Imperfections in Solids [Autosaved]

7/24/2019 Imperfections in Solids [Autosaved]

1/59

Imperfections in

Solids


2/59

Why Study Imperfections inSolids? The properties of some materials are profoundly inuenced b

the presence of imperfections. Consequently, it is important t

have a knoled!e about the types of imperfections that e"ist anthe roles they play in a#ectin! the behavior of materials. $o

e"ample, the mechanical properties of pure metals e"periencsi!ni%cant alterations hen alloyed &i.e., hen impurity atom

are added'(for e"ample, brass &)*+ copper-*+ inc' is mucharder and stron!er than pure copper &Section )./'. 0ls

inte!rated circuit microelectronic devices found in ou

computers, calculators, and home appliances function because hi!hly controlled concentrations of speci%c impurities that ar

incorporated into small, localied re!ions of semiconductinmaterials


3/59

three basic types ofimperfections1 0D --- point defects,

1D --- line defects (or dislocations), and

2D --- surface defects

3D --- bulk/volume defects


4/59

23I4T 56$6CTS

2oint defects are localied disruptions in otherisperfect atomic or ionic arran!ements in a crystastructure

These imperfections may be introduced by movemenof the atoms or ions hen they !ain ener!y by heatin!

durin! processin! of the material, or by the intentionaor unintentional introduction of impurities.


5/59

IM!"I#I$%are elements or compounds that are present from ramaterials or processin!. $or e"ample, silicon crystals !ron inquart crucibles contain o"y!en as an impurity.

D&'#%, on the other hand, are elements or compounds that aredeliberately added, in knon concentrations, at speci%c locations i

the microstructure, ith an intended bene%cial e#ect on propertiesor processin!


6/59

T726S 3$ 23I4T 56$6CTS

8. 90C04CI6S

:. I4T6;STITI0< 0T3=

-. S=0STIT>TI340< 0T3=

@. STIT>TI340< 0T3=

B. $;646< 56$6CT

D. SCE3TT7 56$6CT


7/59

90C04CI6S

0 vacancy is produced hen an atom or an ion is missin! from itsnormal site in the crystal structure


8/59

The equilibrium number of vacancies for a !iven quantity ofmaterial depends on and increases ith temperature accordin! to


9/59

6F0=2


10/59


11/59

6F0=2


12/59


13/59

I4T6;STITI0< 56$6CT

0n interstitial defect is formed hen an e"tra atom orion is inserted into the crystal structure at a normallyunoccupied position


14/59

Interstitial atoms or ions, althou!h much smaller than the atoms oions located at the lattice points, are still lar!er than the interstitialsites that they occupyM consequently, the surroundin! crystal re!iois compressed and distorted.

Interstitial atoms such as hydro!en are often present as impuritieshereas carbon atoms are intentionally added to iron to produce

steel. $or small concentrations, carbon atoms occupy interstitialsites in the iron crystal structure, introducin! a stress in thelocalied re!ion of the crystal in their vicinity


15/59

6F0=2


16/59


17/59


18/59

S>STIT>TI340< 56$6CT

0 substitutional defectis introduced hen one atom oion is replaced by a di#erent type of atom or ion. Thsubstitutional atoms or ions occupy the normal latticsite. Substitutional atoms or ions may either be lar!ethan the normal atoms or ions in the crystal structure, ihich case the surroundin! interatomic spacin!s arreduced, or smaller causin! the surroundin! atoms thave lar!er interatomic spacin!s.


19/59


20/59

3TE6; 23I4T 56$6CTS

0n interstitialcis created hen an atom identical to those at thenormal lattice points is located in an interstitial position. Thesedefects are most likely to be found in crystal structures havin! a lopackin! factor.

0 *renkel defectis a vacancyJinterstitial pair formed hen anion Numps from a normal lattice point to an interstitial site, leavin!behind a vacancy. 0lthou!h, this is usually associated ith ionicmaterials, a $renkel defect can occur in metals and covalentlybonded materials


21/59


22/59

0 %c+ottk defectis unique to ionic materials and is commonlyfound in many ceramic materials. When vacancies occur in anionically bonded material, a stoichiometric number of anions andcations must be missin! from re!ular atomic positions if electricalneutrality is to be preserved. $or e"ample, one =!O: vacancy andone 3J: vacancy in =!3 constitute a Schottky pair. In Pr3:, for onePrO@ vacancy, there ill be to 3J: vacancies.


23/59


24/59


25/59

SC;6W 5IS


26/59


27/59


28/59


29/59

65A6 5IS


30/59


31/59


32/59


33/59

=IF65 5IS


34/59

>;A6;S 96CT3;

JJJJ The displacement vector that Qcloses the loopR hen traversin!an equal number of lattice steps around the defect

JJJJ denoted by QbR

JJJJJ it is parallel in the line of dislocation in scre dislocation and isperpendicular in the line of dislocation in ed!e dislocation


35/59

ur!ers vector in scredislocation


36/59

ur!ers vector in ed!e dislocation


37/59

6"ample1

Calculate the len!th of bur!er vector in copper &$CC crystalstructure'


38/59

S C C S


39/59

S>;$0C6 56$6CTS

Surface defects are the boundaries, or planes, that separate amaterial into re!ions. $or e"ample, each re!ion may have the samecrystal structure but di#erent orientations

8. =aterialL6"ternal Surface

:. Arain oundaries

-. Tin oundaries

@. Stackin! fault

=0T6;I0;$0C6


40/59

=0T6;I0;$0C6

3ne of the most obvious boundaries is the e"ternal surface, alon!hich the crystal structure terminates. Surface atoms are notbonded to the ma"imum number of nearest nei!hbors, and aretherefore in a hi!her ener!y state than the atoms at interiorpositions. The bonds of these surface atoms that are not satis%ed!ive rise to a surface ener!y, e"pressed in units of ener!y per unitarea &Lm: or er!Lcm:'.To reduce this ener!y, materials tend to

minimie, if at all possible, the total surface area. $or e"ample,liquids assume a shape havin! a minimum area(the dropletsbecome spherical. 3f course, this is not possible ith solids, hichare mechanically ri!id.

