THE EVOLUTTCN OF MTCROSTRUCTUREDURING SINTERING OF UO? AND TTS EFFECTUPON MECHANICAL AND Tl^ERMAL PROPEPTIES

By

IVavne D-oualas Tuchig

A Dissert -ition Presented to the Gradirrvtc Coun.the Univer>:ity of Florida

In Pari:5ai Fulfilln'ent ci the Requireiuents fo:

Decree of Doctor of Priilosonliv

Ur^IlVERSITY OF FLORIDA

1972

UNIVERSITY OF FLORIDA

lililillllililillll3 1262 08552 5854

Dedicated to my v-'ife, Candy,and to my parents,

Mr. and Mrs. K. J. Tuohig.

ACKNOWLEDGEMENTS

The author wishes to acknowledge the encouragement

and helpful discussions provided during the course of this

research by his chairnian , Dr. E. D. Whitney, and Dr. R. T.

DeHoff. Thanks are due also to Drs. L. L. Hench, J. J.

Hren, R. W, Gould and J. W. Flowers for serving on the

supervisory committee.

The assistance of S. M. Gehl with all aspects of this

work, and contributions by V.'. H. Halback and R. A, Graham

are sincerely appreciated.

Financial support from the United States Atomic

Energy Commission is gratefully acknowledged.

TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS iii

LIST OF TABLES vi

LIST OF FIGURES . vii

ABSTMCT xii

CHAPTER

I INTRODUCTION 1

1.1. The Nature of the SinteringProcess 1

1.2. Evolution of Microstructure ... 101.3. Effect of MicrostructuTC on

Mechanical and ThermalProperties ..... 17

1.4. Objective of the Present V/ork . . 29

II EXPERIMENTAL PROCEDURE 33

2.1. Material Characterization .... 332.2. Specimen Preparation 572.5. Evaluation of Geometric

Properties 622.4. Evaluation of Mechanical

Properties 752.5. Measurement of Thermal

Conductivity 79

III P.ESl'LTS AND DISCUSSION 85

3.1. Densif icati on Behavior ..... 853.2. The Metric Properties ...... 923.3. Mechanical Properties 1413.4. T-herTr.al Conductivity 157

TABLE OF CONTEXTS (continued)

CHAPTER

IV

APPENDIX

A

B

CONCLUSIONS AND SUMf-lARY

PRECIS I ON LATTICE PARAMETER PROGRAM

INTERPOLATED THEP^MAL CONDUCTIVITYOP PYROCERAM 9 606 IN INCREMENTS OF1° KELVIN OVER THE RANGE 300- 1200 °K

LIST OF REFERENCES

BIOGRAPHICAL SKETCH

Page

164

167

188

215

225

LIST OF TABLES

Table Page

1 Analytical Impurities in the Arc FusedUO- Used in this Investigation 34

2 As-received UO2 Powders were SeparatedInto Lots by Sieving 46

3 Surface Areas of the Three SizeFractions of UO^ 56

4 Metric Properties of UO? SpecimensProduced by Cold Compaction andSubsequent Sintering 93

5 Metric Properties of UO2 SpecimensProduced by Pressure Sintering at 3,000psi for 30 minutes at Various Tempera-tures 115

6 Metric Properties of UO2 SpecimensProduced by Pressure Sintering at 3,000psi at the Indicated Temperature forVarious Times 117

7 Metric Properties of Specimens PressureSintered at 5,000 psi From Fine Po'.vder

Lot 134

LIST OF FIGURES

Figure Page

1 Sequence of states through which asintering four-particle system passes . . 11

2 Structural evolution during usefullife of a UO- fuel pin 32

3 SEM photographs of -6 mesh as-receivedUO- powder 35

4 SF.M photographs of -200 mesh as -receivedpowder 36

5 Photomicrographs of -6 mesh as-receivedpowder 38

6 Photomicrographs of -270 +325 as-received powder 39

7 Phase diagram of the U-0 system for 0/Uratios between 2.0 and 2.25 41

8 Dependence of the lattice constant at25''C upon 0/U ratio for cubic UO- .... 42

9 Sinterings prepared from loose stacksof as-received UO2 sintered at 2250°C . . 48

10 SEM photos of powder from the three sizefractions employed in this investigation . 51

11 Schematic of the B.E.-T. apparatus usedto determine surface area 55

12 B.E.T. plot for fine size fraction ofUO^ powder 56

13 Punch and die assembly used to coldcompact UO^ 59

14 (a) The high temperature Astro sinteringfurnace !! . 61

(b) Centorr vacuum hot press 61

Vll

LIST OF FIGURES (continued)

Figure Page

15 Graphite and boron nitride die assembly-used to pressure sinter UO^ 63

16 Schematic illustration of the countingmeasurements on a sinter structure .... 67

17 Quantim^et display o£ a sintered UO^microstructure ~.

. . . 70

18 Metallograph- vidicon assembly 71

19 Distribution of stresses in a diamet-rally loaded cylinder 77

20 Precision centerless grinder u^ed tomachine UO- specimens 78

21 Comparative cut bar thermal conductivityapparatus 80

22 Temperature dependence of the thermalconductivity of Pyroceran 9606 83

23 Densification of three size fractionsof UO2 at constant heating rate followedby 5 minute arrest at 1800 '^C. pressuresintered at 3,000 psi at 10"^ torr .... 86

24 Variation of volume fraction of porosityas a function of temperature for threesize fractions of UO^ 88

25 Volume fraction of porosity as a

function of tim.e at temperature 90

26 Dependence of pore volum.e fraction ontime for isothermal pressure 3 in te rings . 91

2 7 The fam.il> of curves which define thepath of change during sintering of thesurface area per unit volum.e for theintermediate sized fraction 96

2 8 Ihe approach to the linear relationshipfor a spectrum of initial conditions ... 97

LIST OF FIGURES (continued)

Figure Page

29 Surface area per unit mass as a functionof volume fraction of porosity forspecimens prepared by compaction at theindicated pressure and sintering forvarious times and temperatures 99

30 Variation in microstructure for twodifferent paths of surface change .... 101

31 Evolution of microstructure along a

single path of structural evolution . . . 102

32 The family of curves which define thedependence of surface area on volumefraction of porosity for conventionallysintered coarse UO- powder 104

33 Average moan curvature as a function ofvolu;ne fraction porosity for UQt preparedby conventional sintering from the coarsesize fraction 107

34 Variation of average mean curvature withvolume fraction porosity for conven-tionally sintered interr?.ediate UO^powder T.... 108

35 Comparison of the dependence of curva-ture on pore volume fraction and particlesize for UO^ and dendritic copper .... 109

36 Proposed form of the paths of curvaturechange for a spectrum of initial condi-tions Ill

37 Dependence of the shape parameter onvolume fraction porosity for all conven-tionally sintered UO, specimens 112

38 Dependence of surface area per unitvolum.e upon the pore volume fractionfor the isochronal pressure sinteredseries 119

LIST OF FIGURES (continued)

Figure Page

39 Variation of surface area with porosityfor specimens pressure sintered at theindicated temperature at 3,000 psi forvarious times 121

40 Variation of total curvature with volumefraction porosity for specimens sinteredat 3,000 psi for 30 minutes at varioustemperatures 123

41 Variation of mean curvature with volumefraction porosity for isochronal pres-sure sintered series 124

42 Comparison of mean curi'ature for iso-thermal pressure sinterings and thatobtained in the isochronal series .... 126

43 Variation of the mean pore intercept \

with volume fraction porosity forpressure sintered UO^ 127

44 Photomicrographs of isothermallypressure sintered U0-, specimens 129

45 Dependence of the shape parameter uponvolume fraction of porosity for thepressure sintered isochronal series . . . 131

46 Comparison of the dependence of surfacearea on volum.e fraction porosity forconventional and pressure sinterings . . . 132

47 Comparison of mean curvature for coarseUO2 powder prepared by conventional andpressure sintering techniques 135

48 Comparison of mean curvature values forintermediate UO2 powder prepared bycold oressing and sintering and bypressure sintering 136

49 Comparison of the geometry of (a) a

copper sinter body, and (b) UO2 sinter-ing, both aDDroximatelv 35^ theoreticaldensity .".'.. 138

LIST OF FIGURES (continued)

Figure Page

50 Failure modes in diainetral compression . . 142

51 Variation of fracture strength withpore volume fraction for specimens pre-pared by conver.tional sintering of powder"from the intermediate size fraction . . . 144

52 Dependence of fracture strength onvolume fraction of porosity for specimensconventionally sintered from coarse andfine UG-, powders 145

53 Comparison of the strength-pore volumede-cndence of tliree size fractions ofconventionally sintered U0-, 147

54 Fracture strength of specimens from thepressure sintered isochronal series asa function of pore volume fraction .... 148

55 Variation of fracture strength withvolijjr.e fraction porosity for specimensprepared by isothermal pressure sinter-ing the intermediate UO- powder at3,000 psi : 149

56 SEN! fractographs of intermediate iso-chronal series 150

57 Parli of minimal fracture length forcoarse and intermediate specimens ofcomoarable density 153

58 Dependence of mean grain intercept onpore volume fraction for isochronallypressure sintered series 156

59 Dependence of thermal conductivity ontemperature for UC2 specimens withdifferent pore volum.e fractions 158

60 Thermal conductivirv at 500 'K as func-tion of volume fraction of oorosity . . . 159

61 X-ray images of a second phase foundin UO, sinter bodies 162

Abstract of Dissertation Presented to the Graduate Councilof the University of Florida in Partial Fulfillnent of the

Requirements for the Degree of Doctor of Philosophy

THE EVOLUTION OF MICROSTRUCTUREDURING SINTERING OF UO? ,A.ND ITS EFFECTUPON MECHANICAL .A.\'D THER2>L\L PROPERTIES

By

Wayne Douglas Tuohig

December, 19 72

Chairr^jn: E. D. IVhitneyMajor Department: Materials Science and Engineering

A full range of microstructural states, ranging from

301 to near theoretical density, were produced from UCs

powders. Both conventional and pressure sintering (hot

pressing} techniques were emoloved to tabricate che micro-

structures. Each state was characterized by it? associated

metric properties, i.e., volume fraction of /oid, area of

void- solid interface, curvature, mean pore and m^ean grain

intercepts, as determined by the procedures of quantitative

metallography. Additionally, tensile stiengths at roomi

temperature and theTm.al conductivities over the intermediat;:

temiperature ra^ige were determined.

The viewpoint was adopted that a sequence of states

defined the path of microstructural change. It was found

that sintering in the presence of an applied load (hot

pressing) proceeds along a different path of microstruc-

tural development than does the same material under conven-

tional sintering conditions.

The evolution of nicros tructure during conventional

sintering of U0-, is shown to be qualitatively sir.ilar to

that of metallic systems. The role of preconpaction (cold

pressing) upon the subsequent microstructural development

has been elucidated in terms of the area of pore-solid

interface

.

Tensile strength and thermal conductivity have been

found to be functions of the initial particle size for

densities below about 80"^^ of theoretical. Inspection of

fractured surfaces and microstructures indicates that these

properties are sensitive to minimum cross -sectional areas

in the porous solid network. Evidence is presented to show

that this minimum area is in turn related tc initial par-

ticle size. Properties of specimens grsi^er than 80% dense

showed little dependence on initial particle size. Increases

in grain size are thought to be responsible for decreasing

strengths found at very high densities. A marked decrease

in thermal conductivity found for high density specimens is

attributed to the presence of a second phase, believed to be

the result of contamiinants in the starting material.

CHAPTER I

INTRODUCTION

1.1. T]ie Nat ure of the S in t

e

ring Process

Sintering in the presence of a liquid phase is as old

as the i^ost ancient ceramic artifact. A more raodern conno-

tatiori of the teim "sintering" implies the coalescence of

particulate matter at temperatures below tl^.e melting point

into a solidj colierent body. The driAring force for this

process is the therinodynam.ic tendency of a system to lov;er

its cncrg)' by decreasing free surface area (in tlie absence

of a liquid). The sintering process may be characterized

by:

1) Particle contact -- particles are brouglit intocontact under tlie action of gravity, an exter-nally applied force or vibrating rearrangement.

2) Upon heating to a temperature below the liq-uidus, points of contact between particlesbroaden into areas of contact or necks.

3) The initially continuous network of porositybecomes less continuous.

4) Both 2 and 3 are accompanied by a macroscopiccontraction or shrinkage. As a result, thedensity is observed to increase.

5) The rate of densification decreases rapidlyas theoretical density is approached; averagegrain size increases.

1 . ] . ] . Prc vicus .StiiJics of the Sintering, Process

ProbuMy the earliest work on sinterinp in the absence

of liquid was performed by Wollaston [1] in 1725, on plati-

num sponpe. However, the extent to wliich solid species

were nobile and could interact was not known until Roberts-

Austin's [2] work on the diffusion of gold in lead. The

nucleus of current sintering theory was contained in the

suggestion by Kepler [3] in 1D05 that sintering in the

presence of a liquid phase was brought about by surface

tension forces. Iledvall's [-1] observation of spheroidiza-

tion of Fc'2^'' 1 ^'"'•'l lae led hiin to conclude that the phenome-

non v/as brought about by surface tension. The wcrk of

SmJtli [S] in 1923 produced tlie conclusion that a liquid

phase was not requisite for sintering to occur. In the

ensuing years, studies on single and inulticomponcnt systems

firmly establislied a rel ationsliip between solid state dif-

fusion and sintering. By the early 1940's, a number of

workers had concluded tliat materia] transport occurred

imdcr the action of surface tension [6-8]. V.'retblad and

V/ulff[7] utilised equations of capillarity and concluded

tliat stresses in sintering bodies exceed the elastic limit,

and tlujs plastic deformation occurs. Pines [9] and Shaler

and V.'ul f f [10] distinguished between mechanisms which could

produce slirinkage and tliose wliich jn'oduced only surface

rounding witliout densi fi cation .

Kiiczynski [11], in a classic work, utilized a plate-

sphere model to derive sintering rates for different mecha-

nisms of material transport. According to his analysis

>

the radius of the neck, x, was related to time as follows:

21) viscous flow -- X tx t

2) evaporation -condensation -- x "^ t

3) volume diffusion -- x' «: t

74) surface diffusion -- x °^ t

From his measurements on copper, Kuczynski concluded

that early stages of sintering may be surface diffusion

controlled but that later stages are volume diffusion con-

trolled. A similar experiment [12] v.'ith glass spheres ]ed

him to conclude that tlie predominant mechanism was viscous

flow.

The calculations of MacKenzie and Shuttleworth [13]

introduced the concept of vacancy diffusion to external

sites. The results of these calculations, as well as the

observation that shrinkage was not dependent on specimen

size, led them to conclude that material transport during

sintering occurred by plastic flo\\'. Adopting the formalism

of Bingham flov/, they derived an expression for shrinkage

which contained several parameters. Suitable choice of

these parameters led to reasonably good agreement with

experimental data. Impetus to this view was added by

Clark and White [14], who utilized a similar approach and

achieved quite good agreement with experimentally measured

shrinkage rates.

A median ism proposed by Nabarro [15] and later by

Herring [16] to explain creep at low stresses provided a

means to reconcile both the plastic flow and diffusional

viewpoints. The Nabarro-Herring model [17] suggests that

creep deformation can occur by the diffusion of material

from grain boundaries in compression to grain boundaries

in tension, i.e., a flux of vacancies to grain boundaries

experiencing a compressive stress field. Thus, grain

boundaries become vacancy sinks. Experimental evidence wa--

provided by Udin, Shaler and Wulff [18] and by Greenough [10]

Udin et al . attributed the creep of fine co])per wires to

the Nabarro-Herring mechanism. Greenough repeated the ex-

periments using single cr)'Stal wires and observed creep

rates that were two orders of magnitude smaller than those

measured for polycrystall ine materials.

The close rel ationsliip between sintering and diffu-

sional creep was pointed out by Rhines and Cannon [20],

who found tliat sintering in tlic presence of small compres-

sive loads has the same effect on shrinkage rate that addi-

tional stress has on the rate of creep deformation.

The work of Alexander and Baluffi [21] on twisted wire

compacts, Scigle [22] on porous brass sheets, and Burke [23]

on aluminum oxide provided strong evidence for the grain

boundary siiik model.

An ingenious experiment by Kuc^ynski, Matsumura and

Cullity [24] provided tlie most direct evidence of diffusion

and the role of the curved surfaces during sintering. A

copper- indium alloy wire compact was sintered at tempera-

tures wliere the phase diagram predicts the presence of a

single phase solid solution. A subsequent heat treatment

at lower temperatures produced a precipitate rich in indium

at the weld necks. The diffusion coefficient of indium is

greater than that of copper and thus a Kirkendall effect

is observed. The material transported to tlie v;eld necks

by diffusion \v'as enriched in indium to the extent that the

two-phase boundary was crossed, allowing precipitation to

occur.

