Group Title: evolution of microstructure during sintering of UO₂ and its effect upon mechanical and thermal properties
Title: The Evolution of microstructure during sintering of UO₂ and its effect upon mechanical and thermal properties
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 Material Information
Title: The Evolution of microstructure during sintering of UO₂ and its effect upon mechanical and thermal properties
Physical Description: xiii, 225 leaves. : illus. ; 28 cm.
Language: English
Creator: Tuohig, Wayne Douglas, 1942-
Publication Date: 1972
Copyright Date: 1972
 Subjects
Subject: Uranium compounds   ( lcsh )
Uranium -- Metallurgy   ( lcsh )
Sintering   ( lcsh )
Nuclear fuel elements   ( lcsh )
Materials Science and Engineering thesis Ph. D
Dissertations, Academic -- Materials Science and Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis -- University of Florida.
Bibliography: Bibliography: leaves 215-224.
Additional Physical Form: Also available on World Wide Web
General Note: Typescript.
General Note: Vita.
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Bibliographic ID: UF00097644
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000577405
oclc - 13977930
notis - ADA5100

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THE EVOLUfrCN OF MfCROSTRUCTURE
DURING SINTERING OF C'O AND 'TS EFFECT
UPON MECHANICAL AND TFEH_\MAL PROPERTIES



By


'ayve Douglas Tuchig


A iOisscrt-,j.on Presented to the Cradiu;t Council
the Uniiver;sity o' Ficrj;
In Partial Fulfillment of rthe Requi;res;.nt fcr the
Degree of IDoctor ;fi Phi o-;op)



U41:VERSITY CF FL'JRID.






























Dedicated to my wife, Candy,
and to my parents,
Mr. and Mrs. W. J. Tuohig.












ACKNOWLEDGEMENTS


The author wishes to acknowledge the encouragement

and helpful discussions provided during the course of this

research by his chairman, 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 i. H. Halback and R. A. Graham

are sincerely appreciated.

Financial support from the United States Atomic

Energy Commission is gratefully acknowledged.













TABLE OF CONTENTS


ACKNOWLEDGEMENTS . .

LIST OF TABLES . .

LIST OF FIGURES . .

ABSTRACT . . .

CHAPTER


Page

S. . . . . . iii

. . . . . . . vi

. . . . . . . vii

. . . . . . xii


S INTRODUCTION . . . . . . .

1.1. The Nature of the Sintering
Process . . . . . . .
1.2. Evolution of Microstructure .
1.3. Effect of Microstructure on
Mechanical and Thermal
Properties . . .
1.4. Objective of the Present Work .

II EXPERIMENTAL PROCEDURE ....

2.1. Material Characterization ..
2.2. Specimen Preparation ..
2.3. Evaluation of Geometric
Properties . . .
2.4. Evaluation of Mechanical
Properties .....
2.5. Measurement of Thermal
Conductivity .....

III RESULTS AND DISCUSSION ....

3.1. Densification Behavior ...
3.2. The Metric Properties .. ...
3.3. Mechanical Properties .. ...
3.4. Thermal Conductivity ..







TAB I ; i : J'S (continued)


Page


CONCLH SI :' .' s- ::'L\RY . . .


A PRECISE : 1

Bi I NTI RPOVI
OF PY1, 1 '
1 KL\IN ,:

LIST OF REIIPLNCi S

BIOGRAPHICAL SKETCH .


CHAPTER

IV

APPENDI X


TICE PAAI1E]TI PROGRAM .

Ti "',iL CON )IICTIVTTY
90(. IN INCR E"IFTS CO
1 i ANhl: 300-1200 .












LIST OF TABLES


Table Page

1 Analytical Impurities in the Arc Fused
UO2 Used in this Investigation . . . 34

2 As-received UO2 Powders were Separated
Into Lots by Sieving . . . . ... 46

3 Surface Areas of the Three Size
Fractions of UO2 S............. 56

4 Metric Properties of UO2 Specimens
Produced by Cold Compaction and
Subsequent Sintering . . . . .. 93

5 Metric Properties of U02 Specimens
Produced by Pressure Sintering at 3,000
psi for 30 minutes at Various Tempera-
tures . . . . . . . ... 115

6 Metric Properties of U02 Specimens
Produced by Pressure Sintering at 3,000
psi at the Indicated Temperature for
Various Times . . . . . ... 117

7 Metric Properties of Specimens Pressure
Sintered at 5,000 psi From Fine Powder
Lot . . . . . . . . ... 134












LIST OF FIGURES


Figure Page

1 Sequence of states through which a
sintering four-particle system passes 11

2 Structural evolution during useful
life of a UO2 fuel pin . . . .. 32

3 SEM photographs of -6 mesh as-received
UO2 powder . . . . . . ... 35

4 SEM photographs of -200 mesh as-received
powder . . . . .. . . . 36

5 Photomicrographs of -6 mesh as-received
powder . . . . . . . . . 38

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

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

8 Dependence of the lattice constant at
25C upon O/U ratio for cubic UO2 . 42

9 Sinterings prepared from loose stacks
of as-received U02 sintered at 22500C . 48

10 SEM photos of powder from the three size
fractions employed in this investigation 51

11 Schematic of the B.E.T. apparatus used
to determine surface area . ..... 55

12 B.E.T. plot for fine size fraction of
UO2 powder . . . . . . . . 55

13 Punch and die assembly used to cold
compact UO2 . . ... . . ... 59

14 (a) The high temperature Astro sintering
furnace . . . . .. .. . .. 61
(b) Centorr vacuum hot press ...... 61


vii






LIST OF FIGURES (continued)


igure Page

15 Graphite and boron nitride die assembly
used to pressure sinter UO2 ...... 63

16 Schematic illustration of the counting
measurements on a sinter structure . .. 67

17 Quantimet display of 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 used to
machine UO2 specimens . . . ... 78

21 Comparative cut bar thermal conductivity
apparatus . . . . . . . 80

22 Temperature dependence of the thermal
conductivity of Pyroceram 9606 . . .. 83

23 Densification of three size fractions
of UO2 at constant heating rate followed
by 5 minute arrest at 1800C pressure
sintered at 3,000 psi at 10-4 torr . . 86

