viodeling hot 3 essing o uo2
TRANSCRIPT
NUREG/CR-2023PUR-101R3
.--
Viodeling Hot 3 essing o UO2r
Manuscript Completed: August 1980Date Published: March 1981
Prepared byA. A. Solomon, K. M. Cochran, J. A. Habermeyer
School of Nuclear EngineeringPurdue UniversityWest Lafayette, IN 47907
Prepared forDivision of Reactor Safety ResearchOffice of Nuclear Regulatory ResearchU.S. Nuclear Regulatory CommissionWashington, D.C. 20555NRC FIN B6313
8 &W7@EM
ABSTRACT
Final stage isostatic hot-pressing of nearly stoichimetric UO2 was in-vestigated. The rate of hot-pressing is linearly dependent on the
pressuredrivingforceF=P+h-p,wherePandparetheexternaland internal pressures respectively, y is the average surface energyand r is average pore radius. The apparent activation energy for hot-pressing agrees with that for U bulk diffusion. Grain growth duringhot-pressing follows d a tn, where d is the grain diameter, t is timeand n = 0.2. Grain size is also a function of temperature at constantdensity. The results indicate that Nabarro-Herring creep is the con-trolling mechanism of hot-pressing over the range of variables investi-gated, although the applicability of this model is questioned. Theresults also show that sintered UO can entrap gas that can lead to
2swelling.
For modelling purposes, the isostatic hot-pressing of UO , under the2conditions investigated, is best described by,
A ~1 - p" (exp - Q/RT) F1 dV =2V Ht~ 3 o
where, h h is the volumetric strain-rate in sec-I 3, A = 8 x 10 , d is in
pm, r is the relative density, Q = 480 kJ/g-mole, RT has its usualmean.ng, and F is in pascals.
iii
TABLE OF CONTENTS
iiiAbstract . .... .... . . . . . . . . . . . . . . . .
I. Introduction . 1.... ...................
3II. Experimental . .. . ...... . . . . . . . . .
3A. Materials and Preparation . . . . . . . . . . . .
. . . . . . . . . . . . 4B. Hot-pressing Experiments . .
5III. Results ... ... .... . . . . . . . . . . . . . . .
5A. Porosity Evolution and Sintering Behavior . . . . . . .
5B. Hot-pressing Experiments and Re. cults . . . . . . . . .
(1) Pressure Dependence . . . . . . . . . . . . . . . . 6(2) Temperature Dependence . . . . . . . . . . . 7
(3) Stoici.iometry . ... . . . . . . . . . . . 8
(4) Grain Growth 8. . . . . . . . . . . . . . .
(5) Entrapped Gas and Grain Size Effects . . . . . . . . 8(6) Microstructural Evolution During Hot-pressing . . . 9
IV. Discussion . . .... . . . . . . . . . . . . . . . 9
V. Summary and Conclusions . . . . . . . . . . . 13
Table 1 ... .. . .... . . . . . . 1517Table 2 . .. . .. . . . . . . . . . . . . . .
Table 3 . .. . ..... . . . . . . . 18
Footnotes and Acknowledgement . . . . . . . . . . . . . . 19
References . . .. .. .... . . . . . . . . . . . . 20
v
List of Figures
Page No.
Figure 1. Isostatic pressurization system. 23
Figure 2. Pore closure in U0 fr m immersion density. 242
Figure 3. UO sintered to various densities at 1410 C, 252
Figure 4. SEM photograph of sintered UO * 262
Figure 5. Hot-pressing of U0 at various pressures. 272
0Figure 6. Hot-pressing rates at constant density and 1410 C. 28
Figure 7. Variation in surface tension and internal pressure withdensity at 1A100C. 29
Figure 8. Dependence of strain-rate on driving force. 30
Figure 9. Pressure cycling experiment. 31
Figure 10. Hot-pressing of UO with temperature cycling. 322
UFigure 11. Grain growth in UO during hot-pressing at 1410 C and 1460 C. 332
Figure 12. Time dependence of grain growth during hot- pressing. 34
Figure 13. Hot-pressing and swelling in sintered U0 . 352
Figure 14. As-sintered and hot-pressed UO . 362
Figure 15. Comparison of the results with various models. 37
vii
MODELLING HOT-PRESSING OF UO2
I. Introduction
The dimensional stability of ceramics under combined loads and hightemperatures has assumed increasing importance as more ceramics areused as structural materials in energy-related technologies. Mostengineering ceramics contain some residual porosity, so hot-pressing ordensification under external pressure both during fabrication and inservice is of considerable interest. Hot-pressing is especially impor-tant in oxide nuclear fuels because %5 to 10% porosity is intentionallyincorporated in the fuel to accommodate fission products. Hot-pressingcan occur by interaction with the ft ' cladding or under the initialfuel pin pressure and released gas pressure.t
Surprisingly, there has been very little quantitative study of the hot-pressing behavior of high density UO, relevant to nuclear fuels.