On the basis of extensive theoretical and experimental

work on a variety of materials, it is concluded that lat-

tice diffusion is the dominant mode of material transport

during sintering. Exceptions have been noted [NaCl by

evaporation- condensation , Kingery and Berg (25), g]ass by

viscous flow, Kuczynski (12)], and it is likely that more

than oiie mechanism operates at various stages of the pro-

cess. The following factors have been found to influence

sintering behavior [26]: (1) temperature employed,

(2) particle size and size distribution, (3) particle

niorphojogy, (4) occurrence of discontinuous grain growth,

(5) atmosphere, (5) stoichionetry and defect structure,

(7) impurities and additives, and (8) manner and extent

of compaction.

1.1.2. Pressure Sintering

Pressure sintering or hot pressing is defined as t)ie

application of external pressure to a powder compact while

it is at high temperatures. The synergistic effect of

these two variables has led to increased interest in recent

years to production of materials which cannot be fabricated

by any other technique [27]. Hot pressing provides an

additional A^ariable to control microstructurc , by virtue

of the fact th;<t it increases the driving force for densi-

fi cation of a powder compact without significantly increas-

ing the driving force for grain growtli [28]. As a result,

densities approaching theoretical have been achieved for a

number of materials.

The mechanism of dcnsi

f

ication during hot pressing

has been examined by Vasilos and Spriggs [29], Coble and

Ellis [30], Rossi and Fulrath [31] and Murray e t a

1

. [32].

Altliough simple sintering models are inadequate to describe

the process, most workers are of the opinion tliat at tem-

peratures below 2000°C and pressures below 7,500 psi as

arc normally employed in hot pressing refractory ceramics,

densif ication takes place by a diffusional mechanism.

Evidence for this comes primarily from agreement between

densif ication kinetics and lattice diffusion measurements

[28,29]. The plastic flow model proposed by Murray e t a

1

.

[32], and by McClelland [33] may, however, be applicable

to soft materials such as copper, lead, and N'iO [23].

CobJe and Ellis [30] studied neck growth between pairs of

spherical aluminum oxide single crystals under the applica-

tion of load. They concluded that only the initial stage

of neck growth was a result of plastic flow at points of

contact. Deformation occurred until the effective stress

was reduced below the yield stress. Later stages were the

result of a diffusion controlled process.

Murray e t al . [32] have studied the hot pressing

behavior of stoichiometric and hyperstoichiometric ^'02.

They foun.d that hyperstoichiometric material densified more

rapidly than did the stoichiometric oxide, in agreement with

observations of Williams et al . [34] on conventionally sin-

tered ifiaterial. Maximum reported density was 10. S5 g/cm.

(971 theorcrical density), produced by pressing at 2,000

psi at 1800°C for ten minutes.

1.1.3. Sintering of UO -^

In the late 1950' s, the development of advanced power

reactor designs provided srimulus for extensive study oi

the sintering behavior of UO^ . Interest continues in both

UO^ and mixed oxides of ursnium and plutonium which fuel

the present generation of breeder reactors.

The effects of powder characteristics and processing

variables on densificaticn jnd microstructure have been

discussed elsewhere [35] and will net be repeated here.

In genera], remarks that apply to most sinterable powders

apply to UO2 [36,37]. Ilovever, certain characteristics of

IJO2 are not general in nature and deserve further discussion

By virtue of the multiple oxidation states of uranium,

there are at least four thermodynamical ly stable oxides of

uranium known to exist [38]. Uranium dioxide has the

lowest 0/U ratio of the stable oxides and is the only oxide

wherein bonding is thought to be predominantly ionic in

character. Another consequence of the- multiple valence of

uranium is the hyperstoichi ometry exhibited by UO^ ; i.e.,

its ability to dissolve excess oxygen into the fluorite

lattice without formation of a second phase [39]. Cubic

UO2 may in fact have 0/U ratios of 2 . 00 to 2 . 25 . It is

well established that the 0/U ratio of UO^ has a very

significant effect on both sintering behavior and physical

properties [3G , 37] .

The 0/U ratio of UO,^* may be controlled by controlling

sintering furnace atmosphere and stoi chiometry of starting

material. Strongly reducing atmospheres produce 0/U ratios

close to 2.00. Sintering in inert gas or vacuum atmospheres

tonds to maintain the 0/U ratio of the starting material,

althciigh more precise control is obtained by controlling

oxidation potential with CO/CO-, mixtures [40], H-,/N'2

*U02 will be taken to imply stoichiometric UOt.qOunless otherwise indicated by context or the adjective nonstoichiometric.

mixtures [41] or by steam sintering [38]. Williams e t al .

[34] studied the sintering behavior of oxides in the range

0/U = 2.00 to 2.18. They observed that densif ication in-

creased rapidly between 2.00 and 2.02, but only slightly

above 2.02. The sensitivity of densif ication to stoichi-

ometry is a manifestation of the influence of defect struc-

ture on cationic lattice mobility.

UO.-, is particularly prone to agglomeration, i.e., a

tendency of loose particles to bond together in an assembly,

The bonding forces in agglomerates are generally electi'O-

static in nature as distinguished from an aggregate wherein

particles are welded together [42]. Insofar as aggregates

and/or agglomerates survive processing, they influence the

microstructiire of the sinter body. Steele et al . [43]

have examined UO^ and BcO powder compacts by the Brunauer-

Emmett-Teller (B.E.T.) technique and by permeability deter-

mination of surface area. They found that aggregates of

UO^ survived compaction at 40,000 psi and the result was

a very inhomogeneous distribution of porosity in the sin-

tered microstructure . Although Steele et al . , refer to

"strong aggregates," no attempt was made to disperse the

pov;der

.

Further, the inference is made that since x-ray crys-

tallite size is much smaller than observed for "particles"

in the microscope, the "particles" are aggregates of crys-

tals. It is well known that x-ray crvstallite "size" is

10

not equivalent to the traditional concept of particle size

[44]. It sceins likely, therefore, that in view of the

definitions given earlier, Steele et al . [43] observed

both aggregation and agglomeration.

1.2. l:volution of Microstructure

The path of micros tructural evolution may be defined

as the sequence of nicrostructures which exist in a mate-

rial 3"=; it undergoes a process which produces changes in

structure [45]. Examples are, the formation of crystals

and consumption of the matrix during devitrification of a

glass, the formation and growth of equiaxed strain- free

grains during recrystallizat ion , and solid state reactions

involving a phase change. During the sintering process,

a collection of minute particles are welded together to

form a massive coherent body v;hich ultimately may approach

theoretical density. It is evident that a continuum of

microstructurcs will exist between these two extremes.

This transformation is illustrated for a four-particle

system in Fig. 1.

Tiie kinetics of sintering may be viewed as the rate

at v.'lii.cli tiiis path is traversed by the system [45].

Traditionally, the kinetics of sintering have been studied

by measurement cf shrinkage. As indicated in the i-rcvious

section, shrinkage mc-asurcmcnts on geomet rj cal ly simple

11

^^___ I. 4

c) O

Fig. 1, Sequence of states through which a sinteringfour-particle systen passes. Densificatioiiproceeds as L-, >L2>L,>L .

.

12

systems have been used by nany workers to identify the

mechanisms by which sintering is taking place [11,26,46,47]

These results, however, do not extrapolate well to many-

particle systems. Dilatomotric measurements of shrinkage

have been made on three-dimensional systems composed of

many particles. It is usually found that the data can be

fitted to an equation of the form [48]

fi=Kt" CI. 3)o

where AL = L^ - L(t)

L = initial dimensiono

L(t) = dimension at time t

t = time

n =• the time exponent

and K can be represented as

K'exp # (1.2)

T"

where K" = a constant

T = temperature in degrees Kelvin

R = gas constant

Q = activation in energy for the shrinkageprocess

.

Such measurements, however, provide no inform.ation about

the path of sintering;,

A detailed study of microstructural changes wliich

occur during sintering was first undertaken by Rhines et al

[49]. They observed that tlie total volume of porosity

13

decreased as sintering progressed, but aA^erage pore size

increased. Arthur [50] determined that porosity remained

connected until relatively high densities v;ere attained

.

Burke [23] has observed that exaggerated grain growth

occurs during the latter stages of sintering and can effec-

tively arrest densification . These observations indicate

the complexity of tlie sintering processes and the defi-

ciencies of simple geometric models.

Techniques for quantitatively characterizing the

microstructure of sinter bodies have been available for

some time. However, only recently has systematic study

been undertaken. An additional parameter of particular

significance to sintered structure characterization was

provided by Delloff [51] and by Cahn [52] witli the develop-

ment of a technique for measuring quantitatively the curva-

ture exliibited by tlie interface in a two-phase system (see

section 2.3).

Rhines [53] has slio^vn tliat topological concepts may

be used to characterize the sintering process to an extent

not possible with ordinary geometric concepts. Using the

topological approach, Rhines et al . [45] developed a model

wherein the system of particles, contacts and void channels

is reduced to a node -branch network. It was shown that

the model was applicable to the eiitire process from loosely

stacked particles to a fully dense body. Aigeltinger [54]

has experimentally determined the topological properties

14

of a sinter body using a serial sectioning technique to

synthesize the structure.

Coble [55] has undertaken to describe the path of

microstructural evolution based on bulk diffusion-controlled

processes. He concluded from examination of micrographs

that the sintering process could be treated in three

stages

:

1) Initial stage -- growth of interpart icl e con-tacts into weld necks. The necks broaden tothe extent that grain growth becomes possible,thus signaling the end of the first stage,

2) Intermediate stage -- with the onset of graingrowth , intersect ion of grain boundaries withvoid-solid interfaces begin to assume equi-librium dihedral angles. Porosity is situatedas a continuous network of cylindrical poresalong the lines of intersection of threegrains. During this stage the pores retaincylindrical configurations and simply shrink.Two alternate final stages are proposed bvCoble.

3a) Pores are pinched off and isolated at fourgrain corners. If grain grov/th is inliibitedthe pores can continue to shrink untiltheoretical density is attained.

3b) If discontinuous grain growth occurs, poresare isolated from grain boundaries. Mostporosity is closed and spherical. Regionsadjacent to grain boundaries are relativelyfree of porosity as a result of boundarymigration

.

Using a tetrakaidecahedron as a model for grains and

cylindrical or spherical pore shapes, he calculates shrink-

age rates for intermediate and final stages of sintering.

Reasonably good agreement between diffusion coefficients

calculated from shrinkage rates, based on the model, and

15

those determined from initial stages of sintering were

obtained.

The densification and development of micros tructure

in UO^ v;ere studied by Francois and Kingery [56]. They

found that rapid heating rates produced a microstructure

that consisted of intergranular porosity as opposed to an

intragranul ar microstructure observed for conventionally

fired UO^ . The "intergranular" microstructure was charac-

terized by measurements of dihedral angle, average number

of sides exhibited by a pore intersection with the plane

of polish, average pore size and grain size. Based on

this data and extraction analysis, they concluded that

carbon in trace quantity in the starting material was

responsible for the unusual microstructures observed after

rapid lieating.

Rhines et al . [45] have studied the geometric path of

microstructural change for a number of metallic powders.

Particles of different morphologies, including irregular

dendritic electrolytic copper, spherical copper, nickel

carbonyl and antimony powders, were included in the study.

The effect of particle size, compaction, particle size

distribution and temperature were systematically examined.

The results of these studies are briefly summarized.

1. The sintering process may be divided into three

stages based upon the dominant geometric process which is

occui-ring: Stage 1 - points of contact broaden into weld

16

necks; Stage 2 - continuous channels'of porosity begin to

pinch off, isolating regions of porosity; and Stage 3 -

large isolated pores grow at the expense of smaller pores.

Thus, there is a coarsening of the scale of porosity.

2. A linear relationship between S , surface area

per unit volume, and \', volume fraction of porosity, has

been found to hold for all materials during second- stage

sintering. Thus, for a given system, there exists a unique

path of change for surface area towards which the system

tends. The imposition of constraints such as precompaction

and inhibitors will alter tlie approach to tliis path in a

manner that is qualitatively predictable.

3. Tlie total curvature per unit volume, ^^ , is ini-

tially positive, decreases tlirough zero to a maximum nega-

tive value and approaches zero again as densification

nears completion. (See section 2.3.3 for explanation of

sign convention.

)

Gregg [57] lias measured tlie sintering force (defined

to be the force necessary to balance axial shrinkage) as

a function of density. Somewhat surprisingly, the sinter-

ing force v.'as found to increase witli increasing density,

reaching a maxiiiium before beginning to decrease. Gregg

found that tlie variation in the sintering force could be

correlated with tlie evolution of average mean curvature,

FT, and derived an expression relating capillary forces to

the sintering force, based on a spherical pore model.

17

The evolution of microstructure in a three-dimensional

sinter body can be described by quantitative geometric

properties whicli uniquely characterize the system. These

properties are experimentally measurable and require no

simplifying assumptions.

1.3. Effect of MicTOSt ructur e onMechanical and Thermal Proper tie's

The mechanical and thermal properties of a material

depend nrimarily upon atomistic considerations such as bond-

ing, band structure, and crystal symmetry. Microstruc-

ture can, however, play an important role in determiining

realizable properties for engineering applications. Micro

-

structural features which are expected to influence proper-

ties of polycrystals are: (1) grain size, (?) existence of

preferred orientation or anisotropy, and (3) presence, dis-

tribution and morphology of a. second pliasc. Void phase or

porosity is a special case of feature (3) and has received

a great deal of attention in the ceramic literature.

1.3.1. Me chanical Properties

The basis of the mechanical behavior of brittle mate-

rials is the Griffith Tlieory [58]. Griffith hypothesized

that all materials contained flaws. When a stress is applied

to a body containing thf: flav/, stresses in the vicinity of

the flav/ are very much liighei than would be calculated

18

assuming the body Kas a honogcncous continuum. As a result

stresses approaching theoretical strength are achieved at

the tip of the flaw, causing it to propagate and ultimately

produce fracture of the macroscopic body. Inglis [59],

utilizing a flat elliptical void as a model, computed

stresses in the vicinity of the flaw. The result of this

and similar calculations based on a variety of geometries

was a relation of the form

S « (^)^/2 (1.3)

wheie S = the stress necessary to extend the flaw

a = specific surface energy

li = Young's Modulus

C = characteristic flaw dimension.

Credence was given the flaw theory by observations of

high strengths of pristine glass fibers. Upon prolonged

exposure to the atmosphere, strengths deteriorated by more

than an order of magnitude [60]. The Griffith Theory pre-

dicts tliat failure by brittle fracture is the result of the

extension of flaws inadvertantly introduced prior to, or

nucleated by, the application of a stress.

In light of this hypothesis, the effect of microstruc-

ture on nucleation and propagation of "Griffith cracks"

forms the basis of the present discussion.

It is observed that the fracture strength of "brittle"

materials and the yield strength of "ductile" materials

19

increase as grain size decreases. Several explanations of

this effect have been put forth [61],

1. Grain boundaries serve to limit the length of

cracks that can subsequently propagate. Since, from equa-

tion (1.3). the fracture stress is directly related to the

flaw diniensi.on, smaller grain size materials have smaller

flaws, and tlius exhibit higher strengths.

2. If dislocations are mobile, grain boundaries act

as barriers causing dislocations to pile up and nucleate

a crack according to a mechanism proposed by Zener [62].

Presumably, larger grains present a more formidable barrier

to slip.

3. Residua] stresses across grain boundaries, due to

thermal expansion anisotropy, can be produced on cooling a

polycrystal line body. Again, the level of stresses in-

creases with grain size.

4. Elastic anisotropy may also produce high local

stress fields across grain boundaries when an external load

is applied. The extent of loca] stress is expected to be

proportional to grain size.

5. Surface flaws are generally larger in large -grained

materials

.

In a recent work, Carniglia [63] has examined 46 sets

of published strength versus grain size data for monophasic

oxide bodies. After "normalizing" for porosity, the data

could be represented by an equation of the form:

20

c = c^ * a^G""' (1.4)

where a = the mean strength

G = the grain size

a,, o^ and a = constants.

Equation (1.4) is the Fetch [64] equation for o^ ^ 0(6),

the Orowan equation [65] if a^ = 0(7) and the Knudsen equa-

tion if OL ^ 1/2 [66]. Camiglia concluded that the data

were described by a two-branched curve, one branch described

by the Orowan equation, the other by a Fetch relationship.

-1/2In all cases, strength was proportional to G ' .

The effect of porosity on the mechanical properties

of ceramics has received a good deal of attention in recent

years [67-70]. As a result of these studies, several equa-

tions have been proposed which are in reasonably good agree-

ment with published data. Hashin and Shtrikman [71] de-

rived the expression

^'^oT^ »• = '

where E = Young's modulus for porous bodies

£ = Young's modulus for theoretically dense° material

P = fraction of porosity

A = constant.

Using a dispersed pore model and a Poisson's ratio of 0.2,

Hashin and Shtrikman concluded that A should be equal to 1,

in agreement with the work of Fryxell and Chandler [72] on

21

BeO. Values for the constant. A, for A1_0_ are, however,

in the range 3-5 [73,74].

The most commonly used relationship bet\\?een strength

and porosity was suggested by Ryshkewitch [75] and by

Duckworth [ 76 ]

:

-bP(1.6)

where a = fracture stress, a = fracture stress of theo-

retically dense material, b = constant, and P = volume

fraction of porosity.

Carniglia [63] employed equation (1.6) to normalize

data from strength versus grain size studies. Rudnick e t al .