24 Variation of volume fraction of porosity
as a function of temperature for three
size fractions of UO2 .......... 88

25 Volume fraction of porosity as a
function of time at temperature ... . 90

26 Dependence of pore volume fraction on
time for isothermal pressure sinterings 91

27 The family of curves which define the
path of change during sintering of the
surface area per unit volume for the
intermediate sized fraction ...... 96

28 The approach to the linear relationship
for a spectrum of initial conditions . 97








LIST OF FIGURES (continued)


figure Page

29 Surface area per unit mass as a function
of volume fraction of porosity for
specimens prepared by compaction at the
indicated pressure and sintering for
various times and temperatures . . . 99

30 Variation in microstructure for two
different paths of surface change . 101

31 Evolution of microstructure along a
single path of structural evolution . 102

32 The family of curves which define the
dependence of surface area on volume
fraction of porosity for conventionally
sintered coarse UO2 powder . . ... 104

33 Average mean curvature as a function of
volume fraction porosity for UO2 prepared
by conventional sintering from the coarse
size fraction . . . . ... .. . 107

34 Variation of average mean curvature with
volume fraction porosity for conven-
tionally sintered intermediate UO,
powder . . . . . . . . .. 108

35 Comparison of the dependence of curva-
ture on pore volume fraction and particle
size for UO, and dendritic copper . . 109

36 Proposed form of the paths of curvature
change for a spectrum of initial condi-
tions. .... . . . . .... 111

37 Dependence of the shape parameter on
volume fraction porosity for all conven-
tionally sintered UO2 specimens . . 112

38 Dependence of surface area per unit
volume upon the pore volume fraction
for the isochronal pressure sintered
series . . . . . . .. ... 119







LIST OF FIGURES (continued)


igure Page

39 Variation of surface area with porosity
for specimens pressure sintered at the
indicated temperature at 3,000 psi for
various times . . . . . . . 121

40 Variation of total curvature with volume
fraction porosity for specimens sintered
at 3,000 psi for 30 minutes at various
temperatures . . . . . .. . 123

41 Variation of mean curvature with volume
fraction porosity for isochronal pres-
sure sintered series . . . . .. 124

42 Comparison of mean curvature for iso-
thermal pressure sinterings and that
obtained in the isochronal series . . 126

43 Variation of the mean pore intercept X
with volume fraction porosity for
pressure sintered UO2 ......... 127

44 Photomicrographs of isothermally
pressure sintered UO2 specimens . . 129

45 Dependence of the shape parameter upon
volume fraction of porosity for the
pressure sintered isochronal series . 131

46 Comparison of the dependence of surface
area on volume fraction porosity for
conventional and pressure sinterings . 132

47 Comparison of mean curvature for coarse
UO2 powder prepared by conventional and
pressure sintering techniques . . .. .135

48 Comparison of mean curvature values for
intermediate UO2 powder prepared by
cold pressing and sintering and by
pressure sintering . . . . . . 136

49 Comparison of the geometry of (a) a
copper sinter body, and (b) UO2 sinter-
ing, both approximately 35% theoretical
density. .. . . . . . . .138








LIST OF FIGURES (continued)


.gure Page

50 Failure modes in diametral compression . 142

51 Variation of fracture strength with
pore volume fraction for specimens pre-
pared by conventional sintering of power
from the intermediate size fraction . 144

52 Dependence of fracture strength on
volume fraction of porosity for specimens
conventionally sintered from coarse and
fine UO, powders . . . . ... .... 145

53 Comparison of the strength-pore volume
dependence of three size fractions of
conventionally sintered UO, . . .. 147

54 Fracture strength of specimens from the
pressure sintered isochrenal series as
a function of pore volume fraction . . 148

55 Variation of fracture strength with
vclune fraction corosity fcr snecinens
prepared by isothermal pressure sinter-
ing the intermediate UO, powder at
3, 0OJ psi . . .. . . . . 149

56 SE% fractographs of intermediate iso-
chronal series . . . . . . . 150

57 Path of minimal fracture length for
coarse and intermediate specimens of
comparable density . . . . . . 153

58 Dependence of mean grain intercept on
pore volume fraction for isocbronally
pressure sintered series . . . . 156

59 Dependence of thermal conductivity on
temperature for UDO specimens with
different pore volume fractions ... . 15

60 Thermal conductivity at 500'K as func-
tion of volume fraction of porosity . 159

61 X-ray images of a second phase found
in UO, sinter bodies . ... ..... 162







Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



THE EVOLUTION OF MICROSTRUCTURE
DURING SINTERING OF UO2 AND ITS EFFECT
UPON MECHANICAL AND THER%.AL PROPERTIES


By

Wayne Douglas Tuohig

December, 1972


Chair-.mn: E. D. Whitney
Major Department: Materials Science and Engineering



A full range of microstructural states, ranging from

30% to near theoretical density, were produced from UO,

powders. Both conventional and pressure sintering (hot

pressing) techniques were employed to fabricate the micro-

stru-tures. Each state was characterized by its associated

metric properties, i.e., volume fraction of joid, area of

void-solid interface, curvature, mean pore and mean grain

iT ercepts, as determined by the procedures of quantitative

metallography. Additionally, tensile strengths at room

temperature and thermal conductivities over the intermediate

temperature range 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 microstructure during conventional

sintering of UO, is shown to be qualitatively similar to

that of metallic systems. The role of precompaction (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 SO 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 greater 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 contaminants in the starting material.











CHAPTER I

INTRODUCTION



1.1. The N ture of the Sintering Process


Sintering in the presence of a liquid phase is as old

as the nost ancient Clramic artifact. A more modern conno

tatior of the teot ".sintering" implies the coalescence of

particulate matter at temperatures below the melting point

into a solid, coherent body. The driving force for this

Process is the theriodyna iic tendency of a system to lower

its energy by decreasing free surface area (in the absence

of a liquid). The sintering process may be characterized

by:

1) Particle contact -- particles are brought into
contact under the 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 particles
broaden into areas of contact or necks.

3) The initially continuous network of porosity
becomes less continuous.

