t h r ee

o rde rs o f magn i tude . In v iew o f the h igh d if fusiv it ie s me asu red in nanoc rys ta l l ine s ample s

(cf . Sec t ions 4 .1 and 4 .2), the h igh shr inkag e ra tes o bserv ed appe ar to be cons is tent wi th

a c on ve nti on al s intering m od el as w ell. Sim ilar s tud ies (L65-167) we re p erf or m ed by oth er

au tho rs u t il iz ing pos i t ro n l if e time spec t ro scopy to cha rac te r i ze the de fec t s invo lved in

1 0 3 : • , .

1 ' " . . . 3 0 0 K

= l o 2 ' . . s 2 o K ' " ' . .. .

J . x

0 1 . 1 0 2 3 K " " ' . . . " h ~ .

1 0 o ' . . .

.

z i % ' ~ .

~ ,

~ - 1 0 4 1

1 0 - 2 h _ _ ~ , ,

o . ~ 4

S C A T T E R I N G V E C T O R q [ n m - 1 ]

F IG . 2 4 . S m a l l a n g l e s c a t t e r i n g c r o s s s e c t i o n o f X - r a y s f o r n a n o c r y s t a l l i n e P d , a n n e a l e d a t t h e

tem pe ra tu res indic a ted . {~47)



54


s in te r ing an d g ra in g row th o f nanoc rys ta ll ine N i and Cu . In the in i t ia l s t a t e o f s in te r ing

a n d g r a i n g r o w t h , a h i g h c o n c e n t r a t i o n ( a b o u t

1 0 - 1 )

of exces s vacanc ie s was obse rved .

These vacanc ie s a re p roposed to o r ig ina te f rom bounda ry mig ra t ion . Ev iden t ly , a h igh

c o n c e n t r a t i o n o f v a c a nc i es m a y e n h a n c e t h e r a t e o f si n te r in g b y m a n y o r d e r s o f m a g n i t u d e,

a s was obse rved . A con ce ivab le app l i ca t ion o f th is e f fec t was p ro po sed in t e rms o f the

the s in te r ing o f m ater ia ls wi th h igh mel t ing po ints °68 ~69) such as W , M o, e tc . I f such

ma te r i a l s a re mixed wi th a nanoc rys ta l l ine subs tance wi th the s ame o r w i th d i f fe ren t

chemica l compos i t ion , e .g . W, Mo, N i , e t c . , g ra in o r in t e rphase bounda r i e s be tween the

nanoc rys ta l l ine and the coa rse -g ra ined ma te r i a l a re fo rmed . These in te r face s ac t a s e f f i c i en t

vacan cy source s and thus en hance the d i f fusiv i ty and the s in te r ing ra t e. Th i s idea was t e s t ed

fo r tw o sys tems : W, M o (1 -10 p ro ) w i th add i t ive s o f nanoc rys ta l l ine N i (70 nm) an d c (7 nm) ,

a n d W , M o ( I - 5 / z m ) w i t h a d d i t iv e s o f n a n o c ry s t a ll i n e W ( 39 n m ) a n d M o ( 5 0 n m ) . I n

bo th ca se s the s in te r ing t empera tu re s we re found to be reduced , e .g . fo r W wi th nano-

c rys ta ll ine W by 400°C . The s a me app l i e s fo r the fo rm a t ion o f c a rb ides i f nanoc rys ta l l ine C

has been added .

A va r i a t ion o f the type o f chemica l bond in g w as found to a f fec t the g row th ra t e s igni fi -

can t ly . Fo r example , s i l i con and ge rman ium exh ib i t ed g ra in g rowth a t ambien t t empe ra tu re

whe reas an t imony was s t ab le up to 400°C . Jus t a s in conven t iona l po lyc rys ta l s , g ra in g rowth

in nanoc rys ta l l ine m a te r i a ls m ay be inh ib i t ed by s econd-phase pa r t i c le s and /o r im pur i ty d rag .

The s t ab i l ity o f mu l t iphase nan oc rys ta l l ine ma te r i a l s depend s on the m utua l so lub i l ity o f the

phases invo lved . I f a ll phase s a re mu tua l ly in so lub le and i f t he concen t ra t ion o f e ach phase

i s be low the pe rco la t ion l imi t , t he sys tem canno t exh ib i t g ra in de sp i t e the ene rgy s to red in

the in te rfaces .

An e f fect o f th i s type ha s been no t i ced in the A 1 /AIN sys tem. Cryom i l ling (m echan ica l

a l loying in l iquid n i t roge n) led to a matr ix of A1 wi th a f ine gra in s ize (< 50 nm ) wi th d ispersed

AIN pa r t ic l e s. °7°) Th i s m ic ros t ruc tu re p rov ed to be v e ry re s is t an t ag a ins t coa rs en ing , even a t

t e m p e r a t u r e s a p p r o a c h i n g t h e m e l ti n g p o i n t o f A I.

Sim ilar grain gr ow th effects hav e bee n no tice d in nan ocr ysta ll ine ceram ics. (141-143 171)So fa r

m os t o f the s tud ie s on n anoc rys ta l l ine ce ramics have b een l imi ted to T iO2 (F ig . 9 ) . U p to

abou t 600°C the g ra in s i ze rema ins unchanged . Rap id g rowth t akes p lace a t 800°C o r more .

H o t i sos ta t ic p re s s ing inc rea ses the d r iv ing fo rce fo r dens if i c a tion and reduces g ra in b ou nd a ry

mobi l i ty . Hence , a p re s su re / t empera tu re w indow ex i s t s a t wh ich dense , nanoc rys ta l l ine

ce ramics may be ob ta ined . Dop ing may a l so in f luence g ra in g rowth a s i l l u s t ra t ed in F ig . 9

f o r v a r i o u s a d d i t io n s o f Y t o T i O : . P o s i t r o n s tu d i es o f th e g r a i n g r o w t h p r o c e ss~) (F ig . 10 )

ind ica te tha t the in tens ity o f the l i fe t ime s igna l co r re spo nd ing to vo id - t rapped s t a t e s dec rea se s

more rap id ly w i th t empera tu re in nanoc rys ta l l ine s ample s than in coa rs e r -g ra ined ma te r i a l s .

Th i s re su l t suggest s a m ore rap id dec rea se o f vo id dens i ty . Th e s am e p ic tu re emerges f rom

t h e B E T m e a s u r e m e n t s b y H a h n et al. ~72 Annea l ing a t e l eva ted t empera tu re s was no t i ced

to rem ove the sm a l l es t po re s fi rs t. Th i s beh av io r m ay be ra t iona l ized in t e rms o f the h igh f ree

ene rgy o f the se po re s re su l t ing in Os twa ld r ipen ing o f the po re s .

3.6.

Atornistic Structure

The a tom is t i c s truc tu re o f nanoc rys ta l l ine ma te r i a l s was s tud ied by X-ray d i f f rac tion and

EX A FS expe r imen t s . S t ruc tu ra l inves t iga t ions by means o f h igh re so lu t ion t r ansmis s ion

e lec t ron mic roscopy su f fe r f rom the d i f f i cu l ty tha t a tomic rea r rangemen ts may occur du r ing

spec imen p repa ra t ion . The p rep a ra t ion o f su f fi c ien t ly th in fo i l s ( th icknes s le ss than one

gra in d iam e te r , i .e . le s s than a few nanome te rs ) t r ans fo rm s the th ree -d imens iona l c rys ta l



NANOCRY STALLIN E MATERIALS 255

a r r a n g e m e n t o f th e r e a l m a t e r i a l i n t o a t w o - d i m e n s i o n a l o n e a n d t h u s m a y p e r m i t t h e a t o m s

in the bounda r i e s to rea r range by d i f fus iona l p roces se s du r ing spec imen p repa ra t ion .

3.6,1. X r a y d i f f r a c t i o n s t u d i e s

The purp ose o f the X - ray d i f f rac tion s tud ie s (2) was to ob ta in in fo rm a t ion ab ou t the

s t r u c tu r e o f t h e i n te r fa c ia l c o m p o n e n t b y c o m p a r i n g t h e i n te r fe r e n ce f u n c t i o n d e d u c e d f r o m

the X-ray d i f f rac t ion expe r imen t s w i th the one ca lcu la ted f rom d i f fe ren t s t ruc tu ra l mode l s o f

nanoc rys ta l l ine ma te r i a l s . The s impl i f i c a t ion made in th i s computa t ion i s to a s sume tha t the

nanoc rys ta l l ine ma te r i a l cons i s ts o f c rys ta l s (w i th a pe r fec t c rys ta l s t ruc tu re , F ig . 25 ) and

gra in bo un da ry co re reg ions whe re the a tom s m ay have re l axed aw ay f rom idea l la t t ic e si te s .

A l l c rys ta l s toge the r fo rm the c rys ta l line co m po ne n t o f the ma te r i a l . The a tom s in the

b o u n d a r y c o re s c o n s ti tu t e th e b o u n d a r y c o m p o n e n t . H e n c e th e b o u n d a r y c o m p o n e n t is

a c t u a l l y t h e s u m o v e r n u m e r o u s ( a b o u t 1 0 1 9 p e r c m 3 ) bounda r i e s w i th d i f fe ren t a tomic

s t ruc tu re s ac co rd ing to the idea s d i s cus sed in the f ir s t sec t ion . D ue to the sma l l si ze o f the

c rys ta l l it e s o f a nanoc rys ta l l ine ma te r i a l , t he num bers o f a tom s loca ted in the c rys ta ll ine

c o m p o n e n t a n d i n th e i nt e rr a ci al c o m p o n e n t a r e c o m p a r a b l e . H e n c e , t h e c o m p u t a t i o n o f t h e

X-ra y s ca t t e r ing o f a nanoc rys ta l l ine ma te r i a l r equ i re s the com puta t ion o f the s ca t te r ing due

to the d i f fe ren t ly o r i en ted c rys ta l s a s we l l a s the computa t ion o f the s ca t t e r ing o r ig ina t ing

f rom the in te r fac ia l r eg ions. T he ex i s t ence o f X- ray s ca t te r ing f ro m in te rfac ia l r eg ions and

i ts u sefu lnes s to ob ta in in fo rm a t ion ab ou t the a tomic s t ruc tu re o f in t e r face s ha s been

d e m o n s t r a t e d b y S a s s e t a l . n 7 3 ) I t ha s been show n °75) tha t the s ca t te r ing o f the d i f fe ren t ly

o r i e n t ed c r y s t a ls o f a p o l y c ry s t al l in e m a t e r ia l w i t h a r a n d o m t e x t u re m a y b e c o m p u t e d b y

me ans o f the fo l lowing p rocedu re . A s ing le c rys ta l the s ize o f wh ich is equa l to the av e rage

c rys ta l s iz e o f the p o lyc rys ta l line ma te r i a l i s cons ide red . T h i s c rys ta l r ep re sen t s the ensem ble

ave rage o f the ind iv idua l c rys ta l li t es o f the po lyc rys ta l . Fo r the c rys ta l the in t e rfe rence

func t ion I ( s ) fo r a spec i f i c o r i en ta t ion cha rac te r i zed by a d i f f rac t ion vec to r s o f the c rys ta l

w i th re spec t to the inc iden t X- ray beam i s computed . Th i s p rocedure was repea ted fo r a l l

pos s ib le o r i en ta t ions o f the c rys ta l and the d i f fe ren t re su lt ing in te r fe rence func t ions I ( s) we re

ave raged fo r s = cons t . I f t he ave rag ing p ro cedu re i s r epea ted fo r a l l pos s ib le va lues o f s , the

FIG. 25. Schematic cross section through a nanocrystalline material illustrating the approach used in

Ref. 173 The arrows indicate the interatomic spacings in the boundary core region. For further details

we refer to Section 3.6.1.




re su l ting fu nc t ion I ( s ) i s07s) he in t e r fe rence func t ion o f the po lyc rys t a l w i th a r ando m tex tu re .

By fo l lowing the sam e p ro ce d ur e , t he sca t te r ing f rom the c ryst a l line and in t e rfac ial

com pon en t s o f nanoc rys t a l l ine m a te r i a l was com puted /2 ) In f ac t, fo r the spec if ic c a se o f the

nanoc rys ta l l ine Fe , t he c rys t a l l ine componen t was mode led by a cube -shaped 0 t -Fe - (bcc )

c rys t a l r ep re sen t ing the ensem ble ave rage o f the c rys ta l line comp onen t . The v o lum e o f th i s

cub e was ma tch ed to the ave rage vo lum e o f the c ryst a ll i te s o f the nanoc rys ta l l ine Fe . Th e

e n s e m b l e a v e r ag e o f th e i n t e rf a ci a l c o m p o n e n t w a s s i m u l a t ed b y a n a s s e m b l a g e o f a t o m s

w h o s e s t r u c t u re w a s v a r i e d b e t w e e n t h e t w o c o n c e i v ab l e e x tr e m e s: a n o r d e r e d s t r u c t u r e a n d

a s t ruc tu re w i th ou t a ny o rde r . A va r i a t ion o f the ensemble ave rage be tween o rde r and

d i so rde r cove rs a l l conce ivab le bounda ry s t ruc tu re s . Th i s approach was used a s the exac t

s t ruc tu re o f the ensem ble ave rage ove r a ll boun da r y co re s is no t know n . T he in t e r fac ia l

c o m p o n e n t c o n s i s t e d o f a n a s s e m b l a g e o f a t o m s a r r a n g e d i n t h e f o r m o f t w o la y e rs o f a t o m s

wi th , t -Fe s t ruc tu re a t t a c hed cohe ren t ly a t t he ou te r su r face o f the cube . Subsequen t ly , t he

a toms in the th ree ou te r l aye r s we re d i sp laced by non- l a t t i c e vec to r s in to randomly chosen

d i rec tions . These d i sp lacemen t s do no t imp ly tha t t he a toms in any pa r ti cu la r g ra in bou nd a ry

of a nanoc rys t a l l ine m a te r i a l a re d i sp laced in r and om d i rec t ions f ro m the ir o r ig ina l l a t ti c e

s i te s . °*s ) In f ac t , t he d i sp lacem en t s a re used to m ode l the ave rage o ve r the in t e ra tom ic spac ings

b e t w e e n th e a t o m s i n t h e s u r f a c e r e g i o n o f o n e c r y s ta l r e la t iv e to t h e a to m s i n t h e o p p o s i te

c rys t a l su r face reg ion , i .e . t he in t e ra tomic spac ings ind ica ted by the a r row s in the

bou nda r i e s A and B (F ig . 25 ). As w as po in ted ou t in the f ir s t sec t ion (F igs 4 and 5 ), the mis f it

and the a tomic d i sp lacemen t s in the bounda ry co re s r e su l t i n a r educed dens i ty and a b road

d i s t ri b u t i o n o f in t e r a t o m i c s p ac in g s . B o t h f e a t u re s a r e m o d e l e d b y t h e r a n d o m a t o m i c

d i s p la c e m e n t s o f t h e a t o m s i n th e s u r f a c e r e g io n s o f b o t h c ry s ta l s. I n o t h e r w o r d s , t h e t w o

ou te r l aye r s a re sup pos ed to mo de l the su r face l aye r o f a tom s o f one c rys t a l ( e.g . c rys t a l

A , F ig . 25 ) and the su r fac e l aye r o f a tom s o f the ad jacen t c rys t a l ( e.g . c rys t a l B , F ig . 25 ).

As b o th c rys t a l s have d i ffe ren t c rys t a l log raph ic o r i en ta t ions , a va r i e ty o f in t e ra tom ic spac ings

(a r rows in F ig . 25 ) ex i st be tween the a tom s o f bo th l aye rs . In the co re o f a r ea l g ra in b ou nda ry

the a ssum ed va r i e ty o f in t e ra tom ic spac ings ex i s t a s ma y be seen f rom F igs 4 and 5 in Sec t ion

1 . The d i f fe ren t in t e ra tomic spac ings a re fo rmed because in the bounda ry reg ion two

d i f fe ren t ly o r i en ted c rys t a l l a t ti c e s a re jo ined toge the r . A va r i a t ion o f the num ber o f l aye rs

was used to s imula te b oun da r i e s o f d i f fe ren t w id ths . The e f fec t s o f c rys ta l li t e si ze and

c rys t a l l i t e s i z e d i s t r ibu t ions we re accoun ted fo r by ad jus t ing the s i ze o f the cube to the

me asu red va lues o f the ave rage c rys ta l li t e si ze ob ta ine d b y X- ray d i f f rac t ion an d e l ec t ron

m i c r o s c o p y . B y v a r y i n g th e m a g n i t u d e o f t h e r a n d o m a t o m i c d i s p l ac e m e n t i n t h e s e c o n d a n d

th i rd ou te r l aye r o f the cube , t he e l a s t ic d i sp lacemen t s o f the a tom s in the c rys t a l l a tt i ce s c lose

to the bou nd a ry w e re s imula ted . The low er dens i ty o f the g ra in b ou nd a ry co re reg ion re la t ive

to the den si ty of the c rysta l l i tes (cf . Sec t ions 3 .3 .1 a nd 3 .3 .2) was take n in to a cco un t by

un i fo rm ly lower ing the ave rage a tom ic dens i ty in the su r face l aye r s r ep re sen t ing the

bo un da ry co re s . The the rm a l d i f fuse sca t t er ing o f the c rys t a l line com pon en t a t roo m

t e m p e r a t u r e w a s s i m u l a te d b y r a n d o m l y d i s p l ac i ng t h e c r y s ta l a t o m s b y 3 % o f t h e n ea r e s t

ne ighb or d i s t ance wh ich co r re spo nds to the a t t enua t ion o f the d i f f rac t ion peaks o f o t-Fe a t

ro om tempera tu re . The e f fec t o f in te rpa r t ic l e in t e r fe rence is no t inc luded in the com pute d

in te r fe rence func t ion I ( s ) . In t e rpa r t i c le in t e rfe rence ha s been sho wn to y i e ld on ly non-van i sh -

ing sca t t e r ing in the sma l l -ang le r eg ion °76) wh ich was no t w i th in the scope o f the s tudy . The

in te r fe rence func t ion o f the c rys ta l line and the in t e r fac ia l comp one n t was com pute d in the

c la ss i cal way , by sum ming -up the con t r ibu t ion o f the sca t te r ing ampl i tudes o f al l a tom s wi th

the co r rec t phase fac to r . The computed th ree -d imens iona l func t ion was reduced to a one -

d imens iona l p lo t by ave rag ing ove r many d i f f rac t ion vec to r s . A l l computed in t e r fe rence




f u n c t io n s w e r e c o n v o l u t e d b y a G a u s s i a n i n s t r u m e n t f u n c t io n i n o r d e r t o s i m u l a t e t h e e ff ec t

o f i n s t ru m e n t a l b r o a d e n i n g o f t he d i f f r a c t o m e t e r u s e d f o r t h e e x p e r i m e n ts .

A c o m p a r i s o n o f t h e e x p e r i m e n t a l a n d t h e c o m p u t e d i n t e rf e r e n c e fu n c t io n s i s s h o w n i n

F ig . 2 6 a s s u m i n g a s h o r t - r a n g e - o r d e r e d g r a i n b o u n d a r y s t ru c t u re . N e i t h e r t h e p e a k w i d th ,

p e a k h e i g h t o r t h e b a c k g r o u n d i n t e n s i t y i s r e p r o d u c e d c o r r e c t l y . T h e b o u n d a r i e s w e r e

a s s u m e d t o h a v e a t h ic k n e s s o f f o u r a t o m i c l a ye r s , w h i c h a g r e e s w i th t h e p r e s e n t k n o w l e d g e

o f th e a t o m i c s t r u c t u r e o f g r a i n b o u n d a r i e s i n m e t a l ( s ee f o r e x a m p l e R e f . 1 77 ). I n a s e c o n d

s et o f c o m p u t a t i o n s , a n a t t e m p t w a s m a d e t o m a t c h t h e e x p e r i m e n t a l d a t a b y a s s u m i n g a

g r a i n b o u n d a r y c o m p o n e n t w i t h th e f o l lo w i n g s tr u c t u r e ( F ig . 2 7) . T h e a v e r a g e o v e r th e

i n t e r a t o m i c s p a c i n gs b e t w e e n t h e a t o m s a t t h e s u r f a c e o f o n e c r y s ta l a n d t he s u r f a c e

a t o m s o f t h e s e c o n d cr y s t al (a r r o w s i n F i g. 2 5 ) w e r e a s s u m e d t o b ¢ r a n d o m . T h e r e f o r e , t he

a t o m s o f t h e o u t e r l a y e r w e r e d is p l a ce d b y 5 0 % o f t he n e a r e s t n e i g h b o r d i s t a n ce f r o m t h e i r

l a tt ic e s i te s i n r a n d o m d i r e c ti o n s . T h e r e s u l ti n g w i d e v a r i e t y o f in t e r a t o m i c s p a c i n g s a r e

a s s u m e d t o r e p r e s e n t t h e i n t e r a t o m i c s p a c i n g s i n t h e b o u n d a r y c o r e r e g i o n d u e t o t h e l a t t i c e

m i s f i t a n d d u e t o t h e a t o m i c r e l a x a t i o n s ( F i g s 4 a n d 5 ) . I n o r d e r t o m o d e l t h e s t r a i n a t a n d

n e a r t h e b o u n d a r y c o r e th e a t o m s o f t he s e c o n d a n d t h ir d o u t e r m o s t l a y e rs w e re d is p la c e d

b y 2 5 % o f th e n e a r e s t n e i g h b o r d i s t a n c e f r o m t h e i r l a tt ic e s it es i n r a n d o m d i r e c ti o n s . I t m a y

b e s ee n f r o m F i g . 27 t h a t t h e c o m p u t e d I ( s ) c u r v e r e p r o d u c e s n o t o n l y th e h e i g h t s a n d w i d t h s

o f a ll t h e p e a k s , b u t a l s o m a t c h e s a p p r o x i m a t e l y t h e b a c k g r o u n d i n te n s i ty , e s p e c ia l ly i n t h e

r e g i m e b e t w e e n s = 0 .1 a n d 0 . 4 5 w h e r e t h e fi t w i t h t h e m o d e l a s s u m i n g a s h o r t - r a n g e - o r d e r e d

i n t e rr a c i a l c o m p o n e n t w a s p a r t i c u l a r l y p o o r ( c f. F i g . 2 6 ). F u r t h e r m o r e , i t w a s n o t p o s s i b l e

t o r e p r o d u c e t h e e x p e r i m e n t a l d a t a b y a s s u m i n g a n e n h a n c e d t h e r m a l d i f f u s e s c a t t e r i n g b u t

10

0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 . 4 1 . 6

w a v e v e c t o r 2 s i n @ / A ( ~' )

F IG . 2 6. C o m p a r i s o n o f t he m e a s u r e d ( - - + - - )

and computed ( ) interference func t ions for

nanocrystalline Fe. The m od el system assum ed for the

com putations is a bou ndary structure consisting of four

atomic layers in which atoms are displaced in random

directions. The displacem ent distance of the atoms cor-

responding to the two layers in the boundary core are

assumed to be 15% o f the nearest neighbor distance, in

the two ad jacent layers the displacements are 7 % of the

nearest neighbor distance. The displacement of 15% of

the nearest neighbor distance corresponds to the average

nearest neighbor displacemen t of the atoms in a FesoB20

glass.0

T

10

0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 . 4 1 . 6

w a v e v e c t o r 2 s i n 0 / ~ [A I

FIG. 27. Comparison of the measured ( - - + - - )

and c om puted ( ..... ) interferen ce func tions of nano crys-

tall ine. The mo del computed is a mix ture of 6 nm

(75 vol.%) and 4 nm (25 vol.%) crystals in which the

boundary atoms are displaced in random directions. The

displacement distances were chosen as follows. The o uter

layer of atoms was displaced by 50% and the second and

third layer by 25% of the n earest neighbor distance. The

outer layer is supposed to m odel the interatomic spac-

ings between adjacent crystals (arrows in F ig. 25). The

second layer models the displacements of the boundary

core atom s (o pe n circles in F ig. 25) from their ideal

lattice sites, m)



58


no sca t t e ring o f the bo un da ry reg ion a s w as sugges ted b y o the r s tud ie s . (17s) The accu racy o f

t h e c o m p u t a t i o n s w a s t e s te d b y c o m p a r i n g t h e m e a s u r e d a n d c o m p u t e d i n t er f er e n c e fu n c t io n s

o f 6 n m A u c r y s ta l s w h i ch w e r e i s o la t e d f r o m o n e a n o t h e r b y a t h i n w a t e r l a ye r s o t h a t n o

g r a in b o u n d a r i e s c a n b e f o r m e d . T h e c o m p u t e d a n d e x p e r i m e n t a l d a t a a g r e ed ( n o a d j u s ta b l e

f it pa ram e te r s ) w i th in the accu racy o f the measu rem en t s .

A d i f fe ren t app roa ch to ana lyze the s t ruc tu re o f the .g ra in bou nda r i e s in nanoc rys t a l line

me ta l s ha s r ecen t ly been p r o p o s ed , t179 In com par i so n to Zh u ' s ~3) com puta t ion s , seve ra l

s impl i fi c a tions we re in t roduced . In o rde r to sho r t en the com puta t ion o f the in te r fe rence

func t ion , t he rea l ( th ree -d imens iona l ) nanoc rys t a l l ine m a te r i a l was rep laced by a one -

d imen s iona l m ode l cons i s t ing o f two l inea r a r rays o f sca tt e r s . One a r ray rep re sen t s the

pe r iod ic it i e s in the g ra in in t e rio r , w h i le the o th e r on e , w i th a l a rger pe r iod ic i ty , co r re sp ond s

t o t h e b o u n d a r y r e g io n . T h e v o l u m e f r ac t i o n o f th e b o u n d a r i e s w a s t a k e n i n t o a c c o u n t b y

mu l t ip ly ing the d i f frac t ed am pl i tude o f the bou nd a ry sca t t er s by a co r re spo nd ing w e igh t

fac to r . The d i f fe ren t bounda ry s t ruc tu re s and the dens i ty d i f fe rence be tween the bounda r i e s

a n d t h e c r y s ta l s w a s a c c o u n t e d f o r b y v a r y in g t h e d e n s i t y in t h e b o u n d a r y r e g io n b e t w e e n

60 and 100% o f the bu lk dens i ty . The spac ing be tw een the sca t te r s r anged f rom 50 to 150%

of the sca t t e re r dens i ty in the g ra in in t e r io r . T he rando m or i en ta t ion d i s t r ibu t ion was

appr ox im a ted by a ssum ing tha t eve ry c rys t a l ( row o f sca t t e re r s ) ha s e i the r (111), (200) ,

(220) , (311) o r (311) in t e ra tomic spac ings . A random number gene ra to r was used to ave rage

ove r the spac ings . The measu remen t s we re s impl i f i ed by rep lac ing the commonly used

t ransmiss ion m easu rem en t s a l lowing quan t i t a t ive m easu rem en t s o f the in t e rfe rence func t ion

(wi th the appropr i a t e co r rec t ions) by a r e f l ec t ion measu remen t on a g l a ss s l ide . The

u n a v o i d a b l e b a c k g r o u n d h a d t o b e s u b t r a c te d , w h i c h w a s o n l y p o s s i b le to a l im i t ed e x t en t .

D u e t o t h e n u m e r o u s s i m p li fi c at io n s i n t h e c o m p u t a t i o n a l a n d t h e e x p er i m e n ta l p a r t o f th e

wo rk , no d i rec t comp ar i son (w i tho u t f r ee fi t pa ram e te r s a s in Zh u ' s ° ) wo rk ) was poss ib le .

Hence , t he computed and measu red in t e r fe rence func t ions we re f i t t ed toge the r in a su i t ab le

chosen sca t t e ring ang le , 20. The ang le se l ect ed was 20 = 55 ° , we l l aw ay f rom any Bragg pea k

to ma tch the background a s we l l a s poss ib le . Desp i t e th i s cu rve f i t t i ng p rocedure , t he

c o m p u t e d a n d m e a s u r e d i n te n s it y o f t h e B r a g g p e a k s d e v i at e d b y a f a c t o r b e tw e e n 8 a n d 1 2.

In o rde r to r educe th is d i sc repancy , the a ssum pt ion o f 20% vacanc ie s in the c rys t a l s was

made . Ev iden t ly , t h i s a ssumpt ion appea rs un rea l i s t i c and i s a t va r i ance w i th many obse r -

va t ions e .g . w i th the hydr ogen a bso rp t ion da ta on n anoc rys ta l l ine Pd (c f. Sec t ion 3.7 .4 ). The

p a p e r s e em s t o d e m o n s t r a t e t h a t r e li a bl e in f o r m a t i o n a b o u t t h e g r ai n b o u n d a r y s t r u c tu r e o f

nanoc rys ta l l ine ma te r i a l s c anno t be ob ta ined by s impl i f i ed mode l s and X- ray d i f f rac t ion

measurements l imi ted to re la t ive in tensi t ies only .

The X - ray d i f f rac tion behav io r o f th in nanoc rys ta l l ine Ag- -Cu and A g- G e f i lms gene ra ted

by vap or-q uen chin g has been ana ly zed ~lT8,js°) in te rms o f the in te rfe rence fun c t ion of an

ensemble o f sma l l s t r a ined c rys t a l l i t e s . The bounda r i e s we re mode led by an appropr i a t e ly

chosen D ebye -W al l e r f ac to r fo r the c rys ta l li te s . In o th e r words , t he rea l s truc tu re (bo unda r i e s

and c rys t a l s ) i s mode led a s an a r rangemen t o f sma l l , e l a s t i c a l ly s t r a ined , i so la t ed c rys t a l s .

The bou nda r i e s a re r ep re sen ted by means o f l a t ti c e s t ra ins. A l l o the r b oun da r y fea tu re s

(cf . Sec tion 1 ) a re no t inc luded . A s fa r a s the d i f f rac t ion p rop e r t i e s o f those tw o sys t ems a re

conce rn ed th i s mod e l seems to be sa ti s fac to ry . Neve r the le ss , a mo de l o f th i s k ind d oes no t

s e e m a p p l i ca b l e t o o b t a i n i n f o r m a t i o n a b o u t t h e a t o m i c s t r u c tu r e o f t h e b o u n d a r y c o r e

c o m p o n e n t s . F o r e x a m p l e , th e E X A F S m e a s u r e m e n t s r e p o r t e d i n th e s u b s e q u e n t s e ct io n n o t

o n l y s u g g e s t d i s p la c e m e n t s o f t h e a t o m s i n t h e b o u n d a r y c o r e b u t a l s o a r e d u c t i o n i n t h e

num ber o f nea re s t ne ighbors wh ich canno t be de sc r ibed by a mode l l imi t ed to sma l l s tr a ined

c rys ta l li te s . Fu r th e rm ore , t he app l i ca t ion o f a mod e l a ssuming a nanoc rys ta l l ine m a te r i a l t o



N N O C R Y S T L L I N E M T E R I L S 59

cons i s t o f sma l l , s t r a ined c rys ta l li t e s on ly (w i tho u t any s ca t t e r ing f ro m the b ou nd a ry co re

reg ions ) s eems incons i s t en t w i th the repor t ed sma l l ang le X- ray d i f f rac t ion measu remen t s

(Sec t ions 3 .3 .1.2 and 3 .3 .2 .1 ). The s t ra in requ i red to m a tch the peak w id ths and peak he igh t s

d o e s n o t r e p r o d u c e c o r r e c t ly t h e o b s e r v e d b a c k g r o u n d o f n a n o c r y s ta l li n e F e . T h i s m e a n s

phys ica l ly tha t in add i t ion to the s ca t t e r ing by s t ra ined Fe -c rys ta l l i t e s , t he X- rays a re a l so

sca t t e red by Fe -a toms d i sp laced by l a rge d i s t ances f rom la t t i c e s i t e s .