[61] attribute, in part, the variable dependence of strength

on porosity observed by different workers to differences in

pore size, shape and distribution. Brown et al . [77] have

derived an expression based on the concept of a projected

area fraction of porosity normal to tensile stress. They

considered pore shape and orientation, summing up the pro-

jected areas in the fracture surface on the normal plane.

DeHoff and Gillard [78] examined the rupture strength of

porous copper bodies as a function of porosity. They mea-

sured the area fraction of solid supporting the stress

directly on the fractured surface by quantitative micros-

copy, and concluded that the rupture strength v/as given by

a = a A, - , where a = rupture stress, a = rupture stresso A mm - ' o ^

of solid copper, and A„ . = minimal area fraction of solid

(corresponding to projected area of fracture surface).

22

It is apparent that correlation of properties sinply with

volume fraction of porosity is not completely satisfactory.

The morphology, size and distribution of porosity must be

considered if a truly fundamental correlation is to be

obtained.

1.3.2. Mechanical Properties of UO2

UO^ behaves as a perfectly brittle material at temper-

atures belov: 1000°C. Recent studies by Evans and Davidge

[79] and by Canon, Roberts and Ecals [80] have shown that

UOp exhibits a brittle-ductile transition, the precise tem-

perature of which depends upon the deformation rate.

Burdick and Parker [81] examined the effect of particle

size on the bulk density and strength of UO2 bodies. As

expected, coarser size fraction? produced lower densities

and lower strengths. Final grain size was approximately

equivalent as the result of grain growth in finer size frac-

tion material. Knudson, Parker and Burdick [82] examined

the dependence of flexural strength on porosity and the

effect of Ti02 additions to UO2 bodies prepared from four

different kinds of UO2 powders. They found that their data

(consisting of one microstructural state for each of the

four powders) could be expressed as

S = K G"" e"^P (1.7)

where S = flexural strength in four-point loading

lb

G = average grain size (Martin's diameter)

P = volume fraction of p.orosity

K = 23,700

a = .119 ^ constants (room temperature)

b = 3,17

The above equation also produced satisfactory agreement

with data taken at 1000°C for different values of the con-

stants, K, a and b. At 1000°C, Knudsen et al . report a

value for the grain size exponent, a, of .837. As indi-

cated in the previous section, both Orowan [65] and Fetch

[64] predict a value for a of .5, and values close to this

are observed for a number of ceramic materials [63]. Thus,

the equation of Knudsen et al . must be regarded as empirical.

Forlano, Allen and Beals [83] studied elastic modulus

and internal friction characteristics of sintered UO.^ over

a limited density range (volume fraction porosity .02-. 06).

They determined Young's modulus by a sonic technique and

found reasonable agreement with an equation of the form

E = E^(l-AP) (1.8)

where E = Young's modulus

E = Young's modulus of theoretically densematerial

A = constant

P = volume fraction of porosity.

24

Their data is in good agreement with earlier work of Bowers

ct ril . [S'l], Scott ct al . [85], and V.'achtinan et al . [86].

I:vans and Davidgc [79] reported strength and fracture

characteristics of UO- over a wide range of temperatures.

In the low temperature (brittle) regime, they concluded that

fracture occurred as the result of tlie extension of pre-

existing flav.'s. These fla\vs were thought to be large pores

found on the surface of the three-point bend specimens.

Canon, Roberts and Beals [80] observed a similar result

for materials of three different grain sizes. They attrib-

uted fracture at temperatures below 1000*^0 to flaws in the

form of isolated pockets of lov; density material approxi-

mately 50 to 100 microns in diameter. These flaws are

probably tlie result of aggregates and/or agglomerates in

the starting material, Knudsen et al . [82], Evans and

Davidge [79] and Canon et al. [80] all found that brittle

fracture strength increased with increasing temperature to

the onset of plasticity.

Roberts and Ueda [87] studied the influence of porosity

on deformation and fracture of UO2 • Porosity was produced

by increasing additions oT naphthalene to the starting

material. Resulting microstructures showed isolated, large,

anisotropic voids similar to tliat seen in irradiated fuel.

Tlieir data could be fitted to the Knudsen expression, equa-

tion (l.'l), witli a different choice of constants.

25

1.3.3. Effect of Microstructure onThermal Conductivity

Above loom temperature the conduction of heat in oxide

ceramics occurs by coupling of lattice vibrations called

phonons, and the scattering of these waves by anharmonici-

ties limit energy transfer through the lattice. The thermal

conductivity, K, is given by [88]

K = i C^vX (1.9)

where K = thermal conductivity

C = heat capacity/unit volume

V = wave velocity

X = mean free path

Above the Debye temperature both C and v change very

little with temperature, and th£ thermal conductivity is

sensitive only to the mean free path between scattering

events. Theory predicts that the mean free path should be

proportional to 1/T. Experimentally, over intermediate

temperature regimes, many coirmon oxides do in fact show a

1/T dependence [89]. Typically, mean free paths are of the

order of 10-100 A, and thus while microstructural features

have an effect upon thermal conductivity, the influence of

other variables is m.ore pronounced. The presence of varying

impurity levels can completely mask any differences due

to microstructure [90]

.

Because of the similarity of the phenomenological

theory, there is a strong analogy between dielectric and

26

conduction theories of heterogeneous solids. Models con-

sisting of alternate slabs of different materials have been

solved for heat flow parallel and perpendicular to the

slabs [91]. A parallel tube model was employed by Jackson

and Coriell [92]. Analogous to Maxwell's equations for

heterogeneous dielectrics, Euken [93] has suggested an

equation of the form

1 + 2V

1-

1-V

1

KT

2 j^ . 1^2

(1.10)

where K = material conductivitym '

K, = continuous matrix conductivity

Ky = dispersed phase conductivity

V = volume fraction of continuous (matrix) phase.

This equation applied rigorously to systems of phase 1 con-

taining uniform dispersed spheres of phase 2. Such a model

would be a reasonable representation of a high density

sintered material where porosity is isolated and spherical.

If tlie effective conductivity of the pores is low with

respect to the matrix, the Euken relation reduces to

1 - V .1

K (1.11)

27

Francl and Kingery [94] have suggested that the relatively

simple Loeb [95] expression

K^ = K^^j.^Cl-P) (1.12)

where K ^-j = conductivity of the solidsolid

P = volume fraction of porosity,

would adequately describe experimental data on a number of

materials. This expression is empirical, however, and

without physical basis.

The effect of grain size on thermal conductivity has

not received a great deal of attention by investigators,

probably again due to the m.ore dominant effect of such vari-

ables as impurity levels, test sensitivity and specimen

reproducibility. It is known that single crystals exhibit

much higher thermal conductivity than polycrystalline speci

mens of the same composition [91]. Flynn [88] has pre-

sented a model of a polycrystal comprised of grains sur-

rounded by a boundary region of "width" b. The basis for

such a representation is not clear, but, on the assumption

that the boundary "thickness" and the corresponding conduc-

tivity of the "boundary phase" remain constant, Flynn's

model predicts that conductivity increases with increasing

grain size.

1.3.4. Thermal Conductivity of UO .^

The thermal conductivity of stoichiometric UO2 has

been measured by a number of workers using a variety of

28

experimental tecliniqucs [96-^)9]. There is considerable

discrepancy betv;ccn the values obtained v.hen normalized to

theoretical density by using equation (].12). V.'ork by Ross

[100] and by Deem [101] suggested, however, tliat (1.121 is

not adequate, particularly at Dow densities. Ross [100]

further stated that pore shape and location at grain boun-

daries v.crc probably responsible for the low values he ob-

tained. He noted that, at higher density, his data arc in

agreement with the Loeb expression.

Reiswig [102] measured the thermal conductivity of UO^

in tlic range 800 to 2100°C. A least squares fit of the

data gave an equation of the form

^ " r77r"^f~0TFr ^^-^^^

where K = thermal conductivity l^^vi-"

T = temperatures in °K for specimen 85^tlieorctical density.

Bates [103] reported the findings of the International

Atomic Energy Agency (IAEA) panel tliat critically evaluated

all reported thermal conductivity for UO2 . The panel stated

that the thermal conductivity of UO^ between 20°C and

1300°C could be best represented by

1

11 TWTT^ (1.14)

where K = thermal conductivity in '^o,-'^ cm K

T = temperature in °C for a 9S'i dense specimen.

29

The panel further recommended that the correction for

porosity

,

'^A~

^^B

Pb-Pa(1.15)

be used to normalize all data to 95% theoretical density.

K. = conductivity of specimen of density p.; K^ = conduc-

tivity of test specimen of density p^; Pp -= density of

measured specimen; p^ = the desired density; and B = a

parameter that depends upon specimen "characteristics."

6 values ranging between 1 and 4 have been reported. The

panel selected 2.5 but recommended a study of the depen-

dence of B on microstructure

.

1.4. Objective of the Present U^ork

The continuing development of nuclear reactors has

resulted in ever more stringent demands on various material

components. In an effort to increase efficiency and opti-

mize performance, higher temperatures, increased fluxes and

higher burnup levels are being specified. The Liquid Metal

Fast Breeder Reactor (LMFBR) , now undergoing concentrated

development, will be the primary energy source for the

decades immediately ahead. The breeder reactor lias the9-70

capability of converting nonfissionable U"' to fissionable

239Pu and thus produces more usable fuel than it consumes.

A mixed oxide of uranium and plutonium has been selected

30

by the AEC as the fuel for the prototype LMFBR. Specifi-

cations call for the LMFBR to produce 1,000 megawatts,

achieve 10 « burnup with an output of 100,000 megawatt-days

per ton. The result will be a fission density of 10 cm""^

sec . Liquid sodium will leave the core at 540°C. Eighty

thousand fuel pins having a diameter of one-quarter inch

will operate at surface temperatures of 650°C and center-

line temperatures near the melting point of 2760°C. At

steady state, gradients up to 9000°C/cm will be sustained

1104].

It is estimated that there is a potential production

of one billion pellets of fast breeder fuel over the next

forty years. Shaw [104] has stated that it is essential

that development "proceed in a disciplined manner so as to

achieve predicted performance based on reproducibility of

materials, properties and behavior from the laboratory

bench through all phases of the program, including the oper-

ating reactor."

Reactors for specialized application, such as the

Transient Experimental Test Reactor, may impose very dif-

fererit conditions on the component design than are required

for conventional power reactors. The transient reactor will

utilize U dispersed in stabilized ^r02 to give appro-

priate fission densi ty , resist ance to thermal shock and

thermal conductivity [105].

31

All reactor fuels undergo changes in micros tructure

during operation as the result of exposure to high temper-

atures and large thermal gradients for extended periods

of time, as well as accumulating fission products. Struc-

tural changes which occur during the life of a fuel pin are

illustrated in Figure 2 [106]. It is apparent that these

changes markedly effect performance via changes in both

mechanical and thermal properties.

In summary, fuel technology has as major objectives:

1) microstructural fuel design for optimumperformance

,

2) attainment of reproducibility and uniformityfor large-scale production of fuel, and

3) prediction of microstructural changes occur-ring in pile and the effects of these changeson performance parameters.

The primary objective of the present work is the appli

cation of the techniques of quantitative metallography to

a wide range of sintered UO2 microstructures , providing a

degree of characterization not previously achieved. The

simultaneous determination of room temperature tensile

strengths and of thermal conductivities which correspond

to these structures provides a sound basis for the identi-

fication of structure-property relationships in a real fuel

material. Such a systematic study is a necessary first

step towards the attainment of the goals previously enum-

erated.

32

Shut downafter10 5 MWD/T

Operating between10 and 10 5 f.nVD/T

Operating1-10 MWD/T

Shut downafter10 MWD/Ton

Fig. 2. Structural evolution during useful life of a

UO2 fuel pin [106] .

CHAPTER II

EXPERIMENTAL PROCEDURE

2.1. Mate rial Characterization

2.1.1. Material Specifications

The materia] employed in this investigation was sup-

plied by the United States Atomic Energy Commission. It

was produced by Mallinkiodt Chemical Company by precipita-

tion from solution as ammonium diurinate (ADU) , calcina-

tion to UO^ and reduction to UO^ . The resulting product

was then fused in an electric arc furnace by SpcTicer

Cliemical Company. Analytical impurities determined by

Battelle Memorial Laboratories are given in Table 1. The

as -received powder was classified into -6 mesh, -20 mesh

and -200 mesh (U.S. Standard Series) lots. Scanning elec-

tron photographs .of the as -received materials are shov;n

in Figs. 3 and 4. The follovving observations v/ere made:

1] The particles are angular, faceted polyhedra;i.e., they exhibit very little curvature ofsurface and are roughly e qui axed.

2) There are virtually no open pores or voids inthe parti cles .

3) There is no size dependence of shape ortopography insofar as can be resolved in tlie

scanning electron microscope (SEM)

.

33

34

Table 1

.-\nalytica] Impurities in the Arc Fused UOUsed in this Investigation

Carbon 57 ppm

Aluminum 33

Boron < 0.1

Cadmium < 1.0

Chromium < 5.0

Iron 70

Magnesium < 3.0

Nickel < 3.0

Silicon 33

35

37X

4. OX

Fig. 3. SEM photographs of -6 mesh as-received UO2powder

.

36

800X

4,000X

Fig. 4. SEM photographs of -200 mesh as-received powder.

37

4) There are small particles which appear to beadhering to surfaces of the larger particles.These particles are generally siiialler than5 microns and are physically distiiict fromthe substrate particle.

Similar "surface" particles have been seen by Johari

and Bhattacharyya [107] on electrolytic iron and by Lifshin

et al . [108] on SiC. The latter attribute bonding to elec-

trostatic forces. Ef fectiA^ely , then, each particle is an

agglomerate or assembly of many particles which cannot be

readily separated. It is apparent from tlie surface topog-

rapliy that subsequent to arc fusion the present material

was subjected to a coimninution process, wlierein large fused

grains were cruslied. The small particles observed are

probably the result of this operation.

Figures 5 and 6 are photomicrograplis of -6 m.esh and

-270 +325 m.esh as-received powders. In both cases, nearly

all particles are single crystals, and thus even when

etched are A^irtually featureless. The -6 mesh particles

(Fig, 5) show residual cracks from the crushing operation,

the presence of aggregates (although their number was

judged to be quite small) and occasional closed porosity.

The -270 +325 specimen of powder shown in Fig, 6 indicates

no aggregates preseiit in this size fraction. It is appar-

ent, however, that particles much smaller than the 44 micron

325 sieve oponing have been retained.

Graham [109] has measured the x-ray domain size of

ball milled powder employed in this investigation. Based

58

(a)

(b)

Pig. S. Photomicrographs of -6 mesh as-received powder;(a) cracked grain, (b) particle aggregate.

39

Fig. 6. Photomicrogranhs o£ -270 +325 as-received oowder.

40

on line profile analysis of (200) and (400) reflections,

lie found an effective domain size of 530 A. This result

is in p.ood agreement with results of other Korkcrs [110]

and indicates a relativel)' low preparation temperature of

500° to 600°C [111] .

2.1.2. Stoichiometrv

As a result of the multiple oxidation states of U,

the uranium-oxygen system is among the most complex of

metal -oxide systems. There are at least four thermodynam-

ically stable oxides, and these exhibit polymorphism and

metastability to varying degrees [111]. Several otlier

oxides have been reported, but not confii'med. Only tlic

region between UO2 and U^Og (0/U = 2.00 to 2.25), however,

is of primary interest to tlie nuclear fuel industry.

Although differing in detail, tlie work of Schaner

[38], Blackburn [112], Vaughn ct al . [113], Aronson and

Belle [114] and Gronvold [115] established certain general

features of the phase diagram in the region between DO,

and U^Oq. The diagram according to Schaner [38] is pre-

sented in Fig. 7.

UO2 crystallizes in the fluoritc structure, i.e., the

cation lattice is FCC and 8 oxygen ions are located in the

tetrahedral interstices. As indicated by the diagram,

Fig. 7, UO2 exhibits considerable solid solubility for

oxygen (hyperstoichiometry) . At 900°C cubic UO^ is stable

41

14 "

1200 -

1000 -

Fig. 7. Phase diagram of the U-0 systen for 0/U ratiosbetv/een 2.0 and 2 . 25 , according to Schaner [38]

42

5.480

o«^ 5.470

I-

CD

5.460

cyy HATiD

Fig. 8. Dependence of the lattice constant at 25°C upon

n/LI ratio for cubic UO^ [38].

in the 0/U range 2.00 to 2.20, while at room temperature

there is little or no solubility. Viitiially all proper-

ties o£ UO- are sensitive to some degree to the presence

of excess oxygen in the lattice. Consequently, detei'mina-

tion of 0/U ratio is essential to any study of U0„

.

Precision lattice parameter measurements and thermo-

gravimetric analysis were employed for this purpose.

Reported values of the room> temperature lattice parameter

of stoichiometric UO2 range between 5.473 [38] and 5.469 A

[116], Schaner [38] has determined the lattice parameter

of UO^^ , as a function of knoivn 0/U ratio. His results,

sliown in Fig. 8, are in good agreement with more recent

studies.

