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THE EVOLUTTCN OF MTCROSTRUCTUREDURING SINTERING OF UO? AND TTS EFFECTUPON MECHANICAL AND Tl^ERMAL PROPEPTIES
By
IVavne D-oualas Tuchig
A Dissert -ition Presented to the Gradirrvtc Coun.the Univer>:ity of Florida
In Pari:5ai Fulfilln'ent ci the Requireiuents fo:
Decree of Doctor of Priilosonliv
Ur^IlVERSITY OF FLORIDA
1972
UNIVERSITY OF FLORIDA
lililillllililillll3 1262 08552 5854
Dedicated to my v-'ife, Candy,and to my parents,
Mr. and Mrs. K. J. Tuohig.
ACKNOWLEDGEMENTS
The author wishes to acknowledge the encouragement
and helpful discussions provided during the course of this
research by his chairnian , Dr. E. D. Whitney, and Dr. R. T.
DeHoff. Thanks are due also to Drs. L. L. Hench, J. J.
Hren, R. W, Gould and J. W. Flowers for serving on the
supervisory committee.
The assistance of S. M. Gehl with all aspects of this
work, and contributions by V.'. H. Halback and R. A, Graham
are sincerely appreciated.
Financial support from the United States Atomic
Energy Commission is gratefully acknowledged.
TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS iii
LIST OF TABLES vi
LIST OF FIGURES . vii
ABSTMCT xii
CHAPTER
I INTRODUCTION 1
1.1. The Nature of the SinteringProcess 1
1.2. Evolution of Microstructure ... 101.3. Effect of MicrostructuTC on
Mechanical and ThermalProperties ..... 17
1.4. Objective of the Present V/ork . . 29
II EXPERIMENTAL PROCEDURE 33
2.1. Material Characterization .... 332.2. Specimen Preparation 572.5. Evaluation of Geometric
Properties 622.4. Evaluation of Mechanical
Properties 752.5. Measurement of Thermal
Conductivity 79
III P.ESl'LTS AND DISCUSSION 85
3.1. Densif icati on Behavior ..... 853.2. The Metric Properties ...... 923.3. Mechanical Properties 1413.4. T-herTr.al Conductivity 157
TABLE OF CONTEXTS (continued)
CHAPTER
IV
APPENDIX
A
B
CONCLUSIONS AND SUMf-lARY
PRECIS I ON LATTICE PARAMETER PROGRAM
INTERPOLATED THEP^MAL CONDUCTIVITYOP PYROCERAM 9 606 IN INCREMENTS OF1° KELVIN OVER THE RANGE 300- 1200 °K
LIST OF REFERENCES
BIOGRAPHICAL SKETCH
Page
164
167
188
215
225
LIST OF TABLES
Table Page
1 Analytical Impurities in the Arc FusedUO- Used in this Investigation 34
2 As-received UO2 Powders were SeparatedInto Lots by Sieving 46
3 Surface Areas of the Three SizeFractions of UO^ 56
4 Metric Properties of UO? SpecimensProduced by Cold Compaction andSubsequent Sintering 93
5 Metric Properties of UO2 SpecimensProduced by Pressure Sintering at 3,000psi for 30 minutes at Various Tempera-tures 115
6 Metric Properties of UO2 SpecimensProduced by Pressure Sintering at 3,000psi at the Indicated Temperature forVarious Times 117
7 Metric Properties of Specimens PressureSintered at 5,000 psi From Fine Po'.vder
Lot 134
LIST OF FIGURES
Figure Page
1 Sequence of states through which asintering four-particle system passes . . 11
2 Structural evolution during usefullife of a UO- fuel pin 32
3 SEM photographs of -6 mesh as-receivedUO- powder 35
4 SF.M photographs of -200 mesh as -receivedpowder 36
5 Photomicrographs of -6 mesh as-receivedpowder 38
6 Photomicrographs of -270 +325 as-received powder 39
7 Phase diagram of the U-0 system for 0/Uratios between 2.0 and 2.25 41
8 Dependence of the lattice constant at25''C upon 0/U ratio for cubic UO- .... 42
9 Sinterings prepared from loose stacksof as-received UO2 sintered at 2250°C . . 48
10 SEM photos of powder from the three sizefractions employed in this investigation . 51
11 Schematic of the B.E.-T. apparatus usedto determine surface area 55
12 B.E.T. plot for fine size fraction ofUO^ powder 56
13 Punch and die assembly used to coldcompact UO^ 59
14 (a) The high temperature Astro sinteringfurnace !! . 61
(b) Centorr vacuum hot press 61
Vll
LIST OF FIGURES (continued)
Figure Page
15 Graphite and boron nitride die assembly-used to pressure sinter UO^ 63
16 Schematic illustration of the countingmeasurements on a sinter structure .... 67
17 Quantim^et display o£ a sintered UO^microstructure ~.
. . . 70
18 Metallograph- vidicon assembly 71
19 Distribution of stresses in a diamet-rally loaded cylinder 77
20 Precision centerless grinder u^ed tomachine UO- specimens 78
21 Comparative cut bar thermal conductivityapparatus 80
22 Temperature dependence of the thermalconductivity of Pyroceran 9606 83
23 Densification of three size fractionsof UO2 at constant heating rate followedby 5 minute arrest at 1800 '^C. pressuresintered at 3,000 psi at 10"^ torr .... 86
24 Variation of volume fraction of porosityas a function of temperature for threesize fractions of UO^ 88
25 Volume fraction of porosity as a
function of tim.e at temperature 90
26 Dependence of pore volum.e fraction ontime for isothermal pressure 3 in te rings . 91
2 7 The fam.il> of curves which define thepath of change during sintering of thesurface area per unit volum.e for theintermediate sized fraction 96
2 8 Ihe approach to the linear relationshipfor a spectrum of initial conditions ... 97
LIST OF FIGURES (continued)
Figure Page
29 Surface area per unit mass as a functionof volume fraction of porosity forspecimens prepared by compaction at theindicated pressure and sintering forvarious times and temperatures 99
30 Variation in microstructure for twodifferent paths of surface change .... 101
31 Evolution of microstructure along a
single path of structural evolution . . . 102
32 The family of curves which define thedependence of surface area on volumefraction of porosity for conventionallysintered coarse UO- powder 104
33 Average moan curvature as a function ofvolu;ne fraction porosity for UQt preparedby conventional sintering from the coarsesize fraction 107
34 Variation of average mean curvature withvolume fraction porosity for conven-tionally sintered interr?.ediate UO^powder T.... 108
35 Comparison of the dependence of curva-ture on pore volume fraction and particlesize for UO^ and dendritic copper .... 109
36 Proposed form of the paths of curvaturechange for a spectrum of initial condi-tions Ill
37 Dependence of the shape parameter onvolume fraction porosity for all conven-tionally sintered UO, specimens 112
38 Dependence of surface area per unitvolum.e upon the pore volume fractionfor the isochronal pressure sinteredseries 119
LIST OF FIGURES (continued)
Figure Page
39 Variation of surface area with porosityfor specimens pressure sintered at theindicated temperature at 3,000 psi forvarious times 121
40 Variation of total curvature with volumefraction porosity for specimens sinteredat 3,000 psi for 30 minutes at varioustemperatures 123
41 Variation of mean curvature with volumefraction porosity for isochronal pres-sure sintered series 124
42 Comparison of mean curi'ature for iso-thermal pressure sinterings and thatobtained in the isochronal series .... 126
43 Variation of the mean pore intercept \
with volume fraction porosity forpressure sintered UO^ 127
44 Photomicrographs of isothermallypressure sintered U0-, specimens 129
45 Dependence of the shape parameter uponvolume fraction of porosity for thepressure sintered isochronal series . . . 131
46 Comparison of the dependence of surfacearea on volum.e fraction porosity forconventional and pressure sinterings . . . 132
47 Comparison of mean curvature for coarseUO2 powder prepared by conventional andpressure sintering techniques 135
48 Comparison of mean curvature values forintermediate UO2 powder prepared bycold oressing and sintering and bypressure sintering 136
49 Comparison of the geometry of (a) a
copper sinter body, and (b) UO2 sinter-ing, both aDDroximatelv 35^ theoreticaldensity .".'.. 138
LIST OF FIGURES (continued)
Figure Page
50 Failure modes in diainetral compression . . 142
51 Variation of fracture strength withpore volume fraction for specimens pre-pared by conver.tional sintering of powder"from the intermediate size fraction . . . 144
52 Dependence of fracture strength onvolume fraction of porosity for specimensconventionally sintered from coarse andfine UG-, powders 145
53 Comparison of the strength-pore volumede-cndence of tliree size fractions ofconventionally sintered U0-, 147
54 Fracture strength of specimens from thepressure sintered isochronal series asa function of pore volume fraction .... 148
55 Variation of fracture strength withvolijjr.e fraction porosity for specimensprepared by isothermal pressure sinter-ing the intermediate UO- powder at3,000 psi : 149
56 SEN! fractographs of intermediate iso-chronal series 150
57 Parli of minimal fracture length forcoarse and intermediate specimens ofcomoarable density 153
58 Dependence of mean grain intercept onpore volume fraction for isochronallypressure sintered series 156
59 Dependence of thermal conductivity ontemperature for UC2 specimens withdifferent pore volum.e fractions 158
60 Thermal conductivirv at 500 'K as func-tion of volume fraction of oorosity . . . 159
61 X-ray images of a second phase foundin UO, sinter bodies 162
Abstract of Dissertation Presented to the Graduate Councilof the University of Florida in Partial Fulfillnent of the
Requirements for the Degree of Doctor of Philosophy
THE EVOLUTION OF MICROSTRUCTUREDURING SINTERING OF UO? ,A.ND ITS EFFECTUPON MECHANICAL .A.\'D THER2>L\L PROPERTIES
By
Wayne Douglas Tuohig
December, 19 72
Chairr^jn: E. D. IVhitneyMajor Department: Materials Science and Engineering
A full range of microstructural states, ranging from
301 to near theoretical density, were produced from UCs
powders. Both conventional and pressure sintering (hot
pressing} techniques were emoloved to tabricate che micro-
structures. Each state was characterized by it? associated
metric properties, i.e., volume fraction of /oid, area of
void- solid interface, curvature, mean pore and m^ean grain
intercepts, as determined by the procedures of quantitative
metallography. Additionally, tensile stiengths at roomi
temperature and theTm.al conductivities over the intermediat;:
temiperature ra^ige were determined.
The viewpoint was adopted that a sequence of states
defined the path of microstructural change. It was found
that sintering in the presence of an applied load (hot
pressing) proceeds along a different path of microstruc-
tural development than does the same material under conven-
tional sintering conditions.
The evolution of nicros tructure during conventional
sintering of U0-, is shown to be qualitatively sir.ilar to
that of metallic systems. The role of preconpaction (cold
pressing) upon the subsequent microstructural development
has been elucidated in terms of the area of pore-solid
interface
.
Tensile strength and thermal conductivity have been
found to be functions of the initial particle size for
densities below about 80"^^ of theoretical. Inspection of
fractured surfaces and microstructures indicates that these
properties are sensitive to minimum cross -sectional areas
in the porous solid network. Evidence is presented to show
that this minimum area is in turn related tc initial par-
ticle size. Properties of specimens grsi^er than 80% dense
showed little dependence on initial particle size. Increases
in grain size are thought to be responsible for decreasing
strengths found at very high densities. A marked decrease
in thermal conductivity found for high density specimens is
attributed to the presence of a second phase, believed to be
the result of contamiinants in the starting material.
CHAPTER I
INTRODUCTION
1.1. T]ie Nat ure of the S in t
e
ring Process
Sintering in the presence of a liquid phase is as old
as the i^ost ancient ceramic artifact. A more raodern conno-
tatiori of the teim "sintering" implies the coalescence of
particulate matter at temperatures below tl^.e melting point
into a solidj colierent body. The driAring force for this
process is the therinodynam.ic tendency of a system to lov;er
its cncrg)' by decreasing free surface area (in tlie absence
of a liquid). The sintering process may be characterized
by:
1) Particle contact -- particles are brouglit intocontact under tlie action of gravity, an exter-nally applied force or vibrating rearrangement.
2) Upon heating to a temperature below the liq-uidus, points of contact between particlesbroaden into areas of contact or necks.
3) The initially continuous network of porositybecomes less continuous.
4) Both 2 and 3 are accompanied by a macroscopiccontraction or shrinkage. As a result, thedensity is observed to increase.
5) The rate of densification decreases rapidlyas theoretical density is approached; averagegrain size increases.
1 . ] . ] . Prc vicus .StiiJics of the Sintering, Process
ProbuMy the earliest work on sinterinp in the absence
of liquid was performed by Wollaston [1] in 1725, on plati-
num sponpe. However, the extent to wliich solid species
were nobile and could interact was not known until Roberts-
Austin's [2] work on the diffusion of gold in lead. The
nucleus of current sintering theory was contained in the
suggestion by Kepler [3] in 1D05 that sintering in the
presence of a liquid phase was brought about by surface
tension forces. Iledvall's [-1] observation of spheroidiza-
tion of Fc'2^'' 1 ^'"'•'l lae led hiin to conclude that the phenome-
non v/as brought about by surface tension. The wcrk of
SmJtli [S] in 1923 produced tlie conclusion that a liquid
phase was not requisite for sintering to occur. In the
ensuing years, studies on single and inulticomponcnt systems
firmly establislied a rel ationsliip between solid state dif-
fusion and sintering. By the early 1940's, a number of
workers had concluded tliat materia] transport occurred
imdcr the action of surface tension [6-8]. V.'retblad and
V/ulff[7] utilised equations of capillarity and concluded
tliat stresses in sintering bodies exceed the elastic limit,
and tlujs plastic deformation occurs. Pines [9] and Shaler
and V.'ul f f [10] distinguished between mechanisms which could
produce slirinkage and tliose wliich jn'oduced only surface
rounding witliout densi fi cation .
Kiiczynski [11], in a classic work, utilized a plate-
sphere model to derive sintering rates for different mecha-
nisms of material transport. According to his analysis
>
the radius of the neck, x, was related to time as follows:
21) viscous flow -- X tx t
2) evaporation -condensation -- x "^ t
3) volume diffusion -- x' «: t
74) surface diffusion -- x °^ t
From his measurements on copper, Kuczynski concluded
that early stages of sintering may be surface diffusion
controlled but that later stages are volume diffusion con-
trolled. A similar experiment [12] v.'ith glass spheres ]ed
him to conclude that tlie predominant mechanism was viscous
flow.
The calculations of MacKenzie and Shuttleworth [13]
introduced the concept of vacancy diffusion to external
sites. The results of these calculations, as well as the
observation that shrinkage was not dependent on specimen
size, led them to conclude that material transport during
sintering occurred by plastic flo\\'. Adopting the formalism
of Bingham flov/, they derived an expression for shrinkage
which contained several parameters. Suitable choice of
these parameters led to reasonably good agreement with
experimental data. Impetus to this view was added by
Clark and White [14], who utilized a similar approach and
achieved quite good agreement with experimentally measured
shrinkage rates.
A median ism proposed by Nabarro [15] and later by
Herring [16] to explain creep at low stresses provided a
means to reconcile both the plastic flow and diffusional
viewpoints. The Nabarro-Herring model [17] suggests that
creep deformation can occur by the diffusion of material
from grain boundaries in compression to grain boundaries
in tension, i.e., a flux of vacancies to grain boundaries
experiencing a compressive stress field. Thus, grain
boundaries become vacancy sinks. Experimental evidence wa--
provided by Udin, Shaler and Wulff [18] and by Greenough [10]
Udin et al . attributed the creep of fine co])per wires to
the Nabarro-Herring mechanism. Greenough repeated the ex-
periments using single cr)'Stal wires and observed creep
rates that were two orders of magnitude smaller than those
measured for polycrystall ine materials.
The close rel ationsliip between sintering and diffu-
sional creep was pointed out by Rhines and Cannon [20],
who found tliat sintering in tlic presence of small compres-
sive loads has the same effect on shrinkage rate that addi-
tional stress has on the rate of creep deformation.
The work of Alexander and Baluffi [21] on twisted wire
compacts, Scigle [22] on porous brass sheets, and Burke [23]
on aluminum oxide provided strong evidence for the grain
boundary siiik model.
An ingenious experiment by Kuc^ynski, Matsumura and
Cullity [24] provided tlie most direct evidence of diffusion
and the role of the curved surfaces during sintering. A
copper- indium alloy wire compact was sintered at tempera-
tures wliere the phase diagram predicts the presence of a
single phase solid solution. A subsequent heat treatment
at lower temperatures produced a precipitate rich in indium
at the weld necks. The diffusion coefficient of indium is
greater than that of copper and thus a Kirkendall effect
is observed. The material transported to tlie v;eld necks
by diffusion \v'as enriched in indium to the extent that the
two-phase boundary was crossed, allowing precipitation to
occur.
On the basis of extensive theoretical and experimental
work on a variety of materials, it is concluded that lat-
tice diffusion is the dominant mode of material transport
during sintering. Exceptions have been noted [NaCl by
evaporation- condensation , Kingery and Berg (25), g]ass by
viscous flow, Kuczynski (12)], and it is likely that more
than oiie mechanism operates at various stages of the pro-
cess. The following factors have been found to influence
sintering behavior [26]: (1) temperature employed,
(2) particle size and size distribution, (3) particle
niorphojogy, (4) occurrence of discontinuous grain growth,
(5) atmosphere, (5) stoichionetry and defect structure,
(7) impurities and additives, and (8) manner and extent
of compaction.
1.1.2. Pressure Sintering
Pressure sintering or hot pressing is defined as t)ie
application of external pressure to a powder compact while
it is at high temperatures. The synergistic effect of
these two variables has led to increased interest in recent
years to production of materials which cannot be fabricated
by any other technique [27]. Hot pressing provides an
additional A^ariable to control microstructurc , by virtue
of the fact th;<t it increases the driving force for densi-
fi cation of a powder compact without significantly increas-
ing the driving force for grain growtli [28]. As a result,
densities approaching theoretical have been achieved for a
number of materials.
The mechanism of dcnsi
f
ication during hot pressing
has been examined by Vasilos and Spriggs [29], Coble and
Ellis [30], Rossi and Fulrath [31] and Murray e t a
1
. [32].
Altliough simple sintering models are inadequate to describe
the process, most workers are of the opinion tliat at tem-
peratures below 2000°C and pressures below 7,500 psi as
arc normally employed in hot pressing refractory ceramics,
densif ication takes place by a diffusional mechanism.
Evidence for this comes primarily from agreement between
densif ication kinetics and lattice diffusion measurements
[28,29]. The plastic flow model proposed by Murray e t a
1
.
[32], and by McClelland [33] may, however, be applicable
to soft materials such as copper, lead, and N'iO [23].
CobJe and Ellis [30] studied neck growth between pairs of
spherical aluminum oxide single crystals under the applica-
tion of load. They concluded that only the initial stage
of neck growth was a result of plastic flow at points of
contact. Deformation occurred until the effective stress
was reduced below the yield stress. Later stages were the
result of a diffusion controlled process.
Murray e t al . [32] have studied the hot pressing
behavior of stoichiometric and hyperstoichiometric ^'02.
They foun.d that hyperstoichiometric material densified more
rapidly than did the stoichiometric oxide, in agreement with
observations of Williams et al . [34] on conventionally sin-
tered ifiaterial. Maximum reported density was 10. S5 g/cm.