1Kaufman studied the hot-pressing of UO of 82 to 86%TD at 1850 C and2
s39MPa using a vacuum hot-press and a single-action, graphite, punchand die (lined with tungsten to minimize contamination). In such anarrangement, die wall friction and specinen contamination are uncertain.Using only initial and final densities, he deduced that the linearstrain-rate, c, is given by,
E = A o" (1)where A is a constant, o is the applied stress, and n = 4.5. The con-stant A is usually assumed to contain temperature and structural para-meters (porosity, grain size, point defect concentrations). However,the total driving force, F, for volume change is a function of the ex-ternal pressure, P, the internal pore pressure, p, and the surfacetension term 2y/r, viz.,
F = P - p + 2y/r (2)
tDaring fissioning, fuels may undergo hot-pressing at very low tempera-ture under the same driving forces as discussed here (to be publishedby A.A.S.)
where y is an average surface energy and r is the radius of an assumedspherical pore.2 In Kaufman's experiments, p was presumably negliblein the vacuum hot-press, but the sintering term, 2y/r, was neglected.
A number of workers ,4,5 have been primarily interested in fabricating3
high density UO and (U, Pu)0 by hot-pressing in punch-and-dies, by2 2
hot isostatic pressing or by hot-pressing during a phase change.6Generally, these data do not permit accurate analysis of the stress ortemperature dependencies, but Hart found for his experiments on U0 at2
900 C, that n varies from 1.5 to 4 for 13.8 < o < 41.4 MPa. Similarly,
he found n = 2 to 3 for the data of Warren and Chaklader.6 Hart andRoutbort, et al.7 hav7 also found that n > 1 for (U, Pu)0 . Such
22
results are difficult to rationali:.e with simple theory . Contaminationfrom die n;terials, stoichiometry control, and lack of grain growthmeasurements during testing have been additional complications.
The porosity dependence of hot-pressing has received considerable at-tention, and numrous empirical and analytical forms have been proposed.Although these functions tend to merge at high density, they become veryimportant as theorctical density is approached.
The temperature dependence of hot-pressing is usually given by anArhennius factor, e~ , where Q is the apparent activation energy forbulk or grain-boundary diffusion and RT has its usual meaning. Unfor-tunately, there are essentially no well-controlled measurements of
h t-pressing.specimen stoichiometry and Q for UO2
The purpose of the present investigation, therefore, was to measureisostatic hot-pressing rates in well-controlled experiments on well-characterized high density U0 , and to identify the rate-controlling
2mechanisms in terms of known pressure driving forces that are relevantto nuclear reactor fuels.
_2_
II. Experimental
A. Materials and Preparation.
*
The starting ADU-UO2 powder had a reported + Fisher sub-sieve size of3.16 pm, a bulk density of 2.D g/cc, a surface area of 6.73 m'/gm and adensity of 99.3%. Examinatici, ander scanning electron microscopy, SEM,revealed that the powder was highly agglomerated and apparently muchfiner (s0.12p). An analysis of major impurities is given in Table 1.
Peilets were first formed at 0.7 MPa in a double-action punch and diewnich provided equal displacement of each punch so that a uniform initialgeometry wa; obtained. No binders, lubricants or pore formers were used.The pellets were then isostatically compressed at 345 MPa to a densityof s50"TD to obtain the most uniform green density possible. A smallamount of hourglassing was found after isostatic pressing.