4) Both 2 and 3 are accompanied by a macroscopic
contraction or shrinkage. As a result, the
density is observed to increase.

5) The rate of densification decreases rapidly
as theoretical density is approached; average
grain size increases.












of ]I i id

ll['



Aus 1 1. '

nucl "

so




tiosn; T ]
piC ;9 1

tenc

t i oi 1

no: I E; 1 i

Si lh [ 1 :, 1



ensuing ye rs s"

fio icli es t. h 1 o i

fusion and sinic

workers had coi c

under tile actii

1Wulff[7] utilize,

that stresses in

and thus plastic

and Wulff [10] d

produce shrink fif

rounding without


1 f 't1 Sinterin P'rocess

ii .t w, rk n sintering in the abscice

S1 ly 1', Iaston [1] in 1725, on plati-

1.:' c i I to hLiich solid species

T ; t ;. i I not ho now until Ro i rts-

Ill 'irfu.i;on of gold in lead. The

siw iri t] t] e ry \. :s contained in the

S] in 10i thnt sinterinp in the

] n-" Iv s brought aboit by surface

I', [-1] obsei nation of spheroidiza-

Sled hii to conclude tliat the phenoni

t surface tension. Ihe wcrk of

p ,i',ied tie conclusion that a liquid

iiitc for sintering to occur. In the

is on single and multicomponcnt systems

. : relationship between solid state dif-

it. By the early 1940's, a number of

1id that material transport occurred

of siurace tension [6-8]. liretblad and

equations of capillarity and concluded

sinteing bodies exceed the elastic limit,

deformation occurs. Pines [9] and Shaler

stinguished between mechanisms which could

and those which produced only surface

densi fi cat i on,






Kuczynski [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:
2
1) viscous flow -- x c t

2) evaporation-condensation -- x a3 t

3) volume diffusion -- x a t

4) 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] with glass spheres led

him to conclude that the 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 flow. Adopting the formalism

of Bingham flow, 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 meciha isr propo y N' rro I 1. j nu 1: t- r h

Ilerring [16] to explain creep l ow stresses pr vidru a

means to reconcile both the pl stic flow a1nd diffusion:

viewpoints. The NXburro-llrriln ocd 1 [17] sug "
creep deformation can occur by the diffusion of i -terial

from grain boundaries in coiripressicn to grain bou darics

in tension, i.e., a flux of vacancies to rain hoiindaries

experiencing a conpressile stress field. Tu grain

Ibondarics bconc vacancy sinks. Exiseri iintal cvide c- KI

provided by Udin, Shaler and Wulff [18] an by Gr1cnou [I

Udin et al. attributed the creep of fine copper wires to

the Nabarro-I'Hrring mechanism. Greenolluh repeated th, -

perimnnts using single crystal vires aid observed crece

rates that were two orders of magnitude sr:i]ler than those

measured for polycrystalline materials.

The close relationship between sintering and diffu-

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

who found that sintering in the presence of small comprcs-

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 sink model.

An ingenious experiment by Kuczynski, Matsumura and

Cullity [24] provided the 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 where 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 the weld necks

by diffusion was 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 [NaC1 by

evaporation-condensation, Kingery and Berg (25), glass by

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

than one 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

morphology, (4) occurrence of discontinuous grain growth,

(5) atmosphere, (6) stoichiometry 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 the

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 variable to control microstructure, by virtue

of the fact that it increases the driving force for densi-

fication of a powder compact without significantly increas-

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

densities approaching theoretical have been achieved for a

number of materials.

The mechanism of densification during hot pressing

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

illis [30], Rossi and Fulrath [31] and Murray et al. [32].

Although simple sintering models are inadequate to describe

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

peratures below 20000C and pressures below 7,500 psi as

are normally employed in hot pressing refractory ceramics,

densification takes place by a diffusional mechanism.

Evidence for this comes primarily from agreement between

densification kinetics and lattice diffusion measurements

[28,29]. The plastic flow model proposed by Murray et al.

[32], and by :McClelland [33] may, however, he apolirable

to soft materials such as copper, lead, and NiO [2;].








Coble 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 et al. [32] have studied the hot pressing

behavior of stoichiometric and hyperstoichiometric U02.

They found that hyperstoichiometric material densified more

rapidly than did the stoichiometric oxide, in agreement with

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

tered material. Maximum reported density was 10.55 p/cm3

(97% theoretical density), produced by pressing at 2,000

psi at 1800C for ten minutes.


1.1.3. Sintering of UO2

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

reactor designs provided stimulus for extensive study of

the sintering behavior of UO2. Interest continues in both

UOi2 and mixed oxides of uranium and plutonium which fuel

the present generation of breeder reactors.

The effects of powder characteristics and processing

variables on densification -nd microstructure have been

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








In general, remarks th: apply to nost sinterable powders

apply to U0, [36,37]. 'orevxer, certain characteristics of

lO2 are not general in nature and deserve further discussion.

Py virtue of the i.ul tiple oxidation states of uranium,

there are at least four thernodynanically stable oxides of

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

lowest 0/1) 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 hyperstoichiomctry exhibited by U02; i.e.,

its ability to dissolve excess oxygen into the flucritc

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

U02 may in fact have O/U ratios of 2.00 to 2.25. It is

well established that the 0/U ratio of 102 has a very

significant effect on both sintering behavior and physical

properties [36,37].

The 0/U ratio of U02* may be controlled by controlling

sintering furnace atmosphere and stoichiometry of starting

material. Strongly reducing atmospheres produce O/U ratios

close to 2.00. Sintering in inert gas or vacuum atmospheres

tends to maintain the O/U ratio of the starting material,

although more precise control is obtained by controlling

oxidation potential with CO/CO, mixtures [40], H2/ N



i' ill be taken to imply stoichiometric i02.00
unless otherwise indicated by context ol the adjective he n
s oi chi on c.







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

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

O/U = 2.00 to 2.18. They observed that densification in-

creased rapidly between 2.00 and 2.02, but only slightly

above 2.02. The sensitivity of densification to stoichi-

ometry is a manifestation of the influence of defect struc-

ture on cationic lattice mobility.