A s t h e a t o m i c s t r u c t u re s i n t h e c o r e s o f b o u n d a r i e s d e p e n d s t ro n g l y o n t h e i n t er a t o m i c

fo rce s (cf . Sec t ion 1 ), it m ay we l l be th a t the d i f f rac t ion beh av io r o f chemica l ly d if fe ren t

nanoc rys ta l l ine ma te r i a l s dev ia te s t rong ly f rom one ano the r . Hence any s t ruc tu ra l mode l

dedu ced fo r a pa r t icu la r m a te r i a l c anno t be ex tended to o the r ma te r i a l s un le ss te s t ed

expe r imen ta l ly . Hen ce the d i ff rac t ion o f nanoc rys ta l l ine A g- C u a l loys m ay we l l d i f fe r f rom

nanoc rys ta l l ine F e . On the o the r hand , any m ode l de sc r ib ing the d i ff rac t ion o f nanoc rys ta ll ine

ma te r i a l s in t e rms o f s t ra ined c rys ta ll i te s on ly (w i thou t any s ca t t e r ing con t r ibu t ion f rom the

bo un da ry co re ) s eems incons i s t en t w i th the sma ll ang le X- ray d i f f rac t ion expe r imen t s an d the

w o r k o f S a ss

e t a l

(e.g . Re fs 173 and 181) . These expe r imen t s have d em ons t ra t e d tha t g ra in

bo un da ry co re reg ions g ene ra te spec i fi c d i f f rac tion e f fec ts wh ich o r ig ina te f rom the d i sp lace-

me n t s o f the a tom s in the bo un da ry co re f rom la t ti c e s it es . A s t ra ined c rys ta l li t e m ode l

s eems a lso incons i s t en t w i th the spec t rosco p ic ev idence (Sec t ion 3 .7 ) ind ica t ing tha t nanoc rys -

t a ll ine m a te r i a ls co n ta in a h igh dens i ty o f vacancy- l ike free vo lum e and a cons ide rab le

f rac t ion o f a toms in s it e s w i th non - la t ti c e sym met ry .

3.6.2. E X A F S s tu d ie s

E X A F S s tudies ~19°) ap pe ar to be pa r t icula r ly su i table to inves t iga te the s t ruc tu re o f

nanoc rys ta l l ine ma te r i a l s because they y ie ld in fo rm a t ion ab ou t the sho r t - range o rde r o f a

so l id in t e rms o f the coord in a t ion num bers , t he nea re s t ne ighbor d i s t ances , the Deby e -W al le r

facto rs , e tc . (ls2-1sa) In fact , i f a nan oc ryst all in e m ater ial con sis ts o f an (ord ere d) crystall in e

c o m p o n e n t a n d a g r a i n b o u n d a r y c o m p o n e n t f o r m e d b y a t o m s d i s p l a c e d f r o m t h e i r i d e a l

l a t ti c e si te s , t hen the EX A FS osc i ll a t ions o f a nanoc rys ta l l ine ma te r i a l r e su l t f rom the

c rys ta l l ine componen t on ly , because ma te r i a l s w i th a w ide va r i e ty o f in t e ra tomic spac ings

yie ld li t tle o r no osc i l la t ions in the E X A F S s ignal . °82) He nce , in te rm s o f such a m od el the

a m p l i t u d e s o f th e E X A F S o s c il la t io n s o f a n a n o c r y s ta l li n e m a t e r i a l i n c o m p a r i s o n t o t h e

a m p l i t u d e s o f a c o n v e n t io n a l p o l y c r y s ta l w i th t h e s a m e m a s s a r e e x p e c t e d to b e r e d u c e d b y

a f a c t o r c o m p a r a b l e t o t h e f r a c t io n o f a t o m s l o c a t ed i n t he b o u n d a r y c o r e s i f t h e se a t o m s

are d isplaced s ignif icant ly f ro m idea l la t t ice s i tes and i f the in te ra to m ic spac ings wi th in th e

bounda ry co re (a r rows in F ig . 25 ) a re d i s t r ibu ted randomly . In fac t , i t i s t h i s f ea tu re wh ich

h a s b e e n o b s e r v e d in a ll E X A F S s t ud i e s p e r f o r m e d s o f a r. I n F i g . 2 8 a th e w e i g h t ed E X A F S

osc i l la t ions zk 3 o f nanoc rys ta l l ine and po lyc rys ta l l ine Cu a re com pared . T he co r re spo nd ing

Fo ur ie r t r an s fo rm ed FT (zk 3 ) a re summ ar ized in F ig . 28b . Pd show ed s imi la r r esu l ts . The

fo l lowing th ree fea tu re s a re appa ren t .

( i ) Th e radi i o f the d i f fe rent shel ls in polycrys ta l l ine and nan ocrys ta l l ine m ater ia ls coinc ide ,

the d evia t io n is be low 0 .02 A (Fig . 28b) .

( i i) The amp l i tudes o f FT(z k 3 ) o f the f ir s t she ll a re redu ced by an am ou n t com parab le to

t h e v o l u m e f r a c t io n o f t h e g r ai n b o u n d a r y c o m p o n e n t . T h e s a m e e ff e ct h a s b e e n r e p o r t e d

rece ntly for Fer0Co4o alloy s. °91)

( ii i) The reduc t ion o f the am pl i tude o f FT (zk 3 ) inc rea se s w i th inc rea s ing she ll nu mb er .

These fea tu re s ag ree wi th the idea tha t nanoc rys ta l l ine m a te r i a ls cons i s t o f an (o rde red )

c rys ta l l ine componen t w i th the s ame a tomic a r rangemen t a s in bu lk c rys ta l s and a g ra in




a )

50

2 5

0

2 5

5 0

0

. . . . I . . . . I . . . . I

5 10 15

k [/C~

b )

1500

1 0 0 0

x

I

Ii

5 0 0

4 6 8 10

INTERATOM IC DISTANCES r I /~ ]

F IG. 2 8 . T h e w e i g h t ed E X A F S o s c i l la t i o ns x k 3 a ) an d t h e F o u r i e r t r an s fo rm F T x k 3 ) b ) p h as e s hi f t

i s no t inc luded) o f a nanocry s ta l l ine Cu sample ) c rys ta l line d iam eter = 10 nm) in com par i son

w i t h p o l y c ry st a l li n e C u + + + ) . I n t h e n an o c ry s t al l in e s am p l e t h e am p l i t u d e o f t h e E X A F S

osci l l a t ions and the FT xk 3 ) a re w eaker than in the po lycrys ta l , o9°)

b o u n d a r y c o m p o n e n t w i t h a b r o a d d i s t r i b u t io n o f in t e r a to m i c s p ac in g s. T h e f e a tu r e s (i i) a n d

( i ii ) c an no t be in te rp re ted in t e rms o f in t e rna l su r face s and /o r vo ids because the obse rved

r e d u c t i o n o f t h e E X A F S a m p l i t u d e s w o u l d r e q u i re a n a r e a o f in t e rn a l s u r f a c es o r v o i d s w h i c h

are in con s is tent w i th the resu l ts o f pos i t ro n l i fe time sp ec t ro scop y IsS) and smal l angle

diff rac t ion . (~47,~) Th e X -ray d i f f rac t ion s tudies (S ec t ion 3 .6 .1) indica ted tha t the in te ra tom ic

spac ings in the smal l c rys ta l l i tes de via te l i tt le f ro m the equi l ibr iu m (bulk) va lue , v~sJsT) He nce ,

the rad i i o f the d i f fe ren t she ll s o f po lyc rys tal l ine and nanoc rys ta l l ine m a te r ia l s a re expec ted

to co inc ide a s was obse rved . A tom s wi th a w ide spec t rum o f in t e ra tomic spac ings re l a tive to

t h ei r n e i g h b o r s c a n n o t c o n t r i b u t e t o t h e a m p l i t u d e s o f th e F T ( x k 3 ) . T h u s , t h e r e d u c t io n o f

the am pl i tude o f the f ir s t shel l shou ld be comp arab le to the f rac t ion o f in te r rac ia l a tom s , a s

was obse rved . The re su l t s ru le ou t a g la s sy ( sho r t r ange o rde red ) bounda ry s t ruc tu re . In the

case o f g la s sy bou nd a ry s t ruc tu re s , t he in t ens ity o f the f i r s t shel l o f the F T(x k 3 ) i s r educed

by I0 to 30 in com par i so n to the c rys tal l ine coun te rpa r t . H igh e r o rde r she ll s o f g la sse s in

the FT (xk 3 ) p lo t a re e i the r w eak o r inv is ib le . °u'l ss ) Hence , i f t he b ou nd a ry com pon en t o f a

nanocrys ta l l ine mater ia l would have a g lassy s t ruc ture , the in tens i ty loss of the f i rs t she l l in




the FT(xk 3) should be about 10 to 30 of the fraction of boundary atoms. This was not

observed. Furthermore, a significant reduction of the higher order shells (second, third, etc.)

relative to the first shell should be observed. This was also not the case. The results are not

consistent with a glassy boundary structure wi th a large Debye-Waller factor for the following

reasons. The mean square displacements (static or dynamic) in the Debye-Waller factor

cannot explain a density reduction in the grain boundary component which was deduced to

be about 60 or 70 of the bulk density (cf. Sections 3.3.1.2 and 3.3.2.1). (~47'1~) Recent

measurements at 20 K show the same reduction of the EXAFS amplitudes as at 77 K

indicating that there is, up to 20 K, no temperature dependence of the reduction. This

observation clearly contradicts a Debye-Waller factor being the reason for the amplitude

reduction. Hence, one is led to conclude that the observed deviation of the EXAFS signal

between the polycrystalline and nanocrystalline material is primarily due to a wide distri-

bution of bond lengths in the grain boundaries.

It has been argued on the basis o f hard sphere and soap bubble models ~89) that a structural

model of a nanocrystalline material suggesting a measurable fraction of the boundary

atoms to be displaced by 50 of the nearest neighbor spacing from lattice sites is unrealistic.

This objection seems to be based on a misunderstanding of the model used to compute

the interference function of a nanocrystaUine material, c2) As was pointed out above

(Section 3.6.1), the random atomic displacements of 50 of the nearest neighbor spacing

were used to model the ensemble average over the interatomic spacings between adjacent

crystals (i.e. the spacings indicated by the arrows in Fig. 25). On the other hand, the EXAFS

observations reported in the previous paragraph and the strong background observed for

nanocrystalline Fe seem to indicate unambiguously that a large fraction of the a toms of a

nanocrystalline material are displaced from lattice sites.

3.7. Spec t roscopy

3.7.1. Posi tron l i fet ime spectroscopy

Positron lifetime spectroscopy has been demonstrated to be particularly well suited for

studying defects in crystals°92-~94) and structural fluctuations in amorphous materials°gs)

because they permit an estimate of free volume fluctuations in condensed matter. Hence

positron lifetime spectroscopy appeared to be a promising tool to obtain independent

informat ion about the structure o f nanocrystalline materials. So far, studies of this type were

performed for Cu, Fe, Pd and

Si. 196-2°°)

The lifetime spectra (Fig. 29) measured for the nanocrystalline metals differ from those

obtained on uncompacted crystallites or on the metallic glass Fess B15096) and can be analyzed

with good variances (X2~< 1.1) by three components with lifetimes z~, z2, ~3 and intensities

I~, 12, 13. These parameters are given in Table 1 together with the lifetimes zf in perfect crystals

and ZLV in lattice vacancies and can be interpreted as follows.

The lifetime T~ is attributed to free volumes of the size of about a lattice vacancy as their

values are similar to ZLV (see Table 1). The vacancy-size free volumes are expected to be

located in the interfaces because of their thermal stability and the increase of the ratio 11 12

with compacting (see Ref. 198). The presence of vacancy-size free volumes in NiO grain

boundaries has recently been suggested by a comparison of high-resolution electron

microscopy and image simulation32°~)

The lifetime z2 (Table 1) is attributed to boundary regions at which the local free volume

is larger than a single vacancy. For example, the core of a triple junction between three



2 6 2 P R O G R E S S I N M A T E R I A L S S C I E N C E

Z

o ~ - 2

o - 3

I

6 0 0 700 8 0 0 9 0 0

C h a n n e l n u m b e r 2 5 ,5 p s p e r c h a n n e l )

FIG. 29 . Pos i t ron l i fe t ime spect ra o f. (a ) an unco mp acted (6 nm) i ro n pow der ; (b ) a nanocrys ta t l ine

(6 r im) i ron specimen; (c ) amo rpho us Fess .zBi4 .8 a l loy ; and (d ) po lycrys ta l l ine bu lk i ron , w i th the

back groun d o f the spec t ra subs tracted/ t99~

bou nda r i e s m ay rep re sen t such a r eg ion . The l if e time z2 was a t t r ibu ted to t r ip le junc t ions

because T2 was ob se rved even a f t e r p ro lon ged g ra in g row th . Fo r top o log ica l r e a sons t r ip l e

j u n c t i o n s c a n n o t a n n e a l o u t w h e r e a s o t h e r l a rg e f r ee v o l u m e s , e. g. m i c r o v o i d s in b o u n d a r i e s

m ay disap pear . ~196-2°°) Th e long- l ived co m po ne nt (z3) was in te rpre ted by or t ho -po si t ro nu m

(o-Ps ) f orm at io n in la rger void sY 9s'~99) Som e ind ica t ion of in te rfac ia l f ree volum es s mal le r

than vacanc ie s we re dedu ced f ro m the dec rea se be tw een 295 K and 77 K in nanoc rys ta l line

Fe and in nanoc rys ta l l ine Cu .

3.7.2.

Muon spin rotation studies

I n o r d e r t o o b t a i n s p e c t r o s c o p i c i n f o r m a t i o n a b o u t t h e m i c r o s c o p i c m a g n e t i c s t r u c t u r e

o f nanoc rys t a l l ine m a te r i a ls t he mu on sp in ro t a t ion t e chn ique ( /~ +SR) has b een employe d .

B y t h is m e t h o d - - w h i c h p r o b e s m a g n e t ic f ie ld s a n d t h e i r d y n a m i c s a t t h e + s it es i n

crysta ls~2°2)--st ruc tural defec ts ac t ing as /z + t raps m ay be charac te r ized . Tw o m uo n spin

p recess ion f requenc ie s f~ and f2 and a long i tud ina l m uon sp in re l axa t ion ra t e F lons have b een

obse rved (T ab le 2 ) fo r a f r ac t ion o f the mu ons . The p recess ion f requenc ie sf~ andf~ a re s imi la r

to thos e ob serv ed fo r in te rs t i tia l /~ + in the Fe ( ffy203) and for /z + t rapp ed a t la t t ice vacanc ies

(f~v). ~2°4) Th eref ore , i t wa s a ssu m ed tha t f~ is cha racte rist ic fo r/z + on interst i t ia l si tes in the

c rys t a ll i te s andf~ fo r m uon s t r app ed in we l l-de f ined free vo lum es , name ly o f the si ze o f abou t

a l a t t ic e vacancy , in the in t e r face s . Th i s in t e rp re t a t ion ag ree s w i th the pos i t ron an n ih i l a tion

da ta r epor t ed in the p rev ious sec t ion . The ra t io

ALIA

of the s igna l ampl i tudes o f the

ab le 1 . Pos i t ron L i fe t imes T t (ps) and In tens i t i es I t (% ) M easured on N anocry s ta l l ine Coppe r ,

P a l l ad i u m an d I ro n C o n s o l i d a t ed U n d e r P re s s u re p . F o r C o m p ar i s o n , P o s i t ro n L i f e ti m es

M ea s u red i n t h e F ree B u l k S t a t e (¢ r ) , i n M o n o v acan c i e s (C u e) an d a f t e r P l a s ti c D e fo rm a t i o n

(%,- , t ) in the Correspond ing Bulk Crys ta l s a re G iven (see Ref . 198)

Nan ocrys ta l l ine mater ia l s Crys ta l l ine mater ia l s

p (G Pa) ¢1

( p s ) ¢ 2 ( p S )

1 1 1 I 2

¢ 3 ( p s ) I 3 ( ) ' ~ f ( p S ) ¢ g v ( A D S)

p h s t

( p s )

Cu 5 .0 16 5+ 3 3 2 2 ± 4 0 .57 2600_+300 0 .2__0 .0 112 179 164

Pd 5.0 142_+3 321 ± 6 0.72 7 00 ± 100 2.6_+0.7 96 Pt: 169 171

Fe 4 .5 185 ± 5 33 7± 5 0 .63 4100 4-400 8 . 5± 0 . 5 106 175 167



N A N O C R Y S T A L L I N E M A T E R I A L S 2 63

Table 2 . M u o n S p i n P rece s s i o n F req u en c i e s f l , f 2 an d t h e R a t i o A I A 2

o f t h e i r S i g n a l A m p l i tu d es , a s w e l l a s t h e L o n g i t u d i n a l M u o n S p i n

R e l ax a t i o n R a t e F lo ns a t T w o D i f f e r en t T em p e ra t u re s . T h e P reces si o n

F req u en c i e s f~ an d f i r o f t h e M u o n s a t I n t e r s t i ti a l S it es an d M u o n s

T rap p ed i n V acan c ie s in C ry s t a l li n e I ro n a r e In c l u d ed fo r C o m p ar i s o n

N an o c ry s t a l l i n e F e C ry s t a l li n e F e

T f , f2 F,ons .fF fl y

K )

( M H z ) ( M H z )

A s A I 0 s - I

( M H z ) ( M H z )

3 0 0 4 8 . 9 3 1 . 5 0 . 5 2 . 9 4 8 . 7 *

4 . 2 5 3 . 8 3 2 . 6 2 . 1 0 . 3 5 3 . 3

9 O 2 9 . 5 ?

*Ref. 203.

?Ref . 204 .

frequencies f~, f2 decreasing with increasing temperature indicates that at 300 K more muons

decay in the interfaces and less in the crystallites than at 4.2 K. This result is in qualitative

agreement with the + jump rates(2°3) F (4.2 K) = 4.108 s -~ and F (300 K ) = 10 ~° s -~ making

a diffusion of + to the interfaces more likely at the higher temperature. From higher

precision data combined with a study of the crystallite size distribution, one may even expect

a quanti tative determination of the + diffusivity. Only a fraction of the + was detected in

the + precession signals. The missing fraction was attributed to muons trapped in interfacial

regions with varying interatomic distances and hence a wide distribution of local magnetic

fields leading to a fast relaxation of the +SR signals which is beyond the resolution of the

apparatus.

3.7.3.

M ssbauer spectroscopy

The M6ssbauer spectrum of nanocrystalline iron is shown in Fig. 30. (2o5) Two sub-spectra

were used to fit the experimental data, the hyperfine parameters of which are given in

Table 3. Since wide-angle X-ray scattering and EXAFS (cf. Sections 3.6.1 and 3.6.2) gave

little evidence for large lattice distortions in the center of the crystals, the initial fit parameters

I . O 0

z 0 . 9 5

0 . 9 0

I O 5

1

i

I

5

I o

V E L O C I T Y [ ra m s ]

F IG. 3 0. M 6 s s b au e r s p ec t ru m o f a n an o c ry s t a l li n e i ro n s am p l e . T h e s p ~ t ru m w as m eas u red a t 7 7 K .

Tw o sub-spec t ra 1 , sharp l ines ; 2 , b roa d l ines ) were used to f i t the exper im en ta l da ta squares ) . o°s )

J P M 3 3 / 4 - - D




Table 3 . Hype r t ine Parame ters o f Sub-spect ra I and 2 o f F ig . 30

S u b - s p ec t ru m 1 S u b - s p ec tru m 2

S ram /s) 0 .10 0.14

Linew id th a t ha l f -m ax im um ram/s ) 0 .32 1 .6

H kOe) 343 351

of sub -sp ec t rum 1 were chosen a s the va lues o f c rys ta l l ine i ron wh ich w as conf i rmed b y the f it

p rocedu re ; the f it pa ram e te r s o f sub -spec t rum 2 dev ia ted f rom the c rys ta l line va lues (Tab le 3 ) .

The abso rp t io n in tens ity o f spec t rum 2 re l a tive to spec t rum 1 m ay no t be a re li ab le way

to e s t ima te the f rac t ion o f a tom s loca ted in the in te r face s because magne t i c o rde r ing ex tends

ove r mo re than in te ra tomic d i s tances . Hence , a tom s ins ide the c rysta l s a re a l so in f luenced by

the in te rfac ia l com po nen t even i f t hey have a w e l l o rde red c rys ta l line env i ronmen t . Th i s i s

not so for mater ia ls (e .g . FeF2 which wi l l be d iscussed la te r) in th is sec t ion where the

in te rac t ion wi th the ne ighbor ing a tom s i s o f sho r t r ange cha rac te r .

Sub-spec t rum 2 (Tab le 3 ) shows an enhanced hype r f ine magne t i c f i e ld (H) , a l a rge r

l inewid th , a nd an inc rea sed i some r sh if t

I S )

i n com par i son to the c rys tal l ine comp onen t . A l l

o f t h e s e f e a tu r e s m a y b e u n d e r s t o o d i f i t is a s s u m e d t h a t s u b - s p e c t ru m 2 o r i g in a t es f r o m t h e

in te rfac ia l com po nen t o f the nanoc rys ta l l ine m a te r ia l . Th i s in t e rp re ta t ion ag ree s w i th the

fo l lowing obse rva t ion . I f the g ra in bou nda r i e s a re remov ed f rom a nano c rys ta l line m a te r ia l

(by g ra in gro w th a t e leva ted tem pera tu res ) , sub -spe c t ru m 2 ceases to exis t (Fig . 21) . 038'2°~) Th e

e n h a n c e d

I S

(Tab le 3 ) re f lec ts a r edu c t ion o f the e l ec t ron dens i ty o f the in te r fac ia l com pon en t .

I n c o n t r a s t, f r o m h i g h - p r e ss u r e M f s s b a u e r e x p e r i m e n t s it is k n o w n t h a t c o m p r e s s i o n o f i r o n

leads to a smal le r

1S

valu e as a resu lt o f hig her elec tron den sity. <2°6'2°7) Th e red uc tion o f

e lec t ron dens i ty in the ca se o f nanoc rys ta l l ine Fe m ay be d i rec t ly re la t ed to the o bse rved low er

mass dens i ty wh ich impl i e s a vo lume expans ion in the in te r fac ia l componen t . Th i s re su l t

ag ree s w i th the sma l l ang le sca t te r ing da ta sugges t ing a mass dens i ty o f 60 to 70 in the

boundar ies (of . Sec t ions 3 .3 .1 .2 and 3 .3 .2 .1) . The enhanced hyperf ine f ie ld (H, Table 3) may

a l so be in te rp re ted in t e rms o f the reduced in te r fac ia l dens i ty . The Be the -S la te r cu rve , wh ich

re la t e s the exchange ene rgy to the a tomic geome t ry , suppor t s th i s co r re l a t ion . Aga in ,

h igh -p re s su re expe r imen t s show tha t a com pres s ion o f ~ -F e re su l t s in the op pos i t e e f fec t, i.e .

a redu ced hyperf ine f ie ld . (2°7) Th e bro adn ess o f the M rs sb au er l ines (T able 3) sugges ts the

in te r fac ia l componen t to rep re sen t an a tomic s t ruc tu re in wh ich a w ide r spec t rum o f

in te ra to m ic spac ings exis ts than in the 'g lassy or c rys ta l l ine s ta te o f the chem ica l ly ident ica l

ma te r i a l . A s t ruc tu re o f th i s type shou ld l e ad to a b roa d d i s t r ibu t ion o f hype rf ine fi elds .

F igu re 31 summ ar ize s the measu red t em pera tu re va r i a t ion o f the hype rf ine f ie ld o f bo th

com pon en t s . The l a rge r va lue o f H o f the sub -spec t rum 2 is fo l lowed by a fa st e r dec rea se

which m ay b e in te rp re ted a s a lower Cur ie t em pera tu re T¢ o f the in te rfac ia l compo nen t .

S imi la r cu rves a re known f rom the obse rva t ions on th in f i lms c2°8'2°9) alt ho ug h the te m pe ra tu re

d e p e n d e n c e o f H f o u n d t h e re c o u l d n o t b e c o n f i rm e d f o r n a n o c r y s t al li n e F e . I n o r d e r t o

ob ta in an e s t ima t ion o f th is e ffect , t he to t a l r e sonan t ab so rp t ion o f the samp le was de te rmined

as a func t ion o f t emp e ra tu re by measu r ing the a rea unde r the abso rp t io n l ines . The to ta l

r e s o n a n t a b s o r p t i o n w a s f it te d w i th a D e b y e e q u a t i o n l e a d in g t o a D e b y e t e m p e r a t u r e o f

345 K wh ich has to be co m pa red wi th the bu lk va lue of 467 K. ~21°)

M r s s b a u e r s p e c t r o s c o p y h a s a ls o b e e n a p p l i e d t o s t u d y t h e s t r u c tu r e o f n an o c r y st a U in e

m a t e r i a l s ( F e F 2 , ~ - F e 2 0 3 , ~ - F e 2 0 3 a n d C o O ) w i t h i o n i c b o n d i n g . T h e M 6 s s b a u e r s p e c t r u m

of nanoc ry s ta l l ine FeF2 (ave rage c rys ta l si ze 8 nm, p ro duc ed by ine r t ga s cond ensa t ion ;

F igs 32 an d 33 ) shows a qua dru po le d i s t r ibu t ion . ¢2H) W i th the a s su mp t ion o f an ave rage

va lue fo r the qu adru po le sp l it ti ng , tw o dou b le t s we re iden ti f ied (F ig . 32 ) hav ing nea r ly equa l




3 6 0

bT_ 340

r

- r 3 2 0

0 100 2 0 0 3 0 0

T em p e r o t u r e

[ K ]

FI G . 31 . H ype r f i ne m agn e t i c f i e l d H T) f sub-spectra 1 an d 2 Fig . 34 ) ob tain ed by least -squares

f i ts .Oo5

i s o me r s h i f t . One do ub le t c o r r e s po nds to bu lk Fe F2 . The s e c o nd do ub le t e x h ib i te d a br o a d

dis tr ibution of quadru pole spl i t t ings with an average va lue of 1 .97 m m /sec (Fig . 33). Th is

c o mpo ne nt wa s s ug g e s te d to o r ig ina te fr o m the Fe a to ms lo c a te d in the g r a in bo unda r ie s .

In addit ion, lo w temperature measurem ents indicated an anti ferromagnetic trans it ion temper-

ature extendin g over a bou t 70 K ins tead o f the sharp trans it ion observed in a FeF2 s ingle

crys ta l . (256) Th e smear ing out of the anti ferromag netic trans it ion seems to be an indicat ion of

a wide var ie ty of a tomic (non-latt ice ) configurations in the grain boundaries . A comparable

wid e range o f anti ferrom agnetic trans it ion temperatures (242 K to 135 K) com pared to the

1 . 0 0

0 9 7

Z

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b~

Z

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LO

b

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O

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6 3 0 3 6

V E L O C I T Y [ m m / J

F I G . 3 2 . Q u a d r u p o l e sp l i tt i n g Q . S . ) o f t h e M 6 s s b a u e r s p e c tr a o f a ) c o m m e r c i a l a n d b ) n a n o c r y s -

talline (8 nm) FeF2 specimens3 )




1 .oo

o. 97

z

o 0 . 9 4

Ig

z

1 .00

w

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0 6 0

1

6 3 0 3

V E L O C I T Y [ m m / = ]

I I

i

1 I t

6 0. S 1.3

2 . I 2 . 9

fl S r mm/==

FIG. 33. M 6ssbauer spectra and the Q.S. distributionsof (a) commercial and (b) nan ocrystallineFeF2

specimens.(2t~)

b u l k t r a n s i t i o n a t 2 8 8 K w a s n o t e d i n C o O (258 259)a n d a t t r ib u t e d t o a t o m s i n n o n - l a t t i c e s it e s.

A c o m p a r a b l e d i s t r ib u t i o n w a s n o t i c e d i n t h e h y p e r fi n e fi el d o f n a n o c r y s t a ll i n e a - F e

s u g g e s t i n g t h e n o n - l a t t i c e a r r a n g e m e n t o f a t o m s i n t h e g ra i n b o u n d a r i e s o f m e t a l l i c a s w e l l a s

i o n i c n a n o c r y s t a l l i n e m a t e r i a l s . S i m i l a r r e s u l t s w e r e o b t a i n e d (2 t:) f o r n a n o c r y s t a l l i n e ~ , -F e 2 0 3

a n d ~ - F e 2 0 3 ( 6 n m c r y st a l si ze ) . F i g u r e s 3 4 a n d 3 5 s h o w t h e M 6 s s b a u e r s p e ct ra o f b o t h

m a t e r i a ls . J u s t l ik e i n t h e c a s e o f n a n o c r y s t a l l i n e F e a n d F e F 2 , t h e s p e c t r a d e v i a t e d f r o m t h e

o n e s o f t h e c o r r e s p o n d i n g s i n gl e c r y st a ll in e s u b s t a n c e s w i th t h e s a m e c h e m i c a l c o m p o s i t i o n .

I n a d d i t i o n t o t h e s p e c t ra o f t h e s in g l e c r y s t a l li n e m a t e r ia l , a s e c o n d b r o a d c o m p o n e n t w a s

o b s e r v e d i n t h e n a n o c r y s t a ll i n e f o rm . T h e c h a r ac te r is t i c f e a tu r e s o f t h i s s e c o n d c o m p o n e n t

a r e s u m m a r i z e d i n T a b l e 4 . T h e r e d u c e d h y p e r f i n e fi el d a n d t h e in c r e a s e d l i n e w i d t h s u g g e s t

° V i

? ;

w

j , , 0 .98

t

1 0 5 0 5 1 0

V E L O C I T Y [ m m / s ]

Fro. 34. M 6ssbauer spectrum of nanocrystalline7-Fe203 (5 nm ) recorded at 4.2 K . 2 1 2 ) T h e broken ines

indicate the narrow (latt ice) and broad (bound ary) com ponen t of the spectrum (el. T able 4) .



NANOCRYSTALLINE MATERIALS 267

Z

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.n

,n

0.96

r Y

I l l

>

0.92

_ J

u J

n r

1.00

8 4 o 4 8

VELOC ITY [ rnm/s ]

F I G . 3 5 . M 6 s s b a u e r s p e c t r u m o f n a n o c r y s t a l l i n e ~- F e 20 3 8 n m ) r e c o r d e d a t 1 0 K . 2n~)T h e b r o k e n l i n e s

i n d i c a t e t h e n a r r o w l a t ti c e ) a n d b r o a d b o u n d a r y ) c o m p o n e n t o f t h e s p e c t r u m T a b l e 4 ) .

a spec t rum o f d if fe ren t s i te s w i th non- la t t i c e a r rangem en ts fo r the Fe a to m s in the g ra in

bou nda r i e s o f nanoc rys ta l l ine c ( -Fe203 an d y -Fe2 03 . A s imi la r r educ t ion o f the hype r f ine fi e ld

a s i n d i c a t e d i n T a b l e 4 w a s a l s o r e p o r t e d b y A y y u b e t a / (257) w ho stu die d nan ocr ysta ll ine

( 5 to 7 0 n m d i a m e t e r) a - F e 2 0 3 b y M 6 s s b a u e r s p e c t ro s c o p y . T h e r e s u lt s o f t h e s t ru c t u r a l

s tu d i e s o n n a n o c r y s ta l li n e F e F 2 , ~ - F e 2 0 3 a n d y - F e 2 0 3 a n d C o O s e e m a t v a r i a n c e w i t h

inves t iga t ions by m eans o f R am an s ca t te r ing (c f, Sec t ion 3 .7.5 ) o n nanoc rys ta l l ine T iO 2 .

3.7.4. Hydrogen absorption

In many non-c rys ta l l ine ma te r i a l s hydrogen can be inco rpora ted in to in te r s t i t i a l s i t e s , t he

e n e r g y o f w h i c h d e p e n d s o n t h e lo c a l a t o m i c a r r a n g e m e n t . H e n c e t h e g r a in b o u n d a r y

c o m p o n e n t o f a n a n o c ry s t a ll i n e m a t e r i a l m a y b e e x p e c te d t o e x h ib i t a c o n t i n u o u s s p e c t r u m

of hydrogen s i t e ene rg ie s whe rea s the c rys ta l l i t e s exh ib i t d i s c re te spec t rum o f s i t e s such a s

o c t a h e d r a l a n d / o r t e t ra h e d r a l s it es . I n o t h e r w o r d s , m e a s u r e m e n t s o f t h e h y d r o g e n s o l u b i li ty

a s a func t ion o f the hyd roge n po ten t i a l y i e ld st ruc tu ra l in fo rm a t ion ab ou t a g iven ma te r i a l .