(971 theorcrical density), produced by pressing at 2,000
psi at 1800°C for ten minutes.
1.1.3. Sintering of UO -^
In the late 1950' s, the development of advanced power
reactor designs provided srimulus for extensive study oi
the sintering behavior of UO^ . Interest continues in both
UO^ and mixed oxides of ursnium and plutonium which fuel
the present generation of breeder reactors.
The effects of powder characteristics and processing
variables on densificaticn jnd microstructure have been
discussed elsewhere [35] and will net be repeated here.
In genera], remarks that apply to most sinterable powders
apply to UO2 [36,37]. Ilovever, certain characteristics of
IJO2 are not general in nature and deserve further discussion
By virtue of the multiple oxidation states of uranium,
there are at least four thermodynamical ly stable oxides of
uranium known to exist [38]. Uranium dioxide has the
lowest 0/U ratio of the stable oxides and is the only oxide
wherein bonding is thought to be predominantly ionic in
character. Another consequence of the- multiple valence of
uranium is the hyperstoichi ometry exhibited by UO^ ; i.e.,
its ability to dissolve excess oxygen into the fluorite
lattice without formation of a second phase [39]. Cubic
UO2 may in fact have 0/U ratios of 2 . 00 to 2 . 25 . It is
well established that the 0/U ratio of UO^ has a very
significant effect on both sintering behavior and physical
properties [3G , 37] .
The 0/U ratio of UO,^* may be controlled by controlling
sintering furnace atmosphere and stoi chiometry of starting
material. Strongly reducing atmospheres produce 0/U ratios
close to 2.00. Sintering in inert gas or vacuum atmospheres
tonds to maintain the 0/U ratio of the starting material,
althciigh more precise control is obtained by controlling
oxidation potential with CO/CO-, mixtures [40], H-,/N'2
*U02 will be taken to imply stoichiometric UOt.qOunless otherwise indicated by context or the adjective nonstoichiometric.
mixtures [41] or by steam sintering [38]. Williams e t al .
[34] studied the sintering behavior of oxides in the range
0/U = 2.00 to 2.18. They observed that densif ication in-
creased rapidly between 2.00 and 2.02, but only slightly
above 2.02. The sensitivity of densif ication to stoichi-
ometry is a manifestation of the influence of defect struc-
ture on cationic lattice mobility.
UO.-, is particularly prone to agglomeration, i.e., a
tendency of loose particles to bond together in an assembly,
The bonding forces in agglomerates are generally electi'O-
static in nature as distinguished from an aggregate wherein
particles are welded together [42]. Insofar as aggregates
and/or agglomerates survive processing, they influence the
microstructiire of the sinter body. Steele et al . [43]
have examined UO^ and BcO powder compacts by the Brunauer-
Emmett-Teller (B.E.T.) technique and by permeability deter-
mination of surface area. They found that aggregates of
UO^ survived compaction at 40,000 psi and the result was
a very inhomogeneous distribution of porosity in the sin-
tered microstructure . Although Steele et al . , refer to
"strong aggregates," no attempt was made to disperse the
pov;der
.
Further, the inference is made that since x-ray crys-
tallite size is much smaller than observed for "particles"
in the microscope, the "particles" are aggregates of crys-
tals. It is well known that x-ray crvstallite "size" is
10
not equivalent to the traditional concept of particle size
[44]. It sceins likely, therefore, that in view of the
definitions given earlier, Steele et al . [43] observed
both aggregation and agglomeration.
1.2. l:volution of Microstructure
The path of micros tructural evolution may be defined
as the sequence of nicrostructures which exist in a mate-
rial 3"=; it undergoes a process which produces changes in
structure [45]. Examples are, the formation of crystals
and consumption of the matrix during devitrification of a
glass, the formation and growth of equiaxed strain- free
grains during recrystallizat ion , and solid state reactions
involving a phase change. During the sintering process,
a collection of minute particles are welded together to
form a massive coherent body v;hich ultimately may approach
theoretical density. It is evident that a continuum of
microstructurcs will exist between these two extremes.
This transformation is illustrated for a four-particle
system in Fig. 1.
Tiie kinetics of sintering may be viewed as the rate
at v.'lii.cli tiiis path is traversed by the system [45].
Traditionally, the kinetics of sintering have been studied
by measurement cf shrinkage. As indicated in the i-rcvious
section, shrinkage mc-asurcmcnts on geomet rj cal ly simple
11
^^___ I. 4
c) O
Fig. 1, Sequence of states through which a sinteringfour-particle systen passes. Densificatioiiproceeds as L-, >L2>L,>L .
.
12
systems have been used by nany workers to identify the
mechanisms by which sintering is taking place [11,26,46,47]
These results, however, do not extrapolate well to many-
particle systems. Dilatomotric measurements of shrinkage
have been made on three-dimensional systems composed of
many particles. It is usually found that the data can be
fitted to an equation of the form [48]
fi=Kt" CI. 3)o
where AL = L^ - L(t)
L = initial dimensiono
L(t) = dimension at time t
t = time
n =• the time exponent
and K can be represented as
K'exp # (1.2)
T"
where K" = a constant
T = temperature in degrees Kelvin
R = gas constant
Q = activation in energy for the shrinkageprocess
.
Such measurements, however, provide no inform.ation about
the path of sintering;,
A detailed study of microstructural changes wliich
occur during sintering was first undertaken by Rhines et al
[49]. They observed that tlie total volume of porosity
13
decreased as sintering progressed, but aA^erage pore size
increased. Arthur [50] determined that porosity remained
connected until relatively high densities v;ere attained
.
Burke [23] has observed that exaggerated grain growth
occurs during the latter stages of sintering and can effec-
tively arrest densification . These observations indicate
the complexity of tlie sintering processes and the defi-
ciencies of simple geometric models.
Techniques for quantitatively characterizing the
microstructure of sinter bodies have been available for
some time. However, only recently has systematic study
been undertaken. An additional parameter of particular
significance to sintered structure characterization was
provided by Delloff [51] and by Cahn [52] witli the develop-
ment of a technique for measuring quantitatively the curva-
ture exliibited by tlie interface in a two-phase system (see
section 2.3).
Rhines [53] has slio^vn tliat topological concepts may
be used to characterize the sintering process to an extent
not possible with ordinary geometric concepts. Using the
topological approach, Rhines et al . [45] developed a model
wherein the system of particles, contacts and void channels
is reduced to a node -branch network. It was shown that
the model was applicable to the eiitire process from loosely
stacked particles to a fully dense body. Aigeltinger [54]
has experimentally determined the topological properties
14
of a sinter body using a serial sectioning technique to
synthesize the structure.
Coble [55] has undertaken to describe the path of
microstructural evolution based on bulk diffusion-controlled
processes. He concluded from examination of micrographs
that the sintering process could be treated in three
stages
:
1) Initial stage -- growth of interpart icl e con-tacts into weld necks. The necks broaden tothe extent that grain growth becomes possible,thus signaling the end of the first stage,
2) Intermediate stage -- with the onset of graingrowth , intersect ion of grain boundaries withvoid-solid interfaces begin to assume equi-librium dihedral angles. Porosity is situatedas a continuous network of cylindrical poresalong the lines of intersection of threegrains. During this stage the pores retaincylindrical configurations and simply shrink.Two alternate final stages are proposed bvCoble.
3a) Pores are pinched off and isolated at fourgrain corners. If grain grov/th is inliibitedthe pores can continue to shrink untiltheoretical density is attained.
3b) If discontinuous grain growth occurs, poresare isolated from grain boundaries. Mostporosity is closed and spherical. Regionsadjacent to grain boundaries are relativelyfree of porosity as a result of boundarymigration
.
Using a tetrakaidecahedron as a model for grains and
cylindrical or spherical pore shapes, he calculates shrink-
age rates for intermediate and final stages of sintering.
Reasonably good agreement between diffusion coefficients
calculated from shrinkage rates, based on the model, and
15
those determined from initial stages of sintering were
obtained.
The densification and development of micros tructure
in UO^ v;ere studied by Francois and Kingery [56]. They
found that rapid heating rates produced a microstructure
that consisted of intergranular porosity as opposed to an
intragranul ar microstructure observed for conventionally
fired UO^ . The "intergranular" microstructure was charac-
terized by measurements of dihedral angle, average number
of sides exhibited by a pore intersection with the plane
of polish, average pore size and grain size. Based on
this data and extraction analysis, they concluded that
carbon in trace quantity in the starting material was
responsible for the unusual microstructures observed after
rapid lieating.
Rhines et al . [45] have studied the geometric path of
microstructural change for a number of metallic powders.
Particles of different morphologies, including irregular
dendritic electrolytic copper, spherical copper, nickel
carbonyl and antimony powders, were included in the study.
The effect of particle size, compaction, particle size
distribution and temperature were systematically examined.
The results of these studies are briefly summarized.
1. The sintering process may be divided into three
stages based upon the dominant geometric process which is
occui-ring: Stage 1 - points of contact broaden into weld
16
necks; Stage 2 - continuous channels'of porosity begin to
pinch off, isolating regions of porosity; and Stage 3 -
large isolated pores grow at the expense of smaller pores.
Thus, there is a coarsening of the scale of porosity.
2. A linear relationship between S , surface area
per unit volume, and \', volume fraction of porosity, has
been found to hold for all materials during second- stage
sintering. Thus, for a given system, there exists a unique
path of change for surface area towards which the system
tends. The imposition of constraints such as precompaction
and inhibitors will alter tlie approach to tliis path in a
manner that is qualitatively predictable.
3. Tlie total curvature per unit volume, ^^ , is ini-
tially positive, decreases tlirough zero to a maximum nega-
tive value and approaches zero again as densification
nears completion. (See section 2.3.3 for explanation of
sign convention.
)
Gregg [57] lias measured tlie sintering force (defined
to be the force necessary to balance axial shrinkage) as
a function of density. Somewhat surprisingly, the sinter-
ing force v.'as found to increase witli increasing density,
reaching a maxiiiium before beginning to decrease. Gregg
found that tlie variation in the sintering force could be
correlated with tlie evolution of average mean curvature,
FT, and derived an expression relating capillary forces to
the sintering force, based on a spherical pore model.
17
The evolution of microstructure in a three-dimensional
sinter body can be described by quantitative geometric
properties whicli uniquely characterize the system. These
properties are experimentally measurable and require no
simplifying assumptions.
1.3. Effect of MicTOSt ructur e onMechanical and Thermal Proper tie's
The mechanical and thermal properties of a material
depend nrimarily upon atomistic considerations such as bond-
ing, band structure, and crystal symmetry. Microstruc-
ture can, however, play an important role in determiining
realizable properties for engineering applications. Micro
-
structural features which are expected to influence proper-
ties of polycrystals are: (1) grain size, (?) existence of
preferred orientation or anisotropy, and (3) presence, dis-
tribution and morphology of a. second pliasc. Void phase or
porosity is a special case of feature (3) and has received
a great deal of attention in the ceramic literature.
1.3.1. Me chanical Properties
The basis of the mechanical behavior of brittle mate-
rials is the Griffith Tlieory [58]. Griffith hypothesized
that all materials contained flaws. When a stress is applied
to a body containing thf: flav/, stresses in the vicinity of
the flav/ are very much liighei than would be calculated
18
assuming the body Kas a honogcncous continuum. As a result
stresses approaching theoretical strength are achieved at
the tip of the flaw, causing it to propagate and ultimately
produce fracture of the macroscopic body. Inglis [59],
utilizing a flat elliptical void as a model, computed
stresses in the vicinity of the flaw. The result of this
and similar calculations based on a variety of geometries
was a relation of the form
S « (^)^/2 (1.3)
wheie S = the stress necessary to extend the flaw
a = specific surface energy
li = Young's Modulus
C = characteristic flaw dimension.
Credence was given the flaw theory by observations of
high strengths of pristine glass fibers. Upon prolonged
exposure to the atmosphere, strengths deteriorated by more
than an order of magnitude [60]. The Griffith Theory pre-
dicts tliat failure by brittle fracture is the result of the
extension of flaws inadvertantly introduced prior to, or
nucleated by, the application of a stress.
In light of this hypothesis, the effect of microstruc-
ture on nucleation and propagation of "Griffith cracks"
forms the basis of the present discussion.
It is observed that the fracture strength of "brittle"
materials and the yield strength of "ductile" materials
19
increase as grain size decreases. Several explanations of
this effect have been put forth [61],
1. Grain boundaries serve to limit the length of
cracks that can subsequently propagate. Since, from equa-
tion (1.3). the fracture stress is directly related to the
flaw diniensi.on, smaller grain size materials have smaller
flaws, and tlius exhibit higher strengths.
2. If dislocations are mobile, grain boundaries act
as barriers causing dislocations to pile up and nucleate
a crack according to a mechanism proposed by Zener [62].
Presumably, larger grains present a more formidable barrier
to slip.
3. Residua] stresses across grain boundaries, due to
thermal expansion anisotropy, can be produced on cooling a
polycrystal line body. Again, the level of stresses in-
creases with grain size.
4. Elastic anisotropy may also produce high local
stress fields across grain boundaries when an external load
is applied. The extent of loca] stress is expected to be
proportional to grain size.
5. Surface flaws are generally larger in large -grained
materials
.
In a recent work, Carniglia [63] has examined 46 sets
of published strength versus grain size data for monophasic
oxide bodies. After "normalizing" for porosity, the data
could be represented by an equation of the form:
20
c = c^ * a^G""' (1.4)
where a = the mean strength
G = the grain size
a,, o^ and a = constants.
Equation (1.4) is the Fetch [64] equation for o^ ^ 0(6),
the Orowan equation [65] if a^ = 0(7) and the Knudsen equa-
tion if OL ^ 1/2 [66]. Camiglia concluded that the data
were described by a two-branched curve, one branch described
by the Orowan equation, the other by a Fetch relationship.
-1/2In all cases, strength was proportional to G ' .
The effect of porosity on the mechanical properties
of ceramics has received a good deal of attention in recent
years [67-70]. As a result of these studies, several equa-
tions have been proposed which are in reasonably good agree-
ment with published data. Hashin and Shtrikman [71] de-
rived the expression
^'^oT^ »• = '
where E = Young's modulus for porous bodies
£ = Young's modulus for theoretically dense° material
P = fraction of porosity
A = constant.
Using a dispersed pore model and a Poisson's ratio of 0.2,
Hashin and Shtrikman concluded that A should be equal to 1,
in agreement with the work of Fryxell and Chandler [72] on
21
BeO. Values for the constant. A, for A1_0_ are, however,
in the range 3-5 [73,74].
The most commonly used relationship bet\\?een strength
and porosity was suggested by Ryshkewitch [75] and by
Duckworth [ 76 ]
:
-bP(1.6)
where a = fracture stress, a = fracture stress of theo-
retically dense material, b = constant, and P = volume
fraction of porosity.
Carniglia [63] employed equation (1.6) to normalize
data from strength versus grain size studies. Rudnick e t al .
[61] attribute, in part, the variable dependence of strength
on porosity observed by different workers to differences in
pore size, shape and distribution. Brown et al . [77] have
derived an expression based on the concept of a projected
area fraction of porosity normal to tensile stress. They
considered pore shape and orientation, summing up the pro-
jected areas in the fracture surface on the normal plane.
DeHoff and Gillard [78] examined the rupture strength of
porous copper bodies as a function of porosity. They mea-
sured the area fraction of solid supporting the stress
directly on the fractured surface by quantitative micros-
copy, and concluded that the rupture strength v/as given by
a = a A, - , where a = rupture stress, a = rupture stresso A mm - ' o ^
of solid copper, and A„ . = minimal area fraction of solid
(corresponding to projected area of fracture surface).
22
It is apparent that correlation of properties sinply with
volume fraction of porosity is not completely satisfactory.
The morphology, size and distribution of porosity must be
considered if a truly fundamental correlation is to be
obtained.
1.3.2. Mechanical Properties of UO2
UO^ behaves as a perfectly brittle material at temper-
atures belov: 1000°C. Recent studies by Evans and Davidge
[79] and by Canon, Roberts and Ecals [80] have shown that
UOp exhibits a brittle-ductile transition, the precise tem-
perature of which depends upon the deformation rate.
Burdick and Parker [81] examined the effect of particle
size on the bulk density and strength of UO2 bodies. As
expected, coarser size fraction? produced lower densities
and lower strengths. Final grain size was approximately
equivalent as the result of grain growth in finer size frac-
tion material. Knudson, Parker and Burdick [82] examined
the dependence of flexural strength on porosity and the
effect of Ti02 additions to UO2 bodies prepared from four
different kinds of UO2 powders. They found that their data
(consisting of one microstructural state for each of the
four powders) could be expressed as
S = K G"" e"^P (1.7)
where S = flexural strength in four-point loading
lb
G = average grain size (Martin's diameter)
P = volume fraction of p.orosity
K = 23,700
a = .119 ^ constants (room temperature)
b = 3,17
The above equation also produced satisfactory agreement
with data taken at 1000°C for different values of the con-
stants, K, a and b. At 1000°C, Knudsen et al . report a
value for the grain size exponent, a, of .837. As indi-
cated in the previous section, both Orowan [65] and Fetch
[64] predict a value for a of .5, and values close to this
are observed for a number of ceramic materials [63]. Thus,
the equation of Knudsen et al . must be regarded as empirical.
Forlano, Allen and Beals [83] studied elastic modulus
and internal friction characteristics of sintered UO.^ over
a limited density range (volume fraction porosity .02-. 06).
They determined Young's modulus by a sonic technique and
found reasonable agreement with an equation of the form
E = E^(l-AP) (1.8)
where E = Young's modulus
E = Young's modulus of theoretically densematerial
A = constant
P = volume fraction of porosity.
24
Their data is in good agreement with earlier work of Bowers
ct ril . [S'l], Scott ct al . [85], and V.'achtinan et al . [86].
I:vans and Davidgc [79] reported strength and fracture
characteristics of UO- over a wide range of temperatures.
In the low temperature (brittle) regime, they concluded that
fracture occurred as the result of tlie extension of pre-
existing flav.'s. These fla\vs were thought to be large pores
found on the surface of the three-point bend specimens.
Canon, Roberts and Beals [80] observed a similar result
for materials of three different grain sizes. They attrib-
uted fracture at temperatures below 1000*^0 to flaws in the
form of isolated pockets of lov; density material approxi-
mately 50 to 100 microns in diameter. These flaws are
probably tlie result of aggregates and/or agglomerates in
the starting material, Knudsen et al . [82], Evans and
Davidge [79] and Canon et al. [80] all found that brittle
fracture strength increased with increasing temperature to
the onset of plasticity.
Roberts and Ueda [87] studied the influence of porosity
on deformation and fracture of UO2 • Porosity was produced
by increasing additions oT naphthalene to the starting
material. Resulting microstructures showed isolated, large,
anisotropic voids similar to tliat seen in irradiated fuel.
Tlieir data could be fitted to the Knudsen expression, equa-
tion (l.'l), witli a different choice of constants.