UO2 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 electro-

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

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

have examined UO2 and BeO 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

powder.

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 know that x-ray crystallite "size" is









not equivalent to thi traditional concept of particle size

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

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

both aggregation and apglo-cration.



1.2. Evolution of Mi crostructure


The path of microstructural evolution may be defined

as the sequence of microstructures which exist in a mate-

rial a, it uidergocs a process which produces changes in

structure [IS]. 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 recrystallization, and solid state reactions

involving a phase change. During the sinterini process,

a collection of minute particles are welded together to

form a massive coherent body which ultimately may approach

theoretical density. It is evident that a continuum of

microstructures will exist between these two extremes.

This transformation is illustrated foi a four-particle

systcri in Fig. 1.

The kinetics of sintering mny be viewed as the rate

at which this path is traversed by the system [!5].

Tral i tionally, the linetics of sintering have cbeen s lOiied

hvy measure tcnt cf shrinkage As indicr.ted in the irl\' ( ] i

,cticni, 'srini a 0 n iasure .- .t, on c i c'lrical1y 11 c








A B








c 0 D
LK- LL"










Fig. 1. Sequence of states through which a sintering
four-particle system passes. Densification
proceeds as L1>L 2>L>L4'








system, have been used by nany worker. to identify the

rechanisms by which sintering is taking place [11,26,16,47].

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

particle systems. Dilato irtric measurements of shrinkage

have beei 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]


=- Kt (1.1)


where 'L = L L(t)

L = initial dimension
o
L(t) = dimension at time t

t = time

n = the time exponent

and K can be represented as


K = exp (1.2)


where K" = a constant

T = temperature in degrees Kelvin

R = gas constant

Q = activation in energy for the shrinkage
process.

Such measurcrmnts, however, provide no information about

the path of sinterinL

A detailed study of microstructural changes ,l ich

occur during sinilring was first undertaken Ly Rhl is et A!.

[49]. They ob served thatC the total vcli of poru ity







decreased as sintering progressed, but average pore size

increased. Arthur [50] determined that porosity remained

connected until relatively high densities were 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 the sintering processes and the defi-

ciencies of simple geometric models.

Techniques for quantitatively characterizing the

nicrostructure of sinter bodies have been available for

some tile. However, only recently has systematic study

been undertaken. An additional parameter of particular

significance to sintered structure characterization was

provided by De!loff [51] and by Cahn [52] with the develop-

ment of a technique for measuring quantitatively the curva-

ture exhibited by the interface in a two-phase system (see

section 2.3).

Rhincs [53] has shown that 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 entire process from loosely

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

has experimentally determined the topological properties








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 interparticle con-
tacts into weld necks. The necks broaden to
the extent that grain growth becomes possible,
thus signaling the end of the first stage.

2) Intermediate stage -- with the onset of grain
growth,intersection of grain boundaries with
void-solid interfaces begin to assume equi-
librium dihedral angles. Porosity is situated
as a continuous network of cylindrical pores
along the lines of intersection of three
grains. During this stage the pores retain
cylindrical configurations and simply shrink.
Two alternate final stages are proposed by
Coble.

3a) Pores are pinched off and isolated at four
grain corners. If grain growth is inhibited
the pores can continue to shrink until
theoretical density is attained.

3b) If discontinuous grain growth occurs, pores
are isolated from grain boundaries. Most
porosity is closed and spherical. Regions
adjacent to grain boundaries are relatively
free of porosity as a result of boundary
migration.

Using a tetrakaidecahedron as a model for grains and

cylindrical or spherical pore shapes, he calculates shrink-

age r:tes for intermediate and final stages of sintering.

Peasonably pood agreement between diffusion coefficients

c lcruatcd from shrinkage rates, based on the model, and







those determined from initial stages of sintering were

obtained.

The densification and development of microstructure

in UO2 were studied by Francois and Kingery [56]. They

found that rapid heating rates produced a microstructure

that consisted of intergranular porosity as opposed to an

intragranular microstructure observed for conventionally

fired UO2. 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 heating.

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

occurring: Stage 1 points of contact broaden into weld









nec1 4t

pinch off,

larce is<,

Thus t) cr,


r It
:I in

tic ta


n..-n, : f p :-o ity v :,, in to

f pc ty; jd St; *,e 3 -

tic expense of smaller pores

of the sc-ile of porosity.

ip bet.hcn S surface area

ui fraction of poros'ty, has


I r trials d urin, secondi-sta g

ive system ,i there exists a uti

Sare' towards which the system

ccl1train. ts such as precolpact:

thc appro ch to this path in a

ly predict;ib]c.


3. Tie t t I curiature per unit volume, M\, is ini

tially positive decros o s through zero to a maximum nega-

tive vlue ad ;ror lics zero again as densification

nears coipletio:. (Sce section 2.3.3 for explanation of

sign convention.)

Gryc., [57] has i ;-silred the sintering force (defined

to he the force neces-,iry to balance axial shrinkage) as

a function of d nsity. Some, iat surprisingly, the sinter-

ing force was found to increase with increasing density,

reaching a maxiri 9 before beginning to decrease. Gregg

found that the variation in the sintering force could be

correlated with the evolution of average mean curvature,

FT, and derived an expression relating capillary forces to

the sitinting forme, based on a spherical pore model.


(i








The evolution of microstructure in a three-dimensional

sinter body can be described by quantitative geometric

properties which uniquely characterize the system. These

properties are experimentally measurable and require no

simplifying assumptions.


1.3. Effect of Microstructure on
Mechanical and Thermal Properties


The mechanical and thermal properties of a material

depend primarily upon atomistic considerations such as bond-

ing, band structure, and crystal symmetry. Microstruc-

ture can, however, play an important role in determining

realizable properties for engineering applications. Micro-

structural features which are expected to influence proper-

ties of polycrystals are: (1) grain size, (2) existence of

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

tribution and morphology of a. second phase. 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. Mechanical Pronerties

The basis of the mechanical behavior of brittle mate-

rials is the Griffith Theory [58]. Griffith hypothesized

that all materials contained flaws. When a stress is applied

to a body containing the flaw, stresses in the vicinity of

the flaw are very much higher than would be calculated








assuming the body was a homogeneous 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 (E)1/2 (1.3)


wheie S = the stress necessary to extend the flaw

o = specific surface energy

I = 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 that failure by brittle fracture is the result of the

extension of flaws inadvertently 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"

material and the yield strength of "ductile" materials








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 dimension, smaller grain size materials have smaller

flaws, and thus 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. Residual stresses across grain boundaries, due to

thermal expansion anisotropy, can be produced on cooling a

polycrystalline 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 local 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:








o = o + oG-0 (1.4)


where o = the mean strength

G = the grain size

o1, oa and a = constants.