Th i s m e tho d was app l i ed to s tudy th e s t ruc tu re o f nano c rys ta l l ine Pd . The me asu red (2n3)

so lub i l ity o f hyd roge n in c rys ta l l ine and nanoc rys ta l l ine P d i s com pare d in F ig . 36 . Because

on ly on e typ e o f s it e i s occup ied by hyd roge n in a P d s ing le c rys ta l , t he em f fo l lows Ne rns t ' s

l a w ( e m f l in e a rl y d e p e n d e n t f o r h y d r o g e n c o n c e n t r a ti o n s ). A b o v e 1 h y d r o g e n , a p h a s e

sepa ra t ion occurs a t 293 K in the s ing le c rysta l . Fo r the nanoc rys ta l l ine pa l l ad ium the

h y d r o g e n s o l u b il it y is la r g er b y a b o u t o n e t o t w o o r d e r s o f m a g n i t u d e d u e t o t h e h i g h er

d e n s i ty o f s it es in t o w h i c h t h e h y d r o g e n c a n b e i n c o r p o r a t e d i n t h e b o u n d a r y r e gi o n s. T h i s

resul t i s cons is tent wi th the reduced a tomic dens i ty (c f . Sec t ions 3 .3 .1 .2 and 3 .3 .2 .1) in the

bounda r i e s . As the s i t e s w i th in the g ra ins a re p robab ly the s ame a s in a mac roscop ic s ing le

c rys ta l, t he loca l concen t ra t ion o f hydro gen has to b e the s am e in the g rains a s in the s ing le

c rys ta l fo r a g iven equ i l ib r ium p re s su re o f hydrogen . T he re fo re , f ro m the d i ffe rence be twe en

the to ta l concen t ra t ion in nanoc rys ta l l ine Pd and tha t in s ing le -c rys ta l l ine Pd the amoun t o f

Table 4. M 6ssbauer D ata of Nanocrystalline ~-Fe203 and ~-Fe203

Hyperzne I so m er Quadrupole Line

field sh i f t sp l i t t in g wid th

( k O e ) ( r a m / s ) ( r a m / s ) ( ra m /s)

a-Fe204 (10 K)

-Fe203 (4.2 K)

C r ys t al l in e c o m p o n e n t 5 3 2 0 . 0 9 0 . 43 1 0 . 3 5

I n te rr a ci al o m p o n e n t 5 0 1 0 . 0 5 0 . 4 3 1 0 . 9 3

Crystalline com ponent 505 -0 .0 2 0.46 0.81

Interfacial com ponent 478 +0.01 0.37 1.25




200

F--

. _ oo / /

_ °

z I. Y I I

4 3 : 2 1

log c

CONCENTRATION

F IG. 3 6 . E m f o r ch em i ca l p o t en t i a l o f h y d ro g en i n a s i n g le c ry s ta l o f P d 0 ) an d i n n an o c ry s t a ll i n e

P d O ) a s a fu n c t i o n o f h y d ro g en co n cen t r a t i o n r a t i o o f h y d ro g en t o p a l l ad iu m a t o m s ) a t 2 93 K .

T h e s t r a ig h t l i n e t h ro u g h t h e d a t a p o i n t s fo r t h e s i n gl e c ry s t a l h a s t h e t h eo re t ic a l s lo p e o f RT F

where R i s the gas c~n s tan t and F i s the Fara day cons tan t ) . Th e lines th roug h the da ta po in t s fo r

the nanocry s ta l l ine Pd are ca lcu la ted by assum ing a gauss ian d i s t r ibu t ion o f s i t e energ ies fo r hydrog en

w i t h i n th e g ra i n b o u n d a r ie s - -- , w i t h o u t H - -H i n t e rac t i o n) . m )

h y d r o g en s eg r eg a ted a t g r a i n b o u n d a r i e s may b e ca lcu l a ted . I t h a s b een s h o w n(214) th a t th e

s eg r eg a t ed h y d r o g en d o es n o t f o l l o w a s i mp l e Lan g mu l r - M cLean eq u a t i o n b ecau s e a

spec t rum of s i t e energ i es ex i s t s fo r t he hydrogen a toms in t he g ra in boundar i es whereas t he

La ng m ui r - M cL ea n equat ion assum es a ll sites t o be energe t i ca l ly equ iva l en t . I f a gauss i an

d i s t r i bu t ion fo r t he hyd roge n s ites i n t he boun dar i es wi th a wid th o f 15 kJ (m olH ) -~ is

assumed , t he measured so lub i l i t y may bc descr ibed sa t i s fac to r i l y fo r l ower concen t ra t i ons

(cf . F ig . 36 ) . At h igher concen t ra t i ons , t he concen t ra t i on a t t he g ra in boundar i es becomes

s o h ig h ( g rea t e r t h an 1 0 ) t h a t h y d r o g e n - h y d r o g en i n te r ac t io n s h av e to b e in c l u ded . Th i s

w as d o n e b y t h e q u as i -ch emi ca l ap p r o a ch u s in g t h e i n t e r ac t io n p a r a me t e r o f p o l y c ry s t al li n e

Pd . (214) As m ay be seen f rom Fig . 36 th i s ap proa ch y i e lds r em arkab le ag reem en t be twe en

calculated and measured solubi l i t ies .

I f a p h as e s ep a r a t i o n o ccu r s i n m e t a l / h y d r o g en s y st ems , th e ch emi ca l p o t en t ia l o r t h e

h y d r o g en p r e s s u re r em a i n s co n s t an t w i t h in t h e t w o - p h as e r eg io n , a l t h o u g h t h e t o t a l

hydrogen concen t ra t i on in t he sys t em increases . Th i s behav io r was observed in c rys t a l l i ne

and nano crys t a l l i ne Pd . T he expe r imen ta l resu lt s , p resen ted in F igs 37 and 38, show tha t

the f l phase is fo rm ed in nanoc rys t a l l i ne Pd (F ig . 38 ) as a p l a t eau occurs a t t he sam e

hyd roge n ac t iv i ty a t wh ich the f l phase is fo rm ed in po lycrys t a l li ne Pd (F ig . 37 ) . Howev er ,

l ess hyd roge n is abso rbed in nanocrys t a l l i ne Pd (44 a t ) i n com par i son to a po lycrys ta l l ine

Pd spec imen (58a t ) , be fo re t he ac t iv i ty r ises aga in , wh ich was a t t r i bu t ed to t he exc lus ion

o f a co n s i d e r ab l e v o l u me f r ac t i o n o f t h e s amp l e f r o m t h e p h as e t r an s f o r ma t i o n . Th i s v o l u me

f rac t ion be longs to t he d i s to r t ed r eg ions a t t he g ra in boundar i es . The f l phase fo rms wi th in

the g ra ins o f nanocrys t a l l i ne Pd because they o f fe r t he same oc t ahedra l s i t es fo r hydrogen

occ upa t ion as i n a s ing le c rys t a l o f Pd , sugges t ing tha t t he sm al l c rys ta l li tes do n o t c on ta in

a h igh dens i ty o f defec t s t o wh ich the hyd roge n can seg rega te . The e l ec t ron ic o r e l ast ic

h y d r o g e n - h y d r o g en i n t e rac t i o n cau ses t h e f l p h as e t o f o r m a t t h e s ame h y d r o g en ac t iv i ty ,

whereas t he d i s to r t ed r eg ions i n o r c lose t o t he g ra in boundar i es do no t permi t a phase

t rans fo rm at ion . T he sam e effec t was no t i ced in g l assy meta l s . Th i s r esu l t m ay be un ders tood




2 6 9

E

.

E

U r l

. 0 1 5

u i

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0 0 . 2

0 . i 8 .

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I t

t_

t .

r -

u

I : r t

o

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h y d r o g e n

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FIG. 37.

P r e s s u r e - co m p o s i ti o n i s o t h e r m

3 3 3 K )

for hydr o ge n in p o lyc r ys ta l l ine Pd (aver age d iame te r ,

2 0 # m ) . T h e p r es su r e p l a t e a u b e t w e e n

H / P D = 0 . 0 1 5 a n d 0 . 5 8

c or r e s ponds to the c oe x i s te nc e r ange

of the ~t and fl phases. 213)

i f i t i s a s s u m e d t h a t t h e w i d t h o f t h e d i s t r i b u t i o n o f t h e h y d r o g e n s i t e s i s l a r g e r t h a n t h e

H - H intera ct ion energy . (2~5)

F r o m t h e d i f f e r e n t w i d t h s o f t h e t w o - p h a s e r e g i o n i n p o l y c r y s t a l l i n e a n d n a n o c r y s t a l l i n e

P d ( a v e r a g e gr a i n d i a m e t e r , 2 0 m a n d 1 1 n m ) , th e v o l u m e f ra c t io n o f t h e g r a in b o u n d a r y

r e g i o n s t o w h i c h t h e h y d r o g e n c a n s e g r e g a t e m a y b e c a l c u l a t e d a s s u m i n g t h e b o u n d a r i e s t o

b e e x c l u d e d f r o m t h e f l p h a s e f o r m a t i o n . A v a l u e o f 0 .2 7 i s o b t a i n e d f o r t h e b o u n d a r y v o l u m e

f r a c t io n , (2t6) y i e ld in g a g r a in b o u n d a r y t h i c k n e s s o f a b o u t l n m .

~ n

it

E

~ T

E

0 . 0 3

0 44

a B

A I I

0 0 . 2 0 , 0 . 6 O .B

h y d ro g e n c o n c e n t r t i o n

H/Pd)

v °

.

t .

T Q

0

L

r .

FI G. 38 . Pr e s s ur e -c om pos i t ion i s o the r m (333 K) for hydr oge n in na noc r ys ta l l ine Pd (ave r age gr a in

diame te r , 8 -12 nm ) . T h e pr es s ure p la te au be tw e e n 0 .03 and 0 .44 i s pr opos e d to b e s mal l e r be c aus e the

s o lub i l i ty o f h ydr o ge n i s l ar ge r in the = phas e [4° ) and be c aus e th e ~ ph as e i s for me d wi th in the gr a ins

on ly bu t no t w i th in the gr a in bou nda r y r e g ions . 213)




3.7.5 .

aman scat ter i ng

T h e s t r u c t u r e o f n a n o c r y s t a l l i n e s i l i c o n w a s f o u n d , b y R a m a n s p e c t r o s c o p y , t o c o n s i s t o f

a r e l a t i v e l y s h a r p c r y s t a l l i n e f e a t u r e a n d a m o r e o r l e s s p r o n o u n c e d s h o u l d e r a t l o w e r

frequen c ies a t tr ibuted to an am orp hou s- l ike com po nen t . ~2m7 218) F igure 39 sho w s a se t o f

R a m a n s p e c t r a f o r s a m p l e s d e p o s i t e d a t v a r i o u s t e m p e r a t u r e s , o t h e r d e p o s i t i o n c o n d i t i o n s

b e i n g k e p t c o n s t a n t ( f o r e x p e r i m e n t a l d e t a i ls c f. R e f . 2 1 8 ) . F o r c o m p a r i s o n , s p e c tr a o f s i n g le

crys ta l l ine S i (111) wafer ( labe led c -S i (111) ) and an X-ray amorphous s i l i con , prepared

b y a g l o w d i s c h a r g e d e c o m p o s i t i o n o f s i l a n e ( l a b e l e d a - S i ) , h a v e b e e n i n c l u d e d a s w e l l .

With decreas ing depos i t ion temperature , i . e . w i th decreas ing crys ta l l i t e s i ze , the crys ta l l ine

c o m p o n e n t ( F i g . 3 9 ) b r o a d e n s a n d i t s m a x i m u m s h if ts t o w a r d s l o w e r fr e q u en c y . T h e s h o u l d e r

s e e n i n t h e R a m a n s p e c t ra o n t h e l o w e r f r e q u e n c y s i d e o f t h e m a i n p e a k i s m o r e d if fi cu lt t o

i n t er p r e t u n a m b i g u o u s l y . I n s o m e c a s e s it c a n b e r e so l v e d i n t o t w o c o m p o n e n t s ( e .g . s p ec tr a

5 1 6

I

f /

. . . . . ~ . ~ ° -

T d l ° C ]

8 0

D

0

2

• r I . : •

.

I o °

l

I

3 5 0

5 • ' /

' ~ , , ~ c 5 5 c m - i

I

a - ' , - S i ( 11 1 )

- - ~ - j ~ - - - ~

~ 4 5 0 5 0 0 5 5 0

R o m a n s h i f t A v (c m I )

Fl o . 39 . R am an s pe c tr a o f po l yc r ys t a l l i ne s i li c on f il m s de p os i t e d a t var i ou s te m pe r atur e s be t w e e n 80

a n d 3 5 0 ° C . T h e 1 8 0 ° C s a m p l e w a s d e p o s i t e d o n s in g le -c r ys ta l S i 1 1 1 ) w a f e rs , th e o th e r s o n a m o r p h o u s

m e t a l s . R a m a n s p ec tr a o f s i n g l e c r y s ta l c - S i 1 1 1 ) ) a n d a n X - r a y a m o r p h o u s a - S 0 s i l ic o n a r e s h o w n

f o r c o m p a r i s o n a s w e l l : 2~3)




fo r Td = 180°C , F ig . 39 ). The com po nen t c lose r to the m a in peak m ay be due to su r face

phonons . In mos t c a se s , howeve r , t he fea tu re deno ted s in F ig . 39 canno t be re so lved

unam biguo us ly . Th e in teg ra ted in tens ity o f the com po nen t deno ted a (F ig . 39) inc rease s

and the pos i t ion o f i t s max ima sh i f t s towards lower f requenc ie s w i th dec rea s ing depos i t ion

temp era tu re . I t f ina l ly reaches a va lue o f abo u t 480 cm-~ fo r a s am ple depos i t ed a t 80°C

wh ich is typica l of X -ray am or ph ou s s i licon. (2~a) Th e ra t io o f the in teg ra ted in tens i ties o f

t h is c o m p o n e n t a s w e ll a s o f th e c r y s ta l li n e c o m p o n e n t a l lo w s a r o u g h e s ti m a t e o f th e

r a t io o f th e a m o r p h o u s - l i k e a n d o f t h e c r y st a ll in e c o m p o n e n t in th e sa m p l e , i f p r o p e r

va lues fo r Ra m an s ca t te r ing c ros s s ec t ions a t a g iven f requency o f the exc i ting l as e r

l igh t a re t aken in to accoun t . Th i s ra t io co r re sponds approx ima te ly to the re l a t ive amoun t

o f Si a tom s a t the su r fa ce s o f the S i c rys ta l li t es . Th i s in t e rp re ta t ion i s ba sed on the

fo l lowing s t ruc tu ra l m ode l . T he f i lms a re p rop ose d to con s i s t o f c rystaUi te s em bed ded in

a n a m o r p h o u s m a t r ix . * H o w e v e r , o n th e b a s is o f t h e p r e s e n t d a t a o n e a l so c a n n o t

exc lude the pos s ib i l ity tha t the f i lms a re bu i l t up o f th in , quas i tw o-d im ens iona l c rys ta l li t e s

a s wou ld be expec ted acco rd ing to th e theo re t i c a l mode l o f Kane l li s

et al. 22°)

T h e v o l u m e

f rac t ion o f the am orp hou s - l ike com pon en t a s the c rys ta l s iz e was reduced fina lly merg ing

in to the Ra m an spec t rum o f X- r ay am orp ho us s il icon . ¢2~9) Th i s re su lt m ay be un de rs tood a s

fo l lows . I f t he c rys ta l siz e is r educed fu r the r and fu r the r , t he to t a l f r ee ene rgy s to red in the

bou nda r i e s o f the nanoc rys taUine m a te r i a l f ina l ly becom es l a rge r than the f ree ene rgy o f a

p iece o f g la s sy Si w i th the s ame n um ber o f a tom s . I n th i s c a se , the mis fi t conce n t ra t ed in the

in te rcrys ta l l ine in te rfaces de- loca l izes in to a g lassy s t ruc ture because th is process reduces

the to ta l f ree energy. In the case of s i l icon, th is t rans i t ion was observed a t a c rys ta l s ize of

a b o u t 2 n m . 2 ~8 )

Raman s tud ie s have a l so been pe r fo rmed fo r nanoc rys ta l l ine T iO2 wi th ave rage g ra in

dia m eter s o f ab o u t 10 to 100 nm . ~22~)A l t h o u g h t h e v o l u m e f r a c t io n o f g r a in b o u n d a r i e s v a r i e d

(g ra in s i ze va r i a t ion ) in d i f fe ren t s ample s be tween abou t 3 to 30%, no Raman spec t ra l

c o m p o n e n t w a s o b s e r v e d o t h e r t h a n t h o s e f r o m t h e r u t il e p h a s e o f T i O 2. H e n c e i t w a s

conc luded tha t a l l g ra in bo und a r i e s o f nanoc rys ta l l ine T iO2 a re comp r i s ed o f the loca l a tom ic

s t ruc tu ra l un i t s o f ru t i le an d no o the r type o f d i so rde r ex is ts . Th i s conc lus ion is a t va r iance

w i t h t h e r e p o r t e d r e s u lt s o f X - r a y d i f fr a c ti o n m e a s u r e m e n t s , t h e E X A F S d a t a a n d t h e v a ri o u s

types o f spec t roscop ic s tud ie s . In pa r t i cu la r , t he M6ssbaue r s tud ie s o f FeF2 , ~ t -Fe203 and

7-Fe203 (F igs 32 -35 , Sec t ion 3 .7 .3 ) r evea led unam bigu ous ly 2n ,m) tha t g ra in bo un da r y

s t ruc tu re s in ion ic nanoc rys ta l l ine m a te r i a l s cons i s t o f local a tom ic s t ruc tu ra l un i t s d i f fe ren t

f rom the c rys ta ll ine s t ruc tu re o f FeF2 o r Fe203 (cf . Sec t ion 3 .7 .3 ). Obv ious ly , th i s con t rad ic -

t io n d i s a p p e a r s i f t h e g r a in b o u n d a r y c o m p o n e n t o f t h e TiO 2 h a d a s t r u c t u r e w h i c h w a s n o t

R a m a n a c ti v e, a n d h e n c e n o R a m a n s p e ct r al c o m p o n e n t c a n b e n o ti c e d . U n l es s c o m p l i m e n -

t a r y m e a s u r e m e n t s b y i n fr a -r e d a b s o r p t i o n a r e p e r f o r m e d , t h e p r o p o s e d s t r u c t u r a l i n te r p re t -

a t i o n o f t h e R a m a n d a t a f o r T iO 2 re m a i n s a m b i g u o u s .

3.8. N a n o c r y s t a l l i n e A l l o y s

By ana logy to nanoc rys ta l l ine ma te r i a l s , nanoc rys ta l l ine a l loys may be gene ra ted by

s i m u l t a n e o u s ly e v a p o r a t i n g o r s p u t t e r in g s e ve r al c o m p o n e n t s i n a n e v a p o r a t o r o f t h e k i n d

show n in F ig . 8 . Un de r su i t ab le evap ora t io n cond i t ions (m) a un i fo rm mix tu re o f c rys ta ll i te s

wi th d i f fe ren t chemica l compos i t ions may be ob ta ined . The subsequen t conso l ida t ion re su l t s

in a m ater ia l wh ich has b een te rm ed a nan ocry s ta l l ine a l loy . (223) In fac t , these a l loys a re

*The term amo rphous was u sed in the sense of non-crystalline and doe s not necessarily imply glassy.



7


0 O 0 U

O . . . _

45o 5oO

o . - o

•

~

~

:cc

F IG. 4 0 . S ch em a t i c m o d e l o f a n an o c ry s t a ll i n e A g -F e a l l o y acco rd i n g t o t h e d a t a o f M rs s b au e r

spect roscop y Fig . 41). The a l loy cons i s ts o f a mix tu re o f nanom eter-s ized Ag and Fe crys ta ls .

In the s t ra ined) in ter fac ia l reg ion be tween Ag and F e crys ta l s , so lid so lu t ions o f Fe-a tom s in

A g an d A g -a t o m s i n F e a r e fo rm ed a l t h o u g h b o t h co m p o n en t s a r e i m m i s c ib l e i n t h e l i q u id

an d / o r s o l i d s ta t e . F o r t h e s ak e o f s i m p l i c it y t h e fo rm a t i o n o f A g / F e a l l o y s i n t h e A g an d F e g ra i n

boun dar ies has been om i t ted a l thoug h i t is like ly to occu r as suggested by the g ra in bounda ry

se gr eg at ion 222).

poly crys ta ls wi th a c rys ta l s ize o f a few nano m eters cons is t ing o f c rys ta l l ites d i ffe r ing in

o r i en ta t ion a s we l l a s in chemica l com pos i t ion (F ig . 40 ). I t i s one o f the a t t r ac t ive fea tu re s

o f the se a l loys tha t the chemica l ly d i f fe ren t a tom s (molecu le s) o f the v a r ious c rys ta ll i te s a re

mixed (a l loyed) in the in te rfaces as neares t ne ighbors i r respec t ive of bulk misc ib i l i ty , e tc .

Thus , nanoc rys ta l l ine a l loys pe rm i t fo r exam ple the a l loy ing o f me ta l s and ion ic ma te r i a ls .

Con t ra ry to conven t iona l powder me ta l lu rg ica l a l loys , nanoc rys ta l l ine a l loys a re expec ted to

exh ib i t new p rope r t i e s due to the fo l lowing two fac to rs :

(1 ) The h igh dens i ty o f in t e rphase bou nda r i e s be tween the va r ious compo nen t s . In the se

bounda r i e s , a tomic s t ruc tu re s a re fo rmed which do no t ex i s t i n the c rys ta l l ine and /o r g la s sy

s ta te .

(2) Effec ts due the smal l s ize of the c rys ta l li tes .

An e f fec t o f the f i r s t k ind was recen t ly obse rved in nanoc rys ta l l ine a l loys o f Cu /Fe and

Ag /Fe . Bo th a l loys have been p repa red t222) by co -evapo ra t ing the tw o co m pon en t s in H e

(p re s su re 1 to 20 mb a r ) . The two sys tems were se lected because they have l it tl e (< 100 pp m

C u / F e ) o r n o ( A g / F e ) m e a s u r a b l e m u t u a l s o l u b il i ty a t a m b i e n t t e m p e r a t u r e i n t h e b u lk . I n

fac t , Ag /Fe a re even immisc ib le in the mol ten s t a t e c lose to the me l t ing po in t . The a l loy

c o m p o s i t i o n s s t u d ie d w e r e C u - 6 2 a t F e , C u - 3 3 a t F e a n d C u - 1 6 a t F e . T h e c o n c e n -

t ra t ion o f s eve ra l A g- F e a l loys was le s s than 50 a t Fe . The c rys ta l s iz es in the a l loys va r i ed

b e t w e e n 6 a n d 11 n m f o r F e , b e t w e e n 7 a n d 1 4 n m f o r C u a n d b e t w e e n 6 a n d 8 n m f o r

Ag . E lec t ron m ic rosco py revea led a hom oge neou s spac ial d i s t r ibu t ion o f the c rys ta l l it e s o f

bo th cons t i tuen t s in a l l a l loys s tud ied . Th i s re su l t was conf i rmed by sma l l ang le X- ray

sca tt e ring . In te r fe rence e f fect s be twee n the c rys ta l li t e s o f the con s t i tuen t s w e re no t i ced wh ich

impl ies tha t the c rys ta l l ites a re m ixed on a length sca le ranging be tw een 2 and 50 nm. The

a tomic s t ruc tu re in the v ic in i ty o f the Ag /Fe in te rphase bounda r i e s was s tud ied by means




273

l . O 0

t

0

0 . s g

C

~ 0 . 9 8 -

L

Rg Fe

• ~

2 - 8

T = I O K

4 0 4 8

v e l o c i t U [ m m / s ]

FIG. 41 . M 6ssbau er spec t rum of a na nocrys ta l l ine F e- A g a l loy 30 a t*/ , Fe , 10 K , c rys ta l s ize 8 nm).

The spect rum cons is t s o f the fo l lowing th ree com ponen ts . i ) ~-F e ) , i i ) Fe a tom s d isso lved in

Ag -.-) and i ii ) Ag atom s dissolved in Fe .__)m2).

of M 6ssb aue r spec t ro scopy F ig . 41 ) . The obse rved spec t ra cons is t o f the fo l lowing th ree

c o m p o n e n t s .

i ) Fe a toms s i tua ted in an Fe c rys ta l w i th an ~ -Fe c rys ta l l a t t i c e .

i i ) Fe a tom s in an Fe - -Ag so l id so lu t ion wh ich cons i s t ed p r imar i ly o f Ag a tom s , and

i ii ) F e a t o m s i n a n F e - A g s o li d s o lu t i o n w h i c h c o n s i st e d p r e d o m i n a n t l y o f F e a t o m s a n d

c o n t a i n e d o n l y a f e w A g a t o m s .

The s t ruc tu ra l mode l p roposed to in t e rp re t the se re su l t s i s ind ica ted in F ig . 40 . In the

s t ra ined l a t t ic e reg ions in the v ic in ity o f the Ag /Fe in te rph ase b ound a r i e s , t he so lub i l i ty o f

F e i n A g a n d t h e o n e o f A g i n F e i s p r o p o s e d t o b e e n h a n ce d . * A n e n h a n c e d s o l u te s o l u bi l it y

du e to e las t ic s tra ins has been de m on s tra ted in the pas t theo re t ica l ly m*-nT) and exper-

imen ta l ly ns) fo r va r iou s a l loys . The enhan ced so lub i l ity o f Ag in the s t ra ined F e l a t t ic e and

o f F e i n t h e s t r a in e d A g l a t ti c e w o u l d e x p la i n t h e s e c o n d a n d t h i rd c o m p o n e n t o f t h e

M 6 s s b a u e r s p e c t r u m . N o s u c h c o m p o n e n t s a r e n o t i c e d in c o n v e n t i o n a l p o l y c ry s t a ls w i t h t h e

same chemica l compos i t ion . Hence , the newly fo rmed so l id so lu t ions we re sugges ted to be

fo rm ed a t o r c lose to the in te r fac ia l r eg ions o f the nanoc rys ta l l ine m a te r i a l s a s ind ica ted in

F ig . 40. The a l t e rna tive in te rp re ta t ion in t e rms o f t r apped Fe o r A g a tom s in Ag o r Fe c rys ta l s

d u r i n g e v a p o r a t i o n w a s r u l e d o u t b y s e p a r a t in g t h e v a p o r s o u r c es s o fa r t h a t a ll e v a p o r a t e d

F e a n d A g a t o m s h a d c o n d e n s e d i n s e p a r a te r e g io n s o f t h e e v a p o r a t o r F i g. 8 ) i n t h e fo r m

o f smal l c rys ta l l ites . In fac t , s imi la r in te rfae ia l a l loying e ffec ts have be en rep orte d b y Shingu

e t a l . r ag i n nanoc rys ta l l ine F e -A1 a l loys gene ra ted by ba l l mil ling. I f t he abo ve obse rv a t ions

can be gene ra l i z ed , nanoc rys ta l l ine a l loys wou ld open the way to gene ra te so l id so lu t ions o f

componen t s wh ich a re immisc ib le even in ma te r i a l s ob ta ined by rap id coo l ing . Fo r example ,

A g - F e a l l o y s c a n n o t b e g e n e r a t e d b y r a p i d s o l i d i f i c a t i o n o r e v a p o r a t i o n m e t h o d s . T h e

i n t e r p re t a ti o n o f th e M f s s b a u e r s p e c t r u m i n te r m s o f a n i n te r fa e ia l c o m p o n e n t b e t w e e n F e

and Ag crys ta ls agrees wi th the resul ts of a M6ssbauer s tudy on 0c-Fe /Cu layer s t ruc tures326°)

Th e l aye r s t ruc tu re s exh ib i t ed tw o hype r f ine f ie lds , one o f wh ich was iden t ica l w i th bu lk ~ -F e

346 kO e a t 4 .2 K) and a reduced f i e ld 306 + 8 kOe) w h ich was obse rve d on ly in spec imens

* In ad d i t i o n b o u n d a ry s eg reg a t io n o f A g an d F e a t t h e g ra i n b o u n d a r i e s b e t w een F e an d A g c ry s ta l s m ay a l s o o ccu r.



274

PROGRESS IN M TERI LS SCIENCE

wi th a h igh dens i ty o f ~ t -Fe /Cu in te r face s . The re fo re , th i s com pon en t w as a t tr ibu ted to F e

a tom s loca ted a t , o r in the v ic in i ty o f the a -F e /C u in te rfac ia l reg ion .

Ef fec ts due to the sma l l s iz e o f pa r ti c l es have been repo r ted in num erous pape rs . T he m a in

emp has i s o f th i s f ie ld lie s p re sen t ly on the s tudy and po ten t i a l u se o f quan t i t i z a t ion e f fec t s

due to th e sma l l pa r t i c l e s iz es . The p re sen t s t a t e o f the a r t i n th is f ie ld ha s been sum mar ized

in severa l exce l lent reviews . (23°'~3~) If a sm all c lu ster o f n at om s or di ato m s gro w s into an

sp 3 hybr id ized bu lk s em icond uc to r th ree reg imes m ay be d i s tingu i shed a s fa r a s the ba nd

s t ruc tu re i s conce rned. (232) F or smal l n , c lus te rs ap pea r to be ent i re ly m olecu lar in th a t the

bu lk un i t ce ll i s no t present , and each c lus te r n has a d i f fe rent s t ruc ture . In the seco nd regime,

for ab ou t 102 < n < 5 x 103 a hyb rid mo lecular-sol id s ta te regime occurs . He re , a smal l

c rys ta ll i te w i th the un i t c el l o f the b u lk m a te r i a l i s obse rved ; howeve r , t he e l ec t rons rema in

in d i s c re te molecu la r o rb i t a l s . In bo th the se reg imes , the c lus te r in t e rac t s w i th the e l ec t ro -

magne t i c f i e ld v ia the t r ans i t ion d ipo le moment , a s no rma l ly occurs in the molecu la r

s p e c t ro s c o p y . P o l a r it o n p h e n o m e n a a r e n o t p r e se n t . T h e t h i r d r e g im e s h o u l d o c c u r a t a b o u t

15 nm d iame te r . A t th is po in t , t he c rys ta ll i te in t e rac t ion wi th the f i eld swi tches f rom w eak

to s t rong , so tha t loca l fi e ld e f fec t s and h ighe r mul t ip le mom ents beco m e imp or tan t . Th i s w i ll

have an e f fec t on b o th the l inea r and n on- l inea r spec t roscop y .