25
1.3.3. Effect of Microstructure onThermal Conductivity
Above loom temperature the conduction of heat in oxide
ceramics occurs by coupling of lattice vibrations called
phonons, and the scattering of these waves by anharmonici-
ties limit energy transfer through the lattice. The thermal
conductivity, K, is given by [88]
K = i C^vX (1.9)
where K = thermal conductivity
C = heat capacity/unit volume
V = wave velocity
X = mean free path
Above the Debye temperature both C and v change very
little with temperature, and th£ thermal conductivity is
sensitive only to the mean free path between scattering
events. Theory predicts that the mean free path should be
proportional to 1/T. Experimentally, over intermediate
temperature regimes, many coirmon oxides do in fact show a
1/T dependence [89]. Typically, mean free paths are of the
order of 10-100 A, and thus while microstructural features
have an effect upon thermal conductivity, the influence of
other variables is m.ore pronounced. The presence of varying
impurity levels can completely mask any differences due
to microstructure [90]
.
Because of the similarity of the phenomenological
theory, there is a strong analogy between dielectric and
26
conduction theories of heterogeneous solids. Models con-
sisting of alternate slabs of different materials have been
solved for heat flow parallel and perpendicular to the
slabs [91]. A parallel tube model was employed by Jackson
and Coriell [92]. Analogous to Maxwell's equations for
heterogeneous dielectrics, Euken [93] has suggested an
equation of the form
1 + 2V
1-
1-V
1
KT
2 j^ . 1^2
(1.10)
where K = material conductivitym '
K, = continuous matrix conductivity
Ky = dispersed phase conductivity
V = volume fraction of continuous (matrix) phase.
This equation applied rigorously to systems of phase 1 con-
taining uniform dispersed spheres of phase 2. Such a model
would be a reasonable representation of a high density
sintered material where porosity is isolated and spherical.
If tlie effective conductivity of the pores is low with
respect to the matrix, the Euken relation reduces to
1 - V .1
K (1.11)
27
Francl and Kingery [94] have suggested that the relatively
simple Loeb [95] expression
K^ = K^^j.^Cl-P) (1.12)
where K ^-j = conductivity of the solidsolid
P = volume fraction of porosity,
would adequately describe experimental data on a number of
materials. This expression is empirical, however, and
without physical basis.
The effect of grain size on thermal conductivity has
not received a great deal of attention by investigators,
probably again due to the m.ore dominant effect of such vari-
ables as impurity levels, test sensitivity and specimen
reproducibility. It is known that single crystals exhibit
much higher thermal conductivity than polycrystalline speci
mens of the same composition [91]. Flynn [88] has pre-
sented a model of a polycrystal comprised of grains sur-
rounded by a boundary region of "width" b. The basis for
such a representation is not clear, but, on the assumption
that the boundary "thickness" and the corresponding conduc-
tivity of the "boundary phase" remain constant, Flynn's
model predicts that conductivity increases with increasing
grain size.
1.3.4. Thermal Conductivity of UO .^
The thermal conductivity of stoichiometric UO2 has
been measured by a number of workers using a variety of
28
experimental tecliniqucs [96-^)9]. There is considerable
discrepancy betv;ccn the values obtained v.hen normalized to
theoretical density by using equation (].12). V.'ork by Ross
[100] and by Deem [101] suggested, however, tliat (1.121 is
not adequate, particularly at Dow densities. Ross [100]
further stated that pore shape and location at grain boun-
daries v.crc probably responsible for the low values he ob-
tained. He noted that, at higher density, his data arc in
agreement with the Loeb expression.
Reiswig [102] measured the thermal conductivity of UO^
in tlic range 800 to 2100°C. A least squares fit of the
data gave an equation of the form
^ " r77r"^f~0TFr ^^-^^^
where K = thermal conductivity l^^vi-"
T = temperatures in °K for specimen 85^tlieorctical density.
Bates [103] reported the findings of the International
Atomic Energy Agency (IAEA) panel tliat critically evaluated
all reported thermal conductivity for UO2 . The panel stated
that the thermal conductivity of UO^ between 20°C and
1300°C could be best represented by
1
11 TWTT^ (1.14)
where K = thermal conductivity in '^o,-'^ cm K
T = temperature in °C for a 9S'i dense specimen.
29
The panel further recommended that the correction for
porosity
,
'^A~
^^B
Pb-Pa(1.15)
be used to normalize all data to 95% theoretical density.
K. = conductivity of specimen of density p.; K^ = conduc-
tivity of test specimen of density p^; Pp -= density of
measured specimen; p^ = the desired density; and B = a
parameter that depends upon specimen "characteristics."
6 values ranging between 1 and 4 have been reported. The
panel selected 2.5 but recommended a study of the depen-
dence of B on microstructure
.
1.4. Objective of the Present U^ork
The continuing development of nuclear reactors has
resulted in ever more stringent demands on various material
components. In an effort to increase efficiency and opti-
mize performance, higher temperatures, increased fluxes and
higher burnup levels are being specified. The Liquid Metal
Fast Breeder Reactor (LMFBR) , now undergoing concentrated
development, will be the primary energy source for the
decades immediately ahead. The breeder reactor lias the9-70
capability of converting nonfissionable U"' to fissionable
239Pu and thus produces more usable fuel than it consumes.
A mixed oxide of uranium and plutonium has been selected
30
by the AEC as the fuel for the prototype LMFBR. Specifi-
cations call for the LMFBR to produce 1,000 megawatts,
achieve 10 « burnup with an output of 100,000 megawatt-days
per ton. The result will be a fission density of 10 cm""^
sec . Liquid sodium will leave the core at 540°C. Eighty
thousand fuel pins having a diameter of one-quarter inch
will operate at surface temperatures of 650°C and center-
line temperatures near the melting point of 2760°C. At
steady state, gradients up to 9000°C/cm will be sustained
1104].
It is estimated that there is a potential production
of one billion pellets of fast breeder fuel over the next
forty years. Shaw [104] has stated that it is essential
that development "proceed in a disciplined manner so as to
achieve predicted performance based on reproducibility of
materials, properties and behavior from the laboratory
bench through all phases of the program, including the oper-
ating reactor."
Reactors for specialized application, such as the
Transient Experimental Test Reactor, may impose very dif-
fererit conditions on the component design than are required
for conventional power reactors. The transient reactor will
utilize U dispersed in stabilized ^r02 to give appro-
priate fission densi ty , resist ance to thermal shock and
thermal conductivity [105].
31
All reactor fuels undergo changes in micros tructure
during operation as the result of exposure to high temper-
atures and large thermal gradients for extended periods
of time, as well as accumulating fission products. Struc-
tural changes which occur during the life of a fuel pin are
illustrated in Figure 2 [106]. It is apparent that these
changes markedly effect performance via changes in both
mechanical and thermal properties.
In summary, fuel technology has as major objectives:
1) microstructural fuel design for optimumperformance
,
2) attainment of reproducibility and uniformityfor large-scale production of fuel, and
3) prediction of microstructural changes occur-ring in pile and the effects of these changeson performance parameters.
The primary objective of the present work is the appli
cation of the techniques of quantitative metallography to
a wide range of sintered UO2 microstructures , providing a
degree of characterization not previously achieved. The
simultaneous determination of room temperature tensile
strengths and of thermal conductivities which correspond
to these structures provides a sound basis for the identi-
fication of structure-property relationships in a real fuel
material. Such a systematic study is a necessary first
step towards the attainment of the goals previously enum-
erated.
32
Shut downafter10 5 MWD/T
Operating between10 and 10 5 f.nVD/T
Operating1-10 MWD/T
Shut downafter10 MWD/Ton
Fig. 2. Structural evolution during useful life of a
UO2 fuel pin [106] .
CHAPTER II
EXPERIMENTAL PROCEDURE
2.1. Mate rial Characterization
2.1.1. Material Specifications
The materia] employed in this investigation was sup-
plied by the United States Atomic Energy Commission. It
was produced by Mallinkiodt Chemical Company by precipita-
tion from solution as ammonium diurinate (ADU) , calcina-
tion to UO^ and reduction to UO^ . The resulting product
was then fused in an electric arc furnace by SpcTicer
Cliemical Company. Analytical impurities determined by
Battelle Memorial Laboratories are given in Table 1. The
as -received powder was classified into -6 mesh, -20 mesh
and -200 mesh (U.S. Standard Series) lots. Scanning elec-
tron photographs .of the as -received materials are shov;n
in Figs. 3 and 4. The follovving observations v/ere made:
1] The particles are angular, faceted polyhedra;i.e., they exhibit very little curvature ofsurface and are roughly e qui axed.
2) There are virtually no open pores or voids inthe parti cles .
3) There is no size dependence of shape ortopography insofar as can be resolved in tlie
scanning electron microscope (SEM)
.
33
34
Table 1
.-\nalytica] Impurities in the Arc Fused UOUsed in this Investigation
Carbon 57 ppm
Aluminum 33
Boron < 0.1
Cadmium < 1.0
Chromium < 5.0
Iron 70
Magnesium < 3.0
Nickel < 3.0
Silicon 33
35
37X
4. OX
Fig. 3. SEM photographs of -6 mesh as-received UO2powder
.
36
800X
4,000X
Fig. 4. SEM photographs of -200 mesh as-received powder.
37
4) There are small particles which appear to beadhering to surfaces of the larger particles.These particles are generally siiialler than5 microns and are physically distiiict fromthe substrate particle.
Similar "surface" particles have been seen by Johari
and Bhattacharyya [107] on electrolytic iron and by Lifshin
et al . [108] on SiC. The latter attribute bonding to elec-
trostatic forces. Ef fectiA^ely , then, each particle is an
agglomerate or assembly of many particles which cannot be
readily separated. It is apparent from tlie surface topog-
rapliy that subsequent to arc fusion the present material
was subjected to a coimninution process, wlierein large fused
grains were cruslied. The small particles observed are
probably the result of this operation.
Figures 5 and 6 are photomicrograplis of -6 m.esh and
-270 +325 m.esh as-received powders. In both cases, nearly
all particles are single crystals, and thus even when
etched are A^irtually featureless. The -6 mesh particles
(Fig, 5) show residual cracks from the crushing operation,
the presence of aggregates (although their number was
judged to be quite small) and occasional closed porosity.
The -270 +325 specimen of powder shown in Fig, 6 indicates
no aggregates preseiit in this size fraction. It is appar-
ent, however, that particles much smaller than the 44 micron
325 sieve oponing have been retained.
Graham [109] has measured the x-ray domain size of
ball milled powder employed in this investigation. Based
58
(a)
(b)
Pig. S. Photomicrographs of -6 mesh as-received powder;(a) cracked grain, (b) particle aggregate.
39
Fig. 6. Photomicrogranhs o£ -270 +325 as-received oowder.
40
on line profile analysis of (200) and (400) reflections,
lie found an effective domain size of 530 A. This result
is in p.ood agreement with results of other Korkcrs [110]
and indicates a relativel)' low preparation temperature of
500° to 600°C [111] .
2.1.2. Stoichiometrv
As a result of the multiple oxidation states of U,
the uranium-oxygen system is among the most complex of
metal -oxide systems. There are at least four thermodynam-
ically stable oxides, and these exhibit polymorphism and
metastability to varying degrees [111]. Several otlier
oxides have been reported, but not confii'med. Only tlic
region between UO2 and U^Og (0/U = 2.00 to 2.25), however,
is of primary interest to tlie nuclear fuel industry.
Although differing in detail, tlie work of Schaner
[38], Blackburn [112], Vaughn ct al . [113], Aronson and
Belle [114] and Gronvold [115] established certain general
features of the phase diagram in the region between DO,
and U^Oq. The diagram according to Schaner [38] is pre-
sented in Fig. 7.
UO2 crystallizes in the fluoritc structure, i.e., the
cation lattice is FCC and 8 oxygen ions are located in the
tetrahedral interstices. As indicated by the diagram,
Fig. 7, UO2 exhibits considerable solid solubility for
oxygen (hyperstoichiometry) . At 900°C cubic UO^ is stable
41
14 "
1200 -
1000 -
Fig. 7. Phase diagram of the U-0 systen for 0/U ratiosbetv/een 2.0 and 2 . 25 , according to Schaner [38]
42
5.480
o«^ 5.470
I-
CD
5.460
cyy HATiD
Fig. 8. Dependence of the lattice constant at 25°C upon
n/LI ratio for cubic UO^ [38].
in the 0/U range 2.00 to 2.20, while at room temperature
there is little or no solubility. Viitiially all proper-
ties o£ UO- are sensitive to some degree to the presence
of excess oxygen in the lattice. Consequently, detei'mina-
tion of 0/U ratio is essential to any study of U0„
.
Precision lattice parameter measurements and thermo-
gravimetric analysis were employed for this purpose.
Reported values of the room> temperature lattice parameter
of stoichiometric UO2 range between 5.473 [38] and 5.469 A
[116], Schaner [38] has determined the lattice parameter
of UO^^ , as a function of knoivn 0/U ratio. His results,
sliown in Fig. 8, are in good agreement with more recent
studies.
The lattice parameter of a freshly sintered bulk
specimen from the present study was determined utilizing
a Norelco di f fractometer to scan the region 29 = 70° to
145° at 1/2° 26 per minute. Filtered copper radiation
from a fine focus tube operating at 35 KV and 15 ma was
used; 99.99% annealed gold powder served as an internal
standard. Data obtained were fitted by Cohen's Method of
Least Squares [117] . The calculations were performed by
computer, utilizing a program supplied by Mueller (Argonne
National Laboratory) and reproduced in Appendix A. The
choice of correction terms is indicated on the program,
description. The value obtained for a specimen sintered
in H2 ^vas a^ = 5.4716 ± .0003 X. From Fig. 8, the 0/U
44
ratio was determined to be 2.00 after sintering, in agree-
ment v;ith the general observation that sintering in 11^
produces a stoichiometric material, regardless of the
stoichioinctry of the starting oxide.
The measurement was repeated v/ith ball milled powder
dried in air at 90"C.
The 0/U ratio of the starting material v;as determined
to be 2. 06 based on a lattice parameter of 5.4693 ± .0006 A.
A determination of stoi chiometry v;as also made utiliz-
ing a gravimetric technique described by Scott and Harrison
[]1S]. A precision clectrobalancc* Av'ith a reported sensi-
tivity of better than 10 micrograms was used in this experi-
ment. A sample of approximately 100 mg was carefully
weighed on a platinum pan utilizing class S v.'eights. The
specimen and pan Avere then counter balanced and the micro-
balance recalibrated to yield full scale deflection at 10
mg increase in weight. A null detector** was employed to
indicate balance. The specimen and pan were then trans-
ferred to a platinum boat and oxidized at 450°C in still
air for two hours to produce U^Og (0/U = 2.667). The speci-
men was returned to the balance and the weight increase was
determined. The procedure was rejicatcd to insure that the
reaction had gone to completion. The weight gain expected
if the starting material had been stoicliiometric (0/U = 2.00)
*Cahn Division, Vcntron Instrument Company.
*Kiethly Instrument Company, Model No. 155.
45
was calculated and compared with that observed experimen-
tally. An estimate of stoichiometry could then be made.
This m.ethod gave satisfactory results for a bulk sintered
material (0/U < 2.03). Results for ball milled powders
were not satisfactory, probably because of adsorption on
surfaces. It is believed that this situation could be
corrected by in-situ oxidation and/or oxidation-reduction
in a controlled environment. Scott and Harrison [118] also
reported difficulty with as -received powder, indicating the
problem is not unique to the present investigation.
2.1.3. S ize Reduction and Separation
In an effort to evaluate the sinterability and the
effect of particle size on sintering beliavior, the as-
received -200 mesh powder was sieved and fractionated
according to Table 2.
Initial attempts to sinter loose stacks (uncompacted)
of -325 powders at 1650°C met with limited success. Speci-
mens sintered for two hours and 24 hours showed identical
densities of 5.26 gm/cm"""* (^8% theoretical density).
Although some sintering occurred (loose stack density
4.43 gm/cm"^) , specimens were quite fragile.
In order to explore the effect of temperature, arrange-
ments v.'ere made to use ultrahigh temperature furnace facil-
ities.* Molybdenum cups were loaded with material from
'^Komietco, Inc.
46
Table 2
As-received UO2 Powders were SeparatedInto Lots by Sieving
(1)
(2)
(3)
(4)
(5)
Sieve
47
each powder lot in Table 2 and tapped down manually. The
specimens were sintered in hydrogen at 2250°C for one hour.
The results are sho\\m in Fig. 9. Only 4 and 5 could be
considered strong enough to be handled.
It was clear as a. result of these studies that par-
ticle size reduction would be necessary in order to extend
the range of initial particle sizes and, hence, the range
of accessible microstructures . As a result of the sieving
operation, it was determined that approximately 80^ of the
as-received -200 mesh material was retained on a No. 325
sieve, but would pass a 270 sieve. Tliis material \\'as
selected as a base for all furtlier studies because of the
quantity available, the fairly discrete size distribution,
and evidence of reasonable sinterability in the "as-
received" condition.
Two techniques were employed to produce material of
smaller particle size. A rubber lined ball mill with
Burundum cylinders* was used to wet ball mill the base
material for 16 hours. This was followed by a drying oper-
ation done in air in open Pyrex trays at 90°C for 12 hours.
The powder was then granulated and stored in closed con-
tainers until used.
^^U.S. Stoneware Company.
48
c•H<n
(MMO» Q)
iH
V CO>H•H0) cU'H0)
O Vi
tn 3;« ou(0 a>M >(A O
•H0) in
wo oO 4J
E 4)0*4-1it o
0) Ih
>-i 0)CO .£3
P.E<U 3
Co•H O
49
As an alternative to ball milling, an impact pulver-
izer* v.'as em.ployed. Optimum conditions appeared to be
opposing pressures of 80 and 100 psig of argon at the jets.
Although the process produced a powder less than
1 micron in size, it was found to be inefficient. Maximum
production rates were below 10 grams per hour, which was
deemed inadequate for this investigation.
Examination of wet ball m.illed material indicated
the presence of particles in excess of 10 microns along
with particles of 1 m.icron or less in considerable quantity
It was fe]t tliat if a separation process could be used to
remove particles >5 microns the remaining po\'/der would be
sufficiently different from the ball milled material to
provide a third point in the scale of starting materials.
Separation was accomplished by a sedimentation tech-
nique, i.e., a dispersion of the particles in a fluid,
preferential settling of the larger particles and recovery
of the remaining particles. In order for such a technique
to be effective, agglomerates had to be dispersed com-
pletely, in such a way that neighboring particles did not
interact. It was found that a com.mercial pigment stabil-
izer, polyoxyethylene sorbitan monolaurate , ** in concen-
trations of about 20 ppm in aqueous solution vv'ould
*Gem-T, Trost Equipment Corporation
**Tween 20, Atlas Chemical Com.pany.
50
effectively disperse UO^ . Experimentally, the suspension
is agitated in a small liquid blender and transferred to a
glass column approximately 90 cm in height, allowed to
stand 80 minutes; the supernatant, containing the fine
particles, is then withdrawn and the particles recovered.
The basis for this technique is given by Stokes Law for a
spherical particle:
^ Tir^Cp - Pj2^)g = 67Trnv (2.1)
where r = particle ratio
p = particle density
Pj = liquid density
g = acceleration due to gravity
n = coefficient of viscosity
v = steady state or terminal settling velocity.
For a particle initially at rest a distance h from the
bottoi?. of the vessel, the settling velocity v is
V =^ (2.2)
where t is the time required for a particle to settle the
distance h. Substitute (2.2) into (2.1) and rearrange,
1- _ Ojrymh ., ,^1. -
-^ ^ L-.oj
T ^Y (Pp-P;i)
Using the viscosity of water at 25 °C (9 x 10' poise),
a particle density of 11 gm/cm'^ and the column height of
90 cm, the maximum time required for particles larger than
51
-270 +325(coarse)
Ball milled(intermediate)
Separated(fine)
10 microns
Fig. 10. SEM photos of powder from the three sizefractions employed in this investigation.