Equation (1.4) is the Petch [64] equation for oa f 0(6),

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

tion if a $ 1/2 [66]. Carniglia concluded that the data

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

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

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

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

1-P (1.5)
E = E P (1.)


where E = Young's modulus for porous bodies

E = Young's modulus for theoretically dense
0 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 he equal to 1,

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







BeO. Values for the constant, A, for Al203 are, however,

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

The most commonly used relationship between strength

and porosity was suggested by Ryshkewitch [75] and by

Duckworth [76]:


a = o e-bP (1.6)


where a = fracture stress, 0o = 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 et 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 was given by

o = o AA min, where o = rupture stress, oo = rupture stress

of solid copper, and AA min = minimal area fraction of solid

(corresponding to projected area of fracture surface).







It is apparent that correlation of properties simply 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

UO2 behaves as a perfectly brittle material at temper-

atures below 10000C. Recent studies by Evans and Davidge

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

UO2 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 fractions 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-a e-b (1.7)


where S = flexural strength in four-point loading







G = average grain size (Martin's diameter)

P = volume fraction of porosity

K = 23,700

a =.119 7 constants (room temperature)

b = 3.17 J

The above equation also produced satisfactory agreement

with data taken at 10000C for different values of the con-

stants, K, a and b. At 10000C, 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 Petch

[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 UO2 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 = Eo(l-AP) (1.8)


where E = Young's modulus

E = Young's modulus of theoretically dense
material

A = constant

P = volume fraction of porosity.








Sr d t j.tl e rlier work f r

et [ 1 .' t .n et a [ j.

liv : r 1 lrc t h an f ac I re

charaect i ti l r,,- of te to res.

In the I 1 I. L i thly con iu: c t -It



ci L t
fra ctu( 1 t It e extension of pr-

exi tinp V -. >*;*" tho "Iiht to 1) la e ] r' f "

foui d on I ,' t' 1 i1 spc in .r



fo c It 1 ta a ' n si: a trib-

utCd frbrturi : I ... beli 1(I00C to flaws in tile

forl of0 i cat. 1 a t I o ,,t l no i tsi v teiteria appiroxi-

ratcly 50 to P10 'i ct1cr. These fli;;s are

probably the r it1 a: regacat t ani/or atgloir rates in

the stating mnat i: li .sci ct a 1. [82], Evans and

Davidge [79] a l C .t al. [80] all found that brittle

fracture strength ir -esecd with increasing temperature to

the onset of plnstic.ity.

Roberts and li d:: [87j studied the influence of porosity

on deformation and fr; ctur of UO2. Porosity was produced

by increasing, addit'ons of n:phthalene to the starting

material. Resulling i, icrottructures showed isolated, large,

anisotropic voids si lilar to that seen in irradiated fuel.

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

tion (1.4), with ai different choice of constants.








1.3.3. Effect of Microstructure on
Thermal 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 = CvV (1.9)


where K = thermal conductivity

C = heat capacity/unit volume

v = wave velocity

A = mean free path

Above the Debye temperature both C and v change very

little with temperature, and the 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 common 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 more 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








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





2 T- + 1


1-V




where Km = material conductivity

K1 = continuous matrix conductivity

K2 = 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 the effective conductivity of the pores is low with

respect to the matrix, the Euken relation reduces to

K = K 1 V(
K K1 1--- (1.11)
1 +t~







Francl and Kingery [94] have suggested that the relatively

simple Loeb [95] expression


Km = Ksolid-P) (1.12)


where K soid = conductivity of the solid

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 more 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 UO2

The thermal conductivity of stoichiometric UO2 has

been measured by a number of workers using a variety of








experimental techniques [96- . Ti r. i, c nsid ra;,,l

discrepancy between the values obtained 1 'cn nor; lizs: to

theoretical density by using cqution (1.12). Wor3 by Ross

[100] and by Deem [101] suggested, honi, r, tiat (1.121 is

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

further stated that pore shape and location at grain boun-

daries wcre probably responsible for the loi: values he ob-

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

agreement with the Loeb expression.

Reiswig [102] measured the thermal conductivity of UO2

in the range 800 to 21000C. A least squares fit of the

data gave an equation of the form


K = 17.3 + .06T (1.13)

where K = thermal conductivity atitt-

T = temperatures in K for specimen 85%
theoretical density.

Bates [103] reported the findings of the International

Atomic Energy Agency (IAEA) panel that critically evaluated

all reported thermal conductivity for UO2. The panel stated

that the thermal conductivity of UO2 between 20C and

13000C could be best represented by


K = 11 + .0235T (1.14)

where K = thermal conductivity in watts

T = temperature in C for a 95% dense specimen.







The panel further recommended that the correction for

porosity,


K A KB B (1.15)


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

KA = conductivity of specimen of density PA; KB = conduc-

tivity of test specimen of density PB; pB = density of

measured specimen; pA = the desired density; and B = a

parameter that depends upon specimen "characteristics."

B 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 Work


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 has the

capability of converting nonfissionable U238 to fissionable
239
Pu9 and thus produces more usable fuel than it consumes.

A mixed oxide of uranium and plutonium has been selected








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 1014 cm3
-1
sec Liquid sodium will leave the core at 5400C. Eighty

thousand fuel pins having a diameter of one-quarter inch

will operate at surface temperatures of 6500C and center-

line temperatures near the melting point of 27600C. At

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

[104].

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-

ferent conditions on the component design than are required

for conventional power reactors. The transient reactor will

utilize U235 dispersed in stabilized ZrO2 to give appro-

priate fission density,resistance to thermal shock and

thermal conductivity [105].