In the s econd reg ime , the e l emen ta ry theo ry o f s emiconduc to r c lus t e r s p red ic t s a

nu m ber o f in t e re st ing phe nom ena , a s d i s c re te m olecu la r o rb i t a l e lec t ron ic s t a te s evo lve

in to con t inuous so l id - s t a t e bands wi th inc rea s ing s i ze . The so l id - s t a t e phys ic s communi ty

te rms the se l a rger c lus t er s qu an tum do t s o r z e ro -d im ens iona l exc i tons . These sma l l

c rys tal l it e s show qu an tu m conf inem en t o f the e l ec t ron and ho le in th ree d imens ions ; in the

quantum-wel l th in- layer super la t t ices s tudied extens ive ly by sol id-s ta te phys ic is ts , there i s

one -d imens iona l conf inemen t . Op t i ca l abso rp t ion , f luo re scence , and re sonance Raman

techn iques have p rov en v a luab le fo r cha rac te r i za t ion o f s emicon duc to r c lus te r s in the

second reg ime , in l iqu id co l lo ids , and in t r anspa ren t d ie lec tr i cs . Pe rhap s the m os t in s t ruc t ive

m easurem en t i s the s ize depend ence o f the c rysta ll i te abso rp t ion spec t rum tha t occu rs when

the c lus te r d iame te r i s comparab le to o r sma l l e r than the e l ec t ron -ho le exc i ton d iame te r

in the bu lk s em iconduc to r . These d iam e te r s a re qu i t e l a rge (e .g . abo u t 5 um fo r CdS and

ab ou t 20 nm fo r G aA s ) b ecause o f the s t rong e lec t ron de loca l i za tion and sma l l e f fec tive

masses in these mater ia ls . The c rys ta l l i tes show discre te s ta tes (molecular orbi ta ls ) ins tead

o f c o n t i n u o u s b a n d s i n t h e b a n d - g a p r e g io n . F i g u r e 4 2 s h o w s th e e x p e c te d p a t t e r n o f

m olec ular orbi ta ls for spher ica l c rys ta l l i tes of Cd S (7 nm ) an d G aA s (14 nm). (233)The s t rong ly

a l lowed t rans i t ions conse rve the p r inc ipa l quan tum numbers , g iv ing the expec ted pa t t e rn o f

d i s c re te t r ans i t ions show n a t the bo t to m o f the f igu re. In p rac t i c e, t he b lue sh i ft o f the lowes t

l s to l s exc i ton i s c l ea r ly and ea s ily obse rved (F ig . 43 ). Pa r t i c le s l a rge r than ab ou t 6 nm,

i. e. l a rge r than the s ize o f an exc i ton in the mac roc rys ta l l ine ma te r i a l , s t a r t t o abs o rb c lose

t o 5 15 n m ( o r 2 .4 e V p h o t o n e n e rg y ) , c o r re s p o n d i n g t o t h e b a n d g a p o f b u l k C d S . W i t h

dec rea s ing s i ze , the abso rp t ion th re sho ld sh i f t s to sho r t e r wave leng ths . CdS cons i s t ing o f

pa r t i cl e s be low 2 .2 nm i s co lo r le s s . I t c an b e recove red a s a wh i t e po wd er f rom the aqu eou s

so lu t ion whe re i t was fo rm ed by p rec ip i t a t ing Cd 2+ ions w i th H2 S in the p re sence o f a

s m a ll a m o u n t o f s o d i u m p o l y p h o s p h a t e ( th e s ol id p o w d e r o b t a i n e d a f t e r r e m o v a l o f t h e

so lven t a l so con ta ins the po lyp hosp ha te ; i t p reven t s the sma l l pa r t ic l e s f rom com ing in to c lose

con tac t ) . In the ca se o f s emicondu c to rs hav ing a band gap sma l l e r than tha t o f CdS , the

c o l o r c h a n g e s a r e e v e n m o r e d r a s t i c . F o r e x a m p l e , c a d m i u m p h o s p h i d e , a b l a c k m a t e r i a l

w i th a ba nd gap o f 0 .5 eV , can be m ade in a ll co lo rs o f v i sib le ligh t by va ry ing the pa r t i c l e

s ize be tw een 10 and 2 nm. (2~) Th e f luorescence ba nd of the c olo ids i s a lso b lue-shi f ted w i th

decreasing particle s ize.



N A N O C R Y S T A I , L I N E M A T E R I A L S 75

2

> =

= .

z t

~D

~ p

~S

F 9 . . . .

CdS

MOLECULAR

ORBITALS

(7~m)

z r T _ __ . ~ . - - - - r8

SPa

N -

- - - ' 0 7

ORBIT

mD

~ p

~S

F . . . .

G a A s

MOLECULAR

ORBITALS

) 4 n m )

. . . . / S

~ P I s p l .

I - - - - . S XD 1 ORBIT

- p

D

OPTICAL SPECTRA

o P s

A / x A

3 T E g 2

D PS

I I h l

° °

2 TE9

PHOTON ENERGY (eV)

FIG. 42. Expected pa t tern of mo lecula r orb i tals an d al lowed discrete e lectronic t rans i t ions, for spherical

crystal li tes of C dS (7 nm ) a nd Ga As (14 nm ). 233)

The s t rong t rans i t ions s een in op t i ca l abso rp t ion invo lve in te rna l c rys ta l l i t e mo lecu la r

orb itals tha t ha ve no de s o n the crysta ll i te su rface. (23s'236) Th ese spe ctra are no t se nsit ive to

su r face cond i t ions , no r to ads o rp t io n o f fo re ign molecu le s . The c lus te r luminescence is , by

con t ra s t , qu i t e s ens i t ive to su r face cond i t ions , and appea rs to occur f rom su r face loca l i zed

s ta te s . A l a rge pe rcen tage o f the a toms in a nanom c te r pa r t ic l e a re on the su r face , whe re

dang l ing bond s , ad so rb ed spec ie s, e t c. p rod uce t r aps fo r e l ec t rons and ho le s . The fa t e o f the

cha rge ca r r i e rs g ene ra ted b y l igh t abso rp t ion i s s t rong ly dep ende n t o n the ex i s t ence o f the se

t raps . F lu o re scence expe r imen t s a re su i t ab le to de m ons t ra t e th i s f ac t. F igu re 44 il lu st ra te s an

examp le . The f luo re scence spec t rum o f a CdS s am ple is show n he re be fo re and a f t e r su r face

mod i f i ca tion . C dS co l lo ids made by add ing H2 S to a cadm ium sa l t so lu t ion have gene ra lly

a v e r y w e a k r e d f l u o re s ce n c e, p e a k in g a t a p h o t o n e n e r g y a b o u t 0 . 4 e V b e l o w t h e a b s o r p t i o n

th re sho ld . T h i s f luo re scence i s exp la ined a s rad ia tive reco mb ina t ion o f t r apped cha rge

ca r r ie r s , t he com pe t ing rad ia t ion le ss reco m bina t ion be ing the dom inan t p roces s . Af te r su r face

mo di f i ca t ion by the ad d i t ion o f Cd 2+ ions and an inc rease in pH , a b r igh t g re en -b lue

f luo re scence i s p re sen t , t he qu an t um y ie ld exceed ing 50 . The m ax im um of th i s f luo re scence

li es a t t he abso rp t io n th re sho ld ; i .e . one is dea l ing wi th band -gap recom bina t ion o f the f re¢

charge carr ie rs .

S imi la r e f fec ts have b e .n dem ons t r a t ed fo r CdS e co ve red w i th ph cny l l igands (237) and CdS

w i t h C H 3 S g r o u p s a t t a c h e d t o t h e s u r f a c e . 23s.24°) W h i l e f e w h a r d f a c t s c o n c e r n i n g s u r f a c e




,, \

, .,,,, \

200 300 400 5

w o v e le n g t h k [ n r n ]

F IG . 4 3 . A b s o r p t i o n s p e c t ru m o f C d S i n a q u e o u s s o l

u t i o n : different mean particle sizes.~23°)

[ d S

I t e r a c th tio n

°

~ . . b efo re

t .50 500 S50 600 650

w a v e l e n g t h h [ n r n ]

F IG . 4 4. F l u or e sc e n ce s p e c t r u m o f C d S b e f o r e a n d a f t e r

surface m odification. ~°)

s t a t e s a re p re sen t ly know n , the re is a bo dy o f ind i rec t ev idence tha t su r face ada tom s

a n d / o r v a c a n ci e s, a d s o r b e d m o l e c u l es o f t h e c o r r ec t r e d o x p o t e n t i al s , a n d p o s s i b l y a t o m s a t

ve r t i c e s and /o r on edges , p rov ide loca l i zed su r face s t a t e s tha t t r ap e l ec t rons and ho le s . The

t rapped e lec t ron and ho le can recombine e i the r r ad ia t ive ly o r non- rad ia t ive ly . The emis s ion

i s s t rong ly coup led to l a t t i c e phonons , g iv ing a b road con t inuum s t rong ly red -sh i f t ed

f r o m t h e a b s o r p t i o n s p e c t r u m . T h e n o n - r a d i a t i v e r e c o m b i n a t i o n s h o w s s t r o n g t h e r m a l

ac t iva t ion typ ica l o f s t rong cou p l ing to l a t ti c e pho nons . In C dS c lus te r s , t he re appea rs to be

a c o r r e l a ti o n b e t w e e n t h e d i st a n c e b e t w e e n t h e t r a p p e d c h a r g e s a n d t h e e n e r g y o f th e b r o a d

emis s ions, in a fa sh ion ana lo gou s to tha t o f d i s tan t d ono r -accep ted pa i r emis s ion in bu lk

s e m i c o n d u c t o r s .

R e c e n t w o r k o n t h e c o u p l i n g o f p h o n o n s t o t h e i n te r n a l l s to 1 a b s o r p t i o n t r an s i ti o n i n

a b o u t 4 .5 n m d i a m e t e r C d S e c r y st a ll it e s s h o w s t h er e i s w e a k c o u p l i n g t o L O p h o n o n s , a n d

s t r o n g e r c o u p l in g t o l o w f r e q u e n c y a co u s t i ca l p h o n o n s . A t 4 K t h e h o m o g e n e o u s w i d t h is

o n t h e o r d e r o f 1 00 c m - ~. T h e c o u p l i n g t o L O p h o n o n s a l so s h o w s u p i n t h e r e so n a n c e R a m a n

spec t ra o f the se c rys ta l l i t e s . These re su l t s app ly to i so la t ed , non- in te rac t ing s emiconduc to r

c lus te r s in d ie l ec t r i c med ia . Ve ry l i t t l e i s known abou t the co r re spond ing op t i ca l p rope r t i e s

in the loose aggrega te s tha t a re fo rmed in f loccu la ted co l lo ids . In the ca se o f the pe r iod ic ,

t h r e e- d i m e n s io n a l a r r a y o f Cd S c lus te r s fo rm ed in zeo l i te s , e ach ind iv idua l d us te r in t e ract s

wi th i t s neare s t ne igh bors to f orm a supe rc lus te r . (z41) This in te rac t ion can no t be du e to the

d i rec t ove r l ap o f c lus t e r wave func t ions , s ince the se clus te r s a re s epa ra ted by abo u t 0 .6 and

0 .9 nm in zeo li t e Y and A , re spec tive ly . In s t ead , they in te rac t v i a th rou gh- bon d in te rac t ions .

Qu an t i t a t ive t r ea tm en t o f th is p rob lem h as no t ye t appea red . The non - l inea r op t i ca l

p rope r t i e s o f la rge r (10 nm to 50 nm ) C dS xSe l -x c rys ta l li t es in s il ic a te g la sse s (commerc ia l ly

sold as co lor-g lass f i lte rs) have a t t rac ted wid espre ad exper im enta l in te res t , c242) No n-l in ear

op t i ca l fou r -w ave m ix ing expe r im en t s have show n l a rge th i rd -o rde r X 3 coe f fi c ien t s and

p icosecond re sponse t imes in the ava i l ab le s ample s . The ope ra t ive non- l inea r mechan i sm

is tho ug ht to be a s imp le ba nd fil ling ~24x2~) in the few color -glas s sam ples tha t hav e b een

quan t i t a t ive ly inves t iga ted . Non- l inea r op t i ca l s tud ie s have a l so been done on CdS c lus te r s

in ionomers . I t ha s been shown tha t the s imple band- f i l l i ng mechan i sm i s no t impor tan t

du e to an ext rem ely sh or t carr ie r lifetime3245 2~) The re have been severa l re la ted theore t ica l

pa pe rs on gian t osc il la tor s tren gth C:47) local field effec ts 2~) an d exc itat io n-in du ced blu e

shift.c249)



N N O CRY ST LLI N E M TERI LS

277

In the area of metal clusters, there has been extensive work on the optical properties of

metallic colloidal particles, individually and in flocculated aggregates, 25°) In the diameter

range o f about 2 nm and larger, quantum size effects as described for semiconductors are

generally not present. Nevertheless, observations have been reported ~25~) which suggest

quantum effects to exist even in micron-sized crystals. Photoelectron spectroscopy on

mass-selected metal clusters in supersonic jets has shown a size-dependent development of

band structure in approximate agreement with the simple jellium model.

3.8.1.

Nanomet er sized sandwich structures

In a nanometer-sized sandwich structure~23°) two different semiconductor parts are con-

nected. Illumination into one part may produce a response in the other part or at the interface

between the two. The first example was found in experiments where small amounts of

cadmium salt were added to a ZnS sol. As the solubility product of CdS is smaller than that

of ZnS, Zn 2+ ions are substituted by Cd 2+ ions on the surface of the particles and a layer

of approximate composition CdZnS2 ,is formed. Just a few Cd2+ ions on a ZnS particle

are sufficient to quench the fluorescence of the latter. At higher cadmium amounts the

fluorescence of the 1 : 1 layer of zinc and cadmium sulfide appears upon illumination into

the ZnS part of the sandwich. These findings show that the transfer of charge carriers from

one par t of the sandwich structure to the other is possible. (252) More recently, sandwich

structures between cadmium sulfide as the light-absorbing semiconductor part having a

relatively small band gap and titanium oxide or zinc oxide as the large band gap part have

been described. ~252 253) Such structures form spontaneously when the separately prepared

solutions of the colloids are mixed under certain conditions where there is a large excess of

Cd 2+ ions in alkaline solution, polyphosphate acting as stabilizer in a TiO2 sol. The formation

of the sandwich is recognized by the quenching of the fluorescence of CdS. The effect was

explained as immediate transfer of the electron formed in the illuminated CdS part of the TiO2

part as the conduction band in TiO 2 is on a less negative potential than that of CdS. The

positive hole, on the other hand, cannot move to the TiO2 part as it would be there on a much

higher positive potential than in CdS. The result of this electron transfer is an efficient primary

charge separation. The TiO2-CdS sandwich thus acts as a small diode of almost molecular

dimensions or like an n-p junct ion. Similar effects have been found with sandwich structures

of Cd3 P2 and ZnO.~253) Cadmium phosphide can be made with different band gaps by varying

the particle size.

Quenching o f the fluorescence of cadmium phosphide by ZnO was more efficient the larger

the band gap of the Cd 3P2 part.

A phenomenon quite different from the ones just described was observed in the case of

CdS-Ag2 S 36 and AgI-Ag2 S37~225) structures. Such structures are formed upon the addition o f

silver ions to a CdS sol or H2S to an AgI sol, respectively. In both cases a strong red

fluorescence arises which moves into the infra-red region with increasing size of the Ag2 S part.

This fluorescence is quenched by a small amount of Ag2S. The new red fluorescence peaks

at 850 nm (1.45 eV photon energy) at low Ag2S deposits. A second maximum at 1,050nm

(1.18 eV) appears at higher Ag2S concentrations, which shifts to longer wavelengths with

increasing Ag 2S concentration, and, at almost complete conversion of AgI into Ag2S, a weak

fluorescence at 1,250 nm (0.99 eV) remains tha t corresponds to beh band-gap energy of

non-quantitized Ag2S.

The explanation of these findings seems as follows. Small silver sulfide deposits (a) are

strongly quantitized, the conduction band lying at more negative potential than that of AgI.

The hole generated in illuminated AgI moves to the Ag2S part at the interface, and the 850 nm



78


emi s s io n is b r o u g h t ab o u t b y t h e r eco m b i n a t i o n o f t h e e l ec tr o n i n t h e co n d u c t i o n b an d o f

Ag I wi th t h i s ho l e i n Ag2S. W hen the Ag2S depos i t is su ff ic i en tly l a rge b ) , it s cond uct ion

ban d is a t a l ess nega t ive po ten t i a l and the e l ec t ron can a l so be t r ans fe r red f rom A gI to Ag2 S .

Th e r eco m b i n a t i o n o ccu r s n o w i n t h e A g 2 S p a r t , t h e em i tt ed li g ht h av i n g l o n g e r an d l o n g e r

wave leng ths as t he b and gap o f Ag2 S becom es smal l e r wi th i ncreas ing s ize o f t h is pa r t o f t he

sandwich .

4 . P R O P E R T I E S

I f t he a tomic s t ruc tu re o f nanocrys t a l l i ne mater i a l s d i f f e r s f rom the s t ruc tu res o f g l asses

and crys t a l s , t he s t ruc tu re-dependen t p roper t i es o f nanocrys t a l l i ne mater i a l s a re expec t ed

to be d i f f e ren t f rom the p rope r t i es o f t he chem ica l ly i den t ica l subs t ances i n t he g l assy o r

crys t a l l i ne s t a t e . In t he fo l lowing sec t ions t he ex i s t i ng observa t ions on the p roper t i es o f

nano crys t a l l i ne m ater i a l s wi ll be summ ar i zed . M os t s tud ies have been pe r fo rm ed fo r

nano crys t a l l i ne subs t ances p rod uce d by cons o l ida t ion o f smal l c rys ta l li tes F ig . 8 ).

4 1 S el f Di f fusion

Th e nu m ero us in t e r faces i n nanoc rys t a l l i ne ma ter i a l s p rov ide a h igh dens i ty o f shor t c i r cu i t

d i f fus ion pa ths . Thus , nano crys t a l l i ne ma ter i a l s a re expec t ed to exh ib i t an e nha nced se l f

d i f fus iv ity i n com par i so n to s ing le c rys t a ls o r c onve n t iona l po lycrys t a l s wi th t he sam e

ch emi ca l co mp o s i t io n . Th i s i d ea w as co n f i r med b y s e l f d i ff u si o n me as u r em en t s in n an o -

cr ys ta lli n e c o p p e r. 26~-263)Tab le 5 su m ma r i zes t he me asur ed d i ffus iv i ti es i n nan ocrys t a l l i ne Cu

8 n m crys t a l s ize) i n com par i so n to l a t t ice d i f fus iv ity and to t he d i f fusiv ity i n g ra in b ound ar i es

in Cu b i c rys t a ls . The m easu rem en t s in nano crys t a l l i ne Cu were car r i ed ou t b y us ing the 67Cu

i so tope which was d i f fused f rom the f r ee su r face in to a p l a t e shape d nan ocrys t a l l i ne spec imen

o f C u .

Th e m eas ured d i ffus iv i ti es i n t he nanocrys t a l l i ne Cu are ab ou t 14 to 20 o rder s o f m agn i tude

h i g h e r t h an l a t ti c e d i ff u s io n an d ab o u t 2 t o 4 o r d e r s o f mag n i t u d e l a r g e r th an g r a i n b o u n d a r y

s e l f d i ff u s io n . Th e en h a n cem en t in co mp ar i s o n t o b o u n d a r y d i ff u s io n may r e s u lt f r o m t h e

fo l lowing th ree e f fec t s. In c onve n t iona l g ra in bou ndar i es , r ig id body re l axa t ion~2~) is kn o w n

to reduce the boundary f r ee vo lume. R ig id body re l axa t ion requ i res t r ans l a t i ona l d i sp l ace-

me n t s o f t he l a tt ices o f t he two crys t a ls fo rmin g the bo un da ry re l a ti ve t o one a no the r . C lear ly ,

a t r ans l a t i ona l d i sp l acement i s poss ib l e on ly i f t he d imens ions o f t he c rys t a l s a re l a rge in

com par i son to t he t r ans l a t i ona l d i sp l acem ent wh ich i s i n t he o rder o f a f ew l a t ti ce cons t an t s

o r less . He nce , t he smal l s ize o f t he c rys t a l s in n anoc rys t a l l i ne ma ter i a l s m ay l imi t t he r i g id

body re l axa t ion because the var ious boundar i es su r round ing every c rys t a l r equ i re d i f f e ren t

r ig id bod y re l axa t ions due to t he i r d i f f e ren t a tom ic s t ruc tu re c f. F ig . 6) . Ho wev er , these

d i f fe ren t r e l axa t ions a re no t poss ib l e because the smal l c rys t a l s canno t d i s to r t e l as t i ca l ly

by su f f i c i en t amoun t s t o accoun t fo r t he d i f f e ren t r e l axa t ions o f t he var ious boundar i es

able 5 . S e l f D i f f u s i v i t y m 2 / s ) i n N a n o c r y s t a l l i n e C u , C u G r a i n

B o u n d a r i e s a n d L a t t i c e S e l f D i f f u s i o n i n C u

T e m p e r a t u r e N a n o c r y s ta l l in e G r a i n b o u n d a r y L a t ti c e

K ) c o p p e r 8 n m ) d i f f u s i o n * d i f f u s i o n

393 1 .7 x 10 -17 2 .2 × l0 -19 2 × I0 -31

353 2 x 10 - I s 6 .2 × 10 -21 2 x 10 -34

2 9 3 2 . 6 x 1 0 - 2 ° 4 . 8 x 1 0 - 24 4 x l0 - 4 °

* A s s u m e d b o u n d a r y w i d th a b o u t I n m .



N A N O CRY ST A L L IN E MA T E RIA L S 279

sur rou nd ing the c rys t a l. As a consequence , bound a r i e s con t r ibu t ing to an enhanced d i f fus iv i ty

in nanoc rys ta l l ine ma te r i a l s may d i f fe r s t ruc tu ra l ly f rom bounda r i e s in conven t iona l po ly -

c rys t a l s . The inc rea sed d i f fus ion ra t e may a l so o r ig ina te f rom an enhanced d i f fus iv i ty

a long the t r ip l e junc t ions be tween th ree g ra in bounda r i e s . These t r ip l e junc t ions fo rm a

c o n n e c t iv e n e t w o r k a l o n g w h i c h s h o r t c i r cu i t tr a n s p o r t m a y o c c u r a t h ig h e r r a t es t h a n a l o n g

the g ra in bounda r i e s . Th i rd ly , i n nanoc rys t a l l ine ma te r i a l s , t he impur i ty concen t ra t ion in

g r a in b o u n d a r i e s i s p r o b a b l y l o w e r t h a n i n b o u n d a r i e s o f c o n v e n t i o n a l p o l y cr y s ta l s. I f

a ll impur i t i e s o f a nanoc rys t a l l ine ma te r i a l seg rega te to the bounda r i e s , t he conc en t ra t ion

of imp uri t ies in the bo un da ry cores i s s ti ll less than 10 (cf . Sec t ion 3.1) . Co nv ent io na l

po lyc rys t a l s o f the h ighes t poss ib le pu r i ty con ta in en oug h imp ur i t ie s to seg rega te m ore th an

a m o n o l a y e r o f i m p u r i ti e s i n e v e r y b o u n d a r y . A l t h o u g h t h e a c tu a l c o n c e n t r a ti o n d e p e n d s o n

t e m p e r a t u r e a n d t h e i n te r a c ti o n e n e r g y b e t w e e n th e b o u n d a r y a n d t h e im p u r i t y a t o m s , g r ai n

b o u n d a r y m i g r a t i o n e x p e r i m e n t s s u g g e s t t h a t b o u n d a r i e s i n c o n v e n t i o n a l m a t e r i a l s c o n t a i n

( e ve n a t h ig h t e m p e r a t u r e s ) l a r ge a m o u n t s o f s o lu t e a t o m s w h i c h m a y r e d u c e b o u n d a r y

diffusivity.

I f bou nd a ry d i f fus ion is t he dom inan t m od e o f se lf d i f fus ion in nanoc rys ta l l ine m a te r ia l s ,

t he dep th p ro f i le o f the tr ace r conce n t ra t ion , C x), s h o u l d b e p r o p o r t i o n a l t o e x p -x2 /2Dt )

where x i s t he dep th , measu red f rom the spec imen su r face , D i s t he bounda ry d i f fus iv i ty and

t is t he t ime . T he a bov e re l a t ionsh ip imp l i es tha t t he t r ace r ha s b een d i f fused f rom a f ree

su r face in to the ma te r i a l a t cons tan t t empe ra tu re . Th i s i s t he a r rangemen t u sed in mos t

d i f fusion exp er imen ts . C lose to the f ree surface (x ~< 102nm) a l l expe r imen ta l da ta rep or te d

for na no cry stal l ine m ater ials (261'262) de viat e fro m this relat io nsh ip. Th e rea so n for this

dev ia t ion i s no t ye t unde rs to od . Hen ce , an un am bigu ous eva lua t ion o f the da ta i s d if ficult .

The d i f fus iv i t i e s g iven in Tab le 5 a re ob ta ined by us ing the C x) prof i les a t x /> 102 nm.

Impur i t i e s in the su r face reg ion a s we l l a s g ra in g rowth have been sugges ted to cause the

dev ia t ion . The h igh d i f fus iv it ie s have been conf i rm ed ~273) by N M R me asurem en t s in n ano-

c rys t a ll ine Cu (10 nm c rys t a l si ze ) u t il iz ing the mo t iona l na r row ing o f the N M R l ine s a t h igh

tempe ra tu re s . The n a r rowing re su l ts f rom the ave rag ing o f the tr ace le ss d ipo le in t e rac t ion b y

the m ot i on o f the nuc le i d ur in g d i f fusiona l m ot ion . (2s°'2s2) C om pa rab le low ac t iva t ion

en tha lp ie s a s the ones obse rved in nanoc rys ta l l ine ma te r i a l s have been repor t ed on ly fo r f a s t

ion ic con duc to r s and fo r f a s t d i f fuso rs in me ta l li c a lloys . Thu s , nanoc rys t a l l ine m a te r i a ls m ay

be u t i l ized technologica l ly in a reas where so l ids wi th h igh d i f fusiv i t ies a re needed.

4.2.

Solute Diffusion

In am orp ho us a l loys , t he non-pe r iod ic s t ruc tu re r e su l ts in a spec t rum o f tr app ing s i te s

w h i c h c a n a c c o u n t f o r t h e e x p e r i m e n t a l d a t a o n h y d r o g e n d i f f u s i o n 3 z65-268) S im ilar ef fe ct s

a re no t i ced in nanoc rys ta l l ine m a te r ia l s . In f ac t , s tud ie s o f the hyd rogen so lub i l i ty and

d i f fus ion in nanoc rys ta l l ine Pd have conf i rmed the idea tha t t he s t ruc tu re o f the in t e rface s

o f such m a te r i a ls man i fe s t s i t sel f i n a d i s t r ibu t ion o f s i te s o f d i ffe ren t t r app ing ene rg ie s fo r

hyd rog en. ~269-27t) Figu re 45 sho ws a co m par iso n of the d i f fusion coeff ic ient of hy dro gen in

nanoc rys ta l l ine an d s ing le -c rys ta l line pa ll ad ium. The obse rv ed dependence o f D on the

h y d r o g e n c o n c e n t r a t i o n m a y b e i n t e r p re t e d a s f o l lo w s . A t l o w h y d r o g e n c o n c e n t r a t io n s , t h e

h y d r o g e n a t o m s b e c o m e t r a p p e d i n t h e b o u n d a r i e s a t s it es o f l o w en e r g y. T h e i r d i f fu s iv i ty

i s the re fo re ra the r sma l l. By inc rea s ing the hyd roge n concen t ra t ion , t he t r aps a re g radua l ly

f i l l ed . I f f ina l ly the d i f fus iv i ty o f hydrogen invo lves mig ra t ions be tween ve ry sha l low t raps

on ly beca use a l l deep t r ap s a re f il led, t he va lue o f the d i f fus ion coef f ic i en t i nc rea se s co m pare d

to tha t fou nd fo r the d i f fus ion in a s ing le -c rys ta l . A fu r the r inc rease o f the hydrog en

JPMS 33/4~ E



2 8 0 P R O G R E S S I N M T E R I L S S C I E N C E

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H Y D R O G E N C O N C E N T R A T I O N

Fro. 45. Diffusion coefficientsof hydrogen at 293 K as a

function of hydrogen con centration in single-crystalline

(O ) and nanocrystalline Pd ((3). The curves which are

fitted to the expe rimental data ref er to the cases with

(full line) and w ithout (broken line) hydrogen-hydrogen

interaction.(270)

T E M P E R A T U R E [ o C ]

10_ 9 80 60 40 20 0

l O . m

l--

..~ 10-

10 12 I I J f I

2 . 8 3 1 0 3 2 3 / . 3 1 6

TE M P E RA T URE T -1 [10 -3 K -1 ]

FIG. 46. Arrhenius plot of the hydrogen diffusivity n

nanoerystalline Pd at differe nthydrogenconcentrations.

The upper grap h represents the results at a hydrogen

concentration of 3 × 10-2, th e low er one at 10-3. 263)

c o n c e n t r a t i o n l ea d s t o a n i n c re a s e o f th e h y d r o g e n - h y d r o g e n i n t er a c ti o n , a n d h e n c e t he

d i ff u s io n o f h y d r o g e n b e c o m e s m o r e a n d m o r e i m p e d e d . T h i s b l o c k i n g o f s it es r e d uc e s t h e

d i ff u s iv i ty i f th e h y d r o g e n c o n c e n t r a t i o n e x c e e d s t h e c o n c e n t r a t i o n o f a b o u t 2 .5 × 1 0 - 2 ( F ig .

4 5 ) . T h e e x p e r i m e n t a l d a t a o n n a n o c r y s t a l l i n e m a t e r i a l s c a n b e f i t t e d t o c u r v e s c a l c u l a t e d

u n d e r t h e a s s u m p t i o n o f a g a u s s ia n d i s t r i b u t io n o f s it e e n e r gi e s f o r h y d r o g e n a n d a

q u a s i - c h e m i c a l a p p r o a c h f o r t h e h y d r o g e n - h y d r o g e n i n t e r a c t i o n . (269 27°) T h e d i f f u s i o n c o -

e f fi c ie n t o f h y d r o g e n o b s e r v e d i n n a n o c r y s t a l l i n e P d i s n o t o n l y a f u n c t i o n o f it s c o n c e n t r a t i o n

b u t o f t e m p e r a t u r e , t o o . A p p a r e n t l y , t h e d e p e n d e n c e o f th e d i f fu s i o n c o e ff ic i e nt o n t h e

h y d r o g e n c o n c e n t r a t i o n d o e s n o t c h a n g e i t s c h a r a c t e r w i t h i n th e t e m p e r a t u r e i n t e r v a l 2 7 5 K

t o 3 4 8 K . (272) I n F i g . 4 6 t h e h y d r o g e n d i f f u s i v it y c o e ff i c ie n t s , w h i c h w e r e f o u n d a t c o n c e n -

t r a t i o n s o f 3 x 1 0 - 2 o r 1 0 - 3, r e s p e c t i v e l y , a r e d i s p l a y e d . T h e d a t a m a y b e r e p r e s e n t e d b y

s t r a ig h t l i n es in a n A r r h e n i u s p l o t . T h e a c t i v a t i o n e n t h a l p y o f th e h y d r o g e n d i f f u s i o n a t t h e

l o w e r c o n c e n t r a t i o n ( 1 0 - 3 ) i s 0 .2 5 e V a n d t h u s h i g h e r t h a n t h e o n e a t t h e h i g h e r c o n c e n t r a t i o n

( 3 x 1 0 -2 ) , f o r w h i c h a v a l u e o f 0 . 1 6 e V i s o b t a i n e d . T h e p r e - e x p o n e n t i a l f a c t o r s o f t h e

d i f f u s i o n c o e f fi c i e n t a r e 2 . 5 x 1 0 - 7 m 2 / s a t a h y d r o g e n c o n c e n t r a t i o n o f 3 x 1 0 - 2 a n d 1 0 - 7 m 2 /s

a t 1 0 - 3. T h e f a c t th a t a n A r r h e n i u s b e h a v i o r h a s b e e n o b s e r v e d i n s p i te o f a s p e c t r u m o f

t r a p p i n g - s it e e n e r g i e s m a y b e d u e t o t h e s m a l l t e m p e r a t u r e i n t e r v a l in v e s t ig a t e d ( 73 K ) .

D i f f u s i o n m e a s u r e m e n t s o v e r a m o r e e x t e n d e d t e m p e r a t u r e r e g i m e s h o u l d l e a d t o a p o si t iv e

c u r v a t u r e o f t h e A r r h e n i u s c u r v es . T h e r e f o r e , t h e n u m b e r s g i v e n f o r th e h y d r o g e n d i f f u s io n

r e p r e s e n t e f f e c t i v e v a l u e s , w h i c h a r e l i k e ly t o b e v a l i d i n t h e i n v e s t i g a t i o n r e g i m e o n l y .