Batches of specimcas were then pre-sintered in flowing Ar-5%H in a 99.8%2
U Upure alumina tube at temperatures from 1100 C to 1510 C for 0.5 to 67hou.u. After sintering, immersion density measurements were performed inethyl alcohol' to determine pore closure behavior for the subsequent hot-pressing experiments. Two or more density measurements were made on eachspecimen, and the results were averaged. The immersion densities werereproducible within M. For the hot-pressing experiments, all of the
Uspecimens were pre-sintered at 1510 C for 3 hours in flowing Ar-5%H '2
Ceramography and SEM examination were perforned on pre-sinter. ' specimensand hot-pressed specimens. Specimens were mounted in epoxy ' sndf
polished to 1 pm diamond. Interference microscopy revealed minimum edgerounding after final polishing. Specimens were cooled under pressureafter a hot-pressing experiment to maintain the pore morphology.
Pellet stoichiometry was measured by reduction in 38% C0/62%CD, and by
ignition to 'J 0 in ir, both at 800 C for 12 hours.38
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B. Hot ~'ressing Experiments
The hot-pressing experiments were carried out in a special hot isostaticpressurization system, fig.1, described elsewhere.8 A thoria-dispersedtungsten pressure vessel was used, which yielded < 1 C temperature vari-ation in the specimen at 0.1 MPa pressure. This was measured by moving aW/5%Pe vs. W/26%Re thermocouple thrwgh a hollow dunny specimen. Thetungsten pressure vessel served to establish the oxygen potential sincetraces of condensed blue tungsten ox'de were seen at the cooler regionsof the pressure vessel af ter testing
In a typical experiment, the ir.itial atmo',phere was set by first evacu-ating and back-filling the pressure vessel three times at room tempera-ture to 0.14 MPa with dry Ar-5%Hj; then increasing temperature linearlyin 1 hour to 800 C; holding at 800 C for 1 hour during which a secondevacuntion and back-filling was performed with Ar-5%H , and finally in-
2creasing temperature linearly to the test temperature in 10 minutes andevacuating and back-filling a third time with Ar-5%H , at the test
2temperature. The evacuation and back-filling was perfonned to eliminatewater and other adsorbates from the static pressure vessel atmosphere.The specimen was pressurized with ultra-high-purity argon 30 min. af terreaching Set Point on the programmer. The argon was passed through a
0drier and Zr chip getter-furnace at 800 C before being compressed by thediaphragm pump and fed to the pressure vessel.
An automatic microprocessor furnace programmer was used with an SCRpower supply and a MoSi elem nt furnace to accurately program and con-
20
trol the specimen temperature to within + 1 C in 24 hours. Since V02
9equilibrates chemically in % 1 hour at 800 C , equilibration should havebeen very rapid at the test temperature of 14100C.
Calibration experiments on the TD tungsten vessel were used to correlatethe temperatures in a hollow dummy specimen within the vessel, with thecontrol thermocouple outside the vessel, Fig.1 For temperaturecycling experiments, the specimen temperature was found to change in <2minutes following an abrupt char.ge in the control temperature. The
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specimen also reached the test temperature in c15 min. after the pro-grammer reached the Set Point when heating from 8000C to 14100C in 10minutes.
Pressure changes were made in 5 to 10 seconds either by filling from ahigh pressure accumirtor or by releasing gas to the outside. The pres-sure was measured by a heise Guage and a strain-guage pressure trans-ducer++, both within 0.1% accuracy. Pressure was controlled within +~.7MPa during an experiment by bleeding gas from the accumulator asneeoed.
III. Results
A. Porosity Evolution and Sintering Behavior
Sintering experiments were carried-out in order to examine the evolutionof the microstructure and determine the point of pore closure duringsintering prior to hot-pressing. Specimens were sintered in flowing dry
0Ar-5%H in high pr ity alumina tube at 11000C to 1510 C for 0.5 to 672
hours. Individual specimens in a batch were suspended in Al 0 baskets23
that could be withdrawn from the hot-zone at various times. The 0/Mration after sintering was measured to be 2.004.
Immersion density measurements after sintering revealed typical porosityevolution with pore closure at s 91%TD, Fig. 2. The hot-pressing ex-periments were carried out at >94%TD, at which essentially all the poreswere closed.
Microstructural examination of the porosity indicated that the agglom-erates present in the starting powder were not broken up by the 345 MPaisostatic compaction. Fig. 3 shTs that the agglomerate porositycoarsens significantly from s90 to 95%TD, leaving pockets of large poresas well as very fine pores seen by SEM, Fig. 4.