The lattice parameter of a freshly sintered bulk

specimen from the present study was determined utilizing

a Norelco di f fractometer to scan the region 29 = 70° to

145° at 1/2° 26 per minute. Filtered copper radiation

from a fine focus tube operating at 35 KV and 15 ma was

used; 99.99% annealed gold powder served as an internal

standard. Data obtained were fitted by Cohen's Method of

Least Squares [117] . The calculations were performed by

computer, utilizing a program supplied by Mueller (Argonne

National Laboratory) and reproduced in Appendix A. The

choice of correction terms is indicated on the program,

description. The value obtained for a specimen sintered

in H2 ^vas a^ = 5.4716 ± .0003 X. From Fig. 8, the 0/U

44

ratio was determined to be 2.00 after sintering, in agree-

ment v;ith the general observation that sintering in 11^

produces a stoichiometric material, regardless of the

stoichioinctry of the starting oxide.

The measurement was repeated v/ith ball milled powder

dried in air at 90"C.

The 0/U ratio of the starting material v;as determined

to be 2. 06 based on a lattice parameter of 5.4693 ± .0006 A.

A determination of stoi chiometry v;as also made utiliz-

ing a gravimetric technique described by Scott and Harrison

[]1S]. A precision clectrobalancc* Av'ith a reported sensi-

tivity of better than 10 micrograms was used in this experi-

ment. A sample of approximately 100 mg was carefully

weighed on a platinum pan utilizing class S v.'eights. The

specimen and pan Avere then counter balanced and the micro-

balance recalibrated to yield full scale deflection at 10

mg increase in weight. A null detector** was employed to

indicate balance. The specimen and pan were then trans-

ferred to a platinum boat and oxidized at 450°C in still

air for two hours to produce U^Og (0/U = 2.667). The speci-

men was returned to the balance and the weight increase was

determined. The procedure was rejicatcd to insure that the

reaction had gone to completion. The weight gain expected

if the starting material had been stoicliiometric (0/U = 2.00)

*Cahn Division, Vcntron Instrument Company.

*Kiethly Instrument Company, Model No. 155.

45

was calculated and compared with that observed experimen-

tally. An estimate of stoichiometry could then be made.

This m.ethod gave satisfactory results for a bulk sintered

material (0/U < 2.03). Results for ball milled powders

were not satisfactory, probably because of adsorption on

surfaces. It is believed that this situation could be

corrected by in-situ oxidation and/or oxidation-reduction

in a controlled environment. Scott and Harrison [118] also

reported difficulty with as -received powder, indicating the

problem is not unique to the present investigation.

2.1.3. S ize Reduction and Separation

In an effort to evaluate the sinterability and the

effect of particle size on sintering beliavior, the as-

received -200 mesh powder was sieved and fractionated

according to Table 2.

Initial attempts to sinter loose stacks (uncompacted)

of -325 powders at 1650°C met with limited success. Speci-

mens sintered for two hours and 24 hours showed identical

densities of 5.26 gm/cm"""* (^8% theoretical density).

Although some sintering occurred (loose stack density

4.43 gm/cm"^) , specimens were quite fragile.

In order to explore the effect of temperature, arrange-

ments v.'ere made to use ultrahigh temperature furnace facil-

ities.* Molybdenum cups were loaded with material from

'^Komietco, Inc.

46

Table 2

As-received UO2 Powders were SeparatedInto Lots by Sieving

(1)

(2)

(3)

(4)

(5)

Sieve

47

each powder lot in Table 2 and tapped down manually. The

specimens were sintered in hydrogen at 2250°C for one hour.

The results are sho\\m in Fig. 9. Only 4 and 5 could be

considered strong enough to be handled.

It was clear as a. result of these studies that par-

ticle size reduction would be necessary in order to extend

the range of initial particle sizes and, hence, the range

of accessible microstructures . As a result of the sieving

operation, it was determined that approximately 80^ of the

as-received -200 mesh material was retained on a No. 325

sieve, but would pass a 270 sieve. Tliis material \\'as

selected as a base for all furtlier studies because of the

quantity available, the fairly discrete size distribution,

and evidence of reasonable sinterability in the "as-

received" condition.

Two techniques were employed to produce material of

smaller particle size. A rubber lined ball mill with

Burundum cylinders* was used to wet ball mill the base

material for 16 hours. This was followed by a drying oper-

ation done in air in open Pyrex trays at 90°C for 12 hours.

The powder was then granulated and stored in closed con-

tainers until used.

^^U.S. Stoneware Company.

48

c•H<n

(MMO» Q)

iH

V CO>H•H0) cU'H0)

O Vi

tn 3;« ou(0 a>M >(A O

•H0) in

wo oO 4J

E 4)0*4-1it o

0) Ih

>-i 0)CO .£3

P.E<U 3

Co•H O

49

As an alternative to ball milling, an impact pulver-

izer* v.'as em.ployed. Optimum conditions appeared to be

opposing pressures of 80 and 100 psig of argon at the jets.

Although the process produced a powder less than

1 micron in size, it was found to be inefficient. Maximum

production rates were below 10 grams per hour, which was

deemed inadequate for this investigation.

Examination of wet ball m.illed material indicated

the presence of particles in excess of 10 microns along

with particles of 1 m.icron or less in considerable quantity

It was fe]t tliat if a separation process could be used to

remove particles >5 microns the remaining po\'/der would be

sufficiently different from the ball milled material to

provide a third point in the scale of starting materials.

Separation was accomplished by a sedimentation tech-

nique, i.e., a dispersion of the particles in a fluid,

preferential settling of the larger particles and recovery

of the remaining particles. In order for such a technique

to be effective, agglomerates had to be dispersed com-

pletely, in such a way that neighboring particles did not

interact. It was found that a com.mercial pigment stabil-

izer, polyoxyethylene sorbitan monolaurate , ** in concen-

trations of about 20 ppm in aqueous solution vv'ould

*Gem-T, Trost Equipment Corporation

**Tween 20, Atlas Chemical Com.pany.

50

effectively disperse UO^ . Experimentally, the suspension

is agitated in a small liquid blender and transferred to a

glass column approximately 90 cm in height, allowed to

stand 80 minutes; the supernatant, containing the fine

particles, is then withdrawn and the particles recovered.

The basis for this technique is given by Stokes Law for a

spherical particle:

^ Tir^Cp - Pj2^)g = 67Trnv (2.1)

where r = particle ratio

p = particle density

Pj = liquid density

g = acceleration due to gravity

n = coefficient of viscosity

v = steady state or terminal settling velocity.

For a particle initially at rest a distance h from the

bottoi?. of the vessel, the settling velocity v is

V =^ (2.2)

where t is the time required for a particle to settle the

distance h. Substitute (2.2) into (2.1) and rearrange,

1- _ Ojrymh ., ,^1. -

-^ ^ L-.oj

T ^Y (Pp-P;i)

Using the viscosity of water at 25 °C (9 x 10' poise),

a particle density of 11 gm/cm'^ and the column height of

90 cm, the maximum time required for particles larger than

51

-270 +325(coarse)

Ball milled(intermediate)

Separated(fine)

10 microns

Fig. 10. SEM photos of powder from the three sizefractions employed in this investigation.

52

5 microns to settle is 4,800 seconds! Clearly, smaller

particles near the bottom of the column will also settle

out during this time interval. (Althougli these are poten-

tially recoverable by rej^etitions of the sedimentation

process, no attempt was made to further separate the solids

which settled out of the suspension.) The supernatant was

drawn off to a clean vessel after the prescribed time

period had clasped. Attempts to deflocculate the suspen-

sion using commercial def locculants of the anionic, cationic

and nonionic types were unsuccessful. Recovery of the

solids was effected by evaporation of the liquid in sliallow

Pyrox trays heated at approximately 90°C. Tlic dried cake

was crushed, passed through a 200 -mesh sieve, and stored in

closed containers.

Scanning electron micrographs of the powder lots

employed in the present study are shown in Fig. 10. These

lots are referred to respectively as coarse, intermediate

and fine size fractions in the text.

2.1.4. Specific Surface Area

Tlie surface areas of the three powders employed in

this study were measured by a technique devised by Brunauer,

Emmett and Teller [119]. The B.E.T. measurement is based on

a model for adsorption of a gaseous species on the surface

of a solid. The surface area is related directly to

capacity to adsorb atoms by

53

S = o^ N A X lO"^*^ ' (2.4)Mom ^^ • ^ J

2Avhere S = specific surface m /ga-am

X = monoiayer capacity in grams ofadsoi-bate/grams of adsorbent

M = molecular weight of adsorbate

N •- Avogadro's number

A - area occupied by a single adsorbatemolecule in X2

.

Based on the B.E.T. model, the monolayer capacity of the

solid can be evaluated from [120]

X(p -p) " T~C ' TT p '^•^-'^^ o •

'^ m m i

where X = mass of adsorbate in grams per gramof adsorbent

p = saturated vapor pressure

p = system pressure

X = monolayer capacity

C = constant for the system related toenergy of adsorption of the monolayer.

Accordingly, when p/X(p -p) is plotted against p/p , the

relative pressures, a straight line is formed having a

slope

S = ^ (2.6)m

and an intercept

TT (2.7)m

Solutions of these two equations simultaneously leads to

\ = ^ (2.8)

C =I

* 1 (2.9)

B.E.T. measurenents were performed on the three powder

size fractions described prev^iously, using an apparatus

similar to that shown in Fig. 11. Approximately 10 grams

of material were charged into a quartz specimen bulb.

The surface was then activated by heating to temperatures

in excess of 300*^0 for two hours at 10 mm Hg. The bulb

was then cooled to 77°K in a liquid nitrogen bath and held

at that temperature until measurements were completed.

Dry nitrogen was introduced into the system with the

specimen stopcock closed and the amount of gas determined.

The specimen stopcock was then opened and the system pres-

sure was allowed to equilibrate before the value was

recorded. Subsequent readings are obtained by decreasing

the volume of the system through a series of mercury cham-

bers and an equilibrium pressure recorded for each incre-

ment. A computer program to solve t)ie B.E.T. equation has

been written by Martin [121], incorporating the appropriate

parameters for the apparatus employed here. This program

calculates values for p/x(p -p) and p/Pq. performs a

least squares fit, calculates the slope and intercept of

the B.E.T. equation, and computes specific surface area.

55

To

McLeod gauge-

Gos inlet

(helium or-nitrogen)

Thermometer

Moin vocuum line^

Low temperature bath

—»-To atmosphere

Tomercurydiffusion

pump

Mercury (confining liquid)

Fig. 11. Schematic of the B.E.T. apparatus used todetermine surface area [120].

56

Table 3

Surface Areas of theThree Size Fractions of UO,

As received, -270 +325 (coarse)

Ball rilled (intermediate)

Separated (fine)

0.1-0.3 nr/gram*->

0.87 m''/gram

21 . 54 m /pram

Considerable scatter in the adsorption isoinherent for low values of surface area. All itherms B.E.T. Type IJ at 77°K.

thermso-

.05 1

P/P

• Experimental

O Least squares

1.5

Figure 12. R.L.T. plot for fine size fraction of UO,powder

.

2

57

The values obtained are given in Table 3. Figure 12

is a plot of the B.E.T. data for the fine size fraction.

The data for the intermediate and coarse materials were less

satisfactory because experimental error increases as the

surface area decreases, as discussed by Crowl [122]. It

should be noted that for all three data sets, the parameter

C, as defined by equation (2.9), is larger than 2. This is

a necessary condition for the isotherm to be Type II, thus

permitting the surface area to be calculated.

2.2. Specimen Preparation

Tjiree techniques were employed to prepare specimens

for exam.ination

:

1) loose stack sintering -- sintering of uncom-pacted material in a suitable container,

2) cold pressing and sintering -- compaction ina steel die followed by thermal treatment, and

3) hot pressing or pressure sintering -- sinteringunder an applied load in a die.

2.2.1. Loose Stack Sintering

Powder was poured into specially machined molybdenum

cups approximately one inch in height, .625 inch inside

diameter.

As \JOy powder is not free flowing, it was necessary

to tap down the stack to insure that it filled the cup

uniformly. The conical stack was leveled off even with

58

tile top of the cup and tlic cups were then placed directly

into the furnace. The sintering cycle is discussed fully

in the next section.

2.2.2. Cold Pressin?^

Cold pressed specimens v.'cre prepared by compacting with

and without the aid of a binder-lubricant. Polyvinyl alco-

hol, stearic acid in petroleum ether and polyethylene

glycol were evaluated for use as binder- lubricants . Poly-

ethylene glycol* was selected for its outstanding green

strength, ease of blending, excellent surface finish and

ease of volatilization prior to sintering. The binder was

added to the powder batch in amounts of 1/2 to l-i by weight

and blendod in a polyethylene container. Mixing was

carried out b)' tu;nbling the container on a ball mill drive

for one hour.

Specimens Averc pressed in a specially constructed and

hardened tool steel die. The cylindrical die cavity had

a diameter of .689 inches, incorporated a taper of 8 minutes

per incli, and had an adjustable depth. The die, pressed

into a double acting Ilaller^^'die table, is shown in Fig. 13.

A 75- ton liydraulic arbor press was used to apply pressures

up to 100,000 psi. In practice, compacting pressures above

75,000 psi freciuently produced transverse laminations.

*MallJnkrodt Clicmical Works.

**llaller Division, I'ederal -Mogul Corporation,

59

Fig. 13. Punch and die assembly used to cold compact UO^

60

Severe galling, die chatter and specimen cracking were

observed in the absence of a binder-lubricant above 10,000

psi and, as a result, a binder was employed for nearly all

specimens produced by cold pressing.

Pressed compacts were placed on molybdenum trays and

inserted into the hot zone of an Astro high temperature

furnace,* Fig. 11a. The furnace was evacuated and back

filled with commercial grade hydrogen nrior to heating.

A flowing hydrogen atmosphere was maintained during all

heating and cooling periods. A one-hour hold at 150°-200°C

was utilized to volatilize the binder prior to heating to

the desired sintering temperature. Practical sintering

temperatures were limited to about 1800°C by the -^12^3

muffle. Heating and cooling rates of 20°-40°C per minute

were generally encountered and the sintering "times" that

are presented are the time intervals tliat specimens are at

the sintering temperature. They do not include the heating

and cooling periods.

Temperatures were measured with a micro-optical pyrom-

eter**sighted directly on the specimens. The temperatures

reported are believed to be accurate to ±10°C in the range

of interest.

*A5tro Industries, Model lOOOB.

**Pyrometer Instrument Company, Model 95

61

(a)

(b)

Fig. 14. (a) The high temperature Astro sintering furnace(b) Centorr vacuum hot press.

2.2.3. Hot Pressing

Hot pressed specimens were fabricated in a Centorr

vacuum hot press,* Fig. 14b, using graphite** dies and

punches. Early experimental pressings revealed extensive

reaction between graphite and UO^ , particularly at temper-

atures above 1700^C. This reaction is undoubtedly respon-

sible for hot pressing behavior reported by Murray [32].

The situation was corrected by the use of a boron nitride***

die insert and punch faces. The entire die assembly is

shown in Fig. 15. Pressures up to 5,000 psi and temper-

atures to 2000°C in a vacuum of 10 torr were attained.

Temperatures again were measured with an optical pyrometer

sighted on the die body, giving a probable accuracy of t20°C.

A subsequent heat treatment of 90 minutes at i200°C in

hydrogen insured that the specimens were stoichiometric [125]

2.3. F.v^aluation of -Geometric Properties

2.3.1. Metallography

Microstructural examination was carried cut on speci-

mens which had been fiactured in diametral compression (see

section 2.4). The fracture mode was such that two large

segments of the specimen were recovered. The fracture

*Centorr Associates, Inc.

**Union Carbide Corporation, Grade ATJ

***Union Carbide Corporation.

63

Die body-

Lower punch

Lower ram

Upper ram

Upper punch

BN punch face

BN die liner

Fig. 15. Graphite and boron nitride die assembly usedto pressure sinter U0~

.

64

surface of one of the segments was then ground and mounted

for metallographic examination. The remaining segments

were held for fractographic study.

Metallographic mounts were prepared using a castable

epoxy compound* and a vacuum impregnation process. Speci-

mens were impregnated by immersing them in a beaker of the

epoxy mounting material and placing the beaker in a vacuum

dessicator connected to a mechanical pump. The dessicator

was gently evacuated until air appeared to be removed from

the specimen; air was then readmitted into the dessicator,

forcing the epoxy into the open porosity in the specimen.

It was found necessary to repeat impregnation through

successive polishing steps for samples of low density and/or

low strength as many as three times in order to obtain satis-

factory results. After impregnation, the specimens were

placed in glass cylinders situated on a glass plate and

additional mounting material was poured into the cylinder

to produce a mount of suitable size. The epoxy was cured

at room temperature for 24 hours, then heated to 50°C for

an additional 2-3 hours. It was found that only after the

above curing process could the mount be readily removed

from the glass cylinder.

The metp.llographic procedure employed to polish the

specimens is as follows [124]:

*AB Bueh]er, Ltd,

65

1) Vvct grind on a slov.' wheel with 180-, 320- and600 -grit silicon carbide paper discs.

2) Polish on nylon or silk saturated with 2%chromic acid and suspension of Linde A aluminapowder in 2% cliromic acid using a fast wheelspeed.