F o r s u b s t i t u t io n a l s o l u te a t o m s , n o t r a p p i n g e f fe c ts a r e e x p e c t ed . I n f a c t , t he d i f fu s i o n o f

s il v er i n n a n o c r y s t a l l i n e c o p p e r , w a s m e a s u r e d a t v a r i o u s t e m p e r a t u r e s b e t w e e n 3 0 3 K a n d

373. (279)A s m a y b e s e e n f r o m F i g . 4 7 th e a c t i v a t i o n e n t h a l p y f o r t h e d i ff u s io n is 0 .3 9 e V ( b e l o w

3 4 3 K ) a n d 0 .6 3 e V a b o v e 3 5 3 K i n c o m p a r i s o n t o a b o u t 2 e V f o r l a tt ic e d if f u s io n a n d a b o u t

1 e V f o r g r a in b o u n d a r y d i f f u s i o n o f A g i n C u . A g a i n , t h e e v a l u a t i o n o f t h e C u / A g d a t a

( F i g . 47 ) is n o t u n a m b i g u o u s b e c a u s e c lo s e to t h e f r e e s u r f a c e t h e m e a s u r e d c o n c e n t r a t i o n

p r o f i l e d e v i a t e d f r o m t h e e x p e c t e d

exp -x2/2Dt)

r e l a t i o n s h i p a s w a s t h e c a s e f o r t r a c e r

d i f fu s i o n i n C u . I f a s p e c i m e n c o n t a i n s a l a r g e c o n c e n t r a t i o n o f s o l u te a t o m s ( as w a s t h e c a s e

i n t h e s i l v e r - d if f u s i o n e x p e r i m e n t s ) , d i f f u s i o n a l o n g t h e i n t e r f a c e s m a y c a u s e t h e i n t e r f a c e s t o

m i g r a t e . (274-276) T h i s e f f e c t h a s b e e n t e r m e d d i f f u s i o n - i n d u c e d g r a i n - b o u n d a r y m i g r a t i o n




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2 7

2'8 :~9 30 3'I 32 33 [10-L'K ] T

T'[K]3 >3

3 6 3 , 3 5 3 3 } , 3 3 3 3 3 ~ 3 3 1 3 3 C 3

T E M P E R A T U R E [ K ]

F I G. 4 7 . T e m p e r a t u r e d e p e n d e n c e o f t h e d i ff u s i o n co e f fi c ie n t s o f A g i n n an o c ry s aU i ne C u l 0 n m ) . T h e

ve r t i c a l l i ne s i nd i c a t e t he e r r or bar s o f t he m e as ur e m e nt s . The ac t i va t i on e nt ha l p i e s and t he

pr e - e xpone nt i a l s ar e 0 . 3 9 - t- 0 . 1 e V a n d 1 × 1 0 - n m Z / s , r e spe c ti vel y , f or t e m pe r a t ur e s be l ow 3 4 3 K a n d

0 . 6 3 + 0 . 1 e V a n d 3 x 1 0 - 8

m 2/ s , r e spe c t i ve l y , for t em pe r at ure s abo ve

35 3 K . 279)

( D I G M ) . C o n s i d e r a b le e r ro r s i n b o t h t h e m a g n i t u d e a n d t e m p e r a tu r e d e p e n d e n ce o f t h e

a p p a r e n t d i f f u s i o n c o e f fi c ie n t m a y a r is e i f D I G M i s n e g le c t ed . (274) I n t h e s y s t e m C u - A g , n o

D I G M h a s b e e n re p or te d s o fa r . <276 276)S o l u t e d i f f u s i o n e x p e r i m e n t s h a v e a l s o b e e n p e r f o r m e d

f o r th e d i f f u s i o n o f N i i n n a n o c r y s t a ll i n e C u i n t h e t e m p e r a t u r e r e g im e b e t w e e n 5 0 0 ° C a n d

7 0 0 ° C . (2s3) A l t h o u g h r a p id g r a in g r o w t h o c c u r r e d in t h i s t e m p e r a t u r e r e g im e , t h e d i f f u s iv i ti e s

o b s e r v e d ( v a r y i n g b e t w e e n 3 . 8 x 1 0 - 1 6 c m 2 s - ~ a t 5 0 0 ° C a n d 7 .6 x 1 0 -~ 3 c m 2 s - I a t 7 0 0 ° C) a r e

s ti ll s e v er a l o r d e r s o f m a g n i t u d e l a rg e r t h a n b u l k d i f fu s i o n . D u e t o t h e g r a i n g r o w t h p r o c e s s ,

t h e in t e r p r e t a t io n o f t h e d a t a i s d if fi cu lt . P r e l im in a r y m e a s u r e m e n t s o f s o lu t e d i f f u s iv it i e s in

nan ocr ysta l l ine ceram ics ha ve b een p erfo rm ed for H f d i f fus ion in nan ocr ysta l l in e TiO2 <277.278)

T h e s a m p l e s w e r e p r e p a r e d b y d e p o s i t i n g a t h i n l a ye r o f H f , a b o u t 2 . 5 n m t h ic k , o n t o t h e

f r e e s u r f a c e o f a f l a t n a n o c r y s t a l l in e T iO 2 s p e c im e n . Th e d i f f u s io n p r o f i l e s we r e o b t a in e d b y

u s i n g R u t h e r f o r d b a c k s c a t t e r i n g a n a l y s i s . I n o r d e r t o p r e v e n t f a s t s u r f a c e d i f f u s i o n a n d

m e a s u r e g r a i n b o u n d a r y a n d v o l u m e d i f f u s i o n , t h e s a m p l e s w e r e s i n t e r e d p r i o r t o t h e H f

d e p o s i t i o n u n d e r 1 G P a a t 5 5 0 °C , r e su l t in g i n a d e n s i t y o f 9 8 a n d n o in t e r c o n n e c t e d p o r e s

( c f . F i g . 9 ) . T h e c o r r e s p o n d i n g b a c k s c a t t e r i n g s p e c t r a a r e s h o w n i n F i g . 4 8 . A s e x p e c t e d , n o

d i f f u s io n w a s o b s e r v e d a t t e m p e r a t u r e s b e l o w 5 0 0 ° C . A t 6 5 0 ° C , t h e d i f f u s i o n c o e ff i ci e n t w a s

a b o u t

4 x

1 0 - ~5 c m 2 / s , w h i c h i s a p p r o x i m a t e l y t h e s a m e a s t h a t o f t h e s e l f d i f fu s i o n c o e f f ic i en t

o f T i in s in g l e c r y s t a l l in e r u t i l e . Th e d i f f i c u l t i e s e n c o u n t e r e d in m e a s u r in g t h e d i f f u s io n

8 0 0

555 C

_ - - - 6 , . 5 4 C / ~

6o 0 . .. .. .. . 76 4 c

, ~ 1

~ 2 0 0 ~ I0 I 1 I

LSnm . ~ H t

~

f

850 900 950 IO00

C h o n n e l s

F IO. 4 8 . H f di f f us i on pr o f i l e s i n nanoc r y s t a l l ine T i O 2 m e as ur e d by R ut he r f or d bac ks ca t te r ing f or

di f ferent anneal ing temperatures . T h e T i O 2 w a s s i nt er ed a t 1 G P a a t 5 5 0 ° C p r i o r t o H f d e p o s i t i o n a n d

diffusion.(278)



8


. o [ . f 1 2 ® l s M v e . / 3

o . ~ I I r I R r l

o n o 3 K /: l | I

m~ 34h ~ Bi

- - -

7 5 0 8 0 0 8 5 0 9 0 0

CHANNEL

2 6 o i~ o 6 0 ~ o

DEPTH nm l

F IG . 4 9 . H e b a c k s c a t t e r i n g s p e c t r a f o r a n a n o c r y s t a l l i n e C u s a m p l e 1 0 n m c r y s t a l s iz e) w i t h a 2 0 0 n m

t h i c k B i f i l m d e p o s i t e d o n t o i t s f r e e s u r f a c e a f t e r s p u t t e r c l e a n i n g . T h e s p e c t r a s h o w n i n o n e o f t h e

i n s e r t s i n d i c a t e t h e B i d i s t r i b u t i o n b e f o r e a n n e a l i n g a t 3 7 3 K . T h e b a c k s c a t t e r i n g g e o m e t r y u s e d s

sh ow n in the up pe r inse t . <2s6)

coe f fi c ien t o f nanoc rys ta l l ine ma te r i a l s s eem s imi la r to tho se in g la s sy ma te r ia l s . D ur ing

d i f fusion , the a tomic a r rangem en ts in bounda r i e s m ay change by ana logy to the re l axa t ion

obse rved in g la s sy ma te r i a l s . Sys tema t i c inves t iga t ions o f the d i f fus ion in nanoc rys ta l l ine

ma te r i a l s wh ich have been p re -annea led to d i f fe ren t ex ten t s may he lp to c l a r i fy th i s p rob lem

in a s imi la r way a s was done fo r g la s sy

m a te r ia l s . 284,285)

4.3. n h a n c e d S o l u t e S o l u b i l i t y

The so lub i l ity o f a so lu te , A , in a so lven t B , is con t ro l l ed by the chemica l po ten ti a l/~A o f

A in B . Ob v ious ly , i f t he a tomic s t ruc tu re o f B i s changed , the chemica l po ten t i a l a nd hence

the so lub i l i ty o f A in B ma y be enhanc ed (o r r educed) . In o th e r w ords , the so lu te so lub il i ty

o f nanoc rys ta l l ine ma te r i a l s i s expec ted to be d i f fe ren t f rom the one o f s ing le c rys ta l s o r

g la sse s w i th the s am e chemica l com pos i t ion . F ive example s o f th i s e ffec t have been repor ted

so fa r : t he so lub i l ity o f H in Pd , B i in Cu , Fe in Ag an d Fe in Cu . A ccord ing to F ig . 36 ,

the so lub i l i ty o f H in P d (a t co ncen t ra t ion s o f ~<1 0 - 3 ) i s increased by a fac t or o f 10 to 100

rela tive to a Pd single cry stal, c269)A s imi lar e f fec t was obse rv ed c286) fo r Bi in C u (F ig. 49). T he

solubi l i ty of Bi in c rys ta l l ine Cu is less than 1 0 - 4 a t 100°C. The ver t ica l d isp lac em ent o f the

cu rves (F ig . 49 ) sugges ts a so lub i l i ty o f B i in nanoc rys ta l l ine Cu o f abou t 4 ; i n o the r wo rds ,

a so lubi l i ty en han cem ent by ab ou t 10 ,000 re la t ive to c rys ta l l ine C u. (2s6) St ru c tura l s tudies

o f nanoc rys ta l l ine a l loys (Sec t ion 3 .8 ) ev idenced the fo rma t ion o f Ag /Fe and Cu /Fe so l id

so lu t ions in the nanoc rys ta l l ine s t a t e , whe rea s Ag /Fe a nd Cu /Fe p o lyc rys ta l s exh ib i t v i r tua lly

no sol id so lubi l i ty .

M e a s u r e m e n t s o f t h e h y d r o g e n a c t iv i t y u p t o c o n c e n t r a t io n s o f 0 .7 h a v e b e e n c a rr i ed o u t

recent ly . (27' Th e resul ts o bta ine d a nd the s t ruc tu ra l imp l ica t ions have b een d iscussed in

Section 3.7.4.

4.4. S p e c i f i c H e a t

The cu rves o f the spec if ic hea t a s a func t ion o f tem pe ra tu re me asu red fo r nanoc rys ta l l ine

and polycry s taUine Cu or Pd as wel l as for a m eta l l ic g lass (Pd72Si~sFe l0 ) a re sum mar ized in



N A N O C R Y S T A L L I N E M A T E R IA L S

283

a )

so~

. ~ . ~ - ~ ' ~

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T E M P E R A T U R E T { K )

FIG. 50. a) The specific heat ( C p ) o f p o l y c ry st a l li n e P d i n co m p ar i s o n w i t h n an o e ry s t a ll i n e P d an d a

Pd72SinFe, o meta l l i c g lass. The enha ncem ent

cp

o f t h e n an o m e t e r - s ized cry s t al l in e P d O ) an d t h e

me ta l l i c g lass x ) re la t ive to the po lyerys ta l l ine Pd i s shown in the upper l e f t .hand corner . b ) The

speci fic hea t cp ) o f po lycrys ta l l ine Cu ( O ) in com par i so n wi th nanocrys ta l l ine Cu @). ~7)

Fig. 50.(2s7) Th e en han cem en t o f cp in go ing f ro m the po lycrys t a l li ne to t he nano crys t a l l i ne

s t a t e var i es be tw een 29 and 53 fo r Pd in t he t em pera tu re r ange inves t iga t ed (F ig . 50a).

Th e co r res pon d ing va lues fo r Cu are 9 and 11 (F ig . 50b). Th e cp va lues o f t he po ly -

crys t a l li ne Pd and g l assy s t a te (Pd72SilsFe10) d i f fe r by abo u t 8 and ab ou t 50 o f wh ich

or ig ina t e f rom the d i f f e ren t a tom ic s t ruc tu re . The res idua l po r t i on is due to t he dev ia t ing

ch emi ca l co mp o s i t i o n . C u an d P d a r e d i amag n e t i c an d p a r amag n e t i c me t a l s , r e s p ec t i v e l y .

Hence , e l ec t ron ic and magnet i c con t r ibu t ions t o t he spec i f i c hea t i n t he t empera tu re r ange

betw een 150 and 300 K are negligible. Th e specif ic hea t of nanoc rystal l ine Cu a nd P d i s , thus ,

d u e t o t h e t h e r ma l l y i n d u ced v a r i a ti o n o f t h e v i b r a ti o n a l an d co n f i g u r a ti o n a l en t r o p y o f th e

ma ter i a l s (i. e. d ue to l a t ti ce v ib ra tions , var i a t i on o f equ i l i b r ium defec t conce n t ra t i on , e t c .) .

Th e de v ia t ion o f t he c rys t a l l ine and nano crys t a l l i ne s t a tes i s un like ly t o r esu l t f rom in t e rna l

su r faces because sm al l -ang le X- ra y d i f f r ac t ion (Sec t ion 3 .3.1) , pos i t ron ann ih i l a t i on (Sec t ion

3 .7 .1 ) , and hydrogen so lub i l i t y measuremen t s (Sec t ion 3 .7 .4 ) gave l i t t l e ev idence fo r a

l a rg e a m o u n t o f f r ee i n te r n a l s u r faces , e .g . a t p o r e s. Th e d i ff e r en t en h an c em en t s o f cp o f P d

and Cu in t he na nocrys t aUine s ta t e seem to be cons i s t en t wi th t he d i f f e ren t dens i ti es o f



84


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TEMPERATURE [KI

F IG . 5 1 . E x c e s s s p e c if i c h e a t , A ( s p e c if i c h e a t o f n a n o c r y s t a l l i n e P d m i n u s t h e s p e c if i c h e a t o f s i n g l e

c r y s t a l li n e P d ) o f n a n o c r y s t a l l i n e P d ( 6 n m c r y s t a l s i z a ). ( ~° )

b o t h s u b s t a n c e s . I n f a c t , t h e l o w e r r e l a t i v e d e n s i t y o f n a n o c r y s t a l l i n e P d i n c o m p a r i s o n

t o n a n o c r y s t a l l i n e C u ( p r o d u c e d u n d e r s i m i l a r c o n d i t i o n s ) s u g g e s t s a m o r e o p e n a t o m i c

s t r u c t u r e o f t h e g r a i n b o u n d a r y c o m p o n e n t i n t h e c a s e o f P d , a n d h e n c e w e a k e r i n t e r a t o m i c

c o u p l i n g , w h i c h s h o u l d e n h a n c e Cp T h i s a r g u m e n t i m p l i e s t h a t t h e e n h a n c e m e n t o f cp i s

p r i m a r i ly d u e t o t h e g ra i n b o u n d a r y c o m p o n e n t . I f th i s i s s o , g ra i n g r o w t h s h o u l d r e d u c e t h e

s p e c if i c h e a t o f t h e n a n o c r y s t a Uin e m a t e r ia l s t o t h a t o f p o ly c r y s t a l s . T h i s wa s , in f a c t ,

o b s e r v e d w h e n t h e n a n o c r y s t a l li n e C u a n d P d s a m p l e s w e r e a n n e a l ed a t 7 5 0 K t o i n it ia t e g r ai n

g r o w t h . T h e g r a i n s iz e o f t h e s a m p l e s a f te r a n n e a l i n g w a s 2 0 n m . I n t h e c a s e o f P d , it w a s

a l s o n o t i c e d t h a t d u r i n g th e h e a t - u p c y c le a n c x o t h e r m i c r e a c t io n t o o k p l a c e at a b o u t 3 5 0 K .

S u b s e q u e n t c o o l i n g t o 2 0 0 K r e v e al e d t h a t t h e e n h a n c e m e n t o f t h e sp e c if ic h e a t w a s r e d u c e d

t o a b o u t 5 . T h e s p e c if ic h e a t m e a s u r e m e n t s o n n a n o c r y s t a ll i n e P d h a v e b e e n r e c en t ly

e x p a n d e d i n t o t h e l o w t e m p e r a t u r e r eg i m e i n d i c a t in g a n e n h a n c e m e n t w h i c h d e p e n d s l in e a r ly

o n t h e t e m p e r a t u r e ( F ig . 5 1 ) .

M e a s u r e m e n t s o f t h e sp e c if ic h e a t o f n a n o c r y s t a l li n e m e t a l s ( R u a n d A I R u ) g e n e r a t e d b y

h ig h - e n e r g y b a l l m i l l in g ( c f. S e c t i o n 2 .3 .1 ) in d i c a t e d s im i la r c h a n g e s a s r e p o r t e d a b o v e . (28s)

F ig u r e 5 2 d i s p la y s t h e s p e c if i c h e a t o f R u b e f o r e a n d a f t e r 3 2 h r b a l l m i l lin g v e r s u s

t e m p e r a t u r e . Af t e r 3 2 h r m i l l in g t h e s p e c i fi c h e a t in c r e a s e d b y 1 5 t o 2 0 . Th e s p e c i fi c h e a t

i n c re a s e , A cp , o f R u a n d A I R u a t a c o n s t a n t t e m p e r a t u r e o f 2 1 0 K i s s h o w n i n F i g . 5 3 a s

3 0

o

E

: . 2 5

I Z

o

:z: 20

1 5

1 2 0

I I I I I I I

. ,o... ,o,.. .o,.. -b E

~ o . . , , o , . . ~ } ' °

. ,, o , p

f . 7

~

I I I I I I I

1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0

Tem perature [K ]

F l o . 5 2 . S p e c i f ic h e a t , C p , f o r R u b e f o r e a n d a f t e r 3 2 h r

m i l l i n g a s a f u n c t i o n o f te m p e r a t u r e . T h e s o l i d l i n e

s h o w s d a t a o f a s i n g l e c r y s t a l o f R u . (2 ss)

3G

W

<

5

uJ

r e

z 2o

u. 1c

u I

a .

m

o F l u

• A I R u

o

I

, / o

i

p , /

0.1 0.2

I/d Into I ]

R EZ IPR O C AL C R YST AL S IZ E

Fio. 53. Increase of the specific heat for R u and AIR u

a s a f u n c t i o n o f r e c i p r o c a l c r y s t a l s i z e . m S )




a function of reciprocal crystal size. Acp increased almost linearly with

l i d .

Annealing the Ru

and A1Ru samples with the smallest crystal size, i.e. the largest increase in Acp, for 3 days

at 1,370 K resulted in a partial reduction of

Acp

from 20 to 7 for Ru and from 15 to

5 for A1Ru. Apparently, a significant por tion o f the observed Acp is in fact associated with

the particle-size reduction and lattice disorder produced by the ball milling. The residual

enhancement of the specific heat after long annealing times may be due to Fe impurities

introduced during ball milling. Ru-Fe solid solutions probably have a lower Debye

temperature than pure Ru.

4.4.1.

Low t em pera t ure m easurem en t s o f t he spec i f i c hea t

The specific heat, C, at very low temperatures of nanocrystalline Cu is displayed in

Fig. 54 in a double-logarithmic plot of C vs temperature T for two samples with different

average crystallite sizes. In normal metals (non-magnetic, non-superconducting), the specific

heat at low temperatures is known to be given by

C = ~ T + f i T 3,

yielding for bulk Cu

the solid line shown in Fig. 54. For nanocrystalline samples, C is enhanced by a factor of

5 to 10 relative to bulk Cu, with the larger enhancement occurring in samples with smaller

grain sizes. An enhancement of C at temperatures above 1 K has been reported in the

literature, e.g. for small vanadium crystals, and was attributed to Einstein oscillators due

to weakly bound atoms at the surfaces o f the particles. (3~4) The enhancement seen below

1 K in nanocrystalline Cu (Fig. 54) may be further analyzed by measuring the magnetic-

field dependence of C. This has been done for the sample with a crystal size of 6 nm.

The strong increase of C in a magnetic field B = 6 T with decreasing temperature below

about 0.4 K is due to the Zeeman splitting of 6 Cuand 65Cu nuclei, leading to a contri-

bution C~ =

bN T - 2 .

As may be seen from Fig. 54, C strongly decreases in a magnetic field

of 6 T below 1 K and increases above 1 K. The solid curved line in Fig. 54 is a fit of the

experimental data by the following function:

C = y T fi T 3 Jr bN

T -2

Jr Cs,

where y,/~, b~ and

C s are constants with the following values: 7 = 1.55.10-5 J/gK2, fl = 2.5-10-6 J/gK4 and

bN = 1.3.10

- 6

JK/g for the nanocrystalline Cu. For comparison, for bulk Cu one obtains

~; = 1.09.10 -5 J/gK2, fl = 7.6.10 -7 J/gK4, and bN = 1.8.10 -6 JK/g.

C s

represents a two-level

non-degenerate Schottky anomaly with an energy splitting E =

g/~eB

with B ~ 6 T. This

i i i i I i t i E i i i ~ I i i i

Cu

•

d : 8 n m

B = O T ~

o d : 6 0 n m B = O T , . /

~ . d = 6 0 n m B : 6 T / o °

~ g,o

1 0

~ l t l ] ~ i i i i i i i ~ I I

0 1 1

T E M P E R A T U R E T [K ]

F IG . 54 . LO W t e m p e r a t u r e s p e c if i c h e a t o f n a n o c r y s t a l l i n e C u f o r t w o d i f f e r e n t g r a i n s i z e s 6 n m a n d

8 .5 n m ) . T h e m e a s u r e m e n t s f o r t h e 6 n m C u w e r e c a r r i e d o u t w i t h o u t a m a g n e t i c fi e ld a n d a t 6 T . F o r

c o m p a r i s o n , t h e s o l i d l in e s h o w s t h e s p e c i f i c h e a t o f b u l k C u . 2s9)



86


s u g g e s t s t h a t m a g n e t i c e x c i t a t i o n s m i g h t a c c o u n t f o r t h e a n o m a l o u s l y l a r g e s p e c i f i c h e a t

be l ow 1 K i n B = 0 .

T h e e x c i t a t io n s a r e s u p p r e s s e d i n a l a r g e m a g n e t i c fi el d. A t p r e s e n t , t h e o r i g i n o f th e s e

e x c i ta t io n s i s u n k n o w n . F r o m t h e m a g n i t u d e o f

Cs,

w e i n f e r t h a t 2 . 1 0

1 9 g l

exc i t a t i ons

p a r ti c ip a t e , t h a t is r o u g h l y 0 .2 o f th e to t a l n u m b e r o f a t o m s . M a g n e t i c i m p u r it ie s a t

t h i s le v el w e r e n o t p r e s e n t i n t h e s a m p l e s ( f o r d = 6 n m ; F e : 5 0 p p m , C o : 2 0 p p m , N i :

71 p p m , M n a n d C r : < 10 p p m ) . I s o l a t e d s m a l l p a r t ic l e s w i t h a n o d d n u m b e r o f e l e c tr o n s

sho u l d c a r r y a m agn e t i c m om en t o f 1/~B-(385) W i t h d = 6 nm , t he nu m be r o f c r ys t a l l it e s i s t oo

s m a l l b y m o r e t h a n o n e o r d e r o f m a g n i t u d e i n o r d e r t o a c c o u n t f o r t he o b s e rv e d

Cs,

a p a r t

f r o m t h e f a c t t h a t t h e p r e s e n t n a n o c r y s t a ll i te s a re n o t i s o l at e d . M a g n e t i z a t io n m e a s u r e m e n t s

a t l o w t e m p e r a t u r e s a r e u n d e r w a y t o d i r e c t ly ch e c k f o r m a g n e t i c m o m e n t s i n n a n o c r y s t a ll i n e

C u w h i c h m i g h t p e r h a p s o r i g in a t e f r o m e x t re m e l y w e a k l y b o n d e d C u a t o m s a t g r a in

b o u n d a r i e s . I t m a y b e o f i n te r e st t o n o t e t h a t a s im i l ar a n o m a l o u s b e h a v i o r i n th e

l o w - t e m p e r a t u r e s p e c if ic h e a t w a s f o u n d i n i s o l a te d A g a n d A u c o l l o i d a l p a r t ic l e s o f a b o u t

the sam e s izeY sr)

4.5.

Entropy

Th e m eas u r e d exces s speci fi c hea t ~2s7) o f t h e a s - c om pac t ed nan oc r y s t a l l i ne P d ( 6 nm g r a i n

s iz e ) ( F i g . 5 1) m a y b e u s e d t o c o m p u t e t h e e x ce s s e n t r o p y ( A S ) d u e t o t h e g r a i n b o u n d a r i e s :

= f r A C , d T

a s J r

w h e r e A c , is t h e d i f f e r en c e b e t w e e n t h e s p e c if ic h e a t o f n a n o c r y s t a l l i n e a n d p o l y c r y s t a l li n e P d

a n d T i s t h e a b s o l u t e t e m p e r a t u r e .

I f t he A c vs T cu r ve ( F i g . 51 ) i s ap p r o x i m a t e d b y a s t r a i gh t l i ne w i t h t he s l ope A =

0.77 × 10-25 J /a t K 2 , one ob ta in s A S = A T 0 . A t To = 300 K (Fig . 51): S = 2 .3 × 10-23 J /a t

K . <29°) I f th e v o l u m e f r a c t i o n o f g r a i n b o u n d a r i e s i s a s s u m e d t o b e 5 0 a n d i f t h e a t o m s i n

t h e c e n t e r s o f t h e c r y s t a ll i te s ar e a s s u m e d t o c o n t r i b u t e l i tt le t o t h e e x c e ss e n t r o p y , o n e o b t a i n s

f o r A S = 4 . 6 x 1 0 -23 J / a t K w h i c h i s a b o u t 4 k , w h e r e k i s B o l t z r n a n n ' s c o n s t a n t . F o r m o s t

m e t a l s th e e n t r o p i e s o f f u s i o n a n d e v a p o r a t i o n a r e a b o u t I k a n d 1 0 k , r es p e c ti v e ly ( R i c h a r d s '

a n d T r o u t o n ' s r ul e) . I n o t h e r w o r d s , t h e e x ce ss e n t r o p y o f th e n a n o c r y s t a l li n e P d a t a m b i e n t

t e m p e r a t u r e is la r g er t h a n t h e e n t r o p y o f f u s io n a n d c o m p a r a b l e t o t h e e n t r o p y i n cr e as e

d u r i n g e v a p o r a t i o n . A t t e m p t s t o m e a s u r e t h e a b s o l u t e e n t r o p y o f n a n o c r y s ta l li n e m e t a l s b y

m e a n s o f a n e l e c t ro c h e m i c a l m e t h o d a r e i n p r og r es s .

A t h e o r e t i c a l i n t e r p r e t a t i o n o f t h e l a rg e e n t h a l p i e s a n d e n t r o p i e s o f n a n o c r y s t a l l i n e

m a t e r i a l s h a s been p r o po sed r ecen t l y 291) on t he ba s i s o f t he f o l l ow i ng t w o a s sum pt i ons .

( i ) T h e e n e r g y o f g r a in b o u n d a r i e s s c al es w i t h t h e i r e x ce s s v o l u m e , V .~292) (ii) A un iv er sa l

eq ua t i on o f s t a t e o f a m e t a l m ay be ob t a i ne d by app r op r i a t e s ca l ing . <293) N eg l ec t i ng

t e m p e r a t u r e e f fe c ts , t h e b i n d i n g e n e r g y E p e r a t o m m a y b e r e p r e s e n t e d a s a f u n c t i o n o f a

sca l ing parameter a only3293)

E = A .E a )

(1)

w i t h A b e i n g t h e c o h e s i v e e n e r g y a n d

E a )

t h e b i n d i n g e n e r g y . T h e p r o p o s e d s c a li n g la w i s

g i v e n b y

E a ) = e x p ( - a ) . ( - 1 - a - O .0 5a 3 ) (2 )

w i t h

a = (rl -- r2)/l (3)




where r] and r2 are the radii of the Wigner-Seitz cells at the equilibrium and expanded state, i is

a length scale characteristic for a particular material leading to an equation of state of the

following form:

P V ) = -

•

da ( 4 )

This equation provides a simple relationship between the energy and the free volume.

In fact, it has been shown by comparison with first-principle calculations that the relation-

ship between binding energy and free volume can be quantitatively described in terms of a

simple two-parameter scaling law of a universal funct ion and knowledge of only three input

parameters is required. These input parameters are the equilibrium specific volume per atom,

Vo, the equilibrium bulk modulus, Bo, and a length scale,/, as determined for most metallic

elements and semiconductors according to Ref. 293. The derived universal equation of state

agrees with measured compression data during shock wave consolidation. In order to

compute the properties of nanocrystalline materials, this concept was extended to large

expansions by the application o f a negative hydrosta tic pressure. This model was then utilized

to describe the thermodynamic properties o f atoms located in grain boundaries as function

of the excess volume of these boundaries. Figure 55 shows the computed excess volume as

derived from the above equation of state for Cr if a negative pressure is applied. The excess

volume vs pressure dependence scales with the slope of the energy curve [eq. (1)] and reaches

a minimum of about - 25.8 GPa negative pressure at a critical excess volume of 0.44. At the

critical excess volume, Vc, the grain boundary becomes mechanically unstable. The excess

enthalpy per atom, H, is found to reach values as high as 5 x 1 0 - 1 9 J/at at the critical volume.

This excess entha lpy corresponds to 70 of the enthalpy of sublimation and is characteristic

for the high degree of disorder present in the boundaries . In fact, measurements of the energy

stored in the boundaries of nanocrystalline materialsm4) have indicated energies up to

30 of the heat of fusion. The boundary excess entropy (S) was estimated by using the

relationship for an isothermal volume expansion AS =y

C/In(V/Vo)

where ? is the

Griineisen parameter, V and V0 are the volumes of the solid before and after isothermal

o - 1 0

-2 0 ~

1.

,,

- 3 0

,

I A

1 ,

0.2 0.4 0.6

EXCESS VOLUNE ~V

F I G . 5 5. E q u a t i o n o f s t at e o f a g r a i n b o u n d a r y i n C r .

P r e s s u r e a s a f u n c t i o n o f e x c e s s v o l u m e . ~9~)

4

X ) - -

W

c - 4 i

I

x - 6 l , o ' . 2 . ' o ' . ~ ' ' 0 , 6

EXCESS FREE VOLUME AV

F IG . 5 6. T h e e x c e s s G i b b s f r ee e n e r g y A G a t d i f f e r e n t

t e m p e r a t u r e s r a n g i n g f ro m 0 K t o 1 , 50 0 K p e r C r a t o m

l o c a t ed i n a g r a i n b o u n d a r y ) a s a f u n c t i o n o f t h e e x c e ss

f re e v o l u m e , A V . T h i s c u r v e s u g g e s t s t h a t t h e g r a i n

b o u n d a r i e s c a n b e e n t r o p y - s t a b i l i z e d a t e l e v a t e d t e m -

p e r a t u r e s f o r e x c e s s v o l u m e s c l o s e t o a c r i ti c a l e x c e s s

v o l u m e i n d i c a t e d b y a b r o k e n v e r t ic a l l i n e . a gl )



88

P R O G R E S S IN M A T E R IA L S S C IE N C E

expans ion , and Cv i s the spec if ic hea t a t con s tan t vo lum e . ~, was co m pute d f rom the equa t ion

o f s tate [eq. 4)] by usin g the Slate r ap pr ox im atio n, t295)

F r o m A H a n d A S , t h e e x c e s s G i b b s F r e e E n e r g y , A G p e r C r a t o m l o c a t e d i n t h e g r a i n

bou nda r i e s was com pute d fo r d i ffe ren t t emp e ra tu re s rang ing f rom 0 to 1 ,500 K F ig . 56 ). I t

was found tha t g ra in bounda r i e s a t e l eva ted t empera tu re s w i th exces s vo lume c lose to AVe

b e c o m e m o r e s t a b le t h a n b o u n d a r i e s w i t h s m a l l er e x c es s v o l u m e s . T h e l o c al m i n i m u m o f t h e

en t ropy was p red ic ted to s t ab i l i z e the g ra in bounda r i e s and hence the nanoc rys ta l l ine

s t ruc tu re . The b ou nd a ry en e rgy min imu m i s s epa ra ted f rom the s ing le c rys ta l s t a t e A V = 0 )

b y a n e n e r g y b a r r i er o f a b o u t 2 x l0 19 J / a t 1 eV) . Th i s ba r r i e r p reven t s g ra in g row th fo r

those g ra ins su r rou nde d by bou nda r i e s hav ing l a rge exces s vo lum es , whe rea s ma te r i a l s w i th

g r a in b o u n d a r i e s h a v i n g l o w e x c es s v o l u m e s w o u l d c o a r s e n . T h e t h e r m o d y n a m i c p r o p e r t i e s

m ay be used to exp la in the exp e r imen ta l ly obse rved s t ab i l i ty o f c e r ta in reg ions in nano-

c rys ta ll ine me ta l s up to t em pera tu re s c lose to the me l t ing po in t c f. Sec t ion 3 .5 ).