A;0I4 3>450;I6S


41/59

A;0I4 3>450;I6S

0 rain boundar, the surface that separates the individual !rainis a narro one in hich the atoms are not properly spaced. That to say, the atoms are so close to!ether at some locations in the!rain boundary that they cause a re!ion of compression, and inother areas they are so far apart that they cause a re!ion of tensio

0rain is a portion of the material ithin hich the arran!ement othe atoms is nearly identicalM hoever, the orientation of the atomarran!ement, or crystal structure, is di#erent for each adNoinin!!rain


42/59


43/59

3ne method of controllin! the properties of a material is by controlthe !rain sie. y reducin! the !rain sie, e increase the number

!rains and, hence, increase the amount of !rain boundary area. 0n

dislocation moves only a short distance before encounterin! a !rai

boundary, and the stren!th of the metallic material is increased. Thall-etc+ e.uation relates the !rain sie to the yield stren!th,

here y JJJJ is the yield stren!th &the level of stress necessary to ca certain amount of permanent deformation',

d JJJJJJ is the avera!e diameter of the !rains, and

* and JJJJJJare constants for the metal


44/59

6"ample


45/59

6"ample1

The yield stren!th of mild steel ith an avera!e !rain sie of *.*Bmm is :*,*** psi. The yield stress of the same steel ith a !rainsie of *.**) mm is @*,*** psi. What ill be the avera!e !rain sieof the same steel ith a yield stress of -*,*** psi? 0ssume the Eal2etch equation is valid and that chan!es in the observed yieldstress are due to chan!es in !rain sie.


46/59

& ti l i i t h i th t i d t l i


47/59

&ptical microscop is one technique that is used to reveal microfeatures such as !rain boundaries that require less than about :**

ma!ni%cation. The process of preparin! a metallic sample and obse

recordin! its microstructure is called metallorap+. 0 sample of material is sanded and polished to a mirrorJlike %nish. The surface

e"posed to chemical attack, or etchin!, ith !rain boundaries beinattacked more a!!ressively than the remainder of the !rain.


48/59

3ne manner by hich !rain sie is speci%ed is the 0ST= !rain sienumber &0ST= is the 0merican Society for Testin! and =aterials'.The number of !rains per square inch is determined from aphoto!raph of the metal taken at a ma!ni%cation of 8**. The 0ST=!rain sie number n is calculated as

Where 4 is the number of !rains per square inch for ama!ni%cation of 8**"

n is the number of !rains per square inch.


49/59

0t a ma!ni%cation other than 8**" use1

Where1 4= is the number of !rains per square inch at ma!ni%catio=.

In addition, the inclusion of the term makes use of the fact that, hima!ni%cation is a len!th parameter, area is e"pressed in terms ofunits of len!th squared. 0s a consequence, the number of !rains perunit area increases ith the square of the increase in ma!ni%cation.

6"ample1


50/59

6"ample1

Computations of 0ST= Arain Sie 4umber and 4umber of Arains 2e>nit 0rea

&a' 5etermine the 0ST= !rain sie number of a metal specimen if@B !rains per square inch are measured at a ma!ni%cation of8**"

&b' $or this same specimen, ho many !rains per square inch illthere be at a ma!ni%cation of HB"?

&a'


51/59

&a'

&b'


52/59

&b'

e"ample


53/59

e"ample

Suppose e count 8D !rains per square inch in a photomicro!raphtaken at a ma!ni%cation of :B*". What is the 0ST= !rain sienumber?


54/59

Small 0n!le Arain oundaries


55/59

Small 0n!le Arain oundaries

0 small an!le !rain boundary is an array of dislocationsthat produces a small misorientation beteen theadNoinin! crystals. ecause the ener!y of the surface isless than that of a re!ular !rain boundary, the smallan!le !rain boundaries are not as e#ective in blockin!slip. Small an!le boundaries formed by ed!e dislocation

are called tilt boundaries, and those caused by scredislocations are called tist boundaries


56/59

Tin oundaries


57/59

Tin oundaries

0 tin boundary is a plane across hich there is a special mirrorima!e misorientation of the crystal structure


58/59

Tins result from atomic displacements that are produced fromapplied mechanical shear forces &mechanical tins', and also durinannealin! heat treatments folloin! deformation &annealin! tins'

'nnealin ---- 0 heat treatment that typically involves heatin! ametallic material to a hi!h temperature for an e"tended period oftime in order to loer the dislocation density and hence impart

ductility.

>


59/59

>

Imperfections in Solids [Autosaved]

Documents

Transcript of Imperfections in Solids [Autosaved]