3) Repeat (2) witli Linde B alumina after thor-oughly cleaning the specimen with distilledwater and alcohol.

4) U'asli, dry and examine; the etch used to revealgrain structure was devised by Cain [125]:(a) a solution of one part H2SO4 to nineparts n202 (30%) swabbed on the surface withcotton for 30 seconds, and (b) the surfaceis then immersed for an additional 30-60seconds, washed, dried and examined. Deter-minations of the metric properties of thepore solid network were made on unetchedspecimens, in as much as etching was foundto adversely affect the accuracy of thesemeasurements. Subsequent to these measure-ments, the specimens were etched and thegrain i:)Oundary intercept count was made.

2.3.2. Quantitative Metallograpliic .'\n a lysis

Three quantitative metallographic parameters were

determined in order to characterize the void-solid network:

(1) Pp , the fraction of points of a test grid imposed on

the mi crostructure whicli lies within the feature of inter-

est, e.g., void phase; (2) Ny, the number of intersections

per unit lengtli tliat a test line imposed on the micro-

structure makes with a feature of interest, e.g., void-

solid interface; and (3) T. net, the net number of tangents

that a test line makes with features in the microstructure

,

e.g., pores, wlien swept over a unit area. There are two

kinds of tangents wliich a test line can make with a boundins

66

curve, if an interior and an exterior can be distinguished.

Following Rhines et al . [45], a tangent is considered nega-

tive if the arc at which tlie tangent is made is convex with

respect to the pore phase and positive when concave with

respect to the pore phase. The number of positive and

negative tangents per unit area traversed are tabulated

separately and the value of T, net is then

T^ net = T^^ - T^,

.

(2.10)

T, net may be positive or negative depending on relative

magnitudes of the two tangent counts, and the algebraic

sign of T. net must be included in all calculations involv-

ing the tangent count. The determination of these param-

eters is illustrated schematically on a photomicrograph of

a UO^ specimen in Fig. 16.

The volum.e fraction of void phase may be determined

from the point count and independently from a determination

of the density of the sinter body. A comparison of these

two values v;as used as a criterion to ascertain that the

metallographic section v;as in fact representative of the

three-dimensional sinter body. An agreement between the

point count and bulk density of 3"^ was used as a criterion

for acceptance or rejection of metallographic sections as

representative of the sinter body.

Bulk densities were determined by the liquid displace-

ment technique described in ASTM Standard 328-60. Open

67

Fig. 16. Schematic illustration of the counting measure-ments on a sinter structure.

68

porosity was filled with paraffin prior to determination

of sample volume. Some sample densities were also deter-

mined by displacement of carbon tetrachloride. No impreg-

nant was used and specimens were allowed to equilibrate

for several hours in the carbon tetrachloride prior to

determining immersed weight, thus excluding "open" porosity

from the sample volume.

The determination of the quantitative metal lographic

parameters was made utilizing a Quantimet 720 image analy-

ing computer.* The instrument is capable of performing all

of the counting measurements previously described, by

dividing an image into picture points. Logic circuitry

permits this Quantim.et to recognize picture points in which

the image is darker (or lighter) than a preset level. Thus

if there is a gradation in image intensity, such as there

is between void and solid phase in a sinter body, a point

fraction is obtained by counting the number of picture

points which comprise the void space and dividing by the

total number of picture points utilized to represent the

image. The Quantimet has a capacity of 500,000 picture

points on "Standard Frames," but the size and position of

the computed or "live" frame may be varied. The image is

displayed on a cathode ra)' tube which also incorporates a

digital display of the counting results. Additionally,

*Image .Analysing Computers, Ltd,

69

the detected image and the computed image may also be dis-

played. Figure 17 shows the displayed image of a sintered

UO^ specimen with the digital display in the upper left of

the screen.

Intersections and tangents are also based on pre-

programmed logical analysis of the image as represented by

the array of picture points. Intersections are registered

whenever the computer finds that adjacent picture points

differ by an established intensity. As the raster scans

line by line, top to bottom, the structure is sampled by

the equivalent of a test line whose length is the product

of the number of lines in the live frame and the actual

width of the frame. Similarly, the image is scanned line

by line for "end points" or tangents, equivalent to sweep-

ing a test line over the live frame.

A metallograph* is used to provide the image viewed

by the Quantimet vidicon head. A specially designed mount

supports the vidicon and permits it to be moved along the

bellows track of the met allograph . Figure 18 shows the

met alio graph -vidicon assembly.

Grain boundary intercepts were counted manually using

a grid eyepiece. Measurements were performed on specimens

for which void space characterization had been completed,

and which had subsequently been etched to reveal grain

^Bausch and Lomb , Inc., Research I.

70

Fig. 17. Quantimet display of a sintered UO2 micro-

structure.

71

p.

72

boundaries. Intersections with void-solid boundaries and

grain boundaries between adjacent grains were tabulated

separately.

2.3.4. The Metric Properties

The metric properties are determined directly from the

counting measurements described in the preceding section.

1. The volume fraction, V , is the total volume of

void space contained in a unit volume of microstructure

.

It may be shown that the point fraction P is an unbiased

estimator of volume fraction [126,127]

\ - Pp (2.11)

2. S is the surface area of interface per unit

volume of structure. The number of intersections per unit

length made by a test line with the trace of the surfaces

on a representative test plane is directly related to

Sy by [126,128]

S^ = 2Nl (2.12)

3. The means to experimentally determine mean surface

curvature in a three-dimensional volume containing curved

surfaces was devised by DeHoff [51]. The curvature of a

surface at any point is specified by the principal normal

curvatures, K' and K^ , defined as follows: a normal is

constructed at a point on a surface. All possible planes

73

containing the normal are constructed. The intersection

of the surface with these planes is an arc whose radius is

that of a circle passing through three adjacent points on

the curve. There will exist a plane for which the arc

radius is a maximum and a plane for which the radius is a

minimum. These radii are the principal radii and the

principal normal curvatures are then defined by

h-7^ h'k (2.13)

The mean curvature, H, is just the arithmetic average of

the principal normal curvatures or

H E ^ (K^ + K^) C2.14)

The mean curvature is defined at every point on the sur-

face. The total curvature M of a surface element dS is

dM - HdS (2.15)

Total curvature can be evaluated for a finite surface by

integrating the mean curvature over the surface,

M = // HdS (2.16)

It is convenient to express the total curvature on a per

unit volume basis, M i.e., perform the above integration

over the surface contained in a unit volume of structure.

Since H has a value at every point en the surface, it will

have an average value defined by

74

//_ HdS

//g dS(2.17)

DeHoff [51] has shown that this quantity is related to the

net tangent parameter by

n T, netH = -^ (2.18)

where Ff has the algebraic sign of T^ net (see section

2.3.3). The total curvature per unit voluine , M^, is then

II T. net

\ = n-Sv =

-TNT— -^v ' " T^"^'- ''"'

4. A straight line constructed on a plane section

through a sintered structure will form intersections with

traces of the void-solid interface. In structures composed

of a few large pores, the length of line between adjacent

intersections will be greater than for structures composed

of many small pores. Thus, the chord intercept is an

estimator of the scale of the system. The mean pore inter-

cept is given by [45,129]

4V 2Pr =^=^- (2.20)P ^v -^L

5. Analogous to the mean pore intercept, the mean

grain intercept may be defined as the average chordal dis-

tance between grain perimeters. For systems which contain

porosity, the mean grain intercept is given by

4(1-V^) 2(1-V )

X = v__ ^ v (2.211g <. ap^Tg aa ^^,

o^p^^^^ act

"v ^ V ' L "' L

75

where N "^ is the surface area of pore-solid interface

and N, is the surface area of grain boundary between

solid grains. The latter boundaries are shared by two

grains, hence the factor of two. The simultaneous deter^

minations of these properties provide a complete descrip-

tion of the geometric state of the system.

2.4. Evaluation of Mechanical Properties

The diametral compression test was employed in this

investigation to evaluate the tensile strength of U0-,

sinter bodies at room tem.perature . Diametral compression

was developed in the early 1940 's simultaneously in Japan

and Brazil [130]. It was originally developed to evaluate

concrete, but has since been used on a variety of materials

[131-134]. Using elasticity theory, Frocht [135] derived the

stress distribution of a perfectly elastic cylinder loaded

diametrally. His solution was verified photoelastically

by Love [136]. The stress state, shown schematically in

Fig. 19, is biaxial, having large compressive stresses at

both surfaces and a reasonably uniform tensile stress over

the center of the diametral plane.

The present test has several advantages over the more

commonly used bend tests.

1) Specimens are easier to fabricate; in the caseof nuclear fuel, most fuel elements are in theform of cylindrical pellets. The test may

76

then be performed on production pellets with-out resorting to special fabrication tech-niques [137] .

2) Related to (1) is the fact that specimenstested are representative of those being pro-duced, whereas specimens made especially fortesting may incorporate differences in micro-structure due to density gradients, firingprocedures, etc.

3) Bend tests produce maximum tensile stressesat outer surfaces and thus are sensitive tosurface preparation. Tensile stresses gener-ated by diametral compression are distributedover the entire diametral plane, emergingonly at the ends of the right cylinder.

Testing techniques have been reviewed by Mordfin and

Kerper [130] .Rudnick , Hunter and Holden [138], and by

Rudnick et al . [61]. In the present work, specimens were

loaded in an Tnstron TTD* machine equipped with a CF load

cell in a compression carriage. Hardened steel platens

were constructed to fit tlic Instron crosshcad. Padding to

eliminate concentration of compressive stresses was pro-

vided by two thicknesses of file card stock. Loading rates

of .02 and .002 inches per minute were explored with no

significant effect of loading rate observed. As a result,

a crosshead speed of .02 inch/minute \-.'as employed in all

tests .

Initially, samples in the as-fired state were tested

directly. However, the presence of surface asperities,

slight taper parallel to the cylindrical axis, subsurface

*Instron Corporation

77

Fig, 19. Distribution of stresses in a diametrallyloaded cylinder [130].

78

Fig. 20. Precision centerless grinder used to machineUO2 specimens.

79

defects, etc., indicated a need for precision finishing.

This was accomplished by centerless grinding all specimens

in a specially constructed centerless grinder. The grinder

shown in Fig. 20, was built from a design developed by

DeMeyer [139] at Battelle Northwest Laboratories. Toler-

ances of .0002 inch in diameter along the axis were

achieved with a properly dressed v;heel. Additionally, the

grinder produced excellent surface finishes and revealed

the presence of subsurface defects not apparent on the as

-

fired surface. Cylinder ends were also ground flat and

parallel, utilizing a V-block jig with carbide wear inserts

The tensile strength may be calculated directly from

the applied load at failure, P, according to

where D is the diameter of the cylinder and t is the

thickness

.

,2,5. Measurement of Thermal Conductivity

The thermal conductivity of sintered UO-;, was measured

using a com.parative or cut bar instrument, shown schematic-

ally in Fig. 21. The measurement technique is based on the

establishment of longitudinal heat flow through a composite

consisting of two standard meter bars and the specimen.

F.adial heat floi\/ is minimized by the presence of guard

*Thermophysics Corporation, TC-2200.

80

81

heaters which match tlie gradient of tlie stack. Temperatures

aloiip, the stack are monitored at the points indicated in

Fig. 21, so that temperature gradients and mean temperature

values can be calculated for each stack component. For

longitudinal heat flow, the integral form of the Fourier

equation can be written as [8 8]

Q = kA ^- (2.2 3)

where Q = heat flux

k = thermal conductivity

A = cross -sectional area

AT = temperature differential throughwliicli Q flovvS

t = tliickness of conductor in theflow direction.

Since tlie specimen and the standards are in series,

the heat f]ux is the same in each. Then

AT AT

Q ^ ^st \t rf = W T^St X

where the terms are defined in equation (2.2 3) and the sub-

scripts "st" and "x" refer to the standard meter bar and

the specim.en, respectively. All quantities are known except

k and, assuming cross -sectional areas are identical,

AT t

Pyroceram 9606 was selected as the standard material

for the meter bars in the present investigation for two

reasons

:

1. The conductivity of 9606 is intermediate between

the reported extremes of conductivity of UO^ over the tem-

perature ranpc of interest. Tlius it can be used for all

measurements with reasonable accuracy.

2. There is good agreement between several investi-

gators on absolute conductivity values for 9606 over a wide

range of temperatures [140,141]. Figure 22 presents the

temperature dependence recommended by T.P.R.C. [142].

Based on tabular data accompanying the T.P.R.C. curve

[142], a computer program was devised to interpolate between

the published data points. The program generated a table

of conductivity values for 9606 at one degree intervals

between 300 and 1200°K. This tabulation is reproduced in

Appendix B.

Specimen's selected for measurements were centcrless

ground to 0.625 incli diameter to conform precisely to the

diameter of the meter bars. The ends were ground flat and

parallel through 600 -grit SiC. A precision diamond wafer

saw was used to cut 0.024 inch wide by 0.015 inch deep slots

in the end faces to accommodate platinum/platinum-10°

rhodium thermocouples.* The annular gap between the stack

and the guard was filled with bubbled alumina**. Tlie entire

*Omcga fingineering

,

**Norton Company.

83

102 3 4 5 6 7

Temperature (°K)

Fig. 22. Temperature dependence of the thermal conductivityof Pyroceram 9606 [142].

84

assembly was evacuated to a vacuum of 10 Torr to prevent

oxidation of UO- and eliminate convective heat transfer.

Flynn [88] has discussed possible sources of error

associated with cut bar thermal conductivity measurements.

Errors may result from

1) radial heat exchange

2) shunting heat flow through the insulationsurrounding the stack.

3) inaccurate standards.

4) excessive interfacial resistance to heatflow between stack components.

5) perturbations introduced by thermocouples.

6) uncertainties in the measurement of gagelength.

7) presence of cracks, voids or heterogeneitiesnot ascribable to m.icrostructurc

.

8) measurements under nonequilibrium conditions.

CHAPTER III

RESULTS AND DISCUSSION

The results o£ this investigation have been separated

according to the manner in which the specimens were pre-

pared: (1) compacted and sintered, including loose stack

sinterings, and (2) pressure sintered. The reason for

such division will become apparent in the course of this

discussion. The data are further subdivided according to

initial particle size. All graphical presentations are

consistent in that a triangular plotting symbol refers to

data obtained from a specimen prepared from the coarse

size fraction (particle size is discussed in Section 2.1.3)

Similarly, round plotting symbols are associated with

intermediate size powder and a square symbol refers to

powder from the fine size lot.

3.1. Densif ication Behavior

In view of the paucity of information in the litera-

ture on pressure sintering of UO2 , the densif ication

behavior of the powders em.ployed in the present investiga-

tion was system.atically characterized in a series of exper-

iments .

85

86

2000

1800

o 1600

1400-

1200-

1000

Coarse

Intermediate

Fine

10.5

DENSITY (grams- cm" •*)

Fig. 23. Densi fication of three size fractions of UO2 atconstant heating rate followed by 5-minute arrestat 1800°C, pressure sintered at 3,000 psi at10-4 torr.

87

A dynamic measurement of shrinkage was obtained by

cold compacting powder in the hot press die assembly at

3,000 psi. The die was then heated slowly to 1000°C, where

a pressure of 3,000 psi was reapplied. A dial indicator

gage with .0001 inch graduations was used to measure dis-

placement of the ram. The power to. the induction unit was

then increased to a higher fixed level. Temperature and

ram displacement were monitored as a function of time.

The heating rate was nearly constant at 20°C/minute, being

somewliat less above 16 50°C. Density as a function of tem-

perature under these conditions is presented in Fig. 23.

An arrest at 1800°C for 5 minutes was obtained by reduc-

ing the pov;er input. The ram was then withdrawn and the

die assembly allowed to cool. Figure 23 indicates that

the coarse size fraction is initially more dense, but that

as sintering proceeds, an inversion occurs and the fine

powder exhibits the highest density at all subsequent

stages of tlie process. The initial inversion may be the

result of more efficient packing or a relaxation of one of

the load train components.

Having established a useful range of pressure sinter-

ing conditions, a series of specimens was prepared by

pressing at 3,000 psi for 30 minutes at various tempera-

tures. Again the powder was cold compacted and brought to

temperature before reapplying the load. All specimens were

cooled in the absence of pressure. The results of this

o

2000

1800

1600

A Coarse

• Interne

Fine

S 1400

14J

1200

1000.4

Fig. 24. Variation of volume fraction of porosity as afunction of temperature for three size fractionsof UO2 ; all specimens pressure sintered for30 minutes at 3,000 psi.

89

series are shown in Fig. 24. The volume fraction of

porosity is seen to decrease almost linearly with increas-

ing temperature up to volume fractions of about .1, after

which large increases in temperature produced only nomi-

nally higher densities.

Pressure was found to enhance densif ication signifi-

cantly. A specimen pressed at 1800°C for 30 minutes at

3,000 psi exhibited a density of '^97%. Increasing the

pressure to 5,000 psi produced a specimen in excess of 991

theoretical density. Increasing pressures adversely

affected punch and die life, however.