52
5 microns to settle is 4,800 seconds! Clearly, smaller
particles near the bottom of the column will also settle
out during this time interval. (Althougli these are poten-
tially recoverable by rej^etitions of the sedimentation
process, no attempt was made to further separate the solids
which settled out of the suspension.) The supernatant was
drawn off to a clean vessel after the prescribed time
period had clasped. Attempts to deflocculate the suspen-
sion using commercial def locculants of the anionic, cationic
and nonionic types were unsuccessful. Recovery of the
solids was effected by evaporation of the liquid in sliallow
Pyrox trays heated at approximately 90°C. Tlic dried cake
was crushed, passed through a 200 -mesh sieve, and stored in
closed containers.
Scanning electron micrographs of the powder lots
employed in the present study are shown in Fig. 10. These
lots are referred to respectively as coarse, intermediate
and fine size fractions in the text.
2.1.4. Specific Surface Area
Tlie surface areas of the three powders employed in
this study were measured by a technique devised by Brunauer,
Emmett and Teller [119]. The B.E.T. measurement is based on
a model for adsorption of a gaseous species on the surface
of a solid. The surface area is related directly to
capacity to adsorb atoms by
53
S = o^ N A X lO"^*^ ' (2.4)Mom ^^ • ^ J
2Avhere S = specific surface m /ga-am
X = monoiayer capacity in grams ofadsoi-bate/grams of adsorbent
M = molecular weight of adsorbate
N •- Avogadro's number
A - area occupied by a single adsorbatemolecule in X2
.
Based on the B.E.T. model, the monolayer capacity of the
solid can be evaluated from [120]
X(p -p) " T~C ' TT p '^•^-'^^ o •
'^ m m i
where X = mass of adsorbate in grams per gramof adsorbent
p = saturated vapor pressure
p = system pressure
X = monolayer capacity
C = constant for the system related toenergy of adsorption of the monolayer.
Accordingly, when p/X(p -p) is plotted against p/p , the
relative pressures, a straight line is formed having a
slope
S = ^ (2.6)m
and an intercept
TT (2.7)m
Solutions of these two equations simultaneously leads to
\ = ^ (2.8)
C =I
* 1 (2.9)
B.E.T. measurenents were performed on the three powder
size fractions described prev^iously, using an apparatus
similar to that shown in Fig. 11. Approximately 10 grams
of material were charged into a quartz specimen bulb.
The surface was then activated by heating to temperatures
in excess of 300*^0 for two hours at 10 mm Hg. The bulb
was then cooled to 77°K in a liquid nitrogen bath and held
at that temperature until measurements were completed.
Dry nitrogen was introduced into the system with the
specimen stopcock closed and the amount of gas determined.
The specimen stopcock was then opened and the system pres-
sure was allowed to equilibrate before the value was
recorded. Subsequent readings are obtained by decreasing
the volume of the system through a series of mercury cham-
bers and an equilibrium pressure recorded for each incre-
ment. A computer program to solve t)ie B.E.T. equation has
been written by Martin [121], incorporating the appropriate
parameters for the apparatus employed here. This program
calculates values for p/x(p -p) and p/Pq. performs a
least squares fit, calculates the slope and intercept of
the B.E.T. equation, and computes specific surface area.
55
To
McLeod gauge-
Gos inlet
(helium or-nitrogen)
Thermometer
Moin vocuum line^
Low temperature bath
—»-To atmosphere
Tomercurydiffusion
pump
Mercury (confining liquid)
Fig. 11. Schematic of the B.E.T. apparatus used todetermine surface area [120].
56
Table 3
Surface Areas of theThree Size Fractions of UO,
As received, -270 +325 (coarse)
Ball rilled (intermediate)
Separated (fine)
0.1-0.3 nr/gram*->
0.87 m''/gram
21 . 54 m /pram
Considerable scatter in the adsorption isoinherent for low values of surface area. All itherms B.E.T. Type IJ at 77°K.
thermso-
.05 1
P/P
• Experimental
O Least squares
1.5
Figure 12. R.L.T. plot for fine size fraction of UO,powder
.
2
57
The values obtained are given in Table 3. Figure 12
is a plot of the B.E.T. data for the fine size fraction.
The data for the intermediate and coarse materials were less
satisfactory because experimental error increases as the
surface area decreases, as discussed by Crowl [122]. It
should be noted that for all three data sets, the parameter
C, as defined by equation (2.9), is larger than 2. This is
a necessary condition for the isotherm to be Type II, thus
permitting the surface area to be calculated.
2.2. Specimen Preparation
Tjiree techniques were employed to prepare specimens
for exam.ination
:
1) loose stack sintering -- sintering of uncom-pacted material in a suitable container,
2) cold pressing and sintering -- compaction ina steel die followed by thermal treatment, and
3) hot pressing or pressure sintering -- sinteringunder an applied load in a die.
2.2.1. Loose Stack Sintering
Powder was poured into specially machined molybdenum
cups approximately one inch in height, .625 inch inside
diameter.
As \JOy powder is not free flowing, it was necessary
to tap down the stack to insure that it filled the cup
uniformly. The conical stack was leveled off even with
58
tile top of the cup and tlic cups were then placed directly
into the furnace. The sintering cycle is discussed fully
in the next section.
2.2.2. Cold Pressin?^
Cold pressed specimens v.'cre prepared by compacting with
and without the aid of a binder-lubricant. Polyvinyl alco-
hol, stearic acid in petroleum ether and polyethylene
glycol were evaluated for use as binder- lubricants . Poly-
ethylene glycol* was selected for its outstanding green
strength, ease of blending, excellent surface finish and
ease of volatilization prior to sintering. The binder was
added to the powder batch in amounts of 1/2 to l-i by weight
and blendod in a polyethylene container. Mixing was
carried out b)' tu;nbling the container on a ball mill drive
for one hour.
Specimens Averc pressed in a specially constructed and
hardened tool steel die. The cylindrical die cavity had
a diameter of .689 inches, incorporated a taper of 8 minutes
per incli, and had an adjustable depth. The die, pressed
into a double acting Ilaller^^'die table, is shown in Fig. 13.
A 75- ton liydraulic arbor press was used to apply pressures
up to 100,000 psi. In practice, compacting pressures above
75,000 psi freciuently produced transverse laminations.
*MallJnkrodt Clicmical Works.
**llaller Division, I'ederal -Mogul Corporation,
59
Fig. 13. Punch and die assembly used to cold compact UO^
60
Severe galling, die chatter and specimen cracking were
observed in the absence of a binder-lubricant above 10,000
psi and, as a result, a binder was employed for nearly all
specimens produced by cold pressing.
Pressed compacts were placed on molybdenum trays and
inserted into the hot zone of an Astro high temperature
furnace,* Fig. 11a. The furnace was evacuated and back
filled with commercial grade hydrogen nrior to heating.
A flowing hydrogen atmosphere was maintained during all
heating and cooling periods. A one-hour hold at 150°-200°C
was utilized to volatilize the binder prior to heating to
the desired sintering temperature. Practical sintering
temperatures were limited to about 1800°C by the -^12^3
muffle. Heating and cooling rates of 20°-40°C per minute
were generally encountered and the sintering "times" that
are presented are the time intervals tliat specimens are at
the sintering temperature. They do not include the heating
and cooling periods.
Temperatures were measured with a micro-optical pyrom-
eter**sighted directly on the specimens. The temperatures
reported are believed to be accurate to ±10°C in the range
of interest.
*A5tro Industries, Model lOOOB.
**Pyrometer Instrument Company, Model 95
61
(a)
(b)
Fig. 14. (a) The high temperature Astro sintering furnace(b) Centorr vacuum hot press.
2.2.3. Hot Pressing
Hot pressed specimens were fabricated in a Centorr
vacuum hot press,* Fig. 14b, using graphite** dies and
punches. Early experimental pressings revealed extensive
reaction between graphite and UO^ , particularly at temper-
atures above 1700^C. This reaction is undoubtedly respon-
sible for hot pressing behavior reported by Murray [32].
The situation was corrected by the use of a boron nitride***
die insert and punch faces. The entire die assembly is
shown in Fig. 15. Pressures up to 5,000 psi and temper-
atures to 2000°C in a vacuum of 10 torr were attained.
Temperatures again were measured with an optical pyrometer
sighted on the die body, giving a probable accuracy of t20°C.
A subsequent heat treatment of 90 minutes at i200°C in
hydrogen insured that the specimens were stoichiometric [125]
2.3. F.v^aluation of -Geometric Properties
2.3.1. Metallography
Microstructural examination was carried cut on speci-
mens which had been fiactured in diametral compression (see
section 2.4). The fracture mode was such that two large
segments of the specimen were recovered. The fracture
*Centorr Associates, Inc.
**Union Carbide Corporation, Grade ATJ
***Union Carbide Corporation.
63
Die body-
Lower punch
Lower ram
Upper ram
Upper punch
BN punch face
BN die liner
Fig. 15. Graphite and boron nitride die assembly usedto pressure sinter U0~
.
64
surface of one of the segments was then ground and mounted
for metallographic examination. The remaining segments
were held for fractographic study.
Metallographic mounts were prepared using a castable
epoxy compound* and a vacuum impregnation process. Speci-
mens were impregnated by immersing them in a beaker of the
epoxy mounting material and placing the beaker in a vacuum
dessicator connected to a mechanical pump. The dessicator
was gently evacuated until air appeared to be removed from
the specimen; air was then readmitted into the dessicator,
forcing the epoxy into the open porosity in the specimen.
It was found necessary to repeat impregnation through
successive polishing steps for samples of low density and/or
low strength as many as three times in order to obtain satis-
factory results. After impregnation, the specimens were
placed in glass cylinders situated on a glass plate and
additional mounting material was poured into the cylinder
to produce a mount of suitable size. The epoxy was cured
at room temperature for 24 hours, then heated to 50°C for
an additional 2-3 hours. It was found that only after the
above curing process could the mount be readily removed
from the glass cylinder.
The metp.llographic procedure employed to polish the
specimens is as follows [124]:
*AB Bueh]er, Ltd,
65
1) Vvct grind on a slov.' wheel with 180-, 320- and600 -grit silicon carbide paper discs.
2) Polish on nylon or silk saturated with 2%chromic acid and suspension of Linde A aluminapowder in 2% cliromic acid using a fast wheelspeed.
3) Repeat (2) witli Linde B alumina after thor-oughly cleaning the specimen with distilledwater and alcohol.
4) U'asli, dry and examine; the etch used to revealgrain structure was devised by Cain [125]:(a) a solution of one part H2SO4 to nineparts n202 (30%) swabbed on the surface withcotton for 30 seconds, and (b) the surfaceis then immersed for an additional 30-60seconds, washed, dried and examined. Deter-minations of the metric properties of thepore solid network were made on unetchedspecimens, in as much as etching was foundto adversely affect the accuracy of thesemeasurements. Subsequent to these measure-ments, the specimens were etched and thegrain i:)Oundary intercept count was made.
2.3.2. Quantitative Metallograpliic .'\n a lysis
Three quantitative metallographic parameters were
determined in order to characterize the void-solid network:
(1) Pp , the fraction of points of a test grid imposed on
the mi crostructure whicli lies within the feature of inter-
est, e.g., void phase; (2) Ny, the number of intersections
per unit lengtli tliat a test line imposed on the micro-
structure makes with a feature of interest, e.g., void-
solid interface; and (3) T. net, the net number of tangents
that a test line makes with features in the microstructure
,
e.g., pores, wlien swept over a unit area. There are two
kinds of tangents wliich a test line can make with a boundins
66
curve, if an interior and an exterior can be distinguished.
Following Rhines et al . [45], a tangent is considered nega-
tive if the arc at which tlie tangent is made is convex with
respect to the pore phase and positive when concave with
respect to the pore phase. The number of positive and
negative tangents per unit area traversed are tabulated
separately and the value of T, net is then
T^ net = T^^ - T^,
.
(2.10)
T, net may be positive or negative depending on relative
magnitudes of the two tangent counts, and the algebraic
sign of T. net must be included in all calculations involv-
ing the tangent count. The determination of these param-
eters is illustrated schematically on a photomicrograph of
a UO^ specimen in Fig. 16.
The volum.e fraction of void phase may be determined
from the point count and independently from a determination
of the density of the sinter body. A comparison of these
two values v;as used as a criterion to ascertain that the
metallographic section v;as in fact representative of the
three-dimensional sinter body. An agreement between the
point count and bulk density of 3"^ was used as a criterion
for acceptance or rejection of metallographic sections as
representative of the sinter body.
Bulk densities were determined by the liquid displace-
ment technique described in ASTM Standard 328-60. Open
67
Fig. 16. Schematic illustration of the counting measure-ments on a sinter structure.
68
porosity was filled with paraffin prior to determination
of sample volume. Some sample densities were also deter-
mined by displacement of carbon tetrachloride. No impreg-
nant was used and specimens were allowed to equilibrate
for several hours in the carbon tetrachloride prior to
determining immersed weight, thus excluding "open" porosity
from the sample volume.
The determination of the quantitative metal lographic
parameters was made utilizing a Quantimet 720 image analy-
ing computer.* The instrument is capable of performing all
of the counting measurements previously described, by
dividing an image into picture points. Logic circuitry
permits this Quantim.et to recognize picture points in which
the image is darker (or lighter) than a preset level. Thus
if there is a gradation in image intensity, such as there
is between void and solid phase in a sinter body, a point
fraction is obtained by counting the number of picture
points which comprise the void space and dividing by the
total number of picture points utilized to represent the
image. The Quantimet has a capacity of 500,000 picture
points on "Standard Frames," but the size and position of
the computed or "live" frame may be varied. The image is
displayed on a cathode ra)' tube which also incorporates a
digital display of the counting results. Additionally,
*Image .Analysing Computers, Ltd,
69
the detected image and the computed image may also be dis-
played. Figure 17 shows the displayed image of a sintered
UO^ specimen with the digital display in the upper left of
the screen.
Intersections and tangents are also based on pre-
programmed logical analysis of the image as represented by
the array of picture points. Intersections are registered
whenever the computer finds that adjacent picture points
differ by an established intensity. As the raster scans
line by line, top to bottom, the structure is sampled by
the equivalent of a test line whose length is the product
of the number of lines in the live frame and the actual
width of the frame. Similarly, the image is scanned line
by line for "end points" or tangents, equivalent to sweep-
ing a test line over the live frame.
A metallograph* is used to provide the image viewed
by the Quantimet vidicon head. A specially designed mount
supports the vidicon and permits it to be moved along the
bellows track of the met allograph . Figure 18 shows the
met alio graph -vidicon assembly.
Grain boundary intercepts were counted manually using
a grid eyepiece. Measurements were performed on specimens
for which void space characterization had been completed,
and which had subsequently been etched to reveal grain
^Bausch and Lomb , Inc., Research I.
70
Fig. 17. Quantimet display of a sintered UO2 micro-
structure.
71
p.
72
boundaries. Intersections with void-solid boundaries and
grain boundaries between adjacent grains were tabulated
separately.
2.3.4. The Metric Properties
The metric properties are determined directly from the
counting measurements described in the preceding section.
1. The volume fraction, V , is the total volume of
void space contained in a unit volume of microstructure
.
It may be shown that the point fraction P is an unbiased
estimator of volume fraction [126,127]
\ - Pp (2.11)
2. S is the surface area of interface per unit
volume of structure. The number of intersections per unit
length made by a test line with the trace of the surfaces
on a representative test plane is directly related to
Sy by [126,128]
S^ = 2Nl (2.12)
3. The means to experimentally determine mean surface
curvature in a three-dimensional volume containing curved
surfaces was devised by DeHoff [51]. The curvature of a
surface at any point is specified by the principal normal
curvatures, K' and K^ , defined as follows: a normal is
constructed at a point on a surface. All possible planes
73
containing the normal are constructed. The intersection
of the surface with these planes is an arc whose radius is
that of a circle passing through three adjacent points on
the curve. There will exist a plane for which the arc
radius is a maximum and a plane for which the radius is a
minimum. These radii are the principal radii and the
principal normal curvatures are then defined by
h-7^ h'k (2.13)
The mean curvature, H, is just the arithmetic average of
the principal normal curvatures or
H E ^ (K^ + K^) C2.14)
The mean curvature is defined at every point on the sur-
face. The total curvature M of a surface element dS is
dM - HdS (2.15)
Total curvature can be evaluated for a finite surface by
integrating the mean curvature over the surface,
M = // HdS (2.16)
It is convenient to express the total curvature on a per
unit volume basis, M i.e., perform the above integration
over the surface contained in a unit volume of structure.
Since H has a value at every point en the surface, it will
have an average value defined by
74
//_ HdS
//g dS(2.17)
DeHoff [51] has shown that this quantity is related to the
net tangent parameter by
n T, netH = -^ (2.18)
where Ff has the algebraic sign of T^ net (see section
2.3.3). The total curvature per unit voluine , M^, is then
II T. net
\ = n-Sv =
-TNT— -^v ' " T^"^'- ''"'
4. A straight line constructed on a plane section
through a sintered structure will form intersections with
traces of the void-solid interface. In structures composed
of a few large pores, the length of line between adjacent
intersections will be greater than for structures composed
of many small pores. Thus, the chord intercept is an
estimator of the scale of the system. The mean pore inter-
cept is given by [45,129]
4V 2Pr =^=^- (2.20)P ^v -^L
5. Analogous to the mean pore intercept, the mean
grain intercept may be defined as the average chordal dis-
tance between grain perimeters. For systems which contain
porosity, the mean grain intercept is given by
4(1-V^) 2(1-V )
X = v__ ^ v (2.211g <. ap^Tg aa ^^,
o^p^^^^ act
"v ^ V ' L "' L
75
where N "^ is the surface area of pore-solid interface
and N, is the surface area of grain boundary between
solid grains. The latter boundaries are shared by two
grains, hence the factor of two. The simultaneous deter^
minations of these properties provide a complete descrip-
tion of the geometric state of the system.
2.4. Evaluation of Mechanical Properties
The diametral compression test was employed in this
investigation to evaluate the tensile strength of U0-,
sinter bodies at room tem.perature . Diametral compression
was developed in the early 1940 's simultaneously in Japan
and Brazil [130]. It was originally developed to evaluate
concrete, but has since been used on a variety of materials
[131-134]. Using elasticity theory, Frocht [135] derived the
stress distribution of a perfectly elastic cylinder loaded
diametrally. His solution was verified photoelastically
by Love [136]. The stress state, shown schematically in
Fig. 19, is biaxial, having large compressive stresses at
both surfaces and a reasonably uniform tensile stress over
the center of the diametral plane.
The present test has several advantages over the more
commonly used bend tests.
1) Specimens are easier to fabricate; in the caseof nuclear fuel, most fuel elements are in theform of cylindrical pellets. The test may
76
then be performed on production pellets with-out resorting to special fabrication tech-niques [137] .
2) Related to (1) is the fact that specimenstested are representative of those being pro-duced, whereas specimens made especially fortesting may incorporate differences in micro-structure due to density gradients, firingprocedures, etc.
3) Bend tests produce maximum tensile stressesat outer surfaces and thus are sensitive tosurface preparation. Tensile stresses gener-ated by diametral compression are distributedover the entire diametral plane, emergingonly at the ends of the right cylinder.