B. Hot-pressing Experiments and Results_
The hot-pressing experiments are listed M Table 2. Most of the
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specimens were pre-sintered in flowing Ar-5%H at 1511 C for 3 hrs to2
s 94%TD. Speci%en #S-6 was sintered rapidly at high temperature withinthe pressure vessel as part of a compatibility experiment betweenmagnesium zirconate, platinum, .nd tungsten and exhibited unusual be-havior.
(1) pressure Dependence
The pressure dependence of hot-pressing in UO was determined both by2
pressure cycling a single specimen at constant temperature and by hot-pressing a series of specimens, all pre-sintered identically, at variouspressures. The former method has the advantage of eliminating specimen-to-specimen variations, but requires extrapolation to obtain the dif-ference in strain-rate at a constant structure.
The density during an experiment, p, was calculated from the measuredspecimen length, f, and the measured final imersion density using
E
(f )3 where I and of are the final length and density, res-=f
pectively, and M t-f . The final imersion density was averaged overf
two or more independent measurements. All of the constant pressure ex-0periments conducted at 1410 C are shown in Fig. 5, where least squares
fits are indicated for all pressures except 13.79 MPa to avoid confusion.The test at the highest pressure exhibited leakage so the average pres-sure is indicated. The average initial sintering rate obtained duringa half hour equilibration period prior to pressurizing the specimens isseen to be non-negligible.
When the strain-rates are plotted at constant density, Fig. 6, it isfound that the strain-rate extrapolates to zero at a negative pressure,indicating that surface tension and perhaps internal pressure are con-tributing to the driving force.
Following Eq. 2, the intercept values represent the terms 2l - p, bothr
of which are functions of pore radius or specimen density as shown in
-6-
Fig. 7. Since, for ideal ga: within the pores, p = 1/r , the in-creasing intercept is consistent with increasing values of p anddensity. If the v31ues of the intercepts for each density are added tothe external pressure, the resultant strain rate vs. pressure drivingforce, F, is essentially linear, Fig. 8.
The result of a typical pressure cycling expc:-iment is shown in Fig. 9.Again, the sintering rate is seen to be non-negligible. The pressuredependence for these experiments was determined using n = dlnc/dinF foreach of the pressure changes. To evaluate F, the 2y/r-p tenn must againbe estimated. This was done by assuming a linear c vs. F relation andcomparing the extrapolated sintering and hot pressing strain-rates at
= [P + (2y/r-p)]/(2y/r-p). This10.35 MPa, anti 93.3%TD, i.e., *y/E2yielded a value of 2y/r-p of 4.8 MPa at 93.3%TD which is consistent withthe values determined by extrapolation, Fig. 7. Therefore, values of
2y/r-p at other densities were taken from Fig. 7 te calculate F and n.The resultant n values indicated in Fig. 9 for each pressure change areconsistent both with the value previously obtained of n=1 and with theassumed linear stress dependence.
(2) Temperature Dependence
To determine the temperature dependence of hot-pressing, temperaturecycling was performed on individual specimens during hot-pressing, anda series of specimens were run at different temperatures. The temper-ature cycling experiment has the advantage that data is obtained on asingle specimen and the uncertainty of possible variations in the grain
sizeandthe(h-p)termsatdifferenttemperaturesareavoided.
A typical temperature cycling experiment is shown in Fig.10. Theapparent activation energy, Q = -Rdlnl/d(1/T), was 480 kJ/g-mole fromtwo series of cycling experiments.t
Comparing strain-rates for specimens at different temperatures and con-stant density yielded lower activation energies, (s290 e). However,9-at constant density the grain size varies with temperature, Fig. 11, so
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tThe small change in internal pressure with temperature has been neglected.
this activation energy is inaccurate. To normalize for the grain sizewould require knowledge of the atrain-rate dependence on grain sizewhich was not obtained. The grain size variation with temperature trendis such as to make the activation energy larger and in closer agreementwith the temperature cycling experiments.