In order to explore the effect of time on pressure

sintering, three series of specimens v;ere prepared from

the intermediate size fraction. Specimens were cold com-

pacted at 3,000 psi and heated to the desired temperature

before the load was reapplied. Specimens were held under

load at temperature for periods between 1 and 90 minutes.

The results of these experiments are shown in Fig. 25.

Density is seen to increase at a decreasing rate with time

for each temperature. The data are replotted in Fig. 26,

using a logarithmic time scale. Within experimental error,

these plots are linear and slopes are indistinguishable.

The lack of a common value of volume fraction porosity at

experimentally reliable times prevents the calculation of

an activation energy. Bacmann and Cizeron [48] have deter-

mined a value of approximately 100 kcal/mole for the initial

stage of sintering in the absence of an applied load.

90

Fig. 25, Volume fraction of porosity as a function oftine at temperature. All specimens pressuresintered from interirediate size fractionpowder at 3,000 psi.

91

TOO

Fig. 26. Dependence of pore volume fraction on time

(logarithmic scale) for isothermal pressuresinterings

.

92

3,2. The Metric Properties

The metric properties determined for all specimens

investigated are presented in tabular form. Table 4 sum-

marizes data for specimens prepared by conventional sin-

tering techniques. Table 5 presents data for specimens

from all three size lots pressure sintered at 3,000 psi

for 30 minutes at various temperatures. Table 6 contains

the metric properties of specimens pressure sintered at

3,000 psi for various times. All data are for structures

prepared from tlie intermediate size powder lot sintered

at 1250, 1500 and 1700°C.

3.2.1. The Me tric Properties o

f

Convent J ona lly SinterecPUO -,

Initial studies of tlie sintering characteristics of

UO^ shoKed that only a limited range of densities was

attainable experimentally for a given precompaction pres-

sure and reasonable sintering time and temperature. A

series of specimens ranging from 60°^ to S6% of theoretical

density (10.96 gms/cm"^) was generated for as-received

-270 +525 and ball milled powders by appropriate combina-

tions of the aforementioned variables. Subsequent to

determination of fracture strengths (Section 3.3) and/or

thernial conductivities (Section 3.4), representative spec-

imens were selected for metallographic analysis. Utilizing

the techniques described in Section 2.3.2, the volume frac-

tion of porosity, V , the surface area per unit volume, S^,,

93

Table 4

Metric Properties o£ UO2 Specimens Produced by-

Cold Compaction and Subsequent Sintering

p

94

Table 4 (extended)

llA

95

and the total curvature, M , were experimentally determined.

From these parameters, H, the average mean curvature, X ,

the mean pore intercept, the shape parameter, HT, and X,

the mean solid intercept, were calculated.

The measured values of surface area per unit volume,

S , for specimeiis cold compacted and sintered from the

intermediate size fractiori are sliown in Fig. 27. It is

evident tliat the data does not conform to the hypotlicsis

of a singular functional dependence of surface area u])on

voliine fraction of jiorosity. DeHoff e t a 1 . fl45], and

Gregg [57] have documented the existence of a linear rela-

tionship between surface i-rea and density in metallic sys-

tems. DeHoff et__ci_l_. , attrilvate linearity during second

stage sintering to tlic attainment of a balance between sur-

face rounding and densifi cation .. Rhines, DeHoff and Krons-

bein [AS] examined the effect of precompaction upon tiie

surface area density relationship. They employed the same

powders for v;hich linearity v\'as observed upon sintei'ing

from the uncompacted state. It was determined that compac-

tion produced a surface excess state as shown in Fig. 28.

Precompacted specimens are found to approach the balanced

condition from the "surface excess" direction. It was

further sho'^^n that at any instant the path of change could

be resolved into a vertical component reflecting a change

in surface area with iio cliange in density (surface rouiiding)

and a horizontal component reflecting densi ticaticn without

a change in the surface area.

96

m

o

97

Fig. 28. The approach to the lineai' relationship foi

a spectrum of initial conditions [45].

98

The surface area data in Tig. 27 thus define an enve-

lope of curves rather than a single path. In order to

establish the form of the paths, the intermediate powder

was pressed at 3,000, 30,000 and 80,000 psi without the aid

of a binder. The resulting corripacts wore carefully cut in

haJf di ai!ietrall)'. One half of each S})Ociinen was fired at

1650°C for 30 minutes along with a control group of speci-

mens, containijig a binder, pressed at tlie same pressures.

The remaining unfired portions were metallographically pre-

pared for analysis. The intercept and point fraction counts

were then made in the usual manner (scale of the system pre-

vented a meaningful tangent count) on both fired and unfired

T)ortions of tlie same specimen. Tiiese results established

Icjiown initial conditions from which the si)ectruT. of start-

ing states could be inferred, as well as the general form

of the path. Previous results were found to correlate well

as a function of precompaction , suggest iiig the family of

curves drawn in Fig. 27.

The sam.e data were recast in terms of surface area

per unit mass, S , from which Fig. 29 was constructed. The

most salient feature of this figure is that, within experi-

mental error, S is constant over the ranee of attainableP

green densities. In viev; of the fact that UO^ is brittle

at room temperature (i.e., it cannot be plastically dc-

fornod) , this result is not surprising. A slight tendency

of particles to fragment under high pressures was iioted,

99

o

o c

w

100

but the additiona] surface created was insignificant in

amount and possessed little curvature. Its effect upon

sintering is thus expected to be mininal. The surface area

per pram determined for the intermediate size fraction of

VOy powder was found to be .17 m^/gram, compared to a value

7of ,8? m''/gram obtained from a H.E.T. measurement (see

Section 2.1.4). In view of the disparity in the scales of

observation (atomic vs. microscopic), the agreement is con-

sidered most satisfactory.

Figure 29 contains several interesting features which

warrant discussion:

1) Once the plot is established, any startingstate can be inferred from a measurement ofgreen density.

2) The series of curves which intersect theenvelope of paths are obtained from deter-minations of surface area for equivalentthermal treatments (time and temperature).Fired density may then be predicted for anyspecimen from a knowledge of the green den-sity and firing schedule. In the range1600-1750, it is found that path of surfacechange is independent of temperature. Thisobservation is consistent with the work ofGregg [57], who found the path of surfacearea change for copper to be independentof temperature. Thus, a knowledge ofkinetics of Sp as function of temperaturefor a single initial condition should besufficient to extrapolate to approximatevalues for all other initial conditions.

Figure 30 shows micrographs for specimens from widely

different paths (by virtue of different initial compac-

tions) which were sintered under identical conditions.

Figure 31 sliows micrographs of two states along the same

101

10^ pov.'der

30. Variation, in nicrostriicture for two differentpaths of surface change. Specinens iv'ere con-"pacted to icidely separated starting states andfired under identical conditions.

102

XH .

103

path of surface change. These specimens exhibit very nearly

the same density, but are markedly different in the extent

to \\'hich surface rounding has occurred.

Figure 32 presents the surface area data for cold

pressed and sintered coarse powder. The same general form

is indicated, altliough initial states were not determined.

A single specimen was hot pressed from a volume fraction of

.22 to .13 by an outside source.* Reported conditions were

ISOO^C at 5,000 psi. The direction of change in S, is indi-

cated in Fig. 32, and suggests that hot pressing is capable

of producing microstructural states unattainable by conven-

tional sintering.

The path of curvature change has been discussed by

Rhines et al . [45], and by Gregg [57] in terms of a sequence

of geometric processes which are observed in a system of

particles undergoing sintering. The reader is referred to

Fig. 1, which shov;s the changing geometry for a four-parti-

cle system. Initially in a stack of equiaxed particles,

both total and mean curvatures are positive, the void solid

interface consisting of almost totally convex particle sur-

faces (Fig. 1-A). During early stages of the process necks

form at contacts, producing saddle surfaces (principal

cur^-atures have opposite signs). These contribute eleinents

of large negative cv.rva'?'.are . As the process continues, the

"C a rb o run

d

uri Comp any

104

Fig. 32. The family of curves which define the dependenceof surface area of volume fraction of porosityfor conventionally sintered coarse UO^ powder.

105

necks expand, consuming the convex surfaces of the par-

ticles, and reducing the magnitude of the negative curva-

ture of saddle surfaces. This process is represented in

Fig. 1-B; at some point, the system passes through a condi-

tion where positive and negative curvatures are equal. The

average m.ean curvature is then zero. Positive elements of

curvature continue to be consumed until none remain. Fig.

1-C. At- tills point, the void space is a multiply connected

network, tlie amount of isolated porosity being negligible.

The next event of importance is channel closure, an

event which, according to Rhines e t a

1

. [45], dominates the

second stage. It is interesting to note that simple models

such as that in Fig. 1 cannot illustrate the channel closure

event, because the void space in such a configuration is

sim.ply connected. The interstitial space of an aggregate

of a large num.ber of particles, hov;ever, is necessarily

multiply connected; it is clear that connectivity must

change as sintering proceeds. Connectivity is a topologi-

cal property [53] of a sinter body which can be quanti-

tatively determined only by a serial sectioning technique

[54].

Upon isolation of the void volume by completion of

channel closure, a coarsening of the scale of porosity is

observed to occur. Large pores become larger and small

pores disappear. The magnitude of the curvature deci'eases

as elements of large (negritive) curvature are removed and

106

the curvature associated with remaininp elements decreases

with growth. Thus, the average mean curvature passes

througli a negative maximum and must ultimately approach

zero at theoretical density.

The experimentally determined values of mean curvature

for the coarse and interncdiate size fractions are shown in

Figs. 33 and 34, respectively. As in tlie case of th.e evolu-

tion of surface area, the data indicate a family of curves,

the form of which lias hcen suggested. Tliere are insuffi-

cient data for any single set of initial conditions to

establish a precise path. It can be seen, however, that

H is initially positive, passes through zero for a volume

fraction of porosity between .3 and . ^. , and exliibits a

maximum negative value at about .2 before decreasing (in

magnitude) towards zero. Thus, the form of the curve is

in agreement with that predicted by Rhines et al . , and with

data obtained for metallic systems [45], as shown in Fig. 35,

Figure 35 also allows comparison of the relative values

of FT for two different poudcr sizes. The slope of the

curvature-density plot is seen to increase with decreasing

particle size, as does the magnitude of the maximum (nega-

tive), again in agreement with observations on metallic

systems [45,57]. The extent to which precompaction alters

the form of the path of curvature change is not entirely

clear. The existence of an envelope of patlis , as suggested

by the present data, would seem reasonable in view of the

107

+2

108

Fig. 34. Variation of average mean curvature with volumefraction porosity for conventionally sinteredintermediate UO^ powder.

109

© As-received dendritic Cu (mostly -325)

B -270 +325 dendritic Cu

Fig. 35. Comparison of the dependence of curvature on

pore volume fraction and particle size forUO2 and dendritic copper [45].

110

results of surface area determinations. I'urther, the value

of the mean curvature for the initial stack should be inde-

pendent of the extent of compaction if the particles are

undistorted and not unduly fragmented, and in fact can be

approximated by

2 *-r, T^ r d '

where d is the average particle diameter. Tlie form of the

family of curves defininji the path of curvature change

from the inception of sintering is proposed in Fig. 36.

As indicated in Table 4, experimental determination of

curvature values for unsintered material was deemed not

feasible because the most significant contributions to

total curvature would be from unresolvable features (a dis-

cussion of exnerimcntal techniques is presented in the

latter part of this section). However, it should be pos-

sible to determine values at very early stages in the pro-

cess by sintering at temperatures in the range of 1200-

1400°C for short periods of time. A satisfactory plot

could be generated by obtaining measurements near the jioint

of zero average curvature for several known starting condi-

tions .

Rhines et al . [45], present data for a wide range of

systems for a parameter which they call the shaj^e parameter,

Fit (the product of the mean pore intercept and the mean

curvature). FIX is found (1) to be dimcnsionlcss, (2) to

Ill

Fig. 36. Proposed form of the paths of curvature changefojr a spectrum of initial conditions.

112

+ .1

115

involve all three of the structural parameters (P , N,P ^

and T. ) , (3) to be independent of the scale (size) of

the system, and (4) to be sensitive to shape. Figure 37

presents a plot of ITX as a function of volume fraction at

porosity. The dashed lines define the band of values

determined for a spectrum of equiaxed metallic systems

[45] . The qualitative observation that the UO^ powders

were approximately equiaxed is reasonably well supported

by Fig. 37. Again, the value for a specimen that was sin-

tered and then liot pressed to final density is signifi-

cantly different from values for conventionally sintered

specimens

.

In summary, the evolution of microstructure in UO2

under normal sintering conditions is qualitatively similar

to that observed in metallic systems. The absence of a

linear surface area relationship is attributed to exten-

sive precompaction employed to produce the range of den-

sities .

3.2.2. The Metric Properties ofPressure Sintered UQ ^

A series of specimens was prepared from each of the

three powder lots by pressure sintering at 3,000 psi at

temperatures between 1050 and 2000°C for 30 minutes. The

resulting specimens spanned the range of pore fractions

between .30 and .03. Subsequent to a determination of frac-

ture strength, metallographic analysis was" performed on all

114

specimens from this series. The metric properties of the

members of this series are presented in Tab]e 5.

Although a S])ectrun of structural states extending

beyond those accessible experimentally by conventional

sintering v.-as produced, analysis of the series in terms of

a path would require the assumption that, in fact, the path

was independent of temperature over a range of nearly 1000°C.

In order to establish the veracity of such an assumption, a

second series of pressure sintering experiments was de-

signed. Powder from the intermediate size fraction was

pressure sintered for periods of time ranging between 1 and

90 minutes at three temperatures in the interval of inter-

est. Icnsile strengths of these specimens were established

prior to an analysis of the stiuctural parameters. Results

of the quantitative microscopic measurements on this series

are presented in Table 6. The results of the two pressure

sintered series are presented simultaneously in view of

their interdependent nature. For brevity, the series de-

scribed previously will be designated "isochronal" since

all specimens were sintered for 30 minutes. The latter

series is termed "isothermal" since time is variable at

constant temperature.

The change in surface area per unit volume for the

isochronal series is portrayed in Fig. 38. Again, no pre-

cisely linear region is established, although the inter-

mediate size fraction appears close to linear behavior.

115

Table 5

Metric Properties of UO2 SpecimensProduced by Pressure Sintering at 3,000 psi

for 30 minutes at Various Temperatures

p

(gms/cm )

116

Table 5 (extended)

IT

(cm-l)

117

Table 6

Metric Properties of UO2 SpecimensProduced by Pressure Sintering at 3,000 psi

at the Indicated Temperature for Various Times

p V^ Time S^ S xlO.96 M^

(gms/cm-

}

(minutes) (cm" ^) (cm^/gm) (cm'^)

A. 1500°C

8.55 .22 1

8.87 -.19 3

9.21 .16 109.54 .13 30

10.08 .08 90

B. 1250°C

8.33 .24 10 6.51 8.56 -23.68.43 .23 30 5.81 7.54 -33.68.99 .18 90 3.62 4.41 -18.5

C. 1700°C

5.76x10-^

118

Table 6 (extended)

(cm'^)

P

(cm)

HAg

(cm)

s

(cm)

-6.72X-9.45

119

120

The precipitous change in surface area with density for the

fine powder lot is indicative of an extremely small effec-

tive particle size confirming the general observations of

shrinkage behavior (Section 3.1), B.E.T. measurement (Sec-

tion 2.1.4) and SEM studies (Section 2.1.3). The path of

surface change for coarse powder is significantly different

from that observed for the finer size fractions in that it

appears to approach the balanced state from a "volume

excess" rather than a "surface excess" condition, as illus-

trated by Fig. 28. (A discussion of the meaning of these

terms is presented in tlie previous section.)

Surface area data for the isothermal pressure sinter-

ings appear in Fig. 39. The large symbol from which the

curves emanate was established by cold compaction at 3,000

psi, as discussed in Section 3,2.1. All hot pressings

were preceded by cold compaction in the die prior to heat-

ing and reapplication of load at temperature, thus justify-

ing the choice of initial state. The agreement between

isothermal temperature data is strong evidence that the

path of surface change is not a function of temperature

over a broad range. The data from Fig. 38 for the inter-

mediate size fraction is shown as a dashed line in Fig. 39.

The agreement between the two curves is judged to be within

experimental error, and is the basis for the assumption

that the isochronal specimens lie sequentially on a single

path of surface area development.

121

122

Two curves are shown merging in the range of 751 the-

oretical density in Fig. 39. There is insufficient infor-

mation to indicate whether in fact the initial form of the

curve varies during the very early stages of the process.

Variability may simply reflect changes that occur as a

result of the additional time required to heat the specimen

to higher sintering temperatures.

The- paths of total curvature change arc indicated in

Fig. 40. Additional data for the fine size fraction not

shown in Fig. 40 indicate a maximum negative value consis-

tent with that of the intermediate and coarse values. (See

Table 5.) The calculated values of mean curvature for all

three size fractions are displayed in Fig. 41, The data

indicate that the maximum (negative) value of mean curva-

ture is attained at different levels of porosity for the

various particle sizes. A definite trend toward higher

densities of the maximum (negative) as particle size de-

creases is observed.

Gregg's [57] measurements of the sintering force indi-

cate that the maximum value of the sintering force shows a

similar dependence upon particle size. He was, however,

unable to document the existence of a maximum (negative)

value of mean curvature for his spherical copper powders.