Testing techniques have been reviewed by Mordfin and
Kerper [130] .Rudnick , Hunter and Holden [138], and by
Rudnick et al . [61]. In the present work, specimens were
loaded in an Tnstron TTD* machine equipped with a CF load
cell in a compression carriage. Hardened steel platens
were constructed to fit tlic Instron crosshcad. Padding to
eliminate concentration of compressive stresses was pro-
vided by two thicknesses of file card stock. Loading rates
of .02 and .002 inches per minute were explored with no
significant effect of loading rate observed. As a result,
a crosshead speed of .02 inch/minute \-.'as employed in all
tests .
Initially, samples in the as-fired state were tested
directly. However, the presence of surface asperities,
slight taper parallel to the cylindrical axis, subsurface
*Instron Corporation
77
Fig, 19. Distribution of stresses in a diametrallyloaded cylinder [130].
78
Fig. 20. Precision centerless grinder used to machineUO2 specimens.
79
defects, etc., indicated a need for precision finishing.
This was accomplished by centerless grinding all specimens
in a specially constructed centerless grinder. The grinder
shown in Fig. 20, was built from a design developed by
DeMeyer [139] at Battelle Northwest Laboratories. Toler-
ances of .0002 inch in diameter along the axis were
achieved with a properly dressed v;heel. Additionally, the
grinder produced excellent surface finishes and revealed
the presence of subsurface defects not apparent on the as
-
fired surface. Cylinder ends were also ground flat and
parallel, utilizing a V-block jig with carbide wear inserts
The tensile strength may be calculated directly from
the applied load at failure, P, according to
where D is the diameter of the cylinder and t is the
thickness
.
,2,5. Measurement of Thermal Conductivity
The thermal conductivity of sintered UO-;, was measured
using a com.parative or cut bar instrument, shown schematic-
ally in Fig. 21. The measurement technique is based on the
establishment of longitudinal heat flow through a composite
consisting of two standard meter bars and the specimen.
F.adial heat floi\/ is minimized by the presence of guard
*Thermophysics Corporation, TC-2200.
80
81
heaters which match tlie gradient of tlie stack. Temperatures
aloiip, the stack are monitored at the points indicated in
Fig. 21, so that temperature gradients and mean temperature
values can be calculated for each stack component. For
longitudinal heat flow, the integral form of the Fourier
equation can be written as [8 8]
Q = kA ^- (2.2 3)
where Q = heat flux
k = thermal conductivity
A = cross -sectional area
AT = temperature differential throughwliicli Q flovvS
t = tliickness of conductor in theflow direction.
Since tlie specimen and the standards are in series,
the heat f]ux is the same in each. Then
AT AT
Q ^ ^st \t rf = W T^St X
where the terms are defined in equation (2.2 3) and the sub-
scripts "st" and "x" refer to the standard meter bar and
the specim.en, respectively. All quantities are known except
k and, assuming cross -sectional areas are identical,
AT t
Pyroceram 9606 was selected as the standard material
for the meter bars in the present investigation for two
reasons
:
1. The conductivity of 9606 is intermediate between
the reported extremes of conductivity of UO^ over the tem-
perature ranpc of interest. Tlius it can be used for all
measurements with reasonable accuracy.
2. There is good agreement between several investi-
gators on absolute conductivity values for 9606 over a wide
range of temperatures [140,141]. Figure 22 presents the
temperature dependence recommended by T.P.R.C. [142].
Based on tabular data accompanying the T.P.R.C. curve
[142], a computer program was devised to interpolate between
the published data points. The program generated a table
of conductivity values for 9606 at one degree intervals
between 300 and 1200°K. This tabulation is reproduced in
Appendix B.
Specimen's selected for measurements were centcrless
ground to 0.625 incli diameter to conform precisely to the
diameter of the meter bars. The ends were ground flat and
parallel through 600 -grit SiC. A precision diamond wafer
saw was used to cut 0.024 inch wide by 0.015 inch deep slots
in the end faces to accommodate platinum/platinum-10°
rhodium thermocouples.* The annular gap between the stack
and the guard was filled with bubbled alumina**. Tlie entire
*Omcga fingineering
,
**Norton Company.
83
102 3 4 5 6 7
Temperature (°K)
Fig. 22. Temperature dependence of the thermal conductivityof Pyroceram 9606 [142].
84
assembly was evacuated to a vacuum of 10 Torr to prevent
oxidation of UO- and eliminate convective heat transfer.
Flynn [88] has discussed possible sources of error
associated with cut bar thermal conductivity measurements.
Errors may result from
1) radial heat exchange
2) shunting heat flow through the insulationsurrounding the stack.
3) inaccurate standards.
4) excessive interfacial resistance to heatflow between stack components.
5) perturbations introduced by thermocouples.
6) uncertainties in the measurement of gagelength.
7) presence of cracks, voids or heterogeneitiesnot ascribable to m.icrostructurc
.
8) measurements under nonequilibrium conditions.
CHAPTER III
RESULTS AND DISCUSSION
The results o£ this investigation have been separated
according to the manner in which the specimens were pre-
pared: (1) compacted and sintered, including loose stack
sinterings, and (2) pressure sintered. The reason for
such division will become apparent in the course of this
discussion. The data are further subdivided according to
initial particle size. All graphical presentations are
consistent in that a triangular plotting symbol refers to
data obtained from a specimen prepared from the coarse
size fraction (particle size is discussed in Section 2.1.3)
Similarly, round plotting symbols are associated with
intermediate size powder and a square symbol refers to
powder from the fine size lot.
3.1. Densif ication Behavior
In view of the paucity of information in the litera-
ture on pressure sintering of UO2 , the densif ication
behavior of the powders em.ployed in the present investiga-
tion was system.atically characterized in a series of exper-
iments .
85
86
2000
1800
o 1600
1400-
1200-
1000
Coarse
Intermediate
Fine
10.5
DENSITY (grams- cm" •*)
Fig. 23. Densi fication of three size fractions of UO2 atconstant heating rate followed by 5-minute arrestat 1800°C, pressure sintered at 3,000 psi at10-4 torr.
87
A dynamic measurement of shrinkage was obtained by
cold compacting powder in the hot press die assembly at
3,000 psi. The die was then heated slowly to 1000°C, where
a pressure of 3,000 psi was reapplied. A dial indicator
gage with .0001 inch graduations was used to measure dis-
placement of the ram. The power to. the induction unit was
then increased to a higher fixed level. Temperature and
ram displacement were monitored as a function of time.
The heating rate was nearly constant at 20°C/minute, being
somewliat less above 16 50°C. Density as a function of tem-
perature under these conditions is presented in Fig. 23.
An arrest at 1800°C for 5 minutes was obtained by reduc-
ing the pov;er input. The ram was then withdrawn and the
die assembly allowed to cool. Figure 23 indicates that
the coarse size fraction is initially more dense, but that
as sintering proceeds, an inversion occurs and the fine
powder exhibits the highest density at all subsequent
stages of tlie process. The initial inversion may be the
result of more efficient packing or a relaxation of one of
the load train components.
Having established a useful range of pressure sinter-
ing conditions, a series of specimens was prepared by
pressing at 3,000 psi for 30 minutes at various tempera-
tures. Again the powder was cold compacted and brought to
temperature before reapplying the load. All specimens were
cooled in the absence of pressure. The results of this
o
2000
1800
1600
A Coarse
• Interne
Fine
S 1400
14J
1200
1000.4
Fig. 24. Variation of volume fraction of porosity as afunction of temperature for three size fractionsof UO2 ; all specimens pressure sintered for30 minutes at 3,000 psi.
89
series are shown in Fig. 24. The volume fraction of
porosity is seen to decrease almost linearly with increas-
ing temperature up to volume fractions of about .1, after
which large increases in temperature produced only nomi-
nally higher densities.
Pressure was found to enhance densif ication signifi-
cantly. A specimen pressed at 1800°C for 30 minutes at
3,000 psi exhibited a density of '^97%. Increasing the
pressure to 5,000 psi produced a specimen in excess of 991
theoretical density. Increasing pressures adversely
affected punch and die life, however.
In order to explore the effect of time on pressure
sintering, three series of specimens v;ere prepared from
the intermediate size fraction. Specimens were cold com-
pacted at 3,000 psi and heated to the desired temperature
before the load was reapplied. Specimens were held under
load at temperature for periods between 1 and 90 minutes.
The results of these experiments are shown in Fig. 25.
Density is seen to increase at a decreasing rate with time
for each temperature. The data are replotted in Fig. 26,
using a logarithmic time scale. Within experimental error,
these plots are linear and slopes are indistinguishable.
The lack of a common value of volume fraction porosity at
experimentally reliable times prevents the calculation of
an activation energy. Bacmann and Cizeron [48] have deter-
mined a value of approximately 100 kcal/mole for the initial
stage of sintering in the absence of an applied load.
90
Fig. 25, Volume fraction of porosity as a function oftine at temperature. All specimens pressuresintered from interirediate size fractionpowder at 3,000 psi.
91
TOO
Fig. 26. Dependence of pore volume fraction on time
(logarithmic scale) for isothermal pressuresinterings
.
92
3,2. The Metric Properties
The metric properties determined for all specimens
investigated are presented in tabular form. Table 4 sum-
marizes data for specimens prepared by conventional sin-
tering techniques. Table 5 presents data for specimens
from all three size lots pressure sintered at 3,000 psi
for 30 minutes at various temperatures. Table 6 contains
the metric properties of specimens pressure sintered at
3,000 psi for various times. All data are for structures
prepared from tlie intermediate size powder lot sintered
at 1250, 1500 and 1700°C.
3.2.1. The Me tric Properties o
f
Convent J ona lly SinterecPUO -,
Initial studies of tlie sintering characteristics of
UO^ shoKed that only a limited range of densities was
attainable experimentally for a given precompaction pres-
sure and reasonable sintering time and temperature. A
series of specimens ranging from 60°^ to S6% of theoretical
density (10.96 gms/cm"^) was generated for as-received
-270 +525 and ball milled powders by appropriate combina-
tions of the aforementioned variables. Subsequent to
determination of fracture strengths (Section 3.3) and/or
thernial conductivities (Section 3.4), representative spec-
imens were selected for metallographic analysis. Utilizing
the techniques described in Section 2.3.2, the volume frac-
tion of porosity, V , the surface area per unit volume, S^,,
93
Table 4
Metric Properties o£ UO2 Specimens Produced by-
Cold Compaction and Subsequent Sintering
p
94
Table 4 (extended)
llA
95
and the total curvature, M , were experimentally determined.
From these parameters, H, the average mean curvature, X ,
the mean pore intercept, the shape parameter, HT, and X,
the mean solid intercept, were calculated.
The measured values of surface area per unit volume,
S , for specimeiis cold compacted and sintered from the
intermediate size fractiori are sliown in Fig. 27. It is
evident tliat the data does not conform to the hypotlicsis
of a singular functional dependence of surface area u])on
voliine fraction of jiorosity. DeHoff e t a 1 . fl45], and
Gregg [57] have documented the existence of a linear rela-
tionship between surface i-rea and density in metallic sys-
tems. DeHoff et__ci_l_. , attrilvate linearity during second
stage sintering to tlic attainment of a balance between sur-
face rounding and densifi cation .. Rhines, DeHoff and Krons-
bein [AS] examined the effect of precompaction upon tiie
surface area density relationship. They employed the same
powders for v;hich linearity v\'as observed upon sintei'ing
from the uncompacted state. It was determined that compac-
tion produced a surface excess state as shown in Fig. 28.
Precompacted specimens are found to approach the balanced
condition from the "surface excess" direction. It was
further sho'^^n that at any instant the path of change could
be resolved into a vertical component reflecting a change
in surface area with iio cliange in density (surface rouiiding)
and a horizontal component reflecting densi ticaticn without
a change in the surface area.
96
m
o
97
Fig. 28. The approach to the lineai' relationship foi
a spectrum of initial conditions [45].
98
The surface area data in Tig. 27 thus define an enve-
lope of curves rather than a single path. In order to
establish the form of the paths, the intermediate powder
was pressed at 3,000, 30,000 and 80,000 psi without the aid
of a binder. The resulting corripacts wore carefully cut in
haJf di ai!ietrall)'. One half of each S})Ociinen was fired at
1650°C for 30 minutes along with a control group of speci-
mens, containijig a binder, pressed at tlie same pressures.
The remaining unfired portions were metallographically pre-
pared for analysis. The intercept and point fraction counts
were then made in the usual manner (scale of the system pre-
vented a meaningful tangent count) on both fired and unfired
T)ortions of tlie same specimen. Tiiese results established
Icjiown initial conditions from which the si)ectruT. of start-
ing states could be inferred, as well as the general form
of the path. Previous results were found to correlate well
as a function of precompaction , suggest iiig the family of
curves drawn in Fig. 27.
The sam.e data were recast in terms of surface area
per unit mass, S , from which Fig. 29 was constructed. The
most salient feature of this figure is that, within experi-
mental error, S is constant over the ranee of attainableP
green densities. In viev; of the fact that UO^ is brittle
at room temperature (i.e., it cannot be plastically dc-
fornod) , this result is not surprising. A slight tendency
of particles to fragment under high pressures was iioted,
99
o
o c
w
100
but the additiona] surface created was insignificant in
amount and possessed little curvature. Its effect upon
sintering is thus expected to be mininal. The surface area
per pram determined for the intermediate size fraction of
VOy powder was found to be .17 m^/gram, compared to a value
7of ,8? m''/gram obtained from a H.E.T. measurement (see
Section 2.1.4). In view of the disparity in the scales of
observation (atomic vs. microscopic), the agreement is con-
sidered most satisfactory.
Figure 29 contains several interesting features which
warrant discussion:
1) Once the plot is established, any startingstate can be inferred from a measurement ofgreen density.
2) The series of curves which intersect theenvelope of paths are obtained from deter-minations of surface area for equivalentthermal treatments (time and temperature).Fired density may then be predicted for anyspecimen from a knowledge of the green den-sity and firing schedule. In the range1600-1750, it is found that path of surfacechange is independent of temperature. Thisobservation is consistent with the work ofGregg [57], who found the path of surfacearea change for copper to be independentof temperature. Thus, a knowledge ofkinetics of Sp as function of temperaturefor a single initial condition should besufficient to extrapolate to approximatevalues for all other initial conditions.
Figure 30 shows micrographs for specimens from widely
different paths (by virtue of different initial compac-
tions) which were sintered under identical conditions.
Figure 31 sliows micrographs of two states along the same
101
10^ pov.'der
30. Variation, in nicrostriicture for two differentpaths of surface change. Specinens iv'ere con-"pacted to icidely separated starting states andfired under identical conditions.
102
XH .
103
path of surface change. These specimens exhibit very nearly
the same density, but are markedly different in the extent
to \\'hich surface rounding has occurred.
Figure 32 presents the surface area data for cold
pressed and sintered coarse powder. The same general form
is indicated, altliough initial states were not determined.
A single specimen was hot pressed from a volume fraction of
.22 to .13 by an outside source.* Reported conditions were
ISOO^C at 5,000 psi. The direction of change in S, is indi-
cated in Fig. 32, and suggests that hot pressing is capable
of producing microstructural states unattainable by conven-
tional sintering.
The path of curvature change has been discussed by
Rhines et al . [45], and by Gregg [57] in terms of a sequence
of geometric processes which are observed in a system of
particles undergoing sintering. The reader is referred to
Fig. 1, which shov;s the changing geometry for a four-parti-
cle system. Initially in a stack of equiaxed particles,
both total and mean curvatures are positive, the void solid
interface consisting of almost totally convex particle sur-
faces (Fig. 1-A). During early stages of the process necks
form at contacts, producing saddle surfaces (principal
cur^-atures have opposite signs). These contribute eleinents
of large negative cv.rva'?'.are . As the process continues, the
"C a rb o run
d
uri Comp any
104
Fig. 32. The family of curves which define the dependenceof surface area of volume fraction of porosityfor conventionally sintered coarse UO^ powder.
105
necks expand, consuming the convex surfaces of the par-
ticles, and reducing the magnitude of the negative curva-
ture of saddle surfaces. This process is represented in
Fig. 1-B; at some point, the system passes through a condi-
tion where positive and negative curvatures are equal. The
average m.ean curvature is then zero. Positive elements of
curvature continue to be consumed until none remain. Fig.
1-C. At- tills point, the void space is a multiply connected
network, tlie amount of isolated porosity being negligible.
The next event of importance is channel closure, an
event which, according to Rhines e t a
1
. [45], dominates the
second stage. It is interesting to note that simple models
such as that in Fig. 1 cannot illustrate the channel closure
event, because the void space in such a configuration is
sim.ply connected. The interstitial space of an aggregate
of a large num.ber of particles, hov;ever, is necessarily
multiply connected; it is clear that connectivity must
change as sintering proceeds. Connectivity is a topologi-
cal property [53] of a sinter body which can be quanti-
tatively determined only by a serial sectioning technique
[54].
Upon isolation of the void volume by completion of
channel closure, a coarsening of the scale of porosity is
observed to occur. Large pores become larger and small
pores disappear. The magnitude of the curvature deci'eases
as elements of large (negritive) curvature are removed and
106
the curvature associated with remaininp elements decreases
with growth. Thus, the average mean curvature passes
througli a negative maximum and must ultimately approach
zero at theoretical density.
The experimentally determined values of mean curvature
for the coarse and interncdiate size fractions are shown in
Figs. 33 and 34, respectively. As in tlie case of th.e evolu-
tion of surface area, the data indicate a family of curves,
the form of which lias hcen suggested. Tliere are insuffi-
cient data for any single set of initial conditions to
establish a precise path. It can be seen, however, that
H is initially positive, passes through zero for a volume
fraction of porosity between .3 and . ^. , and exliibits a
maximum negative value at about .2 before decreasing (in
magnitude) towards zero. Thus, the form of the curve is
in agreement with that predicted by Rhines et al . , and with
data obtained for metallic systems [45], as shown in Fig. 35,
Figure 35 also allows comparison of the relative values
of FT for two different poudcr sizes. The slope of the
curvature-density plot is seen to increase with decreasing
particle size, as does the magnitude of the maximum (nega-
tive), again in agreement with observations on metallic
systems [45,57]. The extent to which precompaction alters
the form of the path of curvature change is not entirely
clear. The existence of an envelope of patlis , as suggested
by the present data, would seem reasonable in view of the
107
+2
108
Fig. 34. Variation of average mean curvature with volumefraction porosity for conventionally sinteredintermediate UO^ powder.
109
© As-received dendritic Cu (mostly -325)
B -270 +325 dendritic Cu
Fig. 35. Comparison of the dependence of curvature on
pore volume fraction and particle size forUO2 and dendritic copper [45].
110
results of surface area determinations. I'urther, the value
of the mean curvature for the initial stack should be inde-
pendent of the extent of compaction if the particles are
undistorted and not unduly fragmented, and in fact can be
approximated by
2 *-r, T^ r d '
where d is the average particle diameter. Tlie form of the
family of curves defininji the path of curvature change
from the inception of sintering is proposed in Fig. 36.
As indicated in Table 4, experimental determination of
curvature values for unsintered material was deemed not
feasible because the most significant contributions to
total curvature would be from unresolvable features (a dis-
cussion of exnerimcntal techniques is presented in the
latter part of this section). However, it should be pos-
sible to determine values at very early stages in the pro-
cess by sintering at temperatures in the range of 1200-
1400°C for short periods of time. A satisfactory plot
could be generated by obtaining measurements near the jioint
of zero average curvature for several known starting condi-
tions .