All reactor fuels undergo changes in microstructure

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 optimum
performance,

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

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






















Operating
1-10 MWD/T


Shut down
after
105 MWD/T


Shut down
after
10 MWD/Ton


Operating between
10 and 105 MWD/T


Fig. 2. Structural evolution during useful life of a
UO2 fuel pin [106].












CHAPTER II

EXPERIMENTAL PROCEDURE



2.1. Material Characterization


2.1.1. Material Specifications

The material employed in this investigation was sup-

plied by the United States Atomic Energy Commission. It

was produced by Mallinkrodt Chemical Company by precipita-

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

tion to 110UO and reduction to I'02. The resulting product

was then fused in an electric arc furnace by Spencer

Chemical Company. Analytical ipipurities 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 shown

in Figs. 3 and 4. The following observations were made:

1) The particles are angular, faceted polyhedra;
i.e., they exhibit very little curvature of
surface and are roughly equiaxed.

2) There are virtually no open pores or voids in
the particles.

3) There is no size dependence of shape or
topography insofar as can be resolved in the
scanning electron microscope (SEi).




34



Table 1

Analytical Impurities in the Arc Fused UO
Used 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
















S37X









4,000X


Fig. 3. SEM photographs of -6 mesh as-received UO2
powder.





















800X














4,OOOX


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








4) There are small particles which appear to be
adhering to surfaces of the larger particles.
These particles are generally smaller than
5 microns and are physically distinct from
the substrate particle.

Similar "surface" particles have been seen by Johari

and Bhattacharyya [107] on electrolytic iron and by Lifshin

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

trostatic forces. Effectively, then, each particle is an

agglomerate or assembly of many particles which cannot be

readily separated. It is apparent from the surface topog-

raphy that subsequent to arc fusion the present material

was subjected to a comminution process, wherein large fused

grains were crushed. The small particles observed are

probably the result of this operation.

Figures 5 and 6 are photomicrographs of -6 mesh and

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

all particles are single crystals, and thus even when

etched are virtually 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 present in this size fraction. It is appar-

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

325 sieve opening have been retained.

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

ball milled powder employed in this investigation. Based






















p'A.

^lP -e
>'^f. :'*e

t^:^'1'.
`J.p ^


(b)


Fig. 5. Photomicrographs of -6 mesh as-received powder;
(a) cracked grain, (hV particle aggregate.









































Fig. 6. t ro h of -270 +32 as-received powder.






Fig. 6. Photomicrographs of -270 +325 as-received powder.








on line profile analysis of (200) and (100) reflect ons,

he found an effective domain size of 530 I. This result

is in good agreement with results of other workers [110]

and indicates a relatively low preparation temperature of

5000 to 6000C [111].


2.1.2. Stoichionetrv

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 thermuodynar

ically stable oxides, and these exhibit polymlorphism and

metastability to varying degrees [111]. Several other

oxides have been reported, but not confirmed. Only the

region between UO2 and U409 (0/U = 2.00 to 2.25), however,

is of primary interest to the nuclear fuel industry.

Although differing in detail, the work of Schaner

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

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

features of the phase diagram in the region between UO,

and U409. The diagram according to Schaner [38] is pre-

sented in Fig. 7.

U02 crystallizes in the fluorite 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 900C cubic U02 is stable


























U409-).










2.25


O/U Ratio


Fig. 7. Phase diagram of the U-0 system for O/U ratios
between 2.0 and 2.25,according to Schaner [38].










5.480



o"" 5.470




S1I
E3 S!60 \



" 5.450 \



5.440 _
2.00 2.10 2.20 2.30
UO2 4 09
(/J iO 49


Fig. 8. : of the lattice constant at 2S5C upon
S for cubic UO, [38].






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

there is little or no solubility. Virtually all proper-

ties of UO2 are sensitive to some degree to the presence

of excess oxygen in the lattice. Consequently, determina-

tion of O/U ratio is essential to any study of UO2.

Precision lattice parameter measurements and thermo-

gravimetric analysis were employed for this purpose.

Reported values of the room temperature lattice parameter

of stoichiometric DO2 range between 5.473 [38] and 5.469

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

of UO2+x as a function of known O/U ratio. His results,

shown 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 diffractometer to scan the region 26 = 700 to

1450 at 1/20 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 was a. = 5.4716 .0003 A. From Fig. 8, the O/U







ratio was determined to be 2.0(1 after sint rin in a rce-

nent with the general observation that sintering in 112

produces a stoichiometric material, of the

stoichiometry of the starting oxide.

The measurement was repeated with ball milled powder

dried in air at 900C.

The 0/U ratio of the starting material i:as determined

to be 2.06 based on a lattice parameter of 5.4693 + .0006 ,

A determination of stoichiometry was also made utiliz-

ing a gravimetric technique described by Scott and Harrison

[118]. A precision cloctrobalance* with 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 weights. The

specimen and pan were 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 450C in still

air for two hours to produce U308 (0/U = 2.667). The speci-

men was returned to the balance and the weight increase was

determined. The procedure was repeated to insure that the

reaction had gone to completion. The weight gain expected

if the starting material had been stoichiometric (O/U = 2.00)



*Cahn Division, Ventron Instrument Company.

**Kiethly Instrument Company, Model No. 155.








was calculated and compared with that observed experimen-

tally. An estimate of stoichiometry could then be made.

This method gave satisfactory results for a bulk sintered

material (O/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 [11] also

reported difficulty with as-received powder, indicating the

problem is not unique to the present investigation.


2.1.3. Size Reduction and Separation

In an effort to evaluate the sinterability and the

effect of particle size on sintering behavior, the as-

received -200 mesh powder was sieved and fractionated

according to Table 2.

Initial attempts to sinter loose stacks uncompactedd)

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

mens sintered for two hours and 24 hours showed identical

densities of 5.26 gm/cm3 (48% theoretical density).

Although some sintering occurred (loose stack density

4.43 gm/cm3), specimens were quite fragile.

in order to explore the effect of temperature, arrange-

ments were made to use ultrahigh temperature furnace facil-

ities.* Molybdenum cups were loaded with material from


*Kometco, Inc.