4.6. Therm al Expansion

M easure m en ts o f the the rma l exp ans ion o f nanoc rys ta l l ine coppe r 8 nm c rys ta l s iz e)

h a v e b e e n c a r r ie d o u t b e t w e e n l l 0 K a n d 2 9 3 K , y i el d in g 31 x 1 0 - 6 K - t i n c o m p a r i s o n

to 16 x 10 - 6K fo r co ppe r s ing le crys ta ls329s ) A s imi la r en hancem en t was obse rved fo r

nanoc rys ta l l ine Pd i f t he c rys ta l s iz e was ab ou t 10 nm. Recen t ly , the se re su l t s have be en

ques t ioned on the ba s i s o f d i l a tome t r i c da ta . Ob v ious ly , fu r the r m easu rem en t s a re requ i red

to c l a r i fy the con t rove rs i a l s i tua t ion . As the c rys ta ll ine com po nen t o f a nanoc rys ta l l ine

ma te r i a l s eem s to con t r ibu te in s ign i f ic an tly to the enhancem en t o f the the rma l exp ans ion

c o e ff ic ie n t, t h e av e r a g e t h e rm a l e x p a n s i o n o f th e b o u n d a r y c o m p o n e n t w o u l d b e a b o u t f o u r

t imes la rge r than the l a t ti c e expans ion i f nanoc rys ta l l ine m a te r i a ls a re a s sum ed to exh ib i t an

enhance d expan s ion . In fac t , t h is enhan cem en t w ou ld ag ree wi th d i rec t mea su rem en t s o f the

the rma l expan s ion o f g ra in bou nda r i e s in Cu and A u by d i l a tom e t ry t296) and X-ra y

diff rac t ion . <297) Th e therm al exp ans io n of gra in bo un dar ies in a Cu poly crys ta l 17/~m gra in

s ize) w as fou nd to be ab ou t fo ur t imes the la t t ice expansion3296) Th e exp ans io n o f a 22 .5 ° 001)

t w i st b o u n d a r y l o w e n e r g y b o u n d a r y ) i n A u n o r m a l t o t h e b o u n d a r y p l a n e) w a s X - r a y

diff rac t ion) enh ance d by a f ac to r of three . <297) In fac t , the X -ray d i f f rac t ion da ta indica te a

m e a n s q u a r e d i s p la c e m e n t o f t h e a to m s i n th e g r ai n b o u n d a r i e s u 2) a t 298 K o f abo u t

0 .012 A 2 wh ich i s a lmos t tw ice the b u lk va lue 0 .007 A2) . The d i f fe rence be twe en bo th u 2 )

va lues l e ads to the conc lus ion , tha t the cu rva tu re o f the e f fec tive in te ra tomic po ten t i a l i s le ss

fo r a toms in the bounda r i e s than in the bu lk . In pa s s ing i t s eems wor th no t ing the fo l lowing

two a spec t s o f th is r e su lt . By va ry ing the c rys ta l si ze vo lum e f rac t ion o f the g ra in b ound a r i e s )

and the chemica l comp os i t ion , the the rma l ex pans ion o f nanoc rys ta l l ine ma te r i a ls c an be

tuned to any p re -de te rm ined va lue be tween the expans ion o f the c rysta l la t t ic e and the

b o u n d a r y e x p a n s i o n .

4.7. Op tical and Infra R ed Absorption

O p t i c a l a n d i n f r a - r e d a b s o r p t i o n m e a s u r e m e n t s h a v e b e e n p e r f o r m e d f o r n a n o c r y s t a l l i n e

Si fi lms33°°) Figu re 57 shows a typica l dep end ence o f the ab sor pt io n coeff ic ient on

pho ton ene rgy fo r s ample s depos i t ed a t d i f fe ren t t empe ra tu re s . Each cu rve was ob ta ined

by com bin ing re su l t s f rom seve ra l s ample s o f va r ious th icknes s be tween a few hund red

n a n o m e t e r s a n d 1 2 /a m , d e p o s i t e d u n d e r t h e s a m e c o n d it i o n s. A p r o n o u n c e d r e d s hi ft o f th e

abso rp t ion was no t i ced wi th inc rea sing depos i t ion t em pera tu re up to abo u t 350°C . I f the




• ~ . / / A

I s Z

10 1 2 3

E N E R G Y h v e V )

FiG. 57. Optical absorpt ion of polycrystalline Si films deposited at various temperatures and hydrogen

contents. A: 110°C, ~ 12 ; B: 260°C, ~4 ; C: 350°C, ~ 1 D: 400°C. The hydrogen content was

estimated from the IR data for each curve except at 400°C. Broken curves show the absorption after

annealing in UHV at 650-800°C. The curve labeled c-Si shows the data for a Si single crystal. ~)

depos i t ion t empera tu re was inc rea sed to 400°C a b lue sh i f t i s obse rved . Such a phenomenon

h a s b e e n f o u n d i n h y d r o g e n a t e d a m o r p h o u s S i a s w el l a n d w a s d i s c us s ed in s o m e d e t a il b y

Free m an and Pau l . °°~) F igu re 57 ind ica tes tha t a ll cu rves ex t rapo la te appro x im a te ly to

hv ~ 0.5 eV for ~t - -, 0 . This sugges ts tha t the ab sor pt io n a t low energies i s assoc ia te d w i th

som e ra the r we l l de f ined s t a t e s in the gap wh ich m igh t be , fo r examp le , due to pa i red )

dang l ing bon ds a t the recons t ruc ted ) in t e r face s be tween the c rys ta l li te s . W i th inc reas ing

depos i t ion t empera tu re the re l a t ive amoun t o f the c rys ta l l ine componen t inc rea se s a s we l l a s

the c rys ta l l it e si ze . Th i s migh t exp la in why the o p t i ca l abso r p t ion wi th inc rea sing dep os i t ion

t e m p e r a t u r e p a s s e s t h r o u g h a m a x i m u m , a s t h e to t a l n u m b e r o f w e a k b o n d s o r o t h e r st a te s

a s soc ia t ed wi th the in te r face s ) i s l i ke ly to d i sp lay a max imum. The re su l t s o f the in f ra - red

abso rp t io n mea su rem en t s sugges t the fo l lowing s t ruc tu ra l conc lusions . i ) The wid th o f the

i n d iv i d u a l c o m p o n e n t s o f t h e S i - H s tr e tc h i ng m o d e s o b s e r v e d i n di c at e s t h a t t h e y a re

a s soc ia t ed wi th we l l de f ined s i t e s wh ich a re un l ike ly to be found in an amorphous ne twork

or on in te rna l surface s o f voids . i i ) Th e H co nte nt decreases wi th increas ing c rys ta ll i te s ize

a s does the num ber o f S i a tom s in the in te rc rys tal l ine b oun da r i e s re l at ive to those in the bu lk .

i ii ) T h e p o s i t i o n o f t h e a b s o r p t i o n p e a k s a r o u n d 2 ,1 0 0 c m - J a g r ee s w el l w i t h t h a t o f a b r o a d

ban d due to the hydr ogen adso rbed a t the su r face o f sing le c rys ta l l ine S i . °°2 ) The s t ruc tu re

o f nanoc rys ta l line S i f ilms p repa red by chemica l t r anspo r t in a low p re s su re hydro gen p la sm a

has a l so b een s tud ied b y t ime- re so lved ph o to m od u la t ion s tud ie s . ° °3 ) The t rans ien t pho to -

m o d u l a t i o n s p e c t r a w e r e m e a s u r e d i n t h e t i m e d o m a i n f r o m 10 7 to 10 2 S, spectral range

f rom 0 .25 to 1 .25 eV, and t em pera tu re range f rom 80 to 300 K . T he p rop e r t i e s o f the spec t ra

a r e c o m p a t i b l e w i th t h e p r e s e n ce o f t w o p h a s e s , t e r m e d a m o r p h o u s a n d c r ys ta ll in e . T h e

amorphous phase exh ib i t s many s imi la r i t i e s to amorphous S i . In fac t , bo th ma te r i a l s have

s i m i l a r p h o t o m o d u l a t i o n b a n d s t h a t e x h i b i t t h r e e c o m p o n e n t s : b a n d t a i l , d a n g l i n g b o n d s

a s s o c ia t e d w i t h a b s o r p t i o n ) , a n d b l ea c h in g . T h e t e m p e r a t u r e d e p e n d e n c i e s o f t h e p h o t o -

m o d u l a t i o n b a n d s t re n g t h s i n b o t h m a t e ri a ls o b e y a n e x p o n e n t ia l l a w . A t l o w t e m p e r a t u r e s

the pho to m od u la t ion a t the ban d t a i l s p reva il s , wh i l e a t h igh t em pera tu re s the dang l ing bon ds

domina te . The dependence on the pump in tens i ty i s s imi la r in bo th ma te r i a l s • A lso , the

co r re la t ion ene rg ie s o f the dang l ing b on d de fec t s a re abo u t the s ame ,~0 .4 -0 .5 eV). The re




a re , how eve r , a l so obv ious d i f fe rences be twee n the am orp ho us phase in nanoc rys ta l l ine

S i a n d a m o r p h o u s S i . T h e p h o t o m o d u l a t i o n p e a k i n t h e s t e a d y - s t a t e s p e c t r a i s a t t h e s a m e

ene rgy a s in am orp ho us S i on ly f rom the sma l l e s t g rain s ize. Sam ple s w i th l a rger g ra in s i ze s

dev ia t e f rom th i s va lue ind ica t ing s t ruc tu ra l dev ia t ions be tween bo th ma te r i a l s . In nano-

c rys t a l line S i t he b on d t a i l - con t r ibu t ion i s obse rv ab le up to 150 K , w h i le in am orp ho us S i i t

i s obse rv ab le up to 240 K . The de m arca t ion ene rgy measu red in coa rse r-g ra ined sample s

inc rea se s a t abou t the same ra t e w i th t ime in nanoc rys ta l l ine S i a s in amorphous S i , bu t i s

deepe r in the nanoc rys ta l l ine ma te r i a l . These obse rva t ions a re compa t ib l e w i th a b roade r

expon en t i a l d i s t r ibu t ion o f s t a t e s in the t a i l (59 meV in nanoc rys ta l l ine S i and 46 meV in

amorphous S i ) , i nd ica t ing tha t t he amorphous phase in the nanoc rys ta l l ine S i i s more

d i so rde red than in am orp ho us S i. The re i s, fu r the rmo re , a d i f fe rence in the ene rg ie s o f the

d a n g l in g b o n d s . F o r t h e tr a n s ie n t p h o t o m o d u l a t i o n i n a m o r p h o u s S i t h e o n s e t o f a b s o r p t i o n

assoc ia t ed w i th dang l ing bon ds i s a t 0 .65 eV an d the on se t o f b l each ing a t 1 .1 eV; the

co r re spo nd ing num bers fo r nanoc rys t a l l ine S i a re a roun d 0 .5 and 0 .9 eV and 0 .6 and 1 .0 eV .

I f we a ssume tha t t he gap Eg i s the sum o f the se ene rg ie s , t hen Eg has b e tween 1 .4 eV and

1 .6 eV com pare d to 1 .75 eV in amo rph ou s S i. The sma l l e r gap ma y a l so be re l a t ed to the la rge r

d i so rde r . I t i s no t poss ib le to d i rec t ly measu re

g

o f th e a m o r p h o u s p h a s e i n n a n o c r y st a ll in e

S i to conf i rm th i s conc lus ion .

4.8. Magnetic Properties

M e a s u r e m e n t s o f t h e s a t u r a t i o n m a g n e t i z a t io n ( M s ) o f n a n o c r y st a ll in e i r o n ( 6 n m c r y s ta l

s ize) r evea led a r educ t ion o f Ms by abo u t 40 % re l a tive to the sa tu ra t ion mag ne t i za t ion o f

bu lk a t- iron33°4) F or com pari son , in m eta l l ic i ron g lasses (ext ra pola ted t o pu re i ron) , M , is

o n l y r e d u c e d b y a b o u t 2 % r e la t iv e t o ~ - F e . ( ~ )

A r e d u c t i o n o f t h e C u r i e t e m p e r a t u r e ( T o) o f N i b y a b o u t 4 0 ° C h a s b e e n re p o r t e d i f t h e

crysta l s ize was red uced to a bo ut 70 nm33°5'3°6) This redu c t ion wa s a t t r ib uted to a redu c t ion

of Tc o f the g rain b ou nd a ry reg ions . The in t e r io r o f the c rys t a l s was a ssum ed to have the same

Tc a s a s in g ly c r y s ta l o f N i . T h e m a g n e t i c b e h a v i o r o f s u c h a s y s t e m w a s m o d e l e d b y a L a n d a u

app rox im a t ion sugges t ing a con t in uou s red uc t ion o f Tc w i th dec rea s ing g ra in s i ze .

T h e m a g n e t i c m i c r o s t r u c t u r e o f n a n o c r y s ta l li n e F e w a s f o u n d t o d if fe r f r o m t h e o n e o f

c rys t a ll ine and am orp ho us i ron and i ron a lloys33°7~ I t i s we ll kno wn tha t t he m agne t i c

mic ro s t ruc tu re o f c rys t a l li ne and am orp ho us i ron a s we l l a s iron a l loys cons is t o f f e r romag-

n e ti c d o m a i n s s e p a r a t e d b y d o m a i n w a ll s. I n n a n o c r y s ta l li n e i r o n n o d o m a i n s t r u c tu r e w a s

revea led by app ly ing the B i t t e r t e chn ique , Ke r r mic roscopy and /o r Loren tz e l ec t ron

microscopy33°7) The obse rva t ion s re por t ed sugges t t he fo l low ing magne t i c mic ros t ruc tu re .

Eve ry c rys t a ll i te o f a nanoc rys t a l l ine Fe spec imen i s a s ing le f e r romag ne t i c dom a in . The

mag ne t i za t ion o f ne ighbor ing c rys t a ll i te s i s con t ro l l ed by two fac to r s : t he c rys ta l an i so t rop y

(which t r i es to a l ign the m agne t i za t ion o f eve ry crys t a ll i te in one o f the ea sy d i rec tions) an d

the mag ne t i c in t e rac t ion be twee n ne ighbor ing c rys t a ll i te s (wh ich t r ie s to a l ign the m agne t i za -

t ion o f ad jacen t c rys t a l s i n to a com m on d i rec tion ) . A s the c rys ta l li t e s a re c rys t a l log raph ica l ly

o r i en ted a t r and om , a mag ne t i c mic ros t ruc tu re r e su l ts in wh ich the magne t i za t ion o f the

c rys t a ll i te s i s co r re l a t ed ove r d i s t ances com para b le to a f ew c rys t a l d i ame te r s on ly . Lo ng

range co r re l a t ions re su lt ing in doma in fo rm a t ion a re p reven ted by the rando m c rys t a l

o r i en ta t ion and the c rys t a l an i so t ropy .

Recen t ly , a s tudy(3°s) o f magne t ic ph ase t ra nsi t ion s in nanoc rysta l l ine Er has been carr ied

ou t . F o r nanoc rys t a l l ine Er (10 -70 nm g ra in s ize) , t he th ree no rma l ly o bse rved magn e t i c

t r an s i ti o n s o f e r b i u m v a n i sh a n d a ' n e w l o w - t e m p e r a t u r e t r a n s it io n t o s u p e r p a r a m a g n e t i c




behav io r a r i s e s . On the o the r hand , fo r nanoc rys ta l l ine Er w i th l a rge r g ra in d iame te r s , t he

norma l magne t i c t r ans i t ions re -appea r bu t a t d i f fe ren t t empe ra tu re s , wh i l e the low- tempera -

tu re supe rpa ramagne t i c behav io r i s r e t a ined .

A m e t h o d o f p r o d u c i n g s o f t m a g n e t i c F e - b a s e d a l lo y s b y m e a n s o f n an o c r y s ta l li n e

s t ruc tu re s ha s been p ro pos ed recen tly . ° °9 ) Con ven t ion a l ly u sed a s magn e t i c m a te r i a l s fo r

h igh - f requency t rans fo rmers , magne t i c heads , s a tu rab le reac to rs , e t c . a re ma in ly fe r r i t e s

hav ing the adv an tage o f low eddy cu r ren t lo sse s. Ho we ve r , s ince fe rr i te s have a low sa tu ra t ion

magne t i c f lux dens i ty and poor t empera tu re cha rac te r i s t i c s , i t i s d i f f i cu l t t o min ia tu r i ze

magne t i c co re s made o f fe r r i t e s fo r h igh - f requency t rans fo rmers , e t c . Thus , in the se

app l i ca t ions , a l loys hav ing pa r t i cu la r ly sma l l magne tos t r i c t ion a re de s ired because they have

re la tive ly goo d so f t magne t i c p rop e r t i e s even whe n in te rna l s t r a in rema ins a f t e r impreg na t ion ,

mold ing o r work ing , wh ich t end to de te r io ra te magne t i c p rope r t i e s the reo f . As so f t magne t i c

a l loys hav ing sma l l ma gne tos t r i c t ion , 6 .5 -w t% s i li con s tee l, Fe -S i -A I a l loys, 80 -w t% Ni

Pe rm a l loy , e tc . a re know n w hich have s a tu ra t ion m agne tos t r i c t ion o f nea r ly 0. Recen t ly , a s

an a l t e rna t ive to such conven t iona l magne t i c ma te r i a l s , amorphous magne t i c a l loys hav ing

a h igh s a tu ra t ion magn e t i c f lux dens i ty have been a t t r ac t ing m uch a t t en t ion , and those hav ing

v a r i o u s c o m p o s i t i o n s h a v e b e e n d e v e l o p e d . A m o r p h o u s a l lo y s a re m a i n l y c la ss if ie d i n t o t w o

ca tegor ie s : i ron -base a l loys and coba l t -ba se a l loys . Fe -base amorphous a l loys a re advan-

tageous in tha t they a re l e s s expens ive than Co-base amorphous a l loys , bu t they gene ra l ly

h a v e l a rg e r c o r e lo s s a n d l o w e r p e rm e a b i l i ty a t h i g h f r e q u e n c y t h a n t h e C o - b a s e a m o r p h o u s

a l loys . On the o the r hand , de sp i t e the fac t tha t the Co-base pe rmeab i l i ty va r i e s a s the t ime

pas se s , t h i s po se s p r ob lem s in p rac t i c a l u se. I t w as the re fo re a t t em pted °°~) to gene ra te

nanoc rys ta l l ine Fe -b ase a l loys w i th spec i fi ed mag ne t i c cha rac te r i s ti c s such a s co re lo s s , t ime

va r i ab i l ity o f co re lo s s , l ow magn e tos t r i c t ion wh ich keeps i t f rom su f fe r ing f rom m agne t i c

d e t e r i o r a ti o n b y i m p r e g n a t i o n a n d d e f o r m a t i o n . T h e a l l o y s w e r e g e n e ra t e d b y t h e a d d i t io n

o f C u a n d a t l e as t o n e e le m e n t s e le c te d f r o m t h e g r o u p c o n s i s ti n g o f N b , W , T a , Z r , H f , T i

and M o to an Fe -b ase a lloy hav ing an e s sen t i al com pos i t io n o f Fe -S i -B . In it ia l ly , t he a l loy

has a g la s sy s t ruc tu re ob ta in ed b y me l t - sp inn ing . Du r ing a sub seque n t annea ling t r ea tm en t

in an ine r t g a s a tmo sphe r e (be tween 450°C a nd 700°C fo r 5 min up to 24 h r ), t he a l loy

c rys ta l li z e s to 50% or m ore . T he c rys ta ll i te s have a b cc ~ -Fe s t ruc tu re in wh ich S i, B e t c. a re

d i s so lved . The c rys ta l l it e s a re un i fo rm ly d i s t r ibu ted . The ave rage d iam e te r i s 50 nm o r le ss ,

p re fe ren t ia l ly in the s ize reg ime o f 50 to 20 nm. W hen the ave rage c rys ta l d i ame te r exceeds

100 nm, go od so f t mag ne t i c p rop e r t i e s a re no t ob ta ined . The re su lt ing m a te r i a ls exh ib i t ed

core lo s se s a s low a s 200 m W /cm 3 and e f fec t ive pe rmeab i li t ie s o f 105 o r more .

The m agne t i c p rope r t i e s o f nanoc rys ta l line (40 nm ) y t t r ium i ron ga rne t s (Y IG) were

s tud ied by fe r romagne t i c re sonance . The nanoc rys ta l l ine subs tance was p roduced by sp ray -

d ry ing fo l lowed b y low tem pera tu r e s in te r ing . ° s2 ) The fe r romag ne t i c re sonance l ine w id th

(A H ) w as n ote d to increase l inear ly w i th the loga r i thm of th e c rys ta l s ize . t299) This increase

ind ica te s tha t a cu t -o f f e f fec t fo r sp inwaves is no t the dom inan t mech an i sm con t ro l l ing H .

The increase o f H wa s in te rp re ted (299'3s3) in te rms of th e coup l ing be tw een the un iform

fe r romagne t i c re sonance p reces s ion mode a t k = 0 and the p reces s ion modes o f the s ame

f requency a t k 0 . The cou p l ing cen te r s a re p ropo sed to be the magn e t i c l a t ti c e i r regu la ri t ie s

wh ich ac t as sca t te r ing centers . With decreas ing gra in s ize the dens i ty o f sca t te r ing cen ters

inc rea se s and hence AH shou ld inc rea se inve rse ly p ropor t iona l to the g ra in s i ze .

The phase t r ans i t ion f rom the pa ramagne t i c to the an t i fe r romagne t i c s t a t e (N6e l t empe ra -

ture , TN) has bee n s tudied in nan ocry s ta l l ine FeF2 b y M 6s sba ue r spec t ro scop y. (394) In

com par i so n to the na r row tem pera tu re in t e rva l o f l es s than 2 K in FeF2 s ing le c rys tal s , the

nanoc rys ta l l ine FeF2 (c rys ta l si ze 10 nm) exh ib i ts a r ange o f t r ans fo rm a t ion t emp era tu re s




ex tend ing f rom 78 K to 66 K . In fac t , the ob se rved d i s t r ibu t ion o f N6e l t emp e ra tu re s in the

nanoc rys ta l l ine FeF2 ind ica te s tha t t he e rys t a l l i t e s t r ans fo rm a t t he same N6e l t empe ra tu re

(78 K) a s a bu lk s ing le c rys t a l , whe rea s the Tr~ o f the bou nda r i e s ex tends ove r a t em pe ra tu re

r e g im e o f 1 2 K . T h i s r e s u lt m a y b e u n d e r s t o o d a s f o ll o w s .

TN i s k n o w n t o d e p e n d o n t h e n u m b e r o f n e a re s t n e i g h b o rs ( N ) a n d t h e s p a ci n gs ( S )

b e t w e e n a p a r t ic u l a r a t o m a n d i ts n e ig h b o r i n g a t o m s . A c c o r d i n g t o th e E X A F S a n d s m a ll

angle sca t te r ing ex per im ents (o f Sec t ion 3 .3.1 and 3 .6 .2) N is redu ced and S is exp and ed in

the bounda ry reg ions in compar i son to a FeF~ s ing le c rys t a l . Hence the ave rage sp in / sp in

coup l ing be tween ad jacen t bounda rY a toms i s r educed wh ich lowers TN. The reduc t ion

d e p e n d s o n t h e lo c a l b o u n d a r y s t r u c t u r e a n d t h u s a s p e c t r u m o f N 6 e l t e m p e r a t u r e s r e s ul ts .

T h i s i n t e r p re t a t io n a g r e es w i t h t h e o b s e r v e d r e d u c t i o n o f t h e D e b y e t e m p e r a t u r e f r o m 2 9 8 K

(FeF 2 single cry stal) to 86 K fo r th e n ano cry stal l i ne FeF 2. (394)

4.9.

lec tr ical Res is t iv i ty

Sys tema t i c s tud ie s o f the e l ec t r i c r e s i s t iv i ty o f nanoc rys t a l l ine ma te r i a l s have recen t ly

been p e r fo rm ed fo r nanoc rys t a l l ine Cu , Pd and Fe spec imens . (3~3ss) The c rys t a l s iz es o f the

va r ious m a te r i a ls s tud ied va r i ed be tween 6 nm and 25 nm. The to t a l m e ta ll i c impu r i ty con ten t

o f the Pd spec imens was ~<0.5 a t . T he spec imens con ta ined b e tween 0 .3 a t and 1 a t

oxyge n and ab ou t I a t C . (364) M e taUograp h ic s tud ie s b y means o f scann ing e l ec t ron

m i c r o s c o p y r e v e a le d r e s id u a l p o r o s i ti e s b e t w e e n 1 a n d a b o u t 1 0 i n C u a n d F e , w h e r e a s v e r y

few (< 0 .1 ) po re s we re no t i ced in nano c rys ta l l ine Pd . (365) F igu re 58 shows the e l ec t ri c

de - re s is t iv ity o f nanoc rys t a l l ine P d spec imens a s a func t ion o f t empe ra tu re fo r va r ious g ra in

s izes . The m easu re d t em pe ra tu re coe f fi c ien t o f the e l ec t r ic r e s is t iv i ty o f nanoc rys t a l l ine Pd

and Cu was found to dec rea se when the c rys t a l s i z e was reduced (F ig . 59 ) . The obse rved

tem pera tu re and g ra in s i ze depend ence o f the e l ec tr i c r e s i ti v i ty a s we ll a s the t em pe ra tu re

coe f fi c ien t m ay be un de rs tood in t e rms o f e l ec t ron sca t t e ring in s ide the c rys t al l it e s a s we l l a s

sca t t e ring o f the e l ec t ron by the boun da r i e s by ana log y to the t r ea tm en t o f the e l ect r ic

de-resis t iv i ty of th in meta l l ic f i lms. 067-37s) Th e in te rac t io n o f gra in bo un da r ies wi th co nd uc t ion

e lec t rons ha s been t r ea t ed b y cons ide r ing the bou nda r i e s a s po ten t i a l ba r r i e r s o f a g iven he igh t

and wid th sca t t e r ing the conduc t ion e l ec t rons . Th i s sca t t e r ing may e i the r be de sc r ibed in

t e rms o f the re fl ec tion o f the e l ec trons by the bound a r i e s o r the t ransm iss ion th rough the

60

o

3 -

~ 40

~ 30

W

re 20

u. 10

W

0

. . . . . . . . : ; ;

x

8 x

x

~. ÷ v ¢

,~ ÷ v •

÷ v v

Y

m g • ii m m B

6 s o ~ b o ~ ; 0 2 ~ 0 2 g o 3 6 0

TEMPERATURE [K].

F IG . 5 8. S p e c i fi c e l v c tr i c d e - r e s i s ti v i ty o f n a n o c r y s t a l l i n e P d a s a f u n c t i o n o f t e m p e r a t u r e a n d c r y s t a l

s iz e ( M 1 0 n m , • 1 2 n m , x 1 3 n m , 4 - 2 2 n m , 1 2 5 n m ) in c o m p a r i s o n t o c o a r s e - g r a in e d p u r e P d

p o ly cr y s t a l (D ) . (36s)




293

x10-3

5

k

F -

Z 4

U -

U -

W 3

0

U.I

~ 2

F--

o r

i i i

a . 1

t u

t- -

I , I , I _ = I _ • _ ~ _

10 20 30 40 50

CRYSTAL SIZE Into]

F IG . 5 9. T e m p e r a t u r e c o e f f ic i e n t o f t h e e l e c tr i c d c - r e s is t i v it y o f n a n o c r y s t a l l i n e P d a s a f u n c t i o n o f

crystal size. 365)

bound a r i e s . T he re su l t s o f bo th t r ea tm en t s d i f fe r in deta il s . How eve r , t he ba s ic p red ic t ions

a r e t h e s a m e a n d m a y b e s u m m a r i z e d a s f o l lo w s . (i ) I f t h e g ra i n b o u n d a r y b a r r i e r h e i g h t

and /o r w id th i s inc rea sed , the e l ec t ron s ca t t e r ing by the bounda ry becomes s t ronge r . ( i i ) I f

the c rys ta l s i z e approached o r becomes l e s s than the e l ec t ron mean f ree , the conduc t iv i ty a s

we l l a s the t em pera tu re coe f fi c ien t s dec rea se s . In fac t , even nega t ive va lues o f the t em pera tu re

coefficien ts hav e bee n pre dicte d. (37s)On the o the r hand , i f t he g ra in s ize i s l a rge in com par i son

to the e l ec t ron me an f ree pa th , the conduc t iv i ty and the t em pera tu re coe f f ic i en t due to

bo un da r y s ca t t e r ing a re expec ted to app roa ch the bu lk limi t. I f t he re s is t iv i ty o f nano-

c rys ta ll ine me ta l s i s cons ide red in the l igh t o f the se re su l ts , t he fo l lowing conc lus ions ma y

be d rawn . I f t he c rys ta l si ze is sma l l e r than the e l ec t ron mean f ree pa th , g ra in bo un da r y

sca t te r ing d om ina te s and hence the con duc t iv i ty a s we l l a s the t emp era tu re coe f fi c ien t i s

expec ted to dec rea se a s was obse rved (F ig . 59 ). F o r g ra in s izes la rge r than the e l ec t ron m ean

f ree pa th , the conduc t iv i ty and the t em pera tu re coe f f i ci en t dev ia te cons ide rab ly f rom the

cor re spond ing bu lk va lues . In o the r words , e l ec t ron s ca t t e r ing by vo lume s ca t t e r ing e f fec t s

ins ide o f the c rys ta l s occu rs and becom es the dom inan t s ca t te r ing m od e sugges t ing a h igh

dens i ty o f po in t o r l ine de fec t s in the c rys ta l li t es . The re s idua l impur i ty con ten t o r po ro s i ty

c a n n o t a c c o u n t f o r t h e d e v i a ti o n . T h e o b s e r v e d t e m p e r a t u r e d e p e n d e n c y o f t h e r es is ti v it y w a s

u t il iz ed (364) to dedu ce the D eb ye t em pera tu re o f the nanoc rys ta l l ine ma te r i a l . The D eby e

tem pera tu r e o f nanoc rys ta l l ine P d was fou nd to be reduced by abo u t 100 K re lat ive to a s ing le

c rys ta l o f Pd .

Studies o f the t ransve rsa l m agn etore s is tanc e (3~) indica ted a para bo l ic res is tiv i ty increase in

the magn e t i c f ie ld . Th i s e f fect m ay be un de rs too d i f i t is a s sum ed tha t the g ra in b oun da r i e s

con t r ibu te l i t t l e to the magne to re s i s t ance due to the i r h igh re s i s t iv i ty and hence s t rong

e lec t ron s ca tt e r ing . In o the r words , i t is t he c rys ta l l ine com po nen t o f the ma te r i a l w h ich

con t ro l s the magne t0 re s i s t ance and hence a s imi la r f i e ld dependence i s expec ted fo r a

nanoc rys ta l l ine ma te r i a l and a s ingle c rys ta l. Th i s w as indeed the ca se .

Cry s ta l s ize e ffec ts in p iezoe lec t r ic m ater ia ls were s tudied by M ultani . (379 3s°) PZ T was fou nd

to exh ib i t an enhance d dec rem en t o f the p iezoe lec tr i c t enso r va lue d33 whe n the g ra in s ize

wa s red uced. In fac t , fo r a gra in s ize o f abo ut 40 nm , d33 was a s h igh as 300 ~ C cm-2 . rag)

T h e i n c re a s e w a s i n t e rp r e t e d i n t e r m s o f t h e c u t - o f f o f l o n g w a v e l e n g th m o d e s d u e t o t h e

smal l c rys ta l s ize . In fac t , th is concept has been success fu l ly tes ted for smal l i so la ted PZT




crystals3269) Th e s ignificance of the h igh dens i ty o f gra in bo un dar ie s in nano crys ta l l ine

ma te r i a l s a s p inn ing cen te r s fo r f e r roe lec t r ic d om a in wa l l s ha s been dedu ced 08~) f rom the

obse rv ed enhance me n t o f ene rgy lo s s o f f a s t e l ec t rons tr ave rs ing th rough a fe r roe lec t r ic

me d ium (BaTiO3) whe n hea ted th rough the phase t rans i t ion t em pera tu re . The ene rgy lo s s was

exp la ined in t e rms o f the dom a in swi tch ing t ime which be com es close to the e l ec t ron t rans it

t ime w hen the t em pera tu re app roach es the c r i t ic a l va lue . °81)

4.10.