Rhines et al . [45], present data for a wide range of
systems for a parameter which they call the shaj^e parameter,
Fit (the product of the mean pore intercept and the mean
curvature). FIX is found (1) to be dimcnsionlcss, (2) to
Ill
Fig. 36. Proposed form of the paths of curvature changefojr a spectrum of initial conditions.
112
+ .1
115
involve all three of the structural parameters (P , N,P ^
and T. ) , (3) to be independent of the scale (size) of
the system, and (4) to be sensitive to shape. Figure 37
presents a plot of ITX as a function of volume fraction at
porosity. The dashed lines define the band of values
determined for a spectrum of equiaxed metallic systems
[45] . The qualitative observation that the UO^ powders
were approximately equiaxed is reasonably well supported
by Fig. 37. Again, the value for a specimen that was sin-
tered and then liot pressed to final density is signifi-
cantly different from values for conventionally sintered
specimens
.
In summary, the evolution of microstructure in UO2
under normal sintering conditions is qualitatively similar
to that observed in metallic systems. The absence of a
linear surface area relationship is attributed to exten-
sive precompaction employed to produce the range of den-
sities .
3.2.2. The Metric Properties ofPressure Sintered UQ ^
A series of specimens was prepared from each of the
three powder lots by pressure sintering at 3,000 psi at
temperatures between 1050 and 2000°C for 30 minutes. The
resulting specimens spanned the range of pore fractions
between .30 and .03. Subsequent to a determination of frac-
ture strength, metallographic analysis was" performed on all
114
specimens from this series. The metric properties of the
members of this series are presented in Tab]e 5.
Although a S])ectrun of structural states extending
beyond those accessible experimentally by conventional
sintering v.-as produced, analysis of the series in terms of
a path would require the assumption that, in fact, the path
was independent of temperature over a range of nearly 1000°C.
In order to establish the veracity of such an assumption, a
second series of pressure sintering experiments was de-
signed. Powder from the intermediate size fraction was
pressure sintered for periods of time ranging between 1 and
90 minutes at three temperatures in the interval of inter-
est. Icnsile strengths of these specimens were established
prior to an analysis of the stiuctural parameters. Results
of the quantitative microscopic measurements on this series
are presented in Table 6. The results of the two pressure
sintered series are presented simultaneously in view of
their interdependent nature. For brevity, the series de-
scribed previously will be designated "isochronal" since
all specimens were sintered for 30 minutes. The latter
series is termed "isothermal" since time is variable at
constant temperature.
The change in surface area per unit volume for the
isochronal series is portrayed in Fig. 38. Again, no pre-
cisely linear region is established, although the inter-
mediate size fraction appears close to linear behavior.
115
Table 5
Metric Properties of UO2 SpecimensProduced by Pressure Sintering at 3,000 psi
for 30 minutes at Various Temperatures
p
(gms/cm )
116
Table 5 (extended)
IT
(cm-l)
117
Table 6
Metric Properties of UO2 SpecimensProduced by Pressure Sintering at 3,000 psi
at the Indicated Temperature for Various Times
p V^ Time S^ S xlO.96 M^
(gms/cm-
}
(minutes) (cm" ^) (cm^/gm) (cm'^)
A. 1500°C
8.55 .22 1
8.87 -.19 3
9.21 .16 109.54 .13 30
10.08 .08 90
B. 1250°C
8.33 .24 10 6.51 8.56 -23.68.43 .23 30 5.81 7.54 -33.68.99 .18 90 3.62 4.41 -18.5
C. 1700°C
5.76x10-^
118
Table 6 (extended)
(cm'^)
P
(cm)
HAg
(cm)
s
(cm)
-6.72X-9.45
119
120
The precipitous change in surface area with density for the
fine powder lot is indicative of an extremely small effec-
tive particle size confirming the general observations of
shrinkage behavior (Section 3.1), B.E.T. measurement (Sec-
tion 2.1.4) and SEM studies (Section 2.1.3). The path of
surface change for coarse powder is significantly different
from that observed for the finer size fractions in that it
appears to approach the balanced state from a "volume
excess" rather than a "surface excess" condition, as illus-
trated by Fig. 28. (A discussion of the meaning of these
terms is presented in tlie previous section.)
Surface area data for the isothermal pressure sinter-
ings appear in Fig. 39. The large symbol from which the
curves emanate was established by cold compaction at 3,000
psi, as discussed in Section 3,2.1. All hot pressings
were preceded by cold compaction in the die prior to heat-
ing and reapplication of load at temperature, thus justify-
ing the choice of initial state. The agreement between
isothermal temperature data is strong evidence that the
path of surface change is not a function of temperature
over a broad range. The data from Fig. 38 for the inter-
mediate size fraction is shown as a dashed line in Fig. 39.
The agreement between the two curves is judged to be within
experimental error, and is the basis for the assumption
that the isochronal specimens lie sequentially on a single
path of surface area development.
121
122
Two curves are shown merging in the range of 751 the-
oretical density in Fig. 39. There is insufficient infor-
mation to indicate whether in fact the initial form of the
curve varies during the very early stages of the process.
Variability may simply reflect changes that occur as a
result of the additional time required to heat the specimen
to higher sintering temperatures.
The- paths of total curvature change arc indicated in
Fig. 40. Additional data for the fine size fraction not
shown in Fig. 40 indicate a maximum negative value consis-
tent with that of the intermediate and coarse values. (See
Table 5.) The calculated values of mean curvature for all
three size fractions are displayed in Fig. 41, The data
indicate that the maximum (negative) value of mean curva-
ture is attained at different levels of porosity for the
various particle sizes. A definite trend toward higher
densities of the maximum (negative) as particle size de-
creases is observed.
Gregg's [57] measurements of the sintering force indi-
cate that the maximum value of the sintering force shows a
similar dependence upon particle size. He was, however,
unable to document the existence of a maximum (negative)
value of mean curvature for his spherical copper powders.
The mean curvature is expected to be a measure of the
driving force available for densification. A qualitative
comparison of the shrinkage behavior for the three powders
123
+ 5
o'
10 -
^ -20o
E-30-
-40-
-50
Fig. 40. Variation of total curvature with volume fractionporosity for specimens pressure sintered at
3,000 psi for 30 minutes at various temperatures.
124
Fig. 41. Variation of mean curvature with volume fractionporosity for isochronal pressure sintered series.
125
(Section 3.1) with the ip.easured values of mean curvature
shows a definite correlation. As Gregg [57] has found,
however, the ability of the system to respond to the forces
which exist will vary as sintering proceeds.
Figure 42 presents the variation of H for the iso-
thermally pressure sintered series. The intermediate size
fraction data from the isochronal series from Fig. 41 is
replotted as a dashed curve. Some scatter is apparent,
presumably because of the sensitivity of H near the maximum
to volume fraction porosity. A smooth curve through the
isothermal data is indistinguishable, within probable ex-
perimental error, from the isochronal curve. Thus, the
dependence on the path of curvature change is independent
(or at least insensitive) to temperature.
The three stages of sintering are evident in Fig. 43
wherein the mean pore intercept, A , is shown as a function
of volume fraction porosity for three powders employed in
the isochronal series. An initial decrease in A is asso-
ciated with the formation of additional interparticle con-
tacts formed as the network shrinks; Aigeltinger [54] has
shown that such events in early first stage produce an
increase in the genus per gram (connectivity) . In terms
of X, tv/o adjacent, initially separated particle surfaces
form a contact as a result of the framework shrinking,
thereby dividing a large irregular void into two pores of
smaller "size." Second-stage sintering shows a nominally
126
-2
127
8
128
constant value of X as channel closure occurs. The onsetP
of third stage is indicated by a rapid increase in X as
conglobation of isolated porosity takes place. All three
stages are evident in the series of photomicrographs shown
in Fig. 44. These microstiuctures were produced by pressure
sintering the intermediate size fraction at an intermediate
temperature (1500°C) for increasing periods of time.
The-behavior of the shape parameter HT for pressure
sintered specimens is shown as a function of volume frac-
tion of porosity in Fig. 45. Figure 45 is presented on
the same scale as Fig. 37 (conventionally sintered UO^) to
permit comparison, and includes the dashed equiaxed band
from reference 45. Additionally, the mcir.bers of each series
are joined by a smooth curve. It is clear that the pressure
sintered data do not conform to behavior observed for con-
ventionally sintered materials. This observation suggests
a direct comparison of the metric properties for the same
material as prepared by pressure sintering and by conven-
tional sintering techniques. A comparison of the dependence
of surface area change is presented in Fig. 46. A general
similarity in appearance and magnitude is observed between
the data for pressure sintered material and that corres-
ponding to conventionally sintered specimens cold compacted
at high pressures. The similarity is less apparent for the
coarse size fraction than for the intermediate. The sig-
nificance of relative similarities and their dependence on
129
22
19
Fig. 44. Photomicrographs of isotherinally pressuresintered UO^ specimens.
130
^4#
* .tfl
• 7
.-.••7Fig. 44. (continued)
V = .0'V
131
+.2
+ .1
-.2
-.4
-.6
-.8
-12
-1.4
-1.6
-1.8
-2D
-72
-24
.5
Fig. 45. Dependence of the shape parameter upon volumefraction of porosity for the pressure sinteredisochronal series.
132
10
•^o
'E 4
C^5
Interinediate
.4 Q
V,
Fig. 46, Comparison of the dependence of surface area on
volume fraction porosity for conventional (solid
lines) and pressure (dashed lines) sinterings.
133
particle size is not clear. In order to establish more
satisfying conclusions, the dependence o£ the path of sur-
face area change upon applied pressure during hot pressing
must be known. Limited data, presented in Table 7 for
fine powders, suggest that pressure has a significant
effect upon path. Therefore, the similarity of the surface
area curves for the intermediate size fraction cold pressed
to 90,000 psi and sintered and that determined for pressure
sintering at 3,000 psi may only be fortuitous.
The relative paths of curvature change for the coarse
material prepared by the two techniques is shou'n in Fig.
47. Figure 48 is a similar representation of data for the
intermediate size fraction. It is evident that mean curva-
ture values attained in pressure sintering may differ from
those established by sintering in the absence of an applied
load by as much as a factor of two! In view of tlie close
relationship between mean curvature and the driving force
for sintering, this result is of major significance, and
contains important implications regarding "the mechanism"
of densification during pressure sintering. The attainment
of ultimately higher densities by pressure sintering may
be rationalized simply on the basis that the system contains
a much greater driving force for densification in the vicin-
ity of the transition from second to third-stage sintering.
This further suggests that externally applied loads may
produce structures containing appreciably larger negative
134
Tabic 7
Metric Properties of SpecimensPressure Sintered at 5,000 psi
From Fine Powder Lot
\
135
+2
CO
•e-2
PressureSintered
Fig. 47. Comparison of mean curvature for coarse UO2powder prepared by conventional and pressuresintering techniques.
136
-10
5 ^v 2
PressureSintered
Fig. 48. Comparison of mean curvature values for intermediate UO^ powder prepared by cold pressingand sintering and by pressure sintering.
137
curvature. Enhanced densification would then be antici-
pated even if the pressure were subsequently removed.
3.2.3. Summary of the Metric Properties
The path of microstructural change has been shown to
be a function of compaction and independent of temperature
for conventionally sintered UO^ . Sintering in the presence
of an applied load has been shovvn to fundamentally alter the
path of curvature change. The increased rate of densifi-.
cation and higher "ultimate densities" reported under hot
pressing conditions may simply reflect differences in micro-
structural development rather than pressure enhanced diffu-
sion as proposed by Coble and Ellis [30].
The convergence of paths of change as pore volume
decreases is generally observed for conventionally sintered
UO^ . DeHoff and Rhines [144] have reported that they find
that, irrespective of initial conditions, all sintered
structures at about IS'o porosity become nearly indistin-
guishable, except for a scale factor. The generality of
this observation is supported by Fig. 49, which shows a
copper sinter body prepared from a mixture of two sizes of
spherical powder [145] and a UO- sinter body prepared from
ball milled powder by conventional sintering. The scales
have been adjusted photographically to emphasize the
similarity. Both specimens are approximately 851 of the-
oretical density. The similarity of geometry takes on
13!
» • w
250 /lim
50/xm<.':
(a)
(b)
*•:'.•.\.
Fig. 49. Coinparison of the geometry of (a) a copper sinterbody, and (b) UO? sintering, both approximatelySS'i theoretical density. (N'ote difference in
scale.
)
139
additional significance in light of the fundamental differ-
ences which exist between the two specimens.
1) Copper contains only copper atoms; UO2 is acompound in which diffusion of two atomicspecies must occur.
2) Copper is metallic; UO2 is considered to bepredominantly ionic in character.
3) Copper is "ductile"; UO2 is "brittle" (UO2is ductile at sintering temperatures, how-ever [80]).
4) Effective homologous sintering temperature*for the copper was approximately .97; forUO2 the homologous temperature was approxi-mately . 67
.
5) The copper body was sintered from the loosestack; the UO2 specimen was compacted athigh pressure.
6) The copper sinter body was prepared from amixture of two sizes of spherical particles;the UO2 powder consisted of angular particleshaving a broad size distribution.
The magnitude of the magnification necessary to make
the structures coincide is indicative of the extent to
which geometry and scale are independent.
3.2.4. Comments on Experimental Determinationof The Metric Parameters
The use of an automated image analysis system to per-
form the counting measurements on sinter bodies has been
successfully demonstrated. In order to extend these capa-
bilities over the range of scale encountered, particularly
*Ratio of temperature to that of miolting point on theabsolute scale.
140
in ceramic systens , optimum experimental conditions are
necessary. The first requirement is a high quality optical
system capable of as broad a span of magnification as is
necessary. High resolution optics have been found to be
essential in order to obtain meaningful data from systems
of complex geometry. A third requirement is a uniform,
intense light source.
The present system, shown in Fig. 18, has wide lati-
tude in choice of magnifications, by appropriate selection
of objective, projector lens, and vidicon- to-proj ector
distance. The liglit source is a 300-watt zirconium arc.
Two apertures and a green filter are encountered by the
light prior to entering the system. A tube of suitable
length and an additional aperture comprise the optical
path between the projector and the vidicon.
In obtaining data for a large number of specimens,
it was found expedient to select the minimum number of
magnifications necessary, and thus the time expended in
calibration of the instrument. A standardized choice of
"live frame" size was also found helpful because it allowed
direct comparison of raw data, decreasing the probability
that an error in data reduction would go undetected. In
changing magnifications or resetting threshold detection
levels, repetition of counting measurements on a previously
characterized specimen insures that conditions remain rela-
tively constant, thereby minimizing experimental scatter.
141
During the course of the present investigation, it
was found necessary to employ an 85X oil immersion objec-
tive, producing an image on the display at an effective
m.agnification of nearly 3,000X. As indicated previously,
the structures of two specimens encountered in the present
investigation were deemed not sufficiently resolvable at
the limits of the optical system. The scanning electron
microscope is capable of resolution far beyond that which
is expected to be necessary for micros tructural analysis.
The hardware necessary to interface commercial SEMs and
commercial image analyzing systems is available, thus remov-
ing the barrier presented by light optics to automated
analysis of fine structural features [146].
3. 3 Mechanical Properties
The tensile strength at room temperature corresponding
to virtually every microstructural state produced in this
investigation was determined by means of the diametral com-
pression test described in Section 2.4. Four characteristic
fracture modes. Fig. 50, were observed to occur. Data
obtained from tensile and triple cleft failures were con-
sidered to be valid. Specimens which showed shear or
laminar failures were rejected. Tensile, triple cleft
and shear failures are the result of stress distributions
within the loaded specimens as described by Rudnick et al . [61]
142
143
Laminar failures are the result of severe density gradients
produced by excessive die wall friction during compaction.
The tensile strengths of conventionally prepared
specimens are presented as a function of volume fraction
porosity in Fig. 51 for the intermediate size fraction and
Fig. 52 for coarse and fine size fractions. Tlie smooth
curve in Fig. 51 was established by a least squares fit of
the data using the equation
= eo
proposed by Duckworth [76]. It can be seen that this equa-
tion produces good agreem.ent with the data over the range,
with a value of b equal to 6 and o equal to about 16,000
psi. Reported values of the constant b are of the order
of 4-9 [66], apparently depending on the stress state [78].
The present values are similar to those obtained for UO2 in
diametral compression by Bowers et al . [84], and are sig-
nificantly lower than values obtained in flexure.
A direct correlation between modulus data and data
obtained by diametral compression does not generally exist.
Rudnick et al . [138] report ratios of modulus to diametral
values in the range of 1.3 to 2.9. Roberts [147], in recent
unpublished work, compared modulus and diametral values for
U0~,presumably for specimens prepared from the same powderj
and found a ratio close to 2.8.
144
Fig, 51. Variation of fracture strength with pore volumefraction for specimens prenared by conventionalsintering of powder from the intermediate sizefraction.
145
Fig. 52. Dependence of fracture strength on volume fractionof porosity for specimens conventionally sinteredfrom coarse and fine UO^ powders.
146
The curves of Fij^s. 51 and 52 ai'e compared in Fig. 53.
Data for the fine size fraction are extrapolated to low
densities for purposes of comparison. It is evident that,
for pore fractions in excess of .2, strength at equivalent
density increases v;ith decreasing initial particle size.
In the vicinity of .2 the dependence of strength on particle
size becomes negligible.
The strengths of specimens produced by pressure sinter-
ing for 30 minutes indicate a similar trend, as shown in
Fig. 54. Figure 54 also shows that strength drops rapidly
at high densities. Data for isothermal sinterings are shown
in Fig. 55, and reflect a similar trend at higher densities.
A recent paper by Manning et al . [148], indicated
differences in thermal expansion characteristics between
sintered and liot pressed '^'b20^ bodies. The authors attrib-
uted the differences to microcracks in the conventionally
sintered material. The present investigation revealed no
significant differences in tlic strengths of conventionally
sintered and pressure sintered specimens of equivalent
density. There are, however, insufficient data to statis-
tically establish a curve for pressure sintered materials.
SEM fractographs of the intermediate isochronal pres-
sure sinterings are shown in I'ig. 56, and span the range
from 70 to 976 theoretical density. Inspection of F'ig. 56
reveals that at lower densities the fracture surface is
very irregular. As density increases tlic fracture surface
147
148
Fig. 54. Fracture strength of specimens from the pressuresintered isochronal series as a function of porevolume fraction.
149
10
9
8
7-
CO
150
(c)
(b)
id)
(c)
(f)
Fip. 56. SRM fractographs of intermediate isochronalscries
.
(c) \\ = .21(b) \V = -27
(a) \\ = .30
(d) \v = .IS(e) \y = .16
(f) \\r = .14
151
(h)
(k)
(i)
0)
rig. 56 ( continued)
(h) V^ ~- .08
(g) V-^ - .12(i) V^ .. .01
(j) \\r - .o:
152
becomes more planar, and the fracture becomes transgranular
in character. At higher densities, fracture is almost
totally transgranular and very similar in appearance to
fractopraphs of UO, presented by Canon et al . [SO].