46


Table 2

As-received UO Powders were Separated
Into Lots by Sieving


Sieve
(U.S. Standard)

-140 +200

-200 +230

-230 +270

-270 +325

-325


Maximum
Diameter

149 um

74 pm

63 pm

53 pm

44 um








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

specimens were sintered in hydrogen at 22500C for one hour.

The results are shown 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. This material was

selected as a base for all further 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 900C for 12 hours.

The powder was then granulated and stored in closed con-

tainers until used.


*U.S. Stoneware Company.
















T3
O

C





U 0


ml
3 Q




00
0 r











0,
to


4. J

O 3
U
rf0
tlo

-+,






00



0.0



P.
















(-L


-IS
- k *









As an alternative to ball milling, an impact pulver-

izer* was employed. 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 milled material indicated

the presence of particles in excess of 10 microns along

with particles of 1 micron or less in considerable quantity.

It was felt that if a separation process could be used to

remove particles >5 microns the remaining powder 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 commercial pigment stabil-

izer, polyoxyethylene sorbitan monolaurate,** in concen-

trations of about 20 ppm in aqueous solution would



*Gem-T, Trost Equipment Corporation.

**Tween 20, Atlas Chemical Company.







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:


Sir 3(p p )g = 67rnv (2.1)


where r = particle ratio

p = particle density

(j = 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

bottom of the vessel, the settling velocity v is


v = h (2.2)


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

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

t 6 .= n--- (2.3)
73 1T (Pp-P)

Using the viscosity of water at 25C (9 x 10-3 poise),

a particle density of 11 gm/cm3 and the column height of

90 cm, the maximum time required for particles larger than










-270 +325
(coarse)


Ball milled
(intermediate)












Separated
(fine)





S10 microns


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







5 i.icrons to settle is 4,800 seconds. Clearly, smaller

particles near the bottom of the column will also settle

out during this tine internal. (Although these are poten-

tially recoverahle by repetitions of the sedimentation

process, no attempt was made to further sep'irate the solid

which settled out of the suspension.) The supernatant wias

drawn off to a clean vessel after the prescribed time

period had clasped. Attempts to deflocculate the suspe

sion using commercial deflocculants of the anionic, cationic

and nonionic types were unsuccessful. Recovery of the

solid: was effected by evaporation of the liquid in shallow

Pyrex trays heated at approximately 900C. The 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

The 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







m -20
S = N Am x 10 (2.4)


where S = specific surface m2 /gram

X = monolayer capacity in grams of
m adsorbate/grams of adsorbent

M = molecular weight of adsorbate

N Avogadro's number

A = area occupied by a single adsorbate
molecule in 2.

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

solid can be evaluated from [120]

S1 C-1 (2.5)
-X(c XmC XiC p

where X = mass of adsorbate in grams per gram
of adsorbent

o = saturated vapor pressure

p = system pressure

X = monolayer capacity

C = constant for the system related to
energy of adsorption of the monolayer.

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

relative pressures, a straight line is formed having a

slope


S = C- (2.6)
m
and an intercept

1
1 = TC (2.7)
m







Solutions of these two equations simultaneously leads to


X = (2.8)


C = 1 (2.9)


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

size fractions described previously, 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'C for two hours at 10-5 mm Hg. The bulb

was then cooled to 770K 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 the P.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/Po, performs a

least squares fit, calculates the slope and intercept of

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
























To
McLeod gouge-

Gos inlet
(helium or-
nitrogen)


Man vacuum line,


To
mercury
diffusion
o pump
atmosphere


(confining liquid)


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








Table 3

Surface Areas of the
Three Size Fractions of UO,


As received, -270 +325 (coarse)

Ball milled (intermediate)

Separated (fine)


0.1-0.3 m2/gram*

0.87 m /gram

1.54 m /gram


*Considerable scatter in the adsorption isotherm
inherent for low values of surface area. All iso-
therms B.E.T. Type II at 77K.


z-t0

X


D .05 1 1.5 2

P/Po
Figure 12. B.L.T. plot for fine size fraction of UO,
powder.







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


Three techniques were employed to prepare specimens

for examination:

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

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

3) hot pressing or pressure sintering -- sintering
under 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 UO2 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







the top G th : ,d t cup.; wdre then placed directly

into the furL;..e. The sintering cycle is discussed fully

in the next section.


2.2.2. Cold PrcF sir"

Cold pressed spcci cns were 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-

ethylece 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 1% by weight

and blended in a polyethylene container. Mixing was

carried out by tumbling the container on a ball mill drive

for one hour.

Specimens were 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 inch, and had an adjustable depth. The die, pressed

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

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

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

75,000 psi frequently produced transverse laminations.



*Mallinkrodt Chemical Works.

callerer Division, Federal-Mogul Corporation.


















































Fig. 13. Punch and die assembly used to cold compact UO2.








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. 14a. The furnace was evacuated and back

filled with commercial grade hydrogen prior to heating.

A flowing hydrogen atmosphere was maintained during all

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

was utilized to volatilize the binder prior to heating to

the desired sintering temperature. Practical sintering

temperatures were limited to about 1800C by the A1203

muffle. Heating and cooling rates of 200-400C per minute

were generally encountered and the sintering "times" that

are presented are the time intervals that 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 100C in the range

of interest.




*Astro Industries, Model 1000B.

**Pyrometer Instrument Company, Model 95.





















































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 UO2, particularly at temper-

atures above 17000C. 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 z20*C.

A subsequent heat treatment of 90 minutes at 1200C in

hydrogen insured that the specimens were stoichiometric [123].



2.3. Evaluation of.Geometric Properties


2.3.1. Metallography

Microstructural examination was carried out on speci-

mens which had been fractured 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.






















A Upper ram


Upper punch

BN punch face
BN die liner


Die body


Lower punch

Lower ram


Fig. 15. Graphite and boron nitride die assembly used
to pressure sinter UO2.







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 50C 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 metallographic procedure employed to polish the

specimens is as follows [124]:


*AB Buehler, Ltd.