(3) Stoichiometry
Because of the very small weight changes involved in reducing the speci-mens in C0/CO mixtures ( @.1 mg), it was decided that ignition to U 0
2 38was a more reliable method of measuring specimen stoichiometry. Themeasured 0/M value after hot-pressing was 2.004 + .001. This valueagrees well with equilibrium of tungsten and WO _and WO at 14100C.10
2 3
(4) Grain Growth
Grain growth during hot-pressing was important only for those experimentswhich 'ollow the strain-rate change with time or densi ty. The resultsof the pressure or temperature cycling experiments are thus not affected.In the tests conducted at various pressures but constant temperature, itis tacitly assumed that grain growth is not a function of pressure.However, as pointed out above, for the tests at constant pressure butvariable temperature, one must investigate possible grain size variationsat constant density.
Grain sizes were averaged over 10 random measurements of lingar inter-cepts. Quoted values are the mean linear intercepts x 1.561 The grain
0size, d, at 1410 C (including the 30 min preconditioning), increases withtime, t, at 14100C as dotn, where ns 0.2, Fig. 12.
(5) Entrapped Gas and Grain Size Effects
As mentioned earlier, specimen #5-6, exhibited intriguing results fromtwo points of view. First, it was found that after hot-pressing someamoJnt, when the specimen was unpressurized, it swelled under an apparent
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internal pressure, Fig 13.t Hot-pressing and swellinq could then beperfonned alternately in En almost reversible manner (there was some re-duction in rates with time). This behavior was in marked contrast toall OUw experiments in which hot-pressing, even to very high density>991TD, did t.ot lead tc swelling when the specimen was unloaded.
The second effect of interest was that #5-6 exhibited higher strain-ratethan the other specimens at the same density. Its grain size, Fig. 12,was also smaller, perhap: due to contamination. This would suggest thatthe hot-pressing strain-rate may be grain-size dependent, although othereffects of impurities may also b. ;si bi t .
(6) Microstructural Evolution During Hot-Pressing
The evolution of thc microstructure during hot-pressing is shown in Fig.14. The remnants of agglomerates present af ter sintering are seen tobreak up and disappear durir.9 ho+- p re s si ng . Examination of the openporosity before and af ter hot-pressing, Table 2, shows that the pores donot tend to open while under external pressure. Another point of in-
terest is that most of the pores appear to be located within the grains,and the grains appear equiaxed.
IV. Discussion
linear dependence of the strain-rate on driving force4The ;.-
stro. j . ?sts a mass transport process controlled by diffusion inUO .w conditions investigated. The apparent activation energy'
2
for t ;reep of UO is very sensitive to stoichiometry, but has been2
12measured to be s313 kJ/g-mole for single crystals and %250 kJ/g-mole13for polycrystalline material , both of wnich e lower than the measured
480 kJ/g-mole. On the other hand, the activat. n energy for uranium7, single crystals is %460 kJ/g-mole.I since, .9 theself-diffusion in UO
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tPetent sintering experiments under pressure have shown that UO2 can en-trap gas during heating which later causes swelling at temperature.
present work, the pores are largely intragranular, diffusion through thebulk would appear appropriate, and the activation energy for U diffusionagrees reasonably well with the measured value for hot-pressino.
The decrease in the values of 2y/r-p during densification, Fig. 7, wouldsuggest that an internal pore pressure does exist and increases as 1/r3and offsets the increase in surface tension with density. From the re-sults on Spec. #5-6, it is clear that gases can be entrapped duringsintering. An attempt was therefore made to verify this by unloading atypical specimen hot-pressed to 99.6%TD, but no swolling was detected,perhaps because the rate was too low.
The good agreement between the pressure cycling and the constant pressureexperiments would suggest that the deformation process is not historydependent, and therefore is not controlled by dislocation plasticity be-tween the pores as suggested by Ashby15,
A number of detailed models have been proposed to describe diffusion-controlled hot-pressing. When pores reside on grain boundaries, and masstransport occurs along the boundaries, Wilkinson16 obtains
D
(P E}1 dp 9 6 Bn 1
/ kTd [1-(1-p)1/3) fI 3
where 3 and D are the effective grain boundary " width" and diffusivity,B
respectively, d is the grain size, O is the atomic voluem and kT has itsusual meaning. Note that p / 0 at p = 1.
A similar result is obtained for bulk diffusion between pores located onboundaries and the grain boundaries,10
(E1 do }- 3 i (I~A F (3)/v kTd )77,(), )1/3) q2
17where D is th bulk diffusion coefficient. Coble assumed a morey
-10-
relevant geometry in which pr,res were located within the grains and ob-
tained an identical result, if it is assumed that p = 1 - f and hiscorrection of P to produce an " effective" P is omitted.