Based en the study of a large number of fractures, it
is apparent that for porosity levels greater than .2, frac-
ture occurs preferentially at interparticle contacts. These
contacts. or necks represent minimal load bearing areas,
Balshin [149] has proposed that changes in strength with
porosity do in fact reflect changes in the effective or
critical load bearing areas. DeHoff and Gillard [78]
experimentally determined the load bearing area in copper
sinter bodies. They obtained good correlation with mea-
sured rupture strengths of porous bodies by assuming that
bulk rupture stress was attained in the measured load bear-
ing cross -sectional areas. Unfortunately, the fractured
areas of U0-, are indistinguishable from the rest of the
fracture topography; consequently, a determination of
actual fractured area does not appear experimentally feasible
As an alternative. Fig. 57 shows micrograph? of speci-
mens of approximately equivalent density from the coarse
and intermediate size fractions of U0-, powder. A hypo-
thetical tensile stress is envisioned as being applied
vertically, as shown, in such a manner as to produce frac-
ture, i.e., separation of the structure into two parts.
It is additionally stipulated that the probable crack path
153
^S^:^'r.^^
Fig. 57. Path of miniRai fracture length for coarseand interuiecl J n te speciiTtens of comparabledensity.
154
would be within the confines of the photograph and initiate
and terminate on opposite vertical edges. The probable
crack path is then defined as the path for which the least
amount of solid phase is "cut." The total length of cut
is then measured using dividers. Initiation and termina-
tion points for the probable crack path for structures in
Fig. 5 7 arc shown.
Several such measurements indicate that the "cut
length" to effect fracture is longer for the intermediate
size fraction than for the coarse size fraction at an equi-
valent density. These observations, while they do not con-
stitute experimental proof, are consistent with fractog-
raphy and observed fracture strengths.
In summary, at volume fractions of porosity greater
than .2, fracture strengths are related to minimum cross-
sectional areas, generally corresponding to necks between
particles. At a given density, the finer powders exhibit
greater minimum cross-sectional areas and relatively higher
strengths. The correlation of strength with actual area of
created fracture surface is the basis of the "fracture
energy" or the "work of fracture" concept as discussed,
for example, by Swanson [ISO].
The relationship betAv^ecn strength and initial particle
size suggests a dependence on scale, as reflected by the
mean pore intercept X. However, in light of the dependence
of fracture on a mi nimmn area, rather tlian an average area.
155
such a correlation would not be particularly meaningful,
nor would it necessarily extrapolate to other particle size
distributions.
At porosity levels below .2, a transition in fracture
character occurs between the rupture of individual elements
and fracture by passage of a singular crack front. As
this transition occurs strength data show a dependence only
on porosity. Again, there are an insufficient num.ber of
data points to statistically establish a true curve.
Knudsen et al . [82], report a similar dependence on porosity
level with a difference of less than 81 in modulus at room
temperature for specimens having grain sizes between 10 and
50 microns. Interestingly, these same workers report that
at 1000°C, the modulus varies by 350-o for the same speci-
mens .
As volume fraction of porosity decreases still further,
tensile strengths are observed to drop rapidly. A compari-
son of Figs. 43 and 54 show a close relationship between
maxima in the strength curves and the point where X begins
to increase rapidly. Simultaneously, however, the mean
grain intercept increases sharply, as shown in Fig. 58.
The transgranular appearance of the fracture surface, Fig.
56, at high densities suggests that porosity has little
influence on the path of the fracture, once it has been
nucleated.
156
100
90
80
70f-
g 60o
•^' 50
^^0,40
30
20
10-
Fig. 58. Dependence of mean grain intercept on porevolume fraction for isochronally pressuresintered series.
157
3.4. Thermal Conductivity
Thermal conductivity as a function of temperature was
determined for representative microstructures produced in
this investigation. The data were obtained by a compara-
tive or cut-bar technique, using Pyroceram 9606 as the
standard. Experimental details are discussed in Section
2.5.
The temperature dependence of the thermal conductivity
is represented in Fig. 59 for various volume fractions of
porosity. The data aie bounded by curves from the litera-
ture. The upper curve (A) vras suggested by an I.A.E.A.
panel, as reported by Bates [103], as representative of
"95% dense polycrystalline UO^." Tlie lower curve (B) was
obtained by Boegli and Deissler [151] on an unsintered
powder stack with an apparent density of 631.
The data indicate that a smooth traiisition occurs
between the two curves, A and B, as the volum.e fraction of
porosity increases. For dense specimens, conductivity de-
creases by nearly a factor of 2 over the range 300-700°K.
At low densities the change in conductivity over the same
interval appears nearly negligible.
For purposes of comparison, all conductivity values
are compared at 500°K, as a function of volume fraction
porosity, in Fig. 60. Although there is some scatter, the
data indicate the values for specimens prepared from coarse
158
<M
.iS
.29 j^. A
X/\
3 4 5 6 7 8 9
fig. 59. Dependence of thermal conductivity on terioeraturefor UO2 specimens with different pore volumefractions. (A) Plotted from equation in Rcf. 103
fB) Ref. 151.
159
!0
SI
CO
1
9
8
7
6
5
4
^- 2
^ Literature values
A conventionally sintered*)• ^ J ? coarseA pressure sintered j
» conveo pres
entionally sintered 1 inter- f^
sure sintered j mediate^
B conventionally sintered?
a uressure siiitered ^ °
& ,0
JL.—
„
.1
Fig. 60. Thermal conductivity at 500'''K as function ofvolume traction of oorositv. (.A) Ref. 103,(B^ Ref. 151.
160
powder are somewhat lower than those obtained from the
finer materials. This suggests that interparticle contacts
or areas of minimal cross -section may in fact critically
influence conductivity. Analogy has been made between elec-
trical and thermal conduction because of the similarity of
the phenomenology. The minimal cross -sectional area may
then be viewed as a region of high resistance to carrier
flow.
A sharp decline in conductivity is observed at high
densities as indicated in Fig. 60. The reader will recall
that, although these specimens were produced by pressure
sintering in vacuum, they were subsequently given thermal
treatment in hydrogen to insure stoichiometry. Further,
two independent determinations of the conductivities were
in good agreement, reducing the probability of experimental
error. No external or internal defects, cracks, or inhomo-
geneities were evident prior to or subsequent to the
measurements. Metallographic analysis indicated the pres-
ence of a second phase in the microstructure . This phase
appeared to be situated at grain boundaries and associated
with residual porosity.
MacEwan [152] has found second-phase inclusions upon
heating UO2 to high temperatures in argon. He identified
the inclusion as uranium metal by its appearance, by the
fact that it tarnished upon exposure to air, and from x-ray
diffraction data. MacEwan suggested that the uranium
161
inclusions were the result of the decomposition of UO- into
a hypostoichiometric U0^_ and uranium metal at high tem-
peratures.
In contrast to MacEwan's observation, the inclusions
found in the present investigation were found to be stable
upon exposure to air for several months. An analysis of
the volume fraction of second phases indicates that the
maximum was something less than 0.51, the amount apparently
depending on time and temperature of preparation. X-ray
diffraction failed to show any lines not attributable to
cubic UO^. A microprobe analysis of the inclusions v/as per-
formed to determine their compositions. Positive identifi-
cations of the elements aluminum, silicon and iron were
made for several different inclusions. X-ray im.ages of
representative inclusions for these three elements are
shown in Fig. 61. Inspection of Table 1 reveals that alumi-
num, iron and silicon are principal impurities in the as-
received powder. Subsequent study of the microstructure of
the -6 m.esh as-received grains revealed the presence of
this same phase. The distribution appeared very non-uniform,
with some grains having no observable inclusions and others
having a substantial amount. The m^orphology was that of
islands or clusters wholly contained within what appeared
to be a single grain. Triis suggests that the m.aterial was
present prior to fusion and was not Introduced in subsequent
processing.
162
(a) AlK^
Cb) FeK^
(c) SiK^
10 micronsI
—
A
Fip. 61. X-ray images of a second phase found in UO2sinter bodies. Al , Fe and Si are theprincipal impurities in the UO2 powder employedin this investigation.
163
Abnormally low values of thermal conductivity for high
density specimens (cf necessity produced by heating above
1800°C) are attributed to the presence of an impurity phase
CHAPTER IV
CONCLUSIONS AND SUMMARY
1. The metric path of microstructural development
during sintering of U0-, has been established. A broad
spectrum of microstructures ranging from near theoretical
density to loosely compacted unfired powder stacks has
been examined.
2. The evolution of micros tructure of conventionally
sintered oxide has been found to be qualitatively similar
to that observed for metallic powders.
3. At volume fractions of porosity below about .15,
the similarity of the pore-solid geometry of UO2 and that
of metallic sinterings is striking. This observation is
significant in view of the large differences in scale and
basic physical characteristics which exist between the two
materials
.
4. The role of compaction in establishing the frame-
work or initial state of UO^ has been elucidated. Deter-
mination of surface area of pore-solid interface as a
function of compaction and firing conditions provides quan^
titative information upon which to optimize processing
variables. The present approach has immediate application
164
165
to commercial reactor fuel production, both in design and
quality control.
5. It has been established that pressure sintering
(hot pressing) produces a fundamentally different path of
structural development than that observed for the same
material undergoing conventional (pressureless) sintering.
Significant implications are contained in this observation
regarding the mechanisms of densif ication during hot
pressing.
6. Two regimes of mechanical behavior at room tem-
perature have been observed for porous U0-, sinter bodies.
(1) At porosity levels greater than 20"o, fracture occurs
at necks or contacts betv;een particles. A dependence upon
density and initial particle size' in this regime is thouglit
to be the result of the fracture occurring at a minimal
cross -sectional area. (2) At porosity levels less than
about 20"o, a transition to a transgranular fracture mode
is observed. A dependence only on the volume of porosity
is found and fracture appears to occur by the passage of
a single crack front. Both failure median Jsms are con-
sistent with the concept of fracture energy.
7. Thern;al conductivity in the intermediate tempera-
ture range ( =100 - SOG°Kj , where energy transport occurs by
phoncn conduction, shows a sensitivity to initial particle
size at low densities. This result is rationalized again
in terms of minimal cross -sect ional area'i in the solid
166
network. At high densities, the presence of a second phase
having its origins in the ravs- material obscures possible
microstructural correlation.
APPENDIX A
PRECISION LATTICE PARAMETER PROGRAM
Stoichiometry was determined based on measurement of
the lattice parameter. The following program was employed
in that measurement.
Description of the Problem
This program is intended to calculate the crystal lat-
tice constants and their probable errors by a method of
least squares. The program provides for using as many as
three separate correction terms for various forms of the
systematic errors; however, one, U-io , three, or none at all
could be used. If desired, a weighting factor may also be
used for each reflection, which may include an observation
weight or a trigonometric function or both. Also a refrac-
tion correction may be applied to the observed angular
measurements of lines or spots.
This program is a modified version of the one described
in reference No. 3 with added off-line plotting of v. vs.
20. values. Reference No. 4 describes the plotting tech-
nique used in this program (see "Special Features and
Restrictions")
.
167
168
The program does the following:
given for any i
h., k., Z. - the Miller indices
9^ - the angular measurement of the lines or spots
w. - the observation weight
\. - the wavelength of the observation
and letting
V. = H.A+K.B+L.C+M.D+N.E+O.F+P.G>Q.I+R^J
- ~ [sin'e^+Asin^e^],
i
then 9CE W.vp =
is solved for the coefficients A, B, C, D, E, F, G, I, J.
Their associated variances aT are calculated as
Z W.v-2 i ^ ' -1
where T.
^ is the j diagonal element of the inverseJ J
matrix
.
Thie coefficients G, I, J repre^enc the drift constants
of the systeriiatic errors.
Then using the above equations, the prcgraiii derives
V = 1/(ABC - AF^ - BE*^ - CD^ + ZFED)^''-
and calculates the constants
aQ = V(BC-f2)1/2
b^ = V(A(:-E-)^^^
Cq - VCAB-D^)^/'^
169
-1 .2, .1/2a = cos'-'{(ED-AF)/[(AC-E^)(AB-D")]"' }
3 = cos'^{(DF-BE)/[(AB-d2)(BC-f2)]^/^}
Y = cos'^{(FE-CD)/[(BC-F^)(AC-£-)]^/2}
md their probable errors
P.E.a, 6745
2
^01 _2 ^^0^0
(a^b^cosY)^a^ + (a^CQCOsB)^a^
^O^O^O^(anbnCnCOsa) a^
1/2
P.E.bQ = .67454^0-' K .2^2
0^0 „2
2 ^
+ (a^b^cosY)^a^ ^ (a.b.c„cosS)^a^'0-^0
2 2+ (bQCpCOsa) Cp
D ^"0 0"0
1/2
P.E.c, 67454^0^'
^iio]
I2 ] l^ )
2 2 2,2(a b CgCOSY) aj ^ (aQc5cos6) a^
+ (bJcQCOsal^ap1/2
P.E.a, _ . _ I sinS * sinv |
674^1 ap
'TC sina
p.E.e = ,5745!sina • sinY
' /AC sina "'
170
/XB siny
In the equation for v., H. = hT, K. = kt", L. = tt",^ I'l I'l I'l i'
M^ = 2h.k., N. = 2h^£^, 0^ = 2k^^^, and the correction
terms P^, Q^, R^ represent one of the following trigono-
metric functions
?l-
pj = sin^2e.
^l= i} - e.)sin(TT-2e.)
p^ = cos^e^
Q^ = cos e. sinZe.
q2 = (-J_^ -1 ^ c 1 n (
^)sin2|
Q^ = (sin^2e.)/2e.
qf = cos^e. sine.
Q^ = cos^e. sin^Ze.
sin2e.
rO =
: = cos2e.
2 cos^Bj^
1 smt
The weighting factor W. is calculated from one of the
three desired functions
wO = w.1 1
sin 29.
sin^(TT-29.)cos^(TT-26^)
The refraction correction may be applied using
2
Asin'19.58PZ ^i ^ ,„-6—EM 4- ^ ^°
171
where p is the density, Z is the total number of electrons
in the molecule, and EM is the molecular weight; otherwise
Asin^e. = 0.
The conditions imposed by the crystal systems are as
follows
:
triclinic - no condition
monoclinic (b-axis unique) - D = 0, F =
monoclinic (c-axis unique) - E = 0, F =
rhombohedral -B=A, C=A, D=F, E=Fhexagonal -B = A, = ^^, E=0,F =
orthorhombic -D=0, E=0, F=0tetragonal - B = A , D =
, E = , F =
cubic - B = A, C = A, D = 0, E = 0,
F = 0.
The subroutine MATINV is used to invert the matrix.
References: 1. Determination of Lattice Parameters withthe Aid of a Computer, by Melvin H. Muellerand Leroy Heaton, ANL-6176.
2. 727/MET 124.
3. B 106.
4. Off-line Plotting System Techniques UsingCalcomp Magnetic Tape Plotting System#580, Technical Memorandum No. 70, byClifford leVee and John Ohde , April 20,1964.
Machine: CDC 3600 FORTRAN -SCOPE, with three tape units andCalcoinp Magnetic Tape Plotting System ^580.
The following comment card is supplied v/ith theattac'iied binary deck:
MOUNT CALCOMP TAPE,
172
If no plotting is desired, an additional commentcard, DO NOT SAVE CALCOMP TAPE, is required.
Running Time: About 15 seconds per crystal system.
Input Information Required
CodeName Description
Title - column 1 must beblank.
CardType
173
Ja^'i CodeJX21 Columns Format Name Description
^"^^ KP Correction Term P SelectionFor KP=0 P=0
*1 P=sin22e2 P=(u/2-e)-sin(TT-2e)3 P=cos2e
KQ Correction Term Q SelectionFor KQ=0 Q=0
1 Q=cos2osin2e*2 Q=(l/sine+l/e)sin2e3 Q=Csin229)/2e4 Q=cos2Qsinfi5 Q=cos2esin22e6 Q=sin2e
-'^"^^ KR Correction Term R SelectionFor KR=0* R=0
13-1
25-30 KW
1 R=cos2e2 R=cos2e/sine
Weighting Term W SelectionFor KW-1 W=;v
*2 W=w/sin22e3 W=w/Csin2(Tr-20)
• rnc4('Tr-9Q'i•cos4(7y-2e)
^^^^ KRC Refraction CorrectionSelection
For KRC=0 Asin2 =o1 Asin2 =-19.58.RH0x2/
•a2//i 10-6
^"^'^^ KC Input selection for TE^(see card 5j
For KC=0* TEi=2ei degrees1 TEj^^Si radians
"^^--^S Kl ConstantFor Kl=l* program reads
other cards of tvpe1,2,3,4,5 and 6 '(ifrequired)
For K1=0 program readsonly other cards oftype 5 and 6 (ifrequired)
NOTE: The last Kl must be1 - end of the problem.
174
Card CodeType Columns Format Name Description
49-54 KPL For KPL=0 no off-lineplotting
1 program plotsoff-line
6 1-12 (3F12.0) EM Molecular weight
13-24 Z Total number of electronsin the molecule
25-36 RH0 Density
NOTE: Card type 6 is only required when KRC=1.
Possible OutDUt
a) Printing off-line
1. Title2. Crystal system identification3. The selection of the correction and weighting
termsZ W. V.
. N where N = number of observations(N-K-l)I IV.' and k = number of parameters
N ^
5. E W.
N ^
6. Input data and calculated Vj^ for each datapoint
7. Lattice constants and their probable errors8. Drift constants
b) Plotting off-line
The program plots Vj^ vs. 2ej^, prints, writes thetitle and the selection of correction and weight-ing terms, and draws the axes for each individualcase
.
The scale for plotting is the following:
1. Horizontal axis - 1 inch per degree.2. Vertical axis - the scale is determined for
each set of reflection data. Minimum andmaximum values of Vj are calculated andplotted inside the 8 inches of eacli graph.
175
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APPENDIX B
INTERPOLATED THERMAL CONDUCTIVITYOF PYROCERAM 96 06 IN INCREMENTS OF
1° KELVIN OVER THE R.A.NGE 300-1200°K
The following data are taken from Table 3110R, Data
Book Volume 3, Thermophysical Properties Research Center,
Purdue University, Lafayette, Indiana, 1966.
188
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LIST OF REFERENCES
1. C. Smith in Powder Me t allurgy , ed. by J. Wulff,iijierican Societv for Metals, Cleveland, Ohio, 1942,p. 4.
2. W- Roberts -Austin, Proc. of the Royal Society , 187 a
(1896), 383.
3. G. Kepler, Die Chemische I nd. Nachrecten Ausgabe,
231 (1905), TJT.
4. J. Hedvall, Z. Ar.org. Chem . , 121 (1922), 217.
5. R. Smith, J. o f Chemical Soc . , 125 (1923), 2088.
6. C. Balke, Iron Age, 147 (1941), 23.
7. P. Wretblad and J, Wulff in Powder Metallurgy , ed. byJ. Wulff, American Society for Metals, Cleveland,Ohio, 1942, p. 36.
8. J. Frenkel, J. of Physics U.S.S.R . , 9 (1945), 385.
9. B. Pines, J. of Technical Physics , 16_ (1946), 737.
10. A. Shaier and J. Wulff, Ind. Eng. Chem . , 40 (1948),838.
11. G. Kuc2>Tiski, Trans. A.I.M.E ., 185 (1949), 169.
12. G. Kuczynski, J . A . P.
, n (1950), 532.
13. J. MacKenzie and R. Shuttleworth , P roc. of thePhysical Soc . , 62_ (1949), 833.
14. P. Clark and J. White, Tr ans, of the Bri tish Cerami c
Soc. , 49 (1950), 305.