The mean curvature is expected to be a measure of the

driving force available for densification. A qualitative

comparison of the shrinkage behavior for the three powders

123

+ 5

o'

10 -

^ -20o

E-30-

-40-

-50

Fig. 40. Variation of total curvature with volume fractionporosity for specimens pressure sintered at

3,000 psi for 30 minutes at various temperatures.

124

Fig. 41. Variation of mean curvature with volume fractionporosity for isochronal pressure sintered series.

125

(Section 3.1) with the ip.easured values of mean curvature

shows a definite correlation. As Gregg [57] has found,

however, the ability of the system to respond to the forces

which exist will vary as sintering proceeds.

Figure 42 presents the variation of H for the iso-

thermally pressure sintered series. The intermediate size

fraction data from the isochronal series from Fig. 41 is

replotted as a dashed curve. Some scatter is apparent,

presumably because of the sensitivity of H near the maximum

to volume fraction porosity. A smooth curve through the

isothermal data is indistinguishable, within probable ex-

perimental error, from the isochronal curve. Thus, the

dependence on the path of curvature change is independent

(or at least insensitive) to temperature.

The three stages of sintering are evident in Fig. 43

wherein the mean pore intercept, A , is shown as a function

of volume fraction porosity for three powders employed in

the isochronal series. An initial decrease in A is asso-

ciated with the formation of additional interparticle con-

tacts formed as the network shrinks; Aigeltinger [54] has

shown that such events in early first stage produce an

increase in the genus per gram (connectivity) . In terms

of X, tv/o adjacent, initially separated particle surfaces

form a contact as a result of the framework shrinking,

thereby dividing a large irregular void into two pores of

smaller "size." Second-stage sintering shows a nominally

126

-2

127

8

128

constant value of X as channel closure occurs. The onsetP

of third stage is indicated by a rapid increase in X as

conglobation of isolated porosity takes place. All three

stages are evident in the series of photomicrographs shown

in Fig. 44. These microstiuctures were produced by pressure

sintering the intermediate size fraction at an intermediate

temperature (1500°C) for increasing periods of time.

The-behavior of the shape parameter HT for pressure

sintered specimens is shown as a function of volume frac-

tion of porosity in Fig. 45. Figure 45 is presented on

the same scale as Fig. 37 (conventionally sintered UO^) to

permit comparison, and includes the dashed equiaxed band

from reference 45. Additionally, the mcir.bers of each series

are joined by a smooth curve. It is clear that the pressure

sintered data do not conform to behavior observed for con-

ventionally sintered materials. This observation suggests

a direct comparison of the metric properties for the same

material as prepared by pressure sintering and by conven-

tional sintering techniques. A comparison of the dependence

of surface area change is presented in Fig. 46. A general

similarity in appearance and magnitude is observed between

the data for pressure sintered material and that corres-

ponding to conventionally sintered specimens cold compacted

at high pressures. The similarity is less apparent for the

coarse size fraction than for the intermediate. The sig-

nificance of relative similarities and their dependence on

129

22

19

Fig. 44. Photomicrographs of isotherinally pressuresintered UO^ specimens.

130

^4#

* .tfl

• 7

.-.••7Fig. 44. (continued)

V = .0'V

131

+.2

+ .1

-.2

-.4

-.6

-.8

-12

-1.4

-1.6

-1.8

-2D

-72

-24

.5

Fig. 45. Dependence of the shape parameter upon volumefraction of porosity for the pressure sinteredisochronal series.

132

10

•^o

'E 4

C^5

Interinediate

.4 Q

V,

Fig. 46, Comparison of the dependence of surface area on

volume fraction porosity for conventional (solid

lines) and pressure (dashed lines) sinterings.

133

particle size is not clear. In order to establish more

satisfying conclusions, the dependence o£ the path of sur-

face area change upon applied pressure during hot pressing

must be known. Limited data, presented in Table 7 for

fine powders, suggest that pressure has a significant

effect upon path. Therefore, the similarity of the surface

area curves for the intermediate size fraction cold pressed

to 90,000 psi and sintered and that determined for pressure

sintering at 3,000 psi may only be fortuitous.

The relative paths of curvature change for the coarse

material prepared by the two techniques is shou'n in Fig.

47. Figure 48 is a similar representation of data for the

intermediate size fraction. It is evident that mean curva-

ture values attained in pressure sintering may differ from

those established by sintering in the absence of an applied

load by as much as a factor of two! In view of tlie close

relationship between mean curvature and the driving force

for sintering, this result is of major significance, and

contains important implications regarding "the mechanism"

of densification during pressure sintering. The attainment

of ultimately higher densities by pressure sintering may

be rationalized simply on the basis that the system contains

a much greater driving force for densification in the vicin-

ity of the transition from second to third-stage sintering.

This further suggests that externally applied loads may

produce structures containing appreciably larger negative

134

Tabic 7

Metric Properties of SpecimensPressure Sintered at 5,000 psi

From Fine Powder Lot

\

135

+2

CO

•e-2

PressureSintered

Fig. 47. Comparison of mean curvature for coarse UO2powder prepared by conventional and pressuresintering techniques.

136

-10

5 ^v 2

PressureSintered

Fig. 48. Comparison of mean curvature values for intermediate UO^ powder prepared by cold pressingand sintering and by pressure sintering.

137

curvature. Enhanced densification would then be antici-

pated even if the pressure were subsequently removed.

3.2.3. Summary of the Metric Properties

The path of microstructural change has been shown to

be a function of compaction and independent of temperature

for conventionally sintered UO^ . Sintering in the presence

of an applied load has been shovvn to fundamentally alter the

path of curvature change. The increased rate of densifi-.

cation and higher "ultimate densities" reported under hot

pressing conditions may simply reflect differences in micro-

structural development rather than pressure enhanced diffu-

sion as proposed by Coble and Ellis [30].

The convergence of paths of change as pore volume

decreases is generally observed for conventionally sintered

UO^ . DeHoff and Rhines [144] have reported that they find

that, irrespective of initial conditions, all sintered

structures at about IS'o porosity become nearly indistin-

guishable, except for a scale factor. The generality of

this observation is supported by Fig. 49, which shows a

copper sinter body prepared from a mixture of two sizes of

spherical powder [145] and a UO- sinter body prepared from

ball milled powder by conventional sintering. The scales

have been adjusted photographically to emphasize the

similarity. Both specimens are approximately 851 of the-

oretical density. The similarity of geometry takes on

13!

» • w

250 /lim

50/xm<.':

(a)

(b)

*•:'.•.\.

Fig. 49. Coinparison of the geometry of (a) a copper sinterbody, and (b) UO? sintering, both approximatelySS'i theoretical density. (N'ote difference in

scale.

)

139

additional significance in light of the fundamental differ-

ences which exist between the two specimens.

1) Copper contains only copper atoms; UO2 is acompound in which diffusion of two atomicspecies must occur.

2) Copper is metallic; UO2 is considered to bepredominantly ionic in character.

3) Copper is "ductile"; UO2 is "brittle" (UO2is ductile at sintering temperatures, how-ever [80]).

4) Effective homologous sintering temperature*for the copper was approximately .97; forUO2 the homologous temperature was approxi-mately . 67

.

5) The copper body was sintered from the loosestack; the UO2 specimen was compacted athigh pressure.

6) The copper sinter body was prepared from amixture of two sizes of spherical particles;the UO2 powder consisted of angular particleshaving a broad size distribution.

The magnitude of the magnification necessary to make

the structures coincide is indicative of the extent to

which geometry and scale are independent.

3.2.4. Comments on Experimental Determinationof The Metric Parameters

The use of an automated image analysis system to per-

form the counting measurements on sinter bodies has been

successfully demonstrated. In order to extend these capa-

bilities over the range of scale encountered, particularly

*Ratio of temperature to that of miolting point on theabsolute scale.

140

in ceramic systens , optimum experimental conditions are

necessary. The first requirement is a high quality optical

system capable of as broad a span of magnification as is

necessary. High resolution optics have been found to be

essential in order to obtain meaningful data from systems

of complex geometry. A third requirement is a uniform,

intense light source.

The present system, shown in Fig. 18, has wide lati-

tude in choice of magnifications, by appropriate selection

of objective, projector lens, and vidicon- to-proj ector

distance. The liglit source is a 300-watt zirconium arc.

Two apertures and a green filter are encountered by the

light prior to entering the system. A tube of suitable

length and an additional aperture comprise the optical

path between the projector and the vidicon.

In obtaining data for a large number of specimens,

it was found expedient to select the minimum number of

magnifications necessary, and thus the time expended in

calibration of the instrument. A standardized choice of

"live frame" size was also found helpful because it allowed

direct comparison of raw data, decreasing the probability

that an error in data reduction would go undetected. In

changing magnifications or resetting threshold detection

levels, repetition of counting measurements on a previously

characterized specimen insures that conditions remain rela-

tively constant, thereby minimizing experimental scatter.

141

During the course of the present investigation, it

was found necessary to employ an 85X oil immersion objec-

tive, producing an image on the display at an effective

m.agnification of nearly 3,000X. As indicated previously,

the structures of two specimens encountered in the present

investigation were deemed not sufficiently resolvable at

the limits of the optical system. The scanning electron

microscope is capable of resolution far beyond that which

is expected to be necessary for micros tructural analysis.

The hardware necessary to interface commercial SEMs and

commercial image analyzing systems is available, thus remov-

ing the barrier presented by light optics to automated

analysis of fine structural features [146].

3. 3 Mechanical Properties

The tensile strength at room temperature corresponding

to virtually every microstructural state produced in this

investigation was determined by means of the diametral com-

pression test described in Section 2.4. Four characteristic

fracture modes. Fig. 50, were observed to occur. Data

obtained from tensile and triple cleft failures were con-

sidered to be valid. Specimens which showed shear or

laminar failures were rejected. Tensile, triple cleft

and shear failures are the result of stress distributions

within the loaded specimens as described by Rudnick et al . [61]

142

143

Laminar failures are the result of severe density gradients

produced by excessive die wall friction during compaction.

The tensile strengths of conventionally prepared

specimens are presented as a function of volume fraction

porosity in Fig. 51 for the intermediate size fraction and

Fig. 52 for coarse and fine size fractions. Tlie smooth

curve in Fig. 51 was established by a least squares fit of

the data using the equation

= eo

proposed by Duckworth [76]. It can be seen that this equa-

tion produces good agreem.ent with the data over the range,

with a value of b equal to 6 and o equal to about 16,000

psi. Reported values of the constant b are of the order

of 4-9 [66], apparently depending on the stress state [78].

The present values are similar to those obtained for UO2 in

diametral compression by Bowers et al . [84], and are sig-

nificantly lower than values obtained in flexure.

A direct correlation between modulus data and data

obtained by diametral compression does not generally exist.

Rudnick et al . [138] report ratios of modulus to diametral

values in the range of 1.3 to 2.9. Roberts [147], in recent

unpublished work, compared modulus and diametral values for

U0~,presumably for specimens prepared from the same powderj

and found a ratio close to 2.8.

144

Fig, 51. Variation of fracture strength with pore volumefraction for specimens prenared by conventionalsintering of powder from the intermediate sizefraction.

145

Fig. 52. Dependence of fracture strength on volume fractionof porosity for specimens conventionally sinteredfrom coarse and fine UO^ powders.

146

The curves of Fij^s. 51 and 52 ai'e compared in Fig. 53.

Data for the fine size fraction are extrapolated to low

densities for purposes of comparison. It is evident that,

for pore fractions in excess of .2, strength at equivalent

density increases v;ith decreasing initial particle size.

In the vicinity of .2 the dependence of strength on particle

size becomes negligible.

The strengths of specimens produced by pressure sinter-

ing for 30 minutes indicate a similar trend, as shown in

Fig. 54. Figure 54 also shows that strength drops rapidly

at high densities. Data for isothermal sinterings are shown

in Fig. 55, and reflect a similar trend at higher densities.

A recent paper by Manning et al . [148], indicated

differences in thermal expansion characteristics between

sintered and liot pressed '^'b20^ bodies. The authors attrib-

uted the differences to microcracks in the conventionally

sintered material. The present investigation revealed no

significant differences in tlic strengths of conventionally

sintered and pressure sintered specimens of equivalent

density. There are, however, insufficient data to statis-

tically establish a curve for pressure sintered materials.

SEM fractographs of the intermediate isochronal pres-

sure sinterings are shown in I'ig. 56, and span the range

from 70 to 976 theoretical density. Inspection of F'ig. 56

reveals that at lower densities the fracture surface is

very irregular. As density increases tlic fracture surface

147

148

Fig. 54. Fracture strength of specimens from the pressuresintered isochronal series as a function of porevolume fraction.

149

10

9

8

7-

CO

150

(c)

(b)

id)

(c)

(f)

Fip. 56. SRM fractographs of intermediate isochronalscries

.

(c) \\ = .21(b) \V = -27

(a) \\ = .30

(d) \v = .IS(e) \y = .16

(f) \\r = .14

151

(h)

(k)

(i)

0)

rig. 56 ( continued)

(h) V^ ~- .08

(g) V-^ - .12(i) V^ .. .01

(j) \\r - .o:

152

becomes more planar, and the fracture becomes transgranular

in character. At higher densities, fracture is almost

totally transgranular and very similar in appearance to

fractopraphs of UO, presented by Canon et al . [SO].

Based en the study of a large number of fractures, it

is apparent that for porosity levels greater than .2, frac-

ture occurs preferentially at interparticle contacts. These

contacts. or necks represent minimal load bearing areas,

Balshin [149] has proposed that changes in strength with

porosity do in fact reflect changes in the effective or

critical load bearing areas. DeHoff and Gillard [78]

experimentally determined the load bearing area in copper

sinter bodies. They obtained good correlation with mea-

sured rupture strengths of porous bodies by assuming that

bulk rupture stress was attained in the measured load bear-

ing cross -sectional areas. Unfortunately, the fractured

areas of U0-, are indistinguishable from the rest of the

fracture topography; consequently, a determination of

actual fractured area does not appear experimentally feasible

As an alternative. Fig. 57 shows micrograph? of speci-

mens of approximately equivalent density from the coarse

and intermediate size fractions of U0-, powder. A hypo-

thetical tensile stress is envisioned as being applied

vertically, as shown, in such a manner as to produce frac-

ture, i.e., separation of the structure into two parts.

It is additionally stipulated that the probable crack path

153

^S^:^'r.^^

Fig. 57. Path of miniRai fracture length for coarseand interuiecl J n te speciiTtens of comparabledensity.

154

would be within the confines of the photograph and initiate

and terminate on opposite vertical edges. The probable

crack path is then defined as the path for which the least

amount of solid phase is "cut." The total length of cut

is then measured using dividers. Initiation and termina-

tion points for the probable crack path for structures in

Fig. 5 7 arc shown.

Several such measurements indicate that the "cut

length" to effect fracture is longer for the intermediate

size fraction than for the coarse size fraction at an equi-

valent density. These observations, while they do not con-

stitute experimental proof, are consistent with fractog-

raphy and observed fracture strengths.

In summary, at volume fractions of porosity greater

than .2, fracture strengths are related to minimum cross-

sectional areas, generally corresponding to necks between

particles. At a given density, the finer powders exhibit

greater minimum cross-sectional areas and relatively higher

strengths. The correlation of strength with actual area of

created fracture surface is the basis of the "fracture

energy" or the "work of fracture" concept as discussed,

for example, by Swanson [ISO].

The relationship betAv^ecn strength and initial particle

size suggests a dependence on scale, as reflected by the

mean pore intercept X. However, in light of the dependence

of fracture on a mi nimmn area, rather tlian an average area.

155

such a correlation would not be particularly meaningful,

nor would it necessarily extrapolate to other particle size

distributions.

At porosity levels below .2, a transition in fracture

character occurs between the rupture of individual elements

and fracture by passage of a singular crack front. As

this transition occurs strength data show a dependence only

on porosity. Again, there are an insufficient num.ber of

data points to statistically establish a true curve.

Knudsen et al . [82], report a similar dependence on porosity

level with a difference of less than 81 in modulus at room

temperature for specimens having grain sizes between 10 and

50 microns. Interestingly, these same workers report that

at 1000°C, the modulus varies by 350-o for the same speci-

mens .

As volume fraction of porosity decreases still further,

tensile strengths are observed to drop rapidly. A compari-

son of Figs. 43 and 54 show a close relationship between

maxima in the strength curves and the point where X begins

to increase rapidly. Simultaneously, however, the mean

grain intercept increases sharply, as shown in Fig. 58.

The transgranular appearance of the fracture surface, Fig.

56, at high densities suggests that porosity has little

influence on the path of the fracture, once it has been

nucleated.

156

100

90

80

70f-

g 60o

•^' 50

^^0,40

30

20

10-

Fig. 58. Dependence of mean grain intercept on porevolume fraction for isochronally pressuresintered series.

157

3.4. Thermal Conductivity

Thermal conductivity as a function of temperature was

determined for representative microstructures produced in

this investigation. The data were obtained by a compara-

tive or cut-bar technique, using Pyroceram 9606 as the

standard. Experimental details are discussed in Section

2.5.