If power-law creep of the matrix is controlling and the uniaxial tensilencreep rate of a fully dense specimen is given by c = Ao , then from
Wilkinson and Ashby,18
1 do 3 (I-P) (3 (4)"
(D E} , I A/ [1_(1-p)l/") n 2ng f
c
For n = 1, thir reduces essentially to the result given by Murray et_al.,19
[Ib\ =9 I-P- -A F (5)(odt /c P /
In order to test the validity of these mv. 1s, the va.ue of n = 1 wasused from the present invcstigation, and the other parameters for UO '
2Table 3, were taken from Wilkinson.16 The value of A for fully denseU0 ias obtained fro the results on polycrystalline UO at low2.00? 2hstress by Seltzer et al. Normalizations were made for density (95% to100%TD) using theii mdsured density dependence; for temperature, usingtheir measured activation energy of 251 kJ/g-mole for U02.004; and forgrain size using their measured d- dependence for low stress.
The results using Eqns. 2, 3, & 5 are shown in Fig.15, where a hot-pressing experiment at 13.8MPa is examined. The models for grain boun-dary and bulk diffusion are seen to be 2 to 3 orders of magnitude lowerthan the measured hot-pressing rates. If the fraction of the poreslying on the grain boundaries is considered, the discrepancy would beeven larger. The power-law creep model for n = 1 appears to fit thedata better, perhaps because it is basert on measured creep rates and
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also because it fits the situation of isolated pores far from grain
boundary sinks. Over the range of densities and grain sizes investi-gated, all functions describe the decrease in the strain rate duringhot-pressing reasonably well, but the boundary diffusion model showssomewhat more variation than measured.
This result is especially interesting in view of the conclusion byRoutbort, et al.7 that bulk diffusion controls hot-piessing in (V,Pu)0 '
2
although they find a factor of 30 deviation in some cases. It may bethat the diffusional creep data fr* (U Pu)0 do not permit an accurate
2value of A to be detennined, or tha, die wall friction or contaminationmay have been important.
On the basis of Fig.15, it would appear taat Nabarro-Herring viscouscreep controls final stage hot-pressing i's 00 over the range of
2
variables investigated. The model fits the observed microstructures,gives the measured pressure and temperature dependencies, describes thedecrease in strain-rate with density and, moreover, gives the proper
magnitude. This model, however, is most appropriate for fine-grainedmaterial surrounding relatively large pores. When the reverse is true,
as in the present use, it is difficult to see why vacancy fluxes betweenmore distant grain boundaries should be rate-controlling rather thanfluxes between pores and boundaries. Even if fluxes between boundariescontrol, the presence of the pores should affect the stress state andboundary tractions in the Nabarro-Herring creep model in order to close
2 grainthe pores. An additional test would be to further verify the 1/dsize dependence and porosity dependence over larger density rangesduring hot-pressing, and to investigate variations in stoichiometery,sinct the creep rate is so sensitive to stoichiometry variations.
Another extension of this study would be to evaluate the surface tensionand internal pressure terms. The former could best be determined by
measuring the average pore size in a material that exhibits uniform poresize. Internal pressures could be evaluated by swelling experiments, as
has been done in Zn0.20
hot-pressing has been modelled by the MATPRO - Version 11 (Rev. 1) 1U02
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fuel modelling code under the subroutine FHOTPS. Use of the hot-pressingrelation at low stress,
y exp (-Qy/RT)A a,
c=-2(-0.3/7 + p)d
and, (6)'
+1f-I- -20Qy = 17.88 exp -8 + 72.12in (x-2)
. -)
yields a strain-rate ~ 7.5 orders of magnitude too high. This dis-crepancy appears to arise from an error in the units of Q which arestnted in kJ/g-mole, but appear to be in kcal/g-mole. When units ofkcal/g-mole are used, the predicted strain-rates are 1.2 orders ofmagnitude lower than the measured values. The lcw stress expression wasused because the applied stress was less than the transition stress for
dislocation creep,13 and because of the measured linear dependence off on F.