15. F. Nabarro, Ccnference on Strength of Solids . ThePhysical Socle r.y, London, 194 8, p. 7S.
:l.=J
216
16. C. Herring, J . A .
P
. . n (1950), 437.
17. R. Reed-Hill, Physical Metallurgy Principles , VanN'ostrand, Princeton, N. J. , 196'V, p. 5 73.
18. K. Udin, A. Shaler and J. Wulff, Trans. A.I.M.E .,
1S5 (1949) , 186.
19. A. Greenough, Phil. Mag . , 4^ (1952), 1075.
20. F. Rhines and H. Cannon, Trans. A.I.M.E ., 191 (1951),5 29.
21. B. Alexander and R. Baluffi, Acta Met . , 5_ (1957),666.
22. L. Seigle in Kinetics of High Temperature Processes,
ed. bv W. Kingery"^ Technology Press and Jonn Kilev,New York, 1959, p. 172.
23. J. Burke, J . A . C . S . , 40^ (195?), 80.
24. G. Kuciynski, G. Matsumura and B. Cullitv, Acta Met . .
8 ri960) , 209.
25. W. Kingery and M. Berg, J . A . P . , 26_ (1955), 1205.
26. R. Ccble and J. Burke, in Pro gress in Ceramics,
Vol. 3, ed. by J. Burke, MacMillan, Xev; York, 1963,p. 197.
27. P. Sahm, Powder Metallurgy International , I (1971), 1.
28. R. Coble in Sintering and Related Phenomena , ed. byG. Kuczynski, N. Hootan and C. Gibbon, Gordon andBreach, 'n. Y. , 1967, p. 329.
29. T. Vasilos and R. Spriggs in Sintering and RelatedPhenomena , ed. by G. Kuczynski, N. Hooten and C.
CTiWonTnTordon and Breach, N. Y. , 1967, p. 306.
30. R. Coble and J. Ellis, J . A . C .
S
. , 46 (1963), 438.
31. R. Rossi and R. Fulrath, J.A.C.S . , £8 (1965), 558.
32. P. Murray, D. Livey and J. Williams in CeramicFabrication Pro ce sses , ed. by W. Kingery, JoTm Wileyana Sons', iTew York , r95S, p. 14 7.
217
33. J. McClelland, J.A.C.S . , 4_4 (1961), 526.
34. J. Williams, E. Barnes, R. Scott and A. Hiall, J. ofNuclear Mat . , 1_ (1959), 28.
35. D. Livey, J. O'Neill and A. Hay in Ceramic Mi c re -
structure , ed. by R. Fulrath and J. Pask, John Wileyand Sons, New York, 1968, p. 800.
36. J. Johnson and H. Sowman in Uranium Dioxide: Proper -
ties and Nuclear Applications , ed. by J. Belle,Naval Reactors Division, Atonic Energy Commission,U. S. Govt. Printing Office, Washington, D. C. , 1961,p. 321.
37. M. Bannister, J. of Nuclear Mat . , 26_ (1968), 174.
38. B. Schaner, J. of Nuclear Mat . , 2_ (1960), 110.
39. H. Hoekstra in Uranium Dioxide: Properties andNuclear Applications , ed. by J. Belle, U. ST! Govt.Printing Office, Washington, D. C, 1961, p. 229.
40. L. Jakeshova, Physics of Sintering , 2_ (1970), 33.
41. A. Carrea, J. of Nuclear Mat . , 8_ (1963), 275.
42. D. Lankard and D. Niesz in Characterization ofCeramics , ed. by L. Hench and R. Gould, Marcel Dekker,New York, 1971, p. 350.
43. B. Steele, J. Ware and B. Oldfield, Proc. of Brit.Ceramic Soc . , 3^ (1965), 17.
44. R. Gould in Characterization of Ceramics , ed. byL. Hench and R. Gould, Marcel Dekker, New York, 19 71,
p. 395.
45. F. Rhines, J. Kronsbein and R. DeHoff, Final Report,A. E.G. Contract AT- (40- 1) -2581.
46. R. Coble, J.A.C.S . , U (1958), 55.
47. D. Johnson and T. Clark, Acta Met . , 12_ (1964), 1173.
48. J. Bacmann and G. Cizeron, J.A.C.S . , 51_ (1968), 209.
49. F. Rhines, C. Birchenall and L. Hughes
,
Trans . A.I.M.E .
188 (1950), 378.
218
50. G. Arthur, J. Inst, of .Metals , 83 (1954), 329.
51. R. DeHoff, Trans. A.I.M.E. , 239 (1967), 617.
52. J. Cahn, Trans. A.I.M.E ., 239 (1967), 610.
53. F. Rhines , Plansee Proceedings , 3rd Seminar, Reutte,Tyrol, 1958, p. 38.
54. £. Aigeltinger, Doctoral Dissertation, Universityof Florida, 1969.
55. R. Coble, J . A . P . , 32_ (1961), 787.
56. J. Francois and W. Kingery in Sintering and RelatedPhen omen a , ed. by G. Kuczynski"^ TT. Gibbon and \.
FIooTeTTr^ordon and Breach, New York, 1967, p. 499.
57. R. Gregg, Doctoral Dissertation, University ofFlorida^, 1969.
53. R. Reed -Hill, Physical Metallurgy Principles , VanN'ostrand, Princeton, N. J., 1964.
59. C. Inglis, Trans. Inst. N'aval Arch ., £5_ (1915), 219.
60. W. Kingery, Introduction to Ceramics , John Wiley andSons, New York, 1960, p. 604.
61. A. Rudnick, C. W. Marschall, IV. H. Duckworth andB. R. Emrich, The Evalua.tion and Interp retation of^
Me chanical Properties of Brittle Materials,ATmL-
TR-67-316 (1968J, available through D.C.I.C. as
DCIC 6 8-3.
62. C. Zener in Fracture in Metals , A.S.M. Seminar,A.S.M., Cleveland, Ohio, 1948, p. 3.
63. 3. Carniglia, J.A.C.S . , 5^5_ (1972), 243.
64. N. Fetch, J. of I ron and Steel Inst ., 1^4 (1953), 25,
65. E. Orowan, Rep. Prog. Physics , 12_ (1948), 185.
66. F. Knudsen, J.A.C.S., 4^ (1959), 376.
67. r. Knudsen, J.A.C.S., 4^ (1962), 94.
68. R. Coble and W. Kingery, J . ^. . C ."^
. , 39_ (1956), 377.
219
69. R. Spriggs, J.A.C.S . , 45_ (1962), 454.
70. D. Hasselman, J.A.C.S . , 5_2_ (1969), 457.
71. Z. Hashin and S. Shtrikman, J. of Mech. and Phys
.
of Solids , ]J^ (1963), 27.
72. R. Fryxell and B. Chandler, J.A.C.S ., 47_ (1964), 283,
73. D. Hasselman, J.A.C.S . , 45_ (1962), 451.
74. N. Weil, Hi gh Temperature Technology , But te two rths
,
Washington,^ D. C, 1964, p. 189.
75. E. Ryshkewitch, J .A.C.S . , 36 (1953), 65.
76. W. Duckworth, J.A.C.S . , 36^ (1953), 68.
77. S. Brown, R. Biddulph and P. Wilcox, J.A.C.S . , A7_
(1964), 320.
78. R. DeHoff and J. Gillard in Modern Develop Tnents inPov.'der Meta llurgy, Vol. 4, ed. by H. Hausner, Ple'num
Pr'esT, New Y'ot^, 19 70, p. 2 81.
79. A. Evans and R, Davidge , J. of Nuclear Mat . , 33
(1969) , 249.
80. R. Canon, J. Roberts and R. Beals, J.A.C.S ., 54
(1971), 105.
81. M. Burdick and H. Parker, J.A.C.S . , 3£ (1956), 181.
S2„ F. Knudsen, H. Parker and M. Burdick, J . A . C
,
S . . 43
(1960) , 641.
83. R. Forlano, A. Allen and R. Bcals, J.A.C.S. , 50_
(1967) , 93.
84. D. Bowers, W. Hedden, M. Snyder and W. Duckworth,BMI 1117, Battelle Memorial Inst., Columbus, Ohio,1956.
85. R. Scott, A. Hall and J, Williams, J. Nuc lea r Mat .
,
1 (19 59) , 39 -
86. J. Wachtmdn , Jr., W. Tefft, D. Lam, Jr., and R.
Stinchfield, WADC-TR-59-278 , W.P.A.F.B., Ohio, 1959.
220
87. J. Roberts and Y. Ueda, J.A.C.S . , 5_5 (1972), 117.
88. D. Flynn in Mechanical and Thermal Pro perties ofCeranics , ed"! by J . Wachtman, N.B.S. Special Publ.30 3, U. S. Govt. Printing Office, Washington, D. C.
,
1969, p. 63.
89. V;. Kingery, J.A.C.S ., 38 (1955), 251.
90. W. Kingery, Introduction to Ceramics , John Wiley andSons , New' YorTrrT960, p. 496.
91. W. Kingery, J.A.C.S ., £2^ (1959), 617.
92. J. Jackson and S. Coriell, J. A.
P
. , 39 (1968), 2349.
93. E. Eukcn, Forsch. Gebeite Ingcnieurw , B3 , Forsch,no. 353 (1932), reported by J. MacHwan et al . , J.
of Nuclear Mat . , 24 (1967), 109.
94. J. Franck and W. Kingery, J.A.C.S ., 37 (1954), 99.
95. A. Loeb, J.A.C.S ., 37^ (1954), 96.
96. J. Hedge and I. Fieldhouse, Armour Research Founda-tion Report AECU-3381 (1956), reported in UO2 : Prop -
erti es and Nuclear Application s, ed. by J. Belle,U. S. Govt. Printing Office, Washington, D. C. , 1961,p. 179.
97. R. Scott, AERE-M/R 2526 (1958), reported in U02J_Properties and Nuclear Applications , ed. by J. Belle,W. ^"^ Govt . Printing Office, Washington, U. C.
,
1961, p. 179.
98. W. Kinperv, J. Franck, T. Vasilos and R. Coble,J.A.C.S .
," 57 (1954), 107.
99. T. Godfrey, W. Fulkerson, T. Kollie, J. Moore andD. McElvey, J.A.C.S . , 48_ (1965), 297.
100. A. Ross, C.R.N.L. (Canada), Report CRFD-817 (1960),cited in UO2 : Properties and Nuclear Applications ,
ed. by J. Belle, U.S. Govt. Printing Office, Washing-ton, D. C. , 1961, p. 183.
101. H. Deem, unpublished work cited in UOp : Propertiesand Nuclear Application s, ed. by J. Belle, 0. JTi
Govt. Printing Office, \7ashington, D. C. , 1961, p. 180
102. R. Reiswio, J.A.C.S., 4_4_ (1961), 48.
221
103. J. Bates, 5th Conference on Thermal Conductivity,
1965, V-D-5.
104. M. Shaw in Ceramic Oxide Fuels , ed. by 0. Krueger andA, Kaznoff, American Ceramic Society, Columbus, Ohio,1969, p. 9.
105. B. Frost, Argonne National Laboratory, Privatecommunication.
106. J. Christenson, WADCO, Richland, Washington, AEC Con-tract AT(45-1)-2170, raAN-PR-4 (1970).
107. J. Johari and M. Bhattachryya, Powder Tech . , 2_ (1968),235.
108. E. Lifshin, W. Morris and R. Bolin, J. of Metals , n(12), 1969, 1.
109. R. Graham, University of Florida, Private communi-cation.
110. J. Anderson, E. Harper, S. Moorbath and L. Roberts,A.E.R.E. C/R 886 (1952), reported in UO^ : Propertiesand Nuclear Applications , ed. by J. Belle, U. S.
Govt. Printing Office, Washington, D. C, 1961, p. Ill
111. H. Hoekstra in UP?: Properties and Nuclear Applica -
tions , ed. by J. Belle, U. S. Govt. Printing Office,Washington, D. C, 1961, p. 229.
112. P. Blackburn, J. Phys. Chem . , 6^ (1959), 897.
113. D. Vaughn, J. Bridge and C. Schwartz, B.M.I. -1241,Battelle Memorial Inst., Columbus, Ohio, 1957.
114. S. Aronson and J. Belle, J. Chem. Phys ., 29_ (1958),151.
115. F. Gronvold, J. Inorg. Nuclear Chem ., 1_ (1955), 357.
116. P. Perio, Bull. Soc. Chim . (France), 2^ (1953), 256,cited in UO 2 : Properties and Nuclear Applications
,
ed. by J. Belle, U. S. Govt. Printing Office, Wash-ington, D. C. , 1961.
117. B. Cullity, Elements of X-ray Diffraction , Addison-Wesley Publ. Co., New York, 1956, p. 335.
118. K. Scott and K. Harrison, J. of Nuclear Materials,
8 (1963), 307.
222
119. S. Brumaner, P. Emnett and E. Teller, J. of AmericanChen. Soc. , 60 (1938), 309.
120. S. Gregg and K. Sing, Adsorption, Surface Area andPorositv, Academic Press , London and Xew York, 1967
,
p. 321.'
121. B. Martin, University of Florida, Private communica-tion.
122. V. Growl, Particle Size Analysis , Soc. for AnalyticalGhemistry , London, 1966.
123. R. Holdcn, Ceramic Fuel Elements , A. E.G. monograph,A.S.M., Gordon and Breach, Xew York, 1966, p. 31.
124. T. Wright, Battelle Memorial Institute, Privatecommunication.
125. F. Cain, Jr., V;APD-PMM-197 (1955), reported by T.
Padden in U0 ->: Proper ties and Xuclear Applicati ons
,
ed. by J. Belle, U". S. Govt. Printing Office, IVash-
ington, D. C. , 1961.
126. R. DeHoff in Characterization of Ceramics , ed. byL. Hench and R. Gould, Marcel Dekker, New York, 1971,p. 529.
127. J. Milliard in Quantitative Microscopy , ed. by R.
nclloff and F. Rhines, McGraw-Hill, New York, 1968,p. 45.
128. E. Underwood in Quantitative Microscopy , ed. byR. DeHoff and F. Rhines, McGraw-Hill, New York, 1968,p. 77.
129. R. DeHoff, Techniques in Metals Research , Vol. II,
Interscience , New York, 1968, p. 221
.
130. L. Mordfin and M. Kerper in Mechanical and ThermalProperties of Ceramics , ed. by J. Kachtman, NationalBureau of Standards Special Publ. 302, U. S. Govt.Printing Office, Washington, D. C. , 1969, p. 243.
131. J. Keski, Am. Ceram. Soc. Bulletin , SJ^ (1972), 527.
132. R. Moore, Ph.D. Dissertation, University of Missouri,1962.
133. S. Freiman and L. Hench, J . A . C . S.
, 55 (1972), 86.
223
134. W. Kenny, M.S. Thesis, University of Minnesota, 1959.
135. M. Frocht, Photoelasticity , Vol. 2, J. Wiley andSons, New York, 1948.
136. T. Love, General Dynamics/Convair, Applied ResearchReport 11-131 (1967), as reported by Mordfin andKerper in Ref. 130.
137. J. T. A. Roberts, Argonne National Laboratory,Private communication.
138. A. Rudnick, A. Hunter and F. Holden, Materials Re -
search and Standards , 3 (1963), 283.
139. J. DeMeyer, Report BNWL-1052, Battelle Memorial Insti-tute, Pacific Northwest Laboratories, Richland, Wash-ington, 1969.
140. H. Robinson, 5rd Conference on Thermal Conductivity,
1963, p. 308.
141. D. Flvnn, 2nd Conference on Tliermal Conductivity1962, 'p. 324.
lum
on
142. Thcrmophysical Properties Research Center, Data Book ,
Vol. 3", Purdue University, 1967, p. 3110R.
143. R. DeHoff, R. Rummel, H. LaBuff and F. Rhines inModern Developments in Powder Metallurgy , Vol. 1,ed. by H. Hausner, Plenum Press, New York, 1966.
144. R. DeMoff and F. Rhines, Second European Symposon Powder Metallurgy , May 196 8, p. 1.
145. T. Slean, University of Florida, Private communication
146. S. Bates, University of Florida, Private communication
147. J. T. A. Roberts, Argonne National Laboratory,unpublished work.
148. W. Manning, 0. Hunter, F. Calderwood and D. Stacy,J . A . C . S . , 5_5 (1972), 342.
149. M. Palshin, Doklady Akad. Sci. U .S.S.R., 67 (1949),851, cited in Ref. oF";
150. G. Swanson, J.A.C.S. , 55_ (1972), 48.
224
151. J. Boegli and R. Deissler, NACA-RM-E54L10 ,1955
152. J. MacEwan, J . A . C . S . , 45_ (1962), 37.
BIOGRAPHICAL SKETCH
Wayne Douglas Tuohig was born July 2, 1942, in East
Orange, New Jersey. He lived in Morristown, New Jersey,
until 1954, when his family moved to Jacksonville, Florida.
He attended Landon High School in Jacksonville, and was
graduated in 1960. In the fall of 1960 he entered the
University of Florida, completing the requirements for the
degree of Bachelor of Metallurgical Engineering in 1965.
After brief employment as a powder metallurgist with Reming-
ton Arms Company, he began graduate studies at the Univer-
sity of Florida in pursuit of the degree of Doctor of
Philosophy.
The author is married to the form.er Candace Ruth Herr-
mann and is the father of one daughter. He is a mem.ber of
Tau Beta Pi, Alpha Sigma Mu and Phi Kappa Phi honoraries,
the American Ceramic Society, the American Society for
Metals and the American Institute of Mining, Metallurgical
and Petroleum Engineers.
Upon receipt of his degree, the author will be affili-
ated with Argonne National Laboratory, xlrgonne, Illinois.
225
I certify that I have read this study and that in myopinion it conforns to acceptable standards of scholarlypresentation and is fully adequate, in scope and quality,as a dissertation for the degree of Doctor of Philosophy.
Dow IsTiitney,' Cha i rrTi\n
Associate Professor -of'\aterialsEngineering
I certify that I have read this study and that in myopinion it conforms to acceptable standards of scholarlypresentation and is fully adequate, in scope and quality,as a dissertation for the degree of Doctor of Philosophy.
^v^Ut^M.Robert T. DeHoffProfessor of ^la
Engineering
I certify that I have read this study and that in myopinion it conforms to acceptable standards of scholarlypresentation and is fully adequate, in scope and quality,as a dissertation for the degree of Doctor of Philosophy.
Larry L. HenchProfessor of MaterialsEngineering
I certify that I have read this study and that in myopinion it conforms to acceptable standards of scholarlypresentation and is fully adequate, in scope and quality,as a dissertation for the degree of Doctor of Philosophy.
(^4M^John .T. IlrerT
Professor of MaterialsEngineering
I certify that I have read this study and that in myopinion it conforms to acceptable standards of scholarlypresentation and is fully adequate, in scope and quality,as a dissertation for the degree of Doctor of Philosophy.
Robert W. Gp<ildAssociate-Professor ofMaterials Engineering
I certify that I have read this study and that in myopinion it conforms to acceptable standards of scholarlypresentation and is fully adequate, in scope and quality,as a dissertation for the degree of Doctor of Philosophy.
This dissertation was submitted to the Dean of the Collegeof Engineering and to the Graduate Council, and wasaccepted as partial fulfillment of the requirements forthe degree of Doctor of Philosophy.
December. 1972
De an , College of Engineering
t)ean, Graduate School
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