The temperature dependence of the thermal conductivity

is represented in Fig. 59 for various volume fractions of

porosity. The data aie bounded by curves from the litera-

ture. The upper curve (A) vras suggested by an I.A.E.A.

panel, as reported by Bates [103], as representative of

"95% dense polycrystalline UO^." Tlie lower curve (B) was

obtained by Boegli and Deissler [151] on an unsintered

powder stack with an apparent density of 631.

The data indicate that a smooth traiisition occurs

between the two curves, A and B, as the volum.e fraction of

porosity increases. For dense specimens, conductivity de-

creases by nearly a factor of 2 over the range 300-700°K.

At low densities the change in conductivity over the same

interval appears nearly negligible.

For purposes of comparison, all conductivity values

are compared at 500°K, as a function of volume fraction

porosity, in Fig. 60. Although there is some scatter, the

data indicate the values for specimens prepared from coarse

158

<M

.iS

.29 j^. A

X/\

3 4 5 6 7 8 9

fig. 59. Dependence of thermal conductivity on terioeraturefor UO2 specimens with different pore volumefractions. (A) Plotted from equation in Rcf. 103

fB) Ref. 151.

159

!0

SI

CO

1

9

8

7

6

5

4

^- 2

^ Literature values

A conventionally sintered*)• ^ J ? coarseA pressure sintered j

» conveo pres

entionally sintered 1 inter- f^

sure sintered j mediate^

B conventionally sintered?

a uressure siiitered ^ °

& ,0

JL.—

„

.1

Fig. 60. Thermal conductivity at 500'''K as function ofvolume traction of oorositv. (.A) Ref. 103,(B^ Ref. 151.

160

powder are somewhat lower than those obtained from the

finer materials. This suggests that interparticle contacts

or areas of minimal cross -section may in fact critically

influence conductivity. Analogy has been made between elec-

trical and thermal conduction because of the similarity of

the phenomenology. The minimal cross -sectional area may

then be viewed as a region of high resistance to carrier

flow.

A sharp decline in conductivity is observed at high

densities as indicated in Fig. 60. The reader will recall

that, although these specimens were produced by pressure

sintering in vacuum, they were subsequently given thermal

treatment in hydrogen to insure stoichiometry. Further,

two independent determinations of the conductivities were

in good agreement, reducing the probability of experimental

error. No external or internal defects, cracks, or inhomo-

geneities were evident prior to or subsequent to the

measurements. Metallographic analysis indicated the pres-

ence of a second phase in the microstructure . This phase

appeared to be situated at grain boundaries and associated

with residual porosity.

MacEwan [152] has found second-phase inclusions upon

heating UO2 to high temperatures in argon. He identified

the inclusion as uranium metal by its appearance, by the

fact that it tarnished upon exposure to air, and from x-ray

diffraction data. MacEwan suggested that the uranium

161

inclusions were the result of the decomposition of UO- into

a hypostoichiometric U0^_ and uranium metal at high tem-

peratures.

In contrast to MacEwan's observation, the inclusions

found in the present investigation were found to be stable

upon exposure to air for several months. An analysis of

the volume fraction of second phases indicates that the

maximum was something less than 0.51, the amount apparently

depending on time and temperature of preparation. X-ray

diffraction failed to show any lines not attributable to

cubic UO^. A microprobe analysis of the inclusions v/as per-

formed to determine their compositions. Positive identifi-

cations of the elements aluminum, silicon and iron were

made for several different inclusions. X-ray im.ages of

representative inclusions for these three elements are

shown in Fig. 61. Inspection of Table 1 reveals that alumi-

num, iron and silicon are principal impurities in the as-

received powder. Subsequent study of the microstructure of

the -6 m.esh as-received grains revealed the presence of

this same phase. The distribution appeared very non-uniform,

with some grains having no observable inclusions and others

having a substantial amount. The m^orphology was that of

islands or clusters wholly contained within what appeared

to be a single grain. Triis suggests that the m.aterial was

present prior to fusion and was not Introduced in subsequent

processing.

162

(a) AlK^

Cb) FeK^

(c) SiK^

10 micronsI

—

A

Fip. 61. X-ray images of a second phase found in UO2sinter bodies. Al , Fe and Si are theprincipal impurities in the UO2 powder employedin this investigation.

163

Abnormally low values of thermal conductivity for high

density specimens (cf necessity produced by heating above

1800°C) are attributed to the presence of an impurity phase

CHAPTER IV

CONCLUSIONS AND SUMMARY

1. The metric path of microstructural development

during sintering of U0-, has been established. A broad

spectrum of microstructures ranging from near theoretical

density to loosely compacted unfired powder stacks has

been examined.

2. The evolution of micros tructure of conventionally

sintered oxide has been found to be qualitatively similar

to that observed for metallic powders.

3. At volume fractions of porosity below about .15,

the similarity of the pore-solid geometry of UO2 and that

of metallic sinterings is striking. This observation is

significant in view of the large differences in scale and

basic physical characteristics which exist between the two

materials

.

4. The role of compaction in establishing the frame-

work or initial state of UO^ has been elucidated. Deter-

mination of surface area of pore-solid interface as a

function of compaction and firing conditions provides quan^

titative information upon which to optimize processing

variables. The present approach has immediate application

164

165

to commercial reactor fuel production, both in design and

quality control.

5. It has been established that pressure sintering

(hot pressing) produces a fundamentally different path of

structural development than that observed for the same

material undergoing conventional (pressureless) sintering.

Significant implications are contained in this observation

regarding the mechanisms of densif ication during hot

pressing.

6. Two regimes of mechanical behavior at room tem-

perature have been observed for porous U0-, sinter bodies.

(1) At porosity levels greater than 20"o, fracture occurs

at necks or contacts betv;een particles. A dependence upon

density and initial particle size' in this regime is thouglit

to be the result of the fracture occurring at a minimal

cross -sectional area. (2) At porosity levels less than

about 20"o, a transition to a transgranular fracture mode

is observed. A dependence only on the volume of porosity

is found and fracture appears to occur by the passage of

a single crack front. Both failure median Jsms are con-

sistent with the concept of fracture energy.

7. Thern;al conductivity in the intermediate tempera-

ture range ( =100 - SOG°Kj , where energy transport occurs by

phoncn conduction, shows a sensitivity to initial particle

size at low densities. This result is rationalized again

in terms of minimal cross -sect ional area'i in the solid

166

network. At high densities, the presence of a second phase

having its origins in the ravs- material obscures possible

microstructural correlation.

APPENDIX A

PRECISION LATTICE PARAMETER PROGRAM

Stoichiometry was determined based on measurement of

the lattice parameter. The following program was employed

in that measurement.

Description of the Problem

This program is intended to calculate the crystal lat-

tice constants and their probable errors by a method of

least squares. The program provides for using as many as

three separate correction terms for various forms of the

systematic errors; however, one, U-io , three, or none at all

could be used. If desired, a weighting factor may also be

used for each reflection, which may include an observation

weight or a trigonometric function or both. Also a refrac-

tion correction may be applied to the observed angular

measurements of lines or spots.

This program is a modified version of the one described

in reference No. 3 with added off-line plotting of v. vs.

20. values. Reference No. 4 describes the plotting tech-

nique used in this program (see "Special Features and

Restrictions")

.

167

168

The program does the following:

given for any i

h., k., Z. - the Miller indices

9^ - the angular measurement of the lines or spots

w. - the observation weight

\. - the wavelength of the observation

and letting

V. = H.A+K.B+L.C+M.D+N.E+O.F+P.G>Q.I+R^J

- ~ [sin'e^+Asin^e^],

i

then 9CE W.vp =

is solved for the coefficients A, B, C, D, E, F, G, I, J.

Their associated variances aT are calculated as

Z W.v-2 i ^ ' -1

where T.

^ is the j diagonal element of the inverseJ J

matrix

.

Thie coefficients G, I, J repre^enc the drift constants

of the systeriiatic errors.

Then using the above equations, the prcgraiii derives

V = 1/(ABC - AF^ - BE*^ - CD^ + ZFED)^''-

and calculates the constants

aQ = V(BC-f2)1/2

b^ = V(A(:-E-)^^^

Cq - VCAB-D^)^/'^

169

-1 .2, .1/2a = cos'-'{(ED-AF)/[(AC-E^)(AB-D")]"' }

3 = cos'^{(DF-BE)/[(AB-d2)(BC-f2)]^/^}

Y = cos'^{(FE-CD)/[(BC-F^)(AC-£-)]^/2}

md their probable errors

P.E.a, 6745

2

^01 _2 ^^0^0

(a^b^cosY)^a^ + (a^CQCOsB)^a^

^O^O^O^(anbnCnCOsa) a^

1/2

P.E.bQ = .67454^0-' K .2^2

0^0 „2

2 ^

+ (a^b^cosY)^a^ ^ (a.b.c„cosS)^a^'0-^0

2 2+ (bQCpCOsa) Cp

D ^"0 0"0

1/2

P.E.c, 67454^0^'

^iio]

I2 ] l^ )

2 2 2,2(a b CgCOSY) aj ^ (aQc5cos6) a^

+ (bJcQCOsal^ap1/2

P.E.a, _ . _ I sinS * sinv |

674^1 ap

'TC sina

p.E.e = ,5745!sina • sinY

' /AC sina "'

170

/XB siny

In the equation for v., H. = hT, K. = kt", L. = tt",^ I'l I'l I'l i'

M^ = 2h.k., N. = 2h^£^, 0^ = 2k^^^, and the correction

terms P^, Q^, R^ represent one of the following trigono-

metric functions

?l-

pj = sin^2e.

^l= i} - e.)sin(TT-2e.)

p^ = cos^e^

Q^ = cos e. sinZe.

q2 = (-J_^ -1 ^ c 1 n (

^)sin2|

Q^ = (sin^2e.)/2e.

qf = cos^e. sine.

Q^ = cos^e. sin^Ze.

sin2e.

rO =

: = cos2e.

2 cos^Bj^

1 smt

The weighting factor W. is calculated from one of the

three desired functions

wO = w.1 1

sin 29.

sin^(TT-29.)cos^(TT-26^)

The refraction correction may be applied using

2

Asin'19.58PZ ^i ^ ,„-6—EM 4- ^ ^°

171

where p is the density, Z is the total number of electrons

in the molecule, and EM is the molecular weight; otherwise

Asin^e. = 0.

The conditions imposed by the crystal systems are as

follows

:

triclinic - no condition

monoclinic (b-axis unique) - D = 0, F =

monoclinic (c-axis unique) - E = 0, F =

rhombohedral -B=A, C=A, D=F, E=Fhexagonal -B = A, = ^^, E=0,F =

orthorhombic -D=0, E=0, F=0tetragonal - B = A , D =

, E = , F =

cubic - B = A, C = A, D = 0, E = 0,

F = 0.

The subroutine MATINV is used to invert the matrix.

References: 1. Determination of Lattice Parameters withthe Aid of a Computer, by Melvin H. Muellerand Leroy Heaton, ANL-6176.

2. 727/MET 124.

3. B 106.

4. Off-line Plotting System Techniques UsingCalcomp Magnetic Tape Plotting System#580, Technical Memorandum No. 70, byClifford leVee and John Ohde , April 20,1964.

Machine: CDC 3600 FORTRAN -SCOPE, with three tape units andCalcoinp Magnetic Tape Plotting System ^580.

The following comment card is supplied v/ith theattac'iied binary deck:

MOUNT CALCOMP TAPE,

172

If no plotting is desired, an additional commentcard, DO NOT SAVE CALCOMP TAPE, is required.

Running Time: About 15 seconds per crystal system.

Input Information Required

CodeName Description

Title - column 1 must beblank.

CardType

173

Ja^'i CodeJX21 Columns Format Name Description

^"^^ KP Correction Term P SelectionFor KP=0 P=0

*1 P=sin22e2 P=(u/2-e)-sin(TT-2e)3 P=cos2e

KQ Correction Term Q SelectionFor KQ=0 Q=0

1 Q=cos2osin2e*2 Q=(l/sine+l/e)sin2e3 Q=Csin229)/2e4 Q=cos2Qsinfi5 Q=cos2esin22e6 Q=sin2e

-'^"^^ KR Correction Term R SelectionFor KR=0* R=0

13-1

25-30 KW

1 R=cos2e2 R=cos2e/sine

Weighting Term W SelectionFor KW-1 W=;v

*2 W=w/sin22e3 W=w/Csin2(Tr-20)

• rnc4('Tr-9Q'i•cos4(7y-2e)

^^^^ KRC Refraction CorrectionSelection

For KRC=0 Asin2 =o1 Asin2 =-19.58.RH0x2/

•a2//i 10-6

^"^'^^ KC Input selection for TE^(see card 5j

For KC=0* TEi=2ei degrees1 TEj^^Si radians

"^^--^S Kl ConstantFor Kl=l* program reads

other cards of tvpe1,2,3,4,5 and 6 '(ifrequired)

For K1=0 program readsonly other cards oftype 5 and 6 (ifrequired)

NOTE: The last Kl must be1 - end of the problem.

174

Card CodeType Columns Format Name Description

49-54 KPL For KPL=0 no off-lineplotting

1 program plotsoff-line

6 1-12 (3F12.0) EM Molecular weight

13-24 Z Total number of electronsin the molecule

25-36 RH0 Density

NOTE: Card type 6 is only required when KRC=1.

Possible OutDUt

a) Printing off-line

1. Title2. Crystal system identification3. The selection of the correction and weighting

termsZ W. V.

. N where N = number of observations(N-K-l)I IV.' and k = number of parameters

N ^

5. E W.

N ^

6. Input data and calculated Vj^ for each datapoint

7. Lattice constants and their probable errors8. Drift constants

b) Plotting off-line

The program plots Vj^ vs. 2ej^, prints, writes thetitle and the selection of correction and weight-ing terms, and draws the axes for each individualcase

.

The scale for plotting is the following:

1. Horizontal axis - 1 inch per degree.2. Vertical axis - the scale is determined for

each set of reflection data. Minimum andmaximum values of Vj are calculated andplotted inside the 8 inches of eacli graph.

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APPENDIX B

INTERPOLATED THERMAL CONDUCTIVITYOF PYROCERAM 96 06 IN INCREMENTS OF

1° KELVIN OVER THE R.A.NGE 300-1200°K

The following data are taken from Table 3110R, Data

Book Volume 3, Thermophysical Properties Research Center,

Purdue University, Lafayette, Indiana, 1966.

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BIOGRAPHICAL SKETCH

Wayne Douglas Tuohig was born July 2, 1942, in East

Orange, New Jersey. He lived in Morristown, New Jersey,

until 1954, when his family moved to Jacksonville, Florida.

He attended Landon High School in Jacksonville, and was

graduated in 1960. In the fall of 1960 he entered the

University of Florida, completing the requirements for the

degree of Bachelor of Metallurgical Engineering in 1965.

After brief employment as a powder metallurgist with Reming-

ton Arms Company, he began graduate studies at the Univer-

sity of Florida in pursuit of the degree of Doctor of

Philosophy.

The author is married to the form.er Candace Ruth Herr-

mann and is the father of one daughter. He is a mem.ber of

Tau Beta Pi, Alpha Sigma Mu and Phi Kappa Phi honoraries,

the American Ceramic Society, the American Society for

Metals and the American Institute of Mining, Metallurgical

and Petroleum Engineers.

Upon receipt of his degree, the author will be affili-

ated with Argonne National Laboratory, xlrgonne, Illinois.

225

I certify that I have read this study and that in myopinion it conforns to acceptable standards of scholarlypresentation and is fully adequate, in scope and quality,as a dissertation for the degree of Doctor of Philosophy.

Dow IsTiitney,' Cha i rrTi\n

Associate Professor -of'\aterialsEngineering

I certify that I have read this study and that in myopinion it conforms to acceptable standards of scholarlypresentation and is fully adequate, in scope and quality,as a dissertation for the degree of Doctor of Philosophy.

^v^Ut^M.Robert T. DeHoffProfessor of ^la

Engineering

I certify that I have read this study and that in myopinion it conforms to acceptable standards of scholarlypresentation and is fully adequate, in scope and quality,as a dissertation for the degree of Doctor of Philosophy.

Larry L. HenchProfessor of MaterialsEngineering

I certify that I have read this study and that in myopinion it conforms to acceptable standards of scholarlypresentation and is fully adequate, in scope and quality,as a dissertation for the degree of Doctor of Philosophy.

(^4M^John .T. IlrerT

Professor of MaterialsEngineering

I certify that I have read this study and that in myopinion it conforms to acceptable standards of scholarlypresentation and is fully adequate, in scope and quality,as a dissertation for the degree of Doctor of Philosophy.

Robert W. Gp<ildAssociate-Professor ofMaterials Engineering

I certify that I have read this study and that in myopinion it conforms to acceptable standards of scholarlypresentation and is fully adequate, in scope and quality,as a dissertation for the degree of Doctor of Philosophy.

This dissertation was submitted to the Dean of the Collegeof Engineering and to the Graduate Council, and wasaccepted as partial fulfillment of the requirements forthe degree of Doctor of Philosophy.

December. 1972

De an , College of Engineering

t)ean, Graduate School

3 3

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