1) Wet grind on a slow wheel with 180-, 320-and
600-grit silicon carbide paper discs.

2) Polish on nylon or silk saturated with 2%
chromic acid and suspension of Linde A alumina
powder in 2% chromic acid using a fast wheel
speed.

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

4) Wash, dry and examine;the etch used to reveal
grain structure was devised by Cain [125]:
(a) a solution of one part H2S04 to nine
parts 11202 (30%) swabbed on the surface with
cotton for 30 seconds, and (b) the surface
is then immersed for an additional 30-60
seconds, washed, dried and examined. Deter-
ninations of the metric properties of the
pore solid network were made on unetched
specimens, in as much as etching was found
to adversely affect the accuracy of these
measurements. Subsequent to these measure-
ments, the specimens were etched and the
grain boundary intercept count was made.


2.3.2. Quantitative Metallographic Analysis

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 microstructure which lies within the feature of inter-

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

per unit length that a test line imposed on the micro-

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

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

that a test line makes with features in the microstructure,

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

kinds of tangents which a test line can make with a bounding







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 the 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 TA net is then


TA net = TA TA- (2.10)


TA net may be positive or negative depending on relative

magnitudes of the two tangent counts, and the algebraic

sign of TA 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 UO2 specimen in Fig. 16.

The volume 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 was used as a criterion to ascertain that the

metallographic section was 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-

nint technique described in AST'! Standard 328-60. Open













Vt a

hid'


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








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 metallographic

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 Quantimet 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 ray tube which also incorporates a

digital display of the counting results. Additionally,


*Image Analysing Computers, Ltd.








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

played. Figure 17 shows the displayed image of a sintered

UO2 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 metallograph. Figure 18 shows the

metallograph-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.






















































Fig. 17. Quantimet display of a sintered U02 micro-
structure.







'N








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, Vv, 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]


V = 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

Sv 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, K1 and K2, defined as follows: a normal is

constructed at a point on a surface. All possible planes








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


K1= 1 K2 (2.13)
1 r1 2 r2
1 '2

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

the principal normal curvatures or


H (K1 + 2) (2.14)


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 = If 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 on the surface, it will

have an average value defined by







I/s HdS
1= (2.17)
fIs dS

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

net tangent parameter by
n TA net
FT = --- (2.18)
A=-L

where rI has the algebraic sign of TA net (see section

2.3.3). The total curvature per unit volume, M is then
1 TA net
M = Sv -- --- S = i TA net (2.19)


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 2P
S= v = P (2.20)

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-Vv) 2(1-V)

vF v L ---- (L.l
g Sv"aP+Sv a "La "NI,







where NL"P is the surface area of pore-solid interface

and NLa 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 UO2

sinter bodies at room temperature. 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 case
of nuclear fuel, most fuel elements are in the
form of cylindrical pellets. The test may








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

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

3) Bend tests produce maximum tensile stresses
at outer surfaces and thus are sensitive to
surface preparation. Tensile stresses gener-
ated by diametral compression are distributed
over the entire diametral plane, emerging
only 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 Instron TTD* machine equipped with a CF load

cell in a compression carriage. Hardened steel platens

were constructed to fit the Instron crosshead. 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 was 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.




















































Fig. 19. Distribution of stresses in a diametrally
loaded cylinder [130].


















































Fig. 20. Precision centerless grinder used to machine
U02 specimens.








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 wheel. 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


S=2P (2.22)


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

thickness.



2.5. Measurement of Thermal Conductivity


The thermal conductivity of sintered U02 was measured

using a comparative 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.

Radial heat flow is minimized by the presence of guard


*Thermophysics Corporation, TC-2200.













IA

Guard 2-


3,


4/-


o1
02

03
04

05
0 6

c7


5^ 08








Sink


:1


Main
heater


Upper
standard

Specimen

Lower
standard


Auxiliary
heater








Thermocouple
positions


Fig. 21. Comparative cut bar thermal conductivity
apparatus.








heaters which match the gradient of the stack. Temperatures

along 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 [88]

AT
Q = kA T (2.23)


where Q heat flux

k = thermal conductivity

A = cross-sectional area

AT = temperature differential through
which Q flows

t = thickness of conductor in the
flow direction.

Since the specimen and the standards are in series,

the heat flux is the sane in each. Then

AT AT
Q t st tst = xA Tx

where the terms are defined in equation (2.23) and the sub-

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

the specimen, respectively. All quantities are known except

kx and, assuming cross-sectional areas are identical,

AT t
kx kst T tst (2.24)
x st

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 UO2 over the tem-

perature range of interest. Thus 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 1200K. This tabulation is reproduced in

Appendix B.

Specimens selected for measurements were centerless

ground to 0.625 inch 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**. The entire



*Omega Engineering.

**Norton Company.













10-1 ----- l-_T -

S8 -
7
S6

5-

4










10-2 2
4r


.0





102 2 3 4 5 6 7 103
Temperature (OK)


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







-2
assembly ;wa: evacu ted to a vacuum of 102 Torr to prevent

oxidation of UO2 and eliminate convective heat transfer.

Flynn [88] has discussed possible sources of error

associated with cut bar thermal conductivity measurements.

Errors may result front

1) radial heat exchange

2) shunting heat flow through the insulation
surrounding the stack.

3) inaccurate standards.

4) excessive interfacial resistance to heat
flow between stack components.

5) perturbations introduced by thermocouples.

6) uncertainties in the measurement of gage
length.

7) presence of cracks, voids or heterogeneities
not ascribable to microstructure.

8) measurements under nonequilibrium conditions.













CHAPTER III

RESULTS AND DISCUSSION



The results of 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. Densification Behavior


In view of the paucity of information in the litera-

ture on pressure sintering of UO2, the densification

behavior of the powders employed in the present investiga-

tion was systematically characterized in a series of exper-

iments.




















^1600 -

In

1-1400-

a-

S1200




1000
8 9 10 10.5
DENSITY (grams.cm-3)






Fig. 23. Densification of three size fractions of UO, at
constant heating rate followed by 5-minute arrest
at 1800'C, pressure sintered at 3,000 psi at
10-4 torr.




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