Mechanical Properties

4.10.1.

lastic properties

Th e e las t ic con s tan ts o f n anoc rys ta l l ine ma ter ia ls were m easu red t312'36°) by the fo l lowin g

fo u r in de pe nd en t m et ho ds , t315'36°)

( i ) E la st i c bend in g o f a th in , p l a t e shaped spec imen sup por ted a t bo th ends and loaded wi th

a c o n s t a n t f o r c e in t h e m i d d le . T h e a m o u n t o f b e n d i n g w a s m e a s u r e d i n d u c ti v e ly w i th a n

accuracy o f - t-2/~m. T he accu racy o f the e la s t ic m odu lus ded uced f rom these measu remen t s

w a s ± 4 .

( ii ) M e a s u r e m e n t s o f th e p r o p a g a t i o n v e l o ci ty o f a l o n g i tu d i n a l o r t r a n sv e r s al s o u n d

w a v e ( f r e q u e n c y 1 0 a n d 5 0 M H z ) t h r o u g h n a n o c r y s ta l l in e s p ec im e n s . F r o m t h e m e a s u r e d

s o u n d v e l o c i ty ( a c c u r a c y 2 ) , t h e sh e a r an d t h e Y o u n g ' s m o d u l i w e r e c o m p u t e d b y m e a n s

of the s t anda rd equa t io ns a s sum ing tha t the m a te r i a l is f r ee o f po ros i ty . In fac t, i f a po r t ion

o f t h e l o w e r d e n s i t y o f n a n o c r y s ta l l in e m a t e r i al s w o u l d o r i g i n a te f r o m m a c r o s c o p i c p o r o s i t y ,

t h e e l as ti c c o n s t a n t s c o m p u t e d f r o m t h e m e a s u r e d v e lo c it ie s o f s o u n d c o u l d b e u p t o 5

la rge r than the va lues l i s t ed in Tab le 6 .

( i ii ) In t r anspa re n t spec imens the sound ve loc i ty was de te rm ined by Br i l lou in s ca t te r ing

us ing l a s e r l igh t w i th ~ = 358 nm and a 90 ° d i f frac t ion ge om e t ry .

( iv ) The f ree decay o f to r s iona l o sc i ll a t ions in a to r s ion pen du lu m a t 1 to 5 H z . (36°)

The e la s t i c cons tan t s o f the me ta l l i c nanoc rys ta l l ine ma te r i a l s we re found to be reduced

by 30 o r l es s whe rea s ion ic c rys ta l s show ed a reduc t ion o f m ore than 50 (Tab le 6 ).

These re su l t s we re in te rp re ted a s fo l lows . D ue to the f ree vo lu m e o f a g ra in b oun da ry ,

the ave rage in te ra tomic spac ings in the bounda ry reg ions a re inc rea sed re l a t ive to the

pe r fec t la t ti c e . I f t he in t e ra tomic po ten t i a l i n g ra in bo und a r i e s i s a s sum ed to b e the s ame

as in the pe r fec t la t ti c e , t he e la s t ic cons tan t s ( ave raged o ve r a ll comp onen t s ) o f a nano -

c rys ta l l ine ma te r i a l a re expec ted to be reduced in compar i son to the c rys ta l l ine s t a t e due

to the reduced e la s ti c m odu l i o f the bounda r i e s . In fac t , a fu r the r r edu c t ion o f the mod u lus

m a y r e s u l t f r o m t h e c h a n g e o f th e i n t e ra t o m i c p o t e n t i a l b e t w e e n b o u n d a r y a t o m s i n

com par i so n to the c rys ta l la t ti c e. S uch a change w as sugges ted on the ba s i s o f X- ra y

d i f f r a c t i o n d a t a ~297) ( c f . also Section 4.5).

able 6 . E l a s t i c P ro p e r t i e s o f N an o c ry s t a l l i n e an d C o n v en t i o n a l

Materials(3 2,360)

C ry s t a l Y o u n g s m o d u l u s E S h ea r m o d u l u s G

M ater ia l s ize (nm) (1 ,000 N/ r am 2) (1 ,000 N/ ram 2)

Pd 8 88 (123)* 32-35 (43)*

M g 12 39 (41)* 15 (15)*

C aF 2 38 (111)* 19 (42)*

*The numbers in b rackets ind ica te the va lues fo r an i so top ic con-

ven t ional po lycrys ta l .




In order to test this interpretation, the grain boundaries o f nanocrystalline Mg and Pd were

doped with oxygen and water, by adsorbing (at 20°C) 02 and H20 at the free surfaces of

the small Pd crystals prior to the compaction process (Fig. 8). The interior of the crystals

remained unchanged because both dopants cannot penetrate into the lattice at ambient

temperature. If the elastic constants of the nanocrystalline substances depend primarily on

the elastic properties of the boundaries, the incorporation of 02 and H20 should affect the

elastic constants. Indeed, the doping reduced E and G to 31,000 and 12,000N/mm 2.

Weller e t a l . 0 6 ° measured the shear modulus and the internal friction, Q-l, of nano-

crystalline Pd from the free decay of torsional oscillations in the frequency ( f ) range 1 Hz

to 5 Hz with a maximum strain of e < 10 -5 in an inverted torsion pendulum between 4 K and

650 K. The internal friction was determined from the logarithmic decrement v by Q -~ = v/n.

The absolute value o f the shear modulus G ocf 2 was derived by a comparison of the

oscillation frequencies of the nanocrystall ine and a well annealed coarse-grained Pd specimen,

taking the shear modulus of the latter from the literature. In order to measure the temperature

variation of G and Q- ~ either linear heating or a step-wise heating program with measure-

ments at constant temperature were performed. The value of G at ambient temperature

(35 GPa) agreed with the data obtained by the other methods (Table 6). The observed

temperature variation of G during heating was interpreted in terms of the annealing out of

interfacial defects. The activation enthalpy of this process was found to be 0.72 + 0.05 eV.

This result seems comparable to the activation enthalpies obtained for self and solute

diffusion in nanocrystalline materials (Sections 4.1 and 4.2). It may be noticed that 0.72 eV

is about half the activation enthalpy of grain boundary diffusion in Pd. The theoretical

interpretation of the reduction of the Young's modulus in terms of the reduced atomic density

in the grain boundary region agrees with X-ray diffraction experiments on boundaries in thin

Au bicrystals.(297~ The variation of the intensity o f the X-ray diffraction spots of a 22.5 ° (001)

twist boundary as a function of temperature (between 100K and 275K) suggests an

enhancement of the mean square displacement (u2> of the boundary region relative to the

one of the lattice by almost 50%. Since the Young's modulus is proportional to (u 2>-1 the

elastic modulus of the 22.5 ° (001) twist boundary was suggested to be about 66% of the bulk

value, i.e. 5.3 x 10 ~° Pa under the assumption that all other contr ibutions are to the boundary

modulus equal to their bulk counterparts. The reduction agrees roughly with the data

summarized in Table 6. Recently, three theoretical attempts have been made to understand

the elastic constant of nanocrystalline materials. Fecht(291) computed the elastic constants in

terms of the excess free volume of the grain boundaries (Fig. 55). The excess free volume of

the boundaries is argued to reduce the average interaction forces between the atoms in the

boundary region. This estimated modus reduction based on the assumptions is, however,

more than an order of magnitude larger than the experimental observations (Table 6). In

the second approach, o~4~ the elastic constants were investigated by means of a computer

simulation method, the elastic constants in what was called a grain-boundary superlattice .

Such a (somewhat hypothetical) material consists of a periodic arrangement of thin slabs

A and A' of equal thickness, ;., of the same material. The two crystal slabs were rotated

with respect to one another about the axis normal to the slab by a certain angle, 0. The

computations were performed for a E5(001)-twist boundary (0 = 36.7° rotation, about a

common (001) axis of A and A') in Cu. By computing the elastic response of this system

the elastic modulus of the (001)-twist boundary was deduced. An embedded-atom method

(EAM) potential°~S) as well as a Lennard-Jones (LJ) potential for Cu (316) have been applied.

Both potentials yield an increase in the Young's modulus (Y) and a corresponding decrease

of the shear modulus (G) as 2 becomes smaller. For example, if the slabs A and A' have

JPMS 33 4~F




a th ickness o f t en un i t c ell s, Y i s i nc rea sed by abo u t 20 and G i s r educed by nea r ly

the same amoun t . The phys ica l r e a sons fo r the se changes a re a s fo l lows . Due to the

des t ruc t ion o f the pe r fec t -c rys t a l p l ana r s t a ck ing a t t he in te r face , a tom s wh ich we re

o r ig ina l ly sepa ra t ed by pe r fec t -c rys t a l d i s t ances have been pushed toge the r more c lose ly .

Essen t i a l ly a s a consequence o f Pau l i ' s p r inc ip le , t he b i c rys t a l expands loca l ly fo r a l l bu t

ve ry spec ia l geome t r i es . Ho wev e r , in sp i t e o f the subse quen t inc rea se in the ave rage

in te ra tomic d i s t ances a sign if i can t f r ac t ion o f a tom s i s fou nd a t sep a ra t ions m uch shor t e r (up

to ab ou t 10 ) t han in the pe r fec t c rys t a l. Wi th in a g iven she ll , d is t ances sho r t e r t han the

re l a t ed idea l-c rys t a l va lue a re expec ted to s t r eng then the e l a st ic cons tan t s w he rea s expan ded

d i s t ances re su lt i n the ir so f t en ing . D ue to the anha rm on ic i ty o f the in t e ra tomic p o ten t i a l,

sho r t ened d i s t ances a re we igh ted more heav i ly than the expanded ones and the re fo re the

e l as t ic m o d u l u s o f a b o u n d a r y m a y b e e n h a n c e d a l t h o u g h t h e a v e ra g e a t o m i c d e n s i ty is

reduced . T he e f fec t i s l ess p ro nou nce d fo r the EA M than fo r the LJ po ten t ia l . Recen t ly ,

A d a m s

e t

al . 063 have pe r fo rmed s imi l a r computa t ions . In f ac t , t he e l a s t i c cons tan t s o f a

E5(001) - tw i s t bounda ry in Cu were ca l cu la t ed us ing the EAM. In o rde r to ob ta in the b i ax ia l

Yo ung ' s mo du lus , a sma l l tens il e s t re ss (0 .05 ) was app l ied to the sys t em ( two c rys t a l s and

a b o u n d a r y ) p e r p e n d i c u l a r t o t h e b o u n d a r y p l a n e . T h e a t o m i c p o s i t i o n s w e r e t h e n a d j u s t e d

to min imize the to t a l ene rgy . The m odu lus o f the tw o c rys t a l l a tt i c es we re foun d to be a lm os t

u n a f f e ct e d b y t h e p r e s e n ce o f t h e b o u n d a r y u n le s s a r e g io n o f I n m o n b o t h s id e s o f t h e

b o u n d a r y i s c o n s i d e r e d . H o w e v e r , i n t h i s b o u n d a r y r e g i o n t h e Y o u n g ' s m o d u l u s w a s f o u n d

t o b e e n h a n c e d f r o m a b o u t 0 .7 x 1012e r g / cm 2 t o a b o u t 1 . 05 x 1012

e r g / c r n 2

T h i s e n h a n c e m e n t

o f th e Y o u n g ' s m o d u l u s s e e m s t o r e s u lt f r o m t h e v o l u m e e x p a n s io n i n t h e b o u n d a r y

( c o m p u t e d t o b e a b o u t 1 5 ) . O n t h e o t h e r h a n d , t h is v o l u m e e x p an s i o n w a s f o u n d t o

d e c r e as e t h e s h e a r m o d u l u s o f t h e b o u n d a r y r e g io n f r o m a b o u t 0 . 75 x 1012e rg /cm 3 to a lmos t

zero .

4.10.2. n t e rna l f r i c t i on

The in t e rna l f r i c tion Q - 1 (F ig . 60 ) was m easu red in nanoc rys taUine Pd be low 300 K and

wa s fou nd to be ab ou t 2 to 3 t imes sm al le r than in wel l anne a led coarse-g ra ined Pd. t36°)

In the a s -p repa red spec imen , sm a l l i n t e rna l f r i c tion peaks we re obse rv ed a t 120 K , 220 K ,

and 400 K which annea led ou t a f t e r hea t ing the spec imen onc e to 640 K . A bov e 300 K

15

Z

O

~ '10

o

e~

' 5

z

/

i

/ /

/

/

@,, ®

/

/ /

/ / /

• ~ = = T==~- I - : ' - - - 1 - - - * l

2 0 0 4 0 0

T E M P E R A T U R E [ K ]

I

p J i

J

i

/

OO

FIG. 60. Temperature variation of the internal friction Q -~ of nanocrystalline Pd with a heating rate

of 150 K/hr,(~) (a) after 5 GPa compation at 295 K and (b) in a second run after heating to 640 K.




the internal friction increases steeply and shifts toward higher temperatures after annealing

(Fig. 60). These internal friction phenomena may be interpreted in terms of viscous sliding

of interfacial boundaries. (36t'362) Alternatively they may, however, also be due to some kind

of dislocation movement because in this temperature regime considerable internal friction is

observed in well annealed coarse-grainted Pd, too. The general increase of Q - t above 300 K

as well as the shoulder at 520 K, are shifted to higher temperatures with increasing measuring

frequency. This indicates thermal activat ion of the interfacial loss processes. The maximum

at 520 K may be due to a particular atomic re-ordering process in the interfaces which is

mechanically reversible under the alternating external stress. From the present results, an

activation energy of 1.3 eV is estimated for this process assuming a pre-exponential factor of

1013s -m. However, the temperature shift of the 520 K-process with frequency variation is

smaller than predicted by these activation parameters.

4 10 3 Hardness and fracture

The synthesis of a nanocrystalline ceramic (TiO2 rutile) has been carried

o u t (317'318)

by

producing small titanium crystals and then oxidizing them to TiO2 prior to compaction

(cf. Section 2.1.2). The nanocrystaUine compacts, which are well bonded on consolidation

even at room temperature, densify rapidly above 770 K (Fig. 9) with only a small increase

in grain size, leading to hardness values similar to those of sintered coarser-grained

commercial TiO2, but at temperatures some 600 K lower. The Vickers microhardness of such

specimens measured at ambient temperature is shown in Fig. 61 as a function of sintering

temperature for three different TiO2 (rutile) samples, the nanocrystalline sample with 12 nm

initial average grain size was compacted at 1.4 GPa. The two samples with 1.3 #m initial grain

size were compacted at 1.4 GPa and 0.1 GPa. (27s319) The lat ter sample, prepared essentially in

accord with standard ceramic processing methods, was the only one of these three which was

sintered with the aid of polyvinylalcohol. Obviously, the hardness of the nanocrystalline

sample is about two or more times the hardness of the two other samples due to the faster

sintering. The enhanced hardness of the 1.3 #m sample consolidated at 0.1 GPa above

1600 f '

U 3

U3

~ 1200

0

n ,

<

o = 8

( . )

=E

u )

~ 4 0 0

Y

0 '

0

TiO2

12 n m , l . 4 G P o ~ /

~/'~- 1.3 p.m 1.4 GP a 7 / ~ \ ,

/ ~I I I . 3 u m r O . I G P o

2 0 0 4 00 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0

T E M P E R A T U R E ( ° C )

F IG . 6 I . V i c k e r s m i c r o h a r d n e s s i n k p / m m 2 t o T iO 2 ( r u t il e ) m e a s u r e d a t r o o m t e m p e r a t u r e a s a f u n c t i o n

o f o n e - h a l f h o u r s i n t e r i n g a t s u c ce s s iv e ly i n c r ea s e d t e m p e r a t u r e s . R e s u l t s f o r a n a n o c r y s t a l l i n e s a m p l e

( s q u a r e s ) w i t h a n i n i t i a l a v e r a g e g r a i n s iz e o f 1 2 n m c o m p a c t e d a t 1 .4 G P a a r e c o m p a r e d w i t h t h o s e

f o r c o a r s e r - g r a i n e d c o m p a c t s w i t h 1 .3 m i n i t ia l a v e r a g e g r a i n siz e s i n t e r e d a t 0 .1 G P a w i t h ( d i a m o n d s )

a n d a t 1 .4 G P a w i t h o u t ( c ir c le s ) th e a i d o f p o l y v i n y l a l c o h o l f r o m c o m m e r c i a l p o w d e r . °~ 9)




Table 7 . V ickers Hardness , H , and Frac tu re Toughness , Ktc o f

N an oc ry st al lin e TiO 2 275 319)

Tem pera tu re (°C) as p repare d 600 800 1000

H (Vi cke rs) 210 190 630 925

Ktc (M Pa ~/m ) 0 .8 1 .0 2 .8 2 .8

Poro s i ty (% ) 25 20 10 5

1 ,200°C is due to t he s in t e r ing a id . Fo r r e fe rence , t he V ickers microh ardne ss o f a s ing le c rys ta l

o f TiO2 m easu red und er i den t ica l co nd i t i ons is 1 ,036 + 66 kgf /m m 2. Frac tu re t oughness

s tu d ie s o n t h e s e samp l e s, m ad e b y mea s u r i n g t h e c r ack l en g th s ema n a t i n g f r o m mi c r o i n d en -

t a t i ons a t h ighe r loads , app ear t o conf i rm the s imi l a r o r be t t e r mec han ica l p roper t i es o f t he

TiO2 in com par i son wi th t he c oar ser -g ra ined m ater i a l an d s ing le c rys t a l T iO2 ( ru ti le ) as w ell.

Tab le 7 shows tha t bo th hardness a nd toughne ss increase wi th i ncreas ing s in te r ing t emp era-

tu re (decreas ing poros i ty ) . The va lues o f hardness and f r ac tu re t oughness a f t e r s in t e r ing a t

abo u t 800-900°C are t yp i ca l o f wel l s i n t e red bu lk ceram ics , i nd i ca t ing tha t g ood m echan ica l

p roper t i es ca n be ach ieved in nanoc rys t a l l ine TiO2 af t e r l ow t em pera tu re s in te r ing . Usual ly ,

h a r d en i n g an d f r ac t u r e to u g h n es s d o n o t s ca le ; h a r d en i n g t r ea t men t s t en d t o m ak e m a t e r ia l s

more b r i t t l e wi th r educed f r ac tu re t oughness . In t he p resen t case , however , t he harden ing

and tough en ing resu l t f rom the e l imina t ion o f po ros i ty which increases t he overa l l s t r eng th

o f t h e m a t e ri a l.

Th e resu l ts o f t hese i nves t iga t ions i nd i ca t e t ha t nan ocrys t a l l i ne com pact s , a l t houg h a l r ea dy

r a t h e r w e l l b o n d ed o n c o m p ac t i o n a t r o o m t emp er a t u r e , d en s i fy r ap i d ly ab o v e 5 00 °C , w i t h

only a smal l increase in grain s ize (cf . Fig . 9) . The hardness and

K t c

values ob ta ined a re

comparab le t o o r g rea t e r t han those o f s ing le-crys t a l T iO2 o r coar ser -g ra ined compact s , bu t

a t t empera tu res some 400 to 600°C lower t han conven t iona l s in t e r ing t empera tu res and

wi thou t t he need fo r s in t e r ing a ids .

A f r ac t o g r ap h i c s t u d y02°) of n ano crys tal l ine TiO2, crystal s ize 12 nm (form ed by pos t

ox ida t ion o f smal l T i c rys t a ls ) , i nd i ca t ed som e rem arka b le d i f fe rences be twee n nano-

c r y s ta l li n e an d co n v en t i o n a l T i O 2 ce r amics . Th e s i nt e ri n g t em p er a t u r e f o r co mp l e t e l y

t ransg ranu lar f r ac tu re o f t he nanoc rys t a l l i ne samples was abo u t 1 ,100°C, o r 200°C lower

t h an t h a t o f t h e co m me r c i a l co a r s e r - g ra i n ed ma t e r i a l. F o r s amp l e s s in t e red a t t h e s ame

t emp er a t u r e , t h e v o i d s in t h e co m mer c i a l ma t e r i a l a r e la r g e r an d m o r e n u m er o u s t h an t h o s e

in t he nanocrys t a l l i ne mater i a l . The microhardness o f t he nanocrys t a l l i ne samples (F ig . 61 )

ma y , a t l e as t in p a r t , b e a t t r ib u t ed b y t h e d i f fe r en t v o i d mo r p h o l o g y . T h e f r ac t u r e m o d e

observed ind ica t es t ha t t he ox ida t ion p rocess as wel l as t he par t i c l e co l l ec tion and c om pact ing

procedures p l ay a c ruc i a l ro l e . In o ther words , by per fo rming these s t eps under wel l -

co n t r o l led co n d i t io n s , t h e m a t e r ia l p r o p e r t ie s m ay b e i mp r o v ed . S o m e o f t h e o b s e r v a t i o n s

repor t e d in Sec t ion 4.10 .5 a re c lose ly r e l a t ed to t he h ardness a nd f r ac tu re o f nanocrys t a l l i ne

mater ial s .

4.10.4.

L o w t e m p e r a t u r e d u c t il it y o f n a n o c r ys ta l li n e c e r a m i c s

I t has been observed tha t conven t iona l ly b r i t t l e ceramics become duct i l e , permi t t i ng

l arge ( e.g. 100 ) p l as t i c defo rm at ions a t l ow t em pera tu re (e .g . 293 K) , i f a ceramic ma ter i a l

is gen era t ed in t he nanoc rys t a l l i ne fo rm . °~s) The duc t i li t y ma y to som e ex ten t o r ig ina t e f rom

the d i f fus iona l f low o f a tom s a lon g the i n t e rcrys t aUine in te r faces . The defo rm at ion ra t e i o f

di f fusional creep (Coble creep) by in ter facial d i f fusion i s g iven by

= a I I B 6 D b

d 3 k T .

(5)



N A N O C R Y S T A L L I N E M A T E R I A LS 2 99

H e r e tr is th e t e n s i le s t r es s , t ) t h e a t o m i c v o l u m e , d t h e a v e r a g e c r y s t a l s i ze , B a n u m e r i c a l

c o n s t a n t , D b t h e b o u n d a r y d i f fu s iv i t y, k t h e B o l t z m a n n c o n s t a n t , T th e t e m p e r a t u r e a n d

t~ is t h e t h i c k n e s s o f t h e b o u n d a r i e s . N a n o c r y s t a U i n e c e r a m i c s a r e e x p e c t e d t o e x h i b i t a

d i f f u s io n a l c r e e p r a t e w h i c h is e n h a n c e d r e l a t iv e t o c o n v e n t i o n a l c e r a m i c s b y a f a c t o r o f a b o u t

1 0 tl d u e t o t h e r e d u c t i o n o f d f r o m 1 0 / ~ m i n c o n v e n t i o n a l p o l y c r y s t a l s t o 1 0 n m ) a n d

t h e e n h a n c e m e n t o f t h e b o u n d a r y d i f fu s i v it y c f. S e c t io n s 4 .1 a n d 4 .2 ) . F ig u r e s 6 2 a a n d b s h o w

t h e p la s t i c d e f o r m a t i o n o f n a n o c r y s t a l l i n e C a F 2 a t 3 5 3 K w h i c h r e s u lt s in s in u s o i d a l b e n d i n g

a n d p l a s ti c f lo w i n t o a f i l a m e n t a r y f o r m . T h e s p a c e o n t h e r i g h t si de o f th e n a n o c r y s t a l l i n e

C a F 2 s p e c i m e n i n F i g . 6 2 a is i n it ia l ly e m p t y a n d c l o se s u p d u r i n g c o m p r e s s i o n i n th e

d i r e c t i o n i n d i c a t e d b y t h e a rr o w s . P l a s t ic d e f o r m a t i o n o f n a n o c r y s t a l l i n e T i O 2 b y i n d e n t i n g

w i t h a d i a m o n d i n d e n t e r ) a t a m b i e n t t e m p e r a t u r e is p r e s e n t e d i n F ig . 6 2 c . I n d e n t a t i o n

o f a c o n v e n t i o n a l T i O 2 p o l y c r y s t a l u n d e r t h e s a m e c o n d i t i o n s a s in F i g . 6 2 c r e s u lt e d i n

m u l t i p l e c r a c k i n g F i g . 62 e ). I f t h e d e f o r m a t i o n r a t e is l a r g e r t h a n t h e cr e e p r a t e o f t h e

Fl t. 62. Illustration o f the mechanical properties o f nanocry stalline materials. a) Schematic

draw ing indicating the deformation p rocedure app lied. b) Plastic deform ation o f nanocry stalline

CaF2 by an arrangement as shown in a). Th e deformation was carried out at 353 K and the

deformation t im e was ab out 1 s. c) Indentat ion of nanocrystal line TiO 2 at 293 K load 2 N,

deformation t im e l0 s). The hardness of the material deduced from the size of the indent) was

250 HV . d) Bri t tle behavior o f nanocrystal line TiO 2 293 K, load 2 N). The indentat ion was generated

by reducing the loading time from l0 s c) to l s. e) Indentation of a conventional TiO2 polycrystal

under condit ions similar to those in c) 293 K, load 5 N). Th e hardness deduced was about 800 HV .

The different brightness of the fractured areas results from tilting of these areas relative to incident

light.<3Is)




n a n o c r y s t a l l i n e c e r a m i c , t h e m a t e r i a l s h o u l d e x h i b i t a d u c t i l e - b r i t tl e t r a n s i t io n , a s w a s i n d e e d

obs e r ved ( F i g . 62d ) .

T h e o b s e r v e d p l a s t ic i t y o f t h e n a n o c r y s t a l l i n e c e ra m i c d o e s n o t s e e m t o b e r e l a te d t o

r e s i d u a l p o r o s i t y , a s h a s b e e n p r o p o s e d . I n f a c t, t h e p l a s t ic f l o w o f a n a n o c r y s t a l l i n e C a F 2

s p e c im e n i n t o t h e t r a n s p a r e n t , f i l a m e n t a r y f o r m ( F ig s 6 2 a a n d b ) w o u l d b e h a r d t o u n d e r s t a n d

i n t e r m s o f r e si d u a l p o r o s i t y . F u r t h e r m o r e , n o t c h e d s p e c i m e n s o f n a n o c r y s t a l l i n e T iO 2 h a v e

b e e n t e s te d i n b e n d i n g ~3~s) a n d e x h i b i t e d p l a s t i c d e f o r m a t i o n w i t h o u t a n y c r a c k g r o w t h .

N o t c h e d s p e ci m e n s o f b r it tl e p o r o u s m a t e r ia l s f r a ct u r e w i t h o u t p l a s ti c d e f o r m a t i o n .

T h e p o s s i b i li t y to u t il iz e t h e p l a s t ic i t y o f n a n o c r y s t a l l i n e c e r a m i c s f o r n e t s h a p e f o r m i n g

p r o c e s s e s h a s b e e n d e m o n s t r a t e d r e c e n t l y a t l o w t e m p e r a t u r e s w h e r e l i t t l e o r n o g r a i n

growth occurs. 387)

I f t h e p l as ti c d e f o r m a t i o n i s p e r f o r m e d a t t e m p e r a t u r e s o f a b o u t 5 0 % a t

t h e a b s o l u t e m e l t i n g p o i n t ( e .g . f o r T iO 2 a t a b o u t 8 0 0 °C ) , t o t a l s t r a i n s a s h i g h a s 0 . 6

wer e ob t a i n ed i n a pe r i o d o f a bo u t 15 h r . (38s) F i g u r e 63 s h ow s a nan oc r y s t a l l i ne T i O 2 s am p l e

b e f o r e a n d a f t e r c o m p r e s s i o n f o r 15 h r a t 8 1 0 ° C . D u e t o t h e h i g h t e m p e r a t u r e , t h e g r a i n

s iz e i n c r e a s e d f r o m a b o u t 5 0 n m t o a p p r o x i m a t e l y 1 /~ m . T h e g r a i n s w e r e n o t i c e d t o

r e m a i n e q u i a x e d a n d w i t h t h e e x c e p t i o n o f a fe w r e si d u a l p o r e s a t g r a i n t r ip l e j u n c t i o n s n o

po r os i t y wa s de t ec t ed . S t r a i n r a t e s a s h i g h a s 8 10 - 5 s -1 w e r e obs e r v ed a t t r ue s t r es s e s o f

5 2 M P a . T h e s e r a t e s a r e q u i t e s u f f ic i en t f o r t e c h n o l o g i c a l a p p l ic a t i o n s . T h e i n c r e a si n g g r a i n

s iz e d u r i n g d e f o r m a t i o n w a s n o t e d t o r e d u c e t h e s t r a in r a t e . H o w e v e r , t h i s e f fe c t d o e s n o t

s e e m t o p o s e a b a s i c p r o b l e m , b e c a u s e d o p i n g o f n a n o c r y s t a l l i n e c e ra m i c s ( e. g. T iO 2 b y Y

o r A I ) h a s b e e n d e m o n s t r a t e d t o r e d u c e g r a i n g r o w t h d r a m a t i c a l l y . T h e a v a i l a b l e d a t a d o

n o t y e t p e r m i t t o s p e c i f y t h e m e c h a n i s m s i n v o l v e d i n t h e l o w t e m p e r a t u r e p l a s t i c i t y o f

n a n o c r y s t a l l i n e c e r a m i c s .

G r a i n b o u n d a r y s li di ng , g r a in r o t a t i o n a n d g r a i n s h a p e a c c o m m o d a t i o n b y d if f u si o n a l

p r oces s e s s eem t o p l ay a c r uc i a l r o l e , i . e. p r oces s e s wh i ch a r e t yp i ca l f o r s upe r p l a s t i c i t y . °sg)

I n f a c t , s u p e r p l a s ti c f l o w i n c e ra m i c s h a s b e e n r e p o r t e d p r e v i o u s l y , h o w e v e r , t h e t e m p e r a t u r e s

w e r e c o n s i d e r a b l y h i g h e r a n d t e c h n o l o g i c a l l y m o r e d i ff ic u l t t o a c h i e v e. C r e e p w i t h h i g h s t r ai n s

FIG. 63. N anocrystaUine TiO2-sample befo re and after compression at 810°C for 15 hr w ith a stress

of 40 MPa . The initial crystal size was a bou t 40 nm. ss)




was repor ted in Al203 at 1,750 -1,950 °C, ¢39°) A1 20 3 do pe d wi th Cr203 a n d Y303 at 1,500°C 391)

and M gO do pe d A1203 a t 1 ,420°C. (392) On ly in ce ram ics w i th l iquid phases a t the in te rfaces

was super-p las t ic f low found a t lower tempera tures3393)

Duc t i l e nanoc rys ta l l ine ce ramics may be used a s a new type o f ce ramic ma te r i a l in the i r

ow n r igh t. Ho we ve r , t he p la s t i c i ty may a l so be u t il iz ed fo r p roces s ing by ex t rus ion o r ro l ling.

Subsequen t ly , the ma te r i a l may be fu l ly o r pa r t i a l ly conve r t ed back in to a conven t iona l

ceramic . Par t ia l convers ion (e .g . by surface annea l ing) resul ts in a mater ia l which exhibi ts

a t the su r face the p rope r t i e s (e.g . ha rdnes s and chemica l r e s is t iv i ty ) o f a conven t iona l

ceramic . T he in te r io r o f such a mater ia l w ou ld s ti ll be duc t i le . I f gra in grow th is inhib i ted ,

t h e n a n o c ry s t a ll i n e m o r p h o l o g y a n d p r o p e r t i e s m a y b e m a i n t a i n e d p e r m a n e n t l y a n d a t

t empera tu re s up to the me l t ing po in t .

Th i s ap pro ach dev ia te s f rom the conven t iona l s t r a t egy to de fea t the b r it t lenes s o f c e ramics

b y i m p r o v e m e n t s i n p r o c e s s in g a n d c o m p o s i t io n . M a c r o d e f e c t- f r e e c e m e n t , c h e m i ca l ly

m odi fied s i l icon n itrides an d tra ns fo rm ati on -to ug he ne d zirconia, ~322'323) rep rese nt succe ssful

imp rovem en ts b a sed o n the se two s t rat eg ie s . The l a s t o f the se was o r ig ina l ly p ropo sed ¢324)wi th

the p rovoc a t ive t it le Ce ram ic s t ee l? , because do pe d z i rcon ia , li ke h igh -t ensi le s t ee l, depen ds

on a pa r t i a l phase t r ans fo rma t ion to t emper s t reng th wi th shock re s i s t ance : an advanc ing

c rack t rigge rs a loca l t r ans fo rm a t ion wh ich h inde rs fu r the r p rop aga t io n o f the c rack . Non e

of the se imp rovem en ts ha s gone fa r en ough . J ack (321) de sc r ibed the t e chno log ical , e conom ic

and o rgan iza t iona l p rob lem s , tha t d imm ed the p rom ise o f s il icon n i tr ide, wh ich has now

been the ce ramic o f the decade fo r th ree decades . The ce ramic eng ine , ou t s ide J ap an a t l e as t ,

s t i l l seems a long way from prac t ica l rea l iza t ion . Obvious ly , there i s s t i l l a scope for new

ap pro ach es. 025)

4.10.5.

lastic deform ation o f nanocrystalline metals

Th e plas t ic de for m at io n of na nocry s ta l l ine m eta ls h as been s tudied ~326) for Ni wi th a gra in

s ize o f abo u t 70 nm. The s t re s s - s t ra in cu rves and the pos i t ron l if e time spec t ra we re me asu red

s i m u l t a n e o u sl y i n o r d e r t o o b t a i n i n f o r m a t i o n a b o u t t h e t y p e o f d ef e c ts c o n tr o l li n g t h e

de fo rm a t ion p roces s . The s t re s s - s t ra in cu rve (F ig . 64a ) di f fe r s f rom the one o f po lyc rys ta l line

Ni . I f t he load was rem oved , a r eve rs ib le s tra in recove ry o f abo u t 3% was no t i ced (F ig . 64)

i r re spec tive o f the nu m ber o f load ing cycle s. P rac t i c a lly no w ork ha rden ing occurs du r ing

de fo rm a t ion con t ra ry to po lyc rys ta l s o r sing le crys ta l s o f N i (F ig . 64b) . S imul taneous

mea surem en t s b y pos i t ro n ann ih i l a t ion revea led a h igh concen t ra t ion o f vacancy- like de fec t s

(F ig . 65) . I f t he s t re ss was 1 ,100 M Pa o r m ore , a new co m pon en t (z2 ~ 510 ps) in the po s i t ron

l if e ti m e s p e c t r u m w a s n o t ic e d . T h i s c o m p o n e n t w a s a s s o ci a te d w i t h t h e f o r m a t i o n o f v a c a n c y

c lus te r s . In t e rms o f the se re su l t s , t he de fo rma t ion p roces s was mode led (327'328) a s fo ll ow s.

At sma l l s t r e s s e s (~<I ,100MPa) , g ra in bounda ry s l id ing i s the dominan t de fo rma t ion

mo de re su l t ing in the emis s ion o f vacanc ie s due to c l imb o f g ra in bo un da r y d i s loca tions . A t

h igh s t re ss e s, t he se vacanc ie s conde nse in the fo rm o f c lust e r s. A ggrega te s o f such c luste r s

fo rm mic roc racks wh ich f ina l ly p rov ide the nuc le i fo r the b r i t t l e f rac tu re o f the ma te r i a l .

The re fo re , the p la s ti c i ty and s t reng th o f nanoc rys ta l l ine m a te r i a ls we re sugges ted to be

de te rmined p r imar i ly by the bounda r i e s and the i r phys icochemica l f ea tu re s and no t by

the m icros t ru c ture (e.g. the types of defec ts ) in the gra ins as in polyc rys ta l l ine mater ia ls .

The s t re s s necessa ry to in i ti a t e p la s ti c de fo rm a t ion in nanoc rys ta l l ine and po lyc rys taUine Pd

and Cu a s a func t ion o f g ra in s ize ha s been s tud ied by Ch oks i

et

a13329) n the grain size regime

f rom 25 ~ tm to 6 nm. The ques t ion o f in t e re s t was w he the r o r n o t the y ie ld s t re s s requ i red

to init ia te plastic flow is corre ctly pre dic ted by the H al l-P et ch relatio nsh ip (33°'331) in th e en tire

range o f g ra in s izes . The re su l ts ob ta ine d sugges t a dev ia t ion f ro m th is r e l a t ionsh ip be low




o

8 0 0

n

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2 0 0

t / 3

~ 6 0 o

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o 4 6 8 io

S T R A I N ( )

F it3 . 6 4 . S t r e s s - s t r a i n c u r v e o f a ) n a n o c r y s t a l l i n e N i

7 0 n m c r y s t a l s iz e ) a n d b ) p o l y c r y s ta U i n e N i 2 / ~ m

cry s t a l s i ze ) .°2~)

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m 8 0 0

t ~

n ¢

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350 /.00 1.50 500 x2, nc

POSITRON LIFETIME Ips]

FIG. 65. Positron lifetime in nanoc~stalline Ni (70 nm)

a s a f u n c t i o n o f t h e c o m p r e s s i o n ) st r e ss . T h e m a t e r i a l

i s t h e s a m e a s i n F i g . 6 4 . 326) T h e d e f o r m a t i o n c o r r e -

s p o n d s t o t h e s e c t i o n 1 o f t h e s t r e s s - s t r a i n c u r v e i n

F ig . 6 4 a .

a cr i t ical grain s ize, d* . In fact , for grain s izes d > d* the y ield s t ress increased (Fig . 66a)

inver se ly p rop or t i ona l t o d ~/2 as was p red i c t ed by the Hal l -Pe t ch r e l a t i onsh ip . However , fo r

d < d* the s t ress necess ary to in i t ia te p las tic f low beco m es smal ler as the grain s ize i s redu ced

(F ig . 66b). In o the r words , r educ ing the g ra in s ize hardens t he m ater i a l fo r d > d* a nd so f t ens

i t i n t he s ize r eg ime d < d* . Th i s e f f ec t was i n t e rp re t ed i n t e rms o f g ra in b ou nd ary s li d ing

an d di f fusional creep b y an alo gy to the p las t ici ty obs erve d in nan ocry stal l ine ceram ics 318)

discussed in the previous sect ion .

Na nocry s t a l l i ne i ron whi sker s (5 -30 nm crys t a l size) p rod uce d by a che mica l vapor

depos i t i on t echn ique ,°32) show ex t ao rd inary s t r eng th u p to 8 G P a . (333) Th e g r a i n b o u n d a r i e s

be tween ne ighbor ing 0 t - i ron c rys t a l s and the phase boundar i es be tween the ~ t - i ron and the

prec ip i ta t es seem to be severa l i n t e ra tom ic spac ings wide and seem to co n ta in m ixed meta l li c

an d co v a l en t b o n d i n g .

4 11 K ine t i c E f f e c t s

The observa t ion o f phase t r ans i ti ons a l t e red by the p resence o f a h igh dens i t y o f g ra in

boun dar i es has b een r epo r t ed fo r severa l a l l oy sys t ems wi th and wi tho u t p las t ic defo rm at ion .

A nano crys t a l l i ne mix tu re o f Co and Te c rys t a ls ( average c rys t a l size 50 nm ) sub jec t ed

t o p l a s t i c d e f o r ma t i o n w as n o t i ced°34) to resul t in the form at io n o f the CoTe2 pha se in a

t em pera tu re r eg ime whe re t he d i f fus iv i ty is neglig ib le . The observed ph ase t r ans i t ion was

a t t r i bu t ed t o a h igh su per sa tu ra t i on ( /> 10 -4 ) o f vacanc i es. Gra in bo un da ry m igra t i on was

s u g g es t ed t o b e t h e mech an i s m o f v acan cy f o r m a t i o n . (335-337) Na nocrys t a l l i ne 0 t -Fe ( average

crys t a l size 100 nm ) , de fo rm ed by ro ll ing a t p ressu res o f abo u t 2 ,000 M Pa (a t amb ien t

t emp er a t u r e ) , ex h i b it ed a p o l y mo r p h i c t ran s f o r m a t i o n f ro m ~ ( - F e co n t a i n in g 3 2 7 - F e

(be for e rol l ing) to 0t-Fe co nta inin g 8 7-F e (after rol l ing), 33s)

A th in b i sm uth f ilm depos i t ed on na nocrys t a l l i ne Pd w a s f o u n d (3 7 ) by he l ium back-

sca t t e r ing t o fo rm the equ i l i b r ium in t e rme ta l li c Pd3 B i a t m uch lower t em pera tu re s (395 K)

than in evap ora t ed t h in f i lm samples. S imi l a r ly , in nano crys t a l l i ne mix tu res o f Cu and Er




(a)

25

90

85

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325

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175

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6020 0 5 0.30 0.35 04 0 0.45 ).50 0.20 0.25 0.30 0.35 0.40

d -1/2 [pro) 1/2 d v2 (nm)1/2

F IG . 6 6 . V a r i a t i o n o f h a r d n e s s o f C u a n d P d a s a f u n c t i o n o f g r a i n s i z e i n t h e r e g i m e o f c o n v e n t i o n a l

p o l y c r y s t a l s a ) a n d o f n a n o c r y s t a l l i n e m a t e r i a l s b ) . I t m a y b e n o t i c e d t h a t t h e h a r d n e s s i n c r e a s e s w i t h

d e c r e a s i n g g r a i n s i z e f o r c o n v e n t i o n a l p o l y c r y s t a l s . T h e c o n t r a r y a p p l i e s f o r t h e n a n o c r y s t a l l i n e

samples. 329)

c r y st a ls , t h e f o r m a t i o n o f th e e q u i li b r iu m C u E r c o m p o u n d w a s n o t ic e d ( u si n g X - r a y

d i f f rac t ion ) a f t e r compac t ion . Th i s expe r imen t shows tha t the ine r t ga s condensa t ion me thod

(cf . Sec t ion 2 .1 .2) i s c l ean enough to sub sequen t ly reac t pa r ti c l e s w i th one a no the r , even when

h igh ly reac tive me ta l s l ike Er a re be ing used . I t a l so dem ons t ra t e s tha t the in te rmix ing o f the

pa r t i cl e s o f two m e ta l s in the convec t ive he l ium-gas f low and on the ro ta t ing co ld f inge r is

su f f i c i en t to a lmos t to t a l ly reac t the powder by compac t ion a lone .

T h e f o r m a t i o n o f m e t a s ta b l e f a c e - c e n te r e d -c u b i c ( fc c) c h r o m i u m a n d v a n a d i u m

s t ruc tu re s ha s b een repo r ted fo r th in s andw ich l aye rs o f these ma te r i a ls on fcc subs t ra t e s

(gold , s i lver) (339) and is be l ieved to resul t f rom the e las t ic coupl in g be tw een the subs t ra te

l a t t i c e and the ch romium or vanad ium la t t i c e , r e spec t ive ly . S imi la r obse rva t ions on the

f o r m a t i o n o f n e w p h a s e s h a v e b e e n r e p o r t e d b y T r u s o v

e t a l

fo r o the r a l loy s y s t e m s . (336 337 340)

Fo r example , (34°) annea l ing o f nanoc rys ta l l ine mix tu re s o f Cu (15 nm ) and Ni (50 nm )

hom ogen ized s eve ra l o rde rs o f ma gn i tud e fa s t e r than an t i c ipa ted f rom bu lk d i f fus iv ity .

T h e r a p i d h o m o g e n i z a t i o n w a s i n t e r p r e t e d t o r e s u l t f r o m a h i g h s u p e r s a t u r a t i o n o f

vacanc ies .

Phase t r ans fo rma t ions o f the mar tens i t i c type s eem to be p reven ted by nanoc rys ta l l ine

m o r p o h o l o g i e s . A c o m p a r a t i v e s t u d y b y m e a n s o f h i g h a n d l o w t e m p e r a t u r e X - r a y

diff rac t ion (341) of the ma rtens i t ic pha se t ran s i t ion in F e- N i a l loys wi th N i co nten ts b e tw een

31 and 36 w t wi th a c rys ta l s iz e o f 4n m , a coa rs e -g ra ined po lyc rys ta l and i so la ted

nanom e te r - s i zed (7 nm ) c rys ta l s w i th the s am e chemica l compo s i t ion em bed ded in pa raf f in

led to the fo l lowing re su lt . The mar tens i t i c phase t r ans i t ion f rom ? -F e ( fcc s t ruc tu re ) to c t -Fe

(bcc s t ruc tu re ) obse rved in the coa rse -g ra ined po lyc rys ta l dose no t occu r in the i so la t ed

nanom e te r - s i zed c rys ta l s a s we l l a s in the nanoc rys ta l l ine m a te r i a l o b ta ined by conso l ida t ion

of the nan om e te r - s i zed c rys ta l s . Tw o rea so ns a re conce ivab le fo r th i s e f fec t. The sma l l c rys ta l s

a s we l l a s the nanoc rys ta l l ine ma te r i a l s do no t con ta in su i t ab le nuc lea t ion s i t e s fo r the

a-ph ase . Al te rna t ive ly , the gro w th o f the a -p ha se in inhib i ted . Prev ious s tudies 042-345) on

the nuc lea t ion o f mar tens i t e in nanome te r - s i zed c rys ta ls have g iven ev idence to a l a ck o f

nuc lea t ion s i t e s . Growth inh ib i t ion i s conce ivab le in the nanoc rys ta l l ine ma te r i a l due to

cons t ra in t s fo r the fo l lowing rea sons . Imag ine a po lyc rys ta l l ine s t ruc tu re o f ? -F e c rys tal s

wi th a few nan om e te r d iame te r . I f one o f the se c rys ta l s t r ans fo rm s b y a mar tens i ti c shea r

p roces s in to an c t -Fe s t ruc tu re , i t ha s to be shea red e l a s t i c a l ly , p l a s t i c a l ly o r by bo th shea r



3 4


modes to ma in ta in compa t ib i l i t y w i th the su r round ing (ye t un t rans fo rmed ~-Fe c rys t a l s ) .

Bo th , the e last ic or the p last ic sh ear require unrea l is t ica l ly h igh s hear s t resses . I f the

mar tens i t i c shea r i s 0 .7 , a s imp le e s t ima te shows tha t t he e l a s t i c shea r ene rgy to ma in ta in

com pa t ib i l i t y o f the t r ans fo rm ed c rys t a l w i th the ne ighbor ing o nes wou ld be l a rge r than the

la t en t hea t o f fu s ion . S imi la rly , p l a st i c shea r o f an Fe c rys t a l w i th a d i am e te r o f a f ew nm

requ i re s s t r e sse s c lose to the theo re t i c a l sh ea r s t r e ss due to the ene rgy o f the s lip s t eps

fo rmed a t t he bounda r i e s . As ad jacen t c rys t a l s have d i f fe ren t c rys t a l log raph ic o r i en ta t ions ,

a mar t ens i t i c t r a ns fo rm a t ion by shea r ing seve ra l c rys t a ls coope ra t ive ly seems to be imposs -

ib le . The s t ab i l iz a t ion o f the aus ten i t i c phase by the nanoc rys ta l l ine m orp ho logy m ay be o f

t echno log ica l i n t e res t . T he c r i t ic a l t em pe ra tu re o f A 15 o r B 1 supe rcond uc to r s ( e.g . Nb3 Sn o r

V3 S i ) i nc rea se s i f t he so lu te concen t ra t ion i s enhanced . Ho wev e r , t he enh ancem en t is l imi t ed

by the m artensi t ic pha se t ransi t ion a t h igher Sn or Si concentrat ions335s '359) This marten si t ic

phase t r ans i t ion m ay be p reven ted in nanoc ry s ta l l ine N i3 Sn o r V3Si a l loys .

4.12. R e c r y s t a l l i z a t i o n

The rec rys t a ll i z a tion o f nanoc rys t a l l ine m e ta l s ha s been inves t iga ted by seve ra l au tho rs .

Neve r the le ss , t he unde rs t and ing seems to be s til l f r agm en ta ry and the in t e rp re t a t ion o f the

ex i s ting obse rva t ions i s con t rove rs i a l . S om e o f the expe r imen ta l ob se rva t ion s a re r ev iewed in

Sec t ion 3 .5 on th e the rma l s t ab i l it y o f nanoc rys t a l l ine m a te r ia l s . In a se r ie s o f p a p e r s ~34° 346 347)

pub l i shed in the Sov ie t Un ion , t he v iew i s adv oca ted tha t a h igh supe rsa tu ra t ion o f vacanc ie s

i s the m os t s ign if i can t p roces s occu r r ing du r ing rec rys t a ll i z a tion o f nanoc rys t a l l ine m e ta ls .

Po si t ro n an nihi la t ion m easu rem ents were c la imed ~348) o evidence the vacan cy sup ersa tura t io n

dur ing rec rys t a ll i z a tion o f nanoc rys t a l l ine N i ( c rys t a l s iz e 15 nm) . P r io r to annea l ing the

pos i t ron l i f e time spec t ra o f the nanoc rys ta l l ine N i cons i s t ed o f two co m pon en t s ( l i fe t imes and

intensit ies ~i = 138 + 3 pse c, 11 = 55 + 2% an d z2 = 281 + 10 psec, I = 45 + 2% ) . These

t w o c o m p o n e n t s w e r e in t e r p r et e d t o a r is e f r o m t h e a n n i h i la t io n o f p o s i tr o n s c o m i n g f r o m

the bu lk and the in t e rface s be tw een the N i c rys t a l s , re spec tive ly . Af te r annea l ing the spec imen

fo r 200 min a t 300°C in vacuum , the sp ec t rum show ed a sha rp inc rease o f the li f et ime and

i n te n s i ty o f t h e s h o r t- l iv e d c o m p o n e n t u p t o T I = 1 88 + 6 % p s e c , I~ = 8 6 + 3 % . N i c k e l

fo i l s (99 .99%) sub jec ted to annea l ing and p la s t i c de fo rma t ion (40%) were obse rved to

exh ib i t pos i t ro n l if e times o f 134 and 183 psec , re spec tive ly . Thus , t he hea t ing to 300°C o f the

nanoc rys ta l l ine spec imens was sugges ted to have re su l t ed in a de fec t s t ruc tu re (vacancy

conce n t ra t ion ) ch a rac te r i s ti c o f heav i ly de fo rm ed Ni . S tud ie s o f the mic ro s t ruc tu re b y

scann ing e l ec t ron m ic rosco py revea led c rys t a l g rowth f rom 15 nm (20°C) to 150 nm (300°C)

and 200 nm (500°C) . The phys ica l r e a son fo r the h igh vacancy supe rsa tu ra t ion was p ropo sed

t o b e t h e a t h e rm a l e m i s s io n o f v a c an c i es f r o m g r a i n b o u n d a r y d i s lo c a t io n d u r i n g b o u n d a r y

m igra t ion , t349~ The dr iv ing forc e for th is proce ss w as pr op os ed to b e the redu c t ion o f the

to ta l f r ee ene rgy o f the sy s t em due to g ra in g row th . In f ac t, ev idence fo r the emiss ion o f

non-equ i l ib r ium vacanc ie s by mig ra t ion bounda r i e s ha s been p re sen ted p rev ious ly in

con ven t ion a l polyc rysta ls . °5°> This e ffec t was ra t iona l ized in te rms of gro wt h acc idents ~351)

which i s phys ica lly s imi l a r to the c l imb o f g ra in b ou nd a ry d i s loca tions . Du r ing rec rys t al li z -

a t i o n o f n a n o c ry s t a ll i n e m a t e ri a ls T r u s o v

e t a l . o52-3~

no t i ced the ra t e o f p l a s t ic de fo rm a t ion

to be enha nced by a fac tor o f ab ou t 104 re la t ive to m ater ia ls w i th a gra in s ize of I> 102 m .

Th i s enhan cem en t w as a t t r ibu ted to a h igh supe rsa tu ra t ion o f vacanc ie s . The vacanc ie s a re

proposed to be generated during recrystal l ization of the nanocrystal l ine materials33~'355'356)

The vacanc ie s a re env i s ioned to enhance d i s loca t ion c l imb p rocesse s and thus inc rea se the

ra t e o f p l a s t i c de fo rma t ion .



NANOCR YSTALL INE MATERIALS 305

4 13 Radiation Dam age

The s t ruc tu ra l changes induced by h igh -ene rgy ions (He , Ne , Ar , Xe ) in a nanoc rys t a l l ine

Fer0Cu40 a l loy (8 nm gra in s ize) w ere s tudie d by resis t iv ity me asure m ents . (357) I r rad ia t ion

wi th heavy ions re su l t ed in a r ap id re s i s t iv i ty dec rea se w i th inc rea s ing dose s whe rea s l i gh t

ions had p rac t i c a l ly no e f fec t. Th i s d i f fe rence m ay be unde rs to od in t e rms o f the a tom ic

rea r rangem en t s induced b y the ca scade e f fec t s in the g rain bound a r i e s . T he d iam e te r o f the

cascades was fo r Ne , A r and Xe ab ou t th ree t imes the c rys t a l si ze o f the ma te r i a l. He nce eve ry

cascade com pr i se s seve ra l g ra ins . I f t he in i ti a l h igh re s is t iv i ty ( a bo u t 200 # f~ cm) i s p r imar i ly

d u e t o t h e l o w c o n d u c t i v i t y o f th e b o u n d a r y r e g io n s , t h e m a t e r ia l m a y b e c o n s i d e r ed a s a

t w o c o m p o n e n t s y s t e m c o n si s ti n g o f h i gh l y c o n d u c t i v e c r y st a ls e m b e d d e d i n a m a t r i x o f g r a in

b o u n d a r i e s w i t h l o w c o n d u c t i v i t y . D u r i n g c a s c a d e f o r m a t i o n , a t o m s i n t h e g r a i n s a s w e l l

a s boun da r y a tom s a re d i sp laced l ead ing to a s t ruc tu ra l m od i f i ca t ion o f the in t e r face s . I f

the new in te r fac ia l s t ruc tu re ha s an enhanced e l ec t r i c conduc t iv i ty , c a scade fo rma t ion l e ads

to the fo rm a t ion o f cond uc t ive links be tw een the g rains and f in a l ly - -a t h igh ca scade

c o n c e n t r a t i o n s - - a p p r o a c h e s t h e p e r c o l a ti o n l im i t. T h i s p i c t u r e is s u p p o r t e d b y t w o e x p er -

imen ta l f a c t s . In the ca se o f He ion i r r ad ia t ion no ca scad es and v e ry few a tom ic rea r range -

me n t s a re in t roduced . He nce the c r i ti c a l numb er o f cond uc t ive links cann o t b e ach ieved even

a t h igh dose s and no re s i s t iv i ty dec rea se w i l l be obse rved . On the con t ra ry , fo r heavy ions

and dense d i sp lacemen t ca scades , t he c r i t i c a l l i nk dens i ty w i l l be ach ieved a t l ower dose s i f

heav ie r ions we re imp lan ted . Indeed , t he pe rco la t ion occur red fo r Xe a t 0 .01 dpa in s t ead o f

0 .0 2 d p a f o r A r i o n s o f c o m p a r a b l e e n e rg y .

5 NANOGLASSES

By ana log y to nanoc rys ta l l ine ma te r ia l s , the gene ra t ion o f g l a sse s ca l led nano g la sse s was

recent ly pro po sed . °°'395 396) Th e pro du ct io n of such a g lass w as carr ied ou t by a s imi la r

p roc edu re a s de sc r ibed in F ig . 8 . I f the ma te r i a l e vap ora ted ha s the ab i l i t y to fo rm a g lass

u p o n r a p i d c o o l i n g , t h e e v a p o r a t i o n a n d s u b s e q u e n t r a p i d c o o l i n g p r o c e s s i n t h e h e l i u m

a t m o s p h e r e l e a d s t o t h e f o r m a t i o n o f n a n o m e t e r- s i z ed g l as s y d r o p l e t s r a t h e r t h a n n a n o m e t e r -

s i zed c rys ta l li t es . S ubse quen t con so l ida t ion o f the se d rop le t s r e su l t s i n a g l a ssy so lid w i th

enhanc ed f ree vo lum e . The enhan ced f ree vo lum e o r ig ina tes f ro m the mechan ica l shea r o f the

d r o p l e t s d u r in g c o m p a c t i o n a n d t h e r e g i o ns o f c o n t a c t b e t w e e n a d j a c e n t d r o p le t s. T h e c o n t a c t

reg ion be tween two d rop le t s d i f fe r s s t ruc tu ra l ly and /o r chemica l ly f rom the a tomic s t ruc tu re

in the cen t re o f the d rop le t s fo r the fo l lowing rea son (F ig . 67) . The su r face a toms o f an

i so la t ed g la ssy d rop le t i n a vacuum fo rm a g la ssy ( sho r t r ange o rde red ) a tomic a r rangemen t

wi th the a tom s in the in t e rio r o f the d rop le t so tha t c e r t a in in t e ra tomic spac ings a re p re fe r red

be tw een the su r face a toms and the a tom s in the in te r io r, I f two (o r ig inal ly i so la t ed ) g l assy

drop le t s a re b roug h t in to con tac t ( e .g . con tac t r eg ion be twee n A and B) , t he in t e ra tomic

spac ings be tween the su r face a toms be long ing o r ig ina l ly to the two d i f fe ren t d rop le t s d ev ia t e

f rom the in t e ra tomic spac ings be tween the a toms in the in t e r io r due to the mis f i t be tween A

a n d B . A l t h o u g h s o m e r e l a x a ti o n a l m o t i o n o f th e a t o m s i n t h e r e g io n o f c o n t a c t o c c ur s , a

d i f fe ren t d i s t r ibu t ion o f in t e ra tomic spac ings in the in t e rfac ial r eg ions re su l t s in com par i son

to a bu lk g la ss w i th the same chemica l compos i t ion . S imi la r a rgumen t s app ly to the a tomic

s t ruc tu re o f a reg ion in wh ich a g l a ssy d rop le t i s mech an ica l ly shea red du r ing c om pac t ion .

D ue to the non-pe r iod ic s t ruc tu re o f a g l ass , a r eg ion o f enhanced f ree vo lum e is gene ra ted

as is know n f ro m the s t ruc tu re o f shea r ban ds in me ta l l ic g l asse s. In f ac t, by ana logy to the

s t ruc tu re o f nanoc rys t a l l ine m a te r ia l s , t he a tom ic s t ruc tu re o f the in t e rfac ia l r eg ions be twe en




B

FIG. 67. Schematic cross section through a two-d imensional nanog lass. The atoms are rep resented by

circles. Th e material con sists o f sma ll regions in the interior o f which full circles) the interatomic

spacings are similar to a bulk glass. In the interfacial region broken lines, open circles) a bro ad

spectrum of interatomic spacings exists.

t h e d r o p l e t s a n d t h e r e g io n s o f m e c h a n i c a l s h e a r a r e p r o p o s e d t o e x h ib i t a b r o a d d i s tr i b u t i o n

o f i n t e r a t o m i c s p a c i n g s F i g . 6 7 ). T h i s s p e c u l a t i o n a g r e e s w i t h r ec e n t m e a s u r e m e n t s b y

M 6 s s b a u e r s p e c t r o s c o p y . 396)

T h e o b s e r v e d M 6 s s b a u e r s p e c t r a o f a Pd 75 Si2 5 n a n o g l a s s d o p e d w i th F e a n d t h e co r r e s -

p o n d i n g q u a d r u p o l e s p l i tt in g d i s t r ib u t i o n a r e s h o w n i n F ig . 68 b , in c o m p a r i s o n t o th e

s p e c t r u m o f a c h e m i c a l ly id e n t i ca l g la s s p r e p a r e d b y m e l t s p i n n i n g F i g . 68 a ). O b v i o u s l y b o t h

m a t e r i a l s e x h i b i t d i f f e re n t s p e c t r a a n d d i f fe r e n t d i s tr i b u t i o n s o f t h e q u a d r u p o l e s p l i tt in g .

I n f ac t , t h e q u a d r u p o l e s p l i t t i n g o f th e n a n o g l a s s m a y b e c o n s i d e r e d a s a s u p e r p o s i t i o n

o f t h e f o l lo w i n g tw o c o m p o n e n t s ; o n e n a r r o w ) c o m p o n e n t s o li d l i ne i n F ig . 6 8 b ) w h i c h

1 . 0 0

0 .98

._o

•~ 0.96

r-

1 . 0 0

_~ 0.97

¢u

n -

0.94

f I I I , , 1 I

-2 -1 0 1 2 0 1

Vel0ci~y [mm/s] 0S [ram/s]

FIG. 68. a) M6ssb auer spectrum a nd distribution, p QS), o f the quadrupole spl i tt ing SQ ) of a

m elt spu n PdToFe3Si27 me tallic glass ,o~) b) M6ssbauer spectrum and distribution,

p QS),

of the

quadrupole spl it ting QS ) of a nanoglass with the same chemical composit ion as in a). The diameter

of the droplets used to generate the glass was about 4 nm .o~) The q uadrupole spl it ting consists of two

components. A narrow one sol id l ine) similar to the quadrupole spl it ting of a) and a b road

com ponen t broken line, hatched area) which is observed in the nanog lass only.o~)

,q

D

t:2.

I

2



N NOC RYST LL INE M TERI LS

307

corresponds to a conventional (e.g. melt-spun) glass, and a second broad component (broken

line in Fig. 68b) which is observed in the nanoglass only. This result may be understood as

follows. The quadrupole splitting is known to depend on the nearest neighbor configuration

only. Hence, the nanoglass consists structurally of two components. One component in which

the atoms are arranged similarly to a Pd-Si-glass generated by melt spinning. In the second

component, the distribution of the interatomic spacings between nearest neighbors is

much wider than in the melt-spun glass as suggested by the broad distributions of the

quadrupole splitting. If this broad distribution is due to the interdroplet region, the structure

of the nanoglass may be manipulated in a controlled way as follows. The volume fraction

of the interdroplet region decreases if the droplet size is made larger. As a consequence, by

varying the diameter and/or chemical composition of the consolidated glassy droplets, the

relative volume fractions of the glassy and the broad second component can be manipulated.

In other words, by varying the size of the glassy droplets used for consolidation, one may

be able to vary (at constant chemical composition) the atomic structure of nanoglasses

continuously between the short-range ordered structure of a conventional glass and structure

with a broad distribut ion of interatomic spacings. If the chemical composition of the surface

region of an isolated glass droplet differs from the interior o f the droplet (e.g. due to surface

segregation effects), the interfacial regions deviate chemically as well as structurally from

the center.

Although the atomic structure of nanoglasses has been discussed in similar terms as

was done for nanocrystalline materials, there seems to be the following fundamental

difference between both materials. As was pointed out in the first section, nano-

crystalline systems preserve the low energy structure in the interior o f the crystallites at the

expense of the boundary regions where the misfit between adjacent crystal lattices is

concentrated so that a structure far away from equilibrium (with a large free volume and a

broad distribut ion of interatomic spacings) is formed. In the case of nanoglasses, the glassy

interior of the droplets (Fig. 67) is not a low energy structure. Hence the atomic misfit of

the transition region between adjacent glassy droplets (e.g. between A and B in Fig. 67)

in the as-consolidated state may not remain in this region if the nanoglass is held for

some time at ambient temperature. In fact, the diffusional rearrangement of individual

atoms may allow the system to redistribute the misfit and free volume from the interfacial

regions to other regions within the structure in order to reduce the total free energy of the

systems. Hence some time after consolidation, the nanoglass may have lost its structural

memory to the initial state in the sense that the free volume distribution of the as-compacted

state is replaced by a new free volume distribution of lower free energy. In fact, such

rearrangements have been observed in computer simulations of glassy structures into which

vacancies or dislocations have been introduced by removing an atom or by local shear.

In other words, nanoglasses may exhibit structural features which differ from the ones of

nanocrystalline materials as well as from glasses prepared by one of the conventional

methods.

CKNOWLEDGEMENTS

The financial support by the BMFT (Contract No. 03 M 00234) and the Deutsche

Forschungsgemeinschaft (G. W. Leibniz program) is gratefully acknowledged. The author

appreciates the numerous helpful discussions with colleagues from various laboratories in

Germany, Japan and the United States. He also would like to thank Professor P. Haasen

for reading the manuscript and for suggesting several modifications.



3 8


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