From our results the best empirical relationship for hot-pressing is,
hh =h2 I-P (exp - Q/RT) F
where,fhisthevolumetricstrain-rateinsec -1 3, A = 8 x 10 , d is in
pm, p is the relative density, Q = 480 kJ/g-mole, RT has its usualmeaning, and F is in Pascals.
V. Summary and Conclusions
(1) The isostatic hot-pressing rate in U0 is linearly proportional to2
the pressure driving force P + 21 - p.
(2) Both pressure cycling and tests at different pressures yield thesame pressure dependence indicating no history dependence in the flow
-13-
process as might be present for dislocation controlled flow.
(3) The apparent activation energy for hot-pressing is 480 kJ/;-molewhich agrees best with the volume diffusion of uranium in U0 "
2
(4) Grain gra tn curing hot-pressing follows a relation d a t" wheren ~ 0.2.
(5) The grain size at constant density is temperature dependent.
(6) Under conditions of rapid sintering and impurity contamination, U02can entrap significant gas pressures which subsequently can causeswelling.
(7) Models for hot -ressing by vacancy fluxes between poras and grainboundaries underestimate the hot-pressing rates by 2 to 3 orders ofmagnitude.
(8) The hot-pressing of U0 at pressures from 0.14 to 27.6MPa ano2.004temperatures from 1360 to 1460cc was quantitatively best described byNabarro-Herring creep of the matrix material surrounding the pores.However, this model is questioned on theoretical grounds. Also, theagreement may be fortuitous because actual creep data are used ratherthan highly uncertain activation parameters.
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Table 1
_AEMICAL AND PHYSICAL DATA
ADU - UO2 (depleted)P. O. No. Q04091Lot No. 450728Specification Y-12 Analysis
Uranium Content (st%) 86.0 min. 86.6826
Isotopic Analysis (wt%)U-234 - < 0.010U-235 Depleted 0.195U-236 - < 0.010U-232 - 99.884
Imp:irities (ppm U basis)Element Max. ppm
Aluminum 100 15.0Boron ... 0,2Ca rbon 150 65.0Calcium + Magnesium 125 < 12.0Cadmium < 0.1---
Chlorine + Fluorine 125 3.0ChromiJm 200 < 2.0Cobalt 100 < 1.0Copper --- 10.0Ha fnium --- < 0.1Iron 400 200.0Lithium , --- < 0.2Mancanese --- 10.2Nict.ei 200 2.0Nitrogren 200 18.0Silicon 200 40.0Silver --- < 1.0Tantalum --- 1.0Titanium --- 1.0Tungsten --- 7.0Vanadium --- 0.6Zinc --- 3.0
Rare Earth
Dysprosium --- < 0.10Europium --- < 0.06
< 0.08Gadolinium ---
Samarium --- < 0.10
TOTALS 1500 max. < 393.0
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Table 1 (cont.)
CHEMICAL AND PHYSICAL DATA
P. O. No. Q04091Lot No. 450728
Ar,U-UO2 (Depleted)Specification Y-12 Analysis
Moisture Content (wt'!,) 0.80 max. 0.80
0/U 9a'io (calculated %) --- 2.11
Particle Size Pass through Pass through20 Mesh Screen 53 Mesh Screen
Avg. Particle Size (by Fishersub-sleve-sizer) --- 3.16p
Density (Toluene)(gm/cc) --- 10.617Density (Bulk)(gm/cc) --- 2.11
2Surface Area (M /gm) --- 6.73Porosity (%) --- 0.725
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Table 2. Hot-Pressing Experiments
Pre-sioter Conditions Hot-Press. Condio.'as
*T t 7 Open T+ P i Open
U5pec. C mir, iTD Por. C MPa %TD Por.-
5- 6 1600 420 94.9 0.1 1410 6.90 91.1 1.1
5-3 1300 4000 93.6 1.5 1410 6.90 90.8 2.63-6 1511 182 95.0 1.0 AT AP 94.9 3.1
3-5 1511 30 91.5 4.7 AT 20.69 98.1 0.77-10 1511 172 94.3 1.6 ; 1410 AP 96.9 2.07-12 1911 172 94.2 1.2 1410 AP 98.3 .7
7-14 1511 172 95.0 0.7 1410 20.69 98.7 0.37-9 1511 172 93.2 1.5 1410 6.90 97.4 0.67-2 1511 li! 93.8 2. 3 1410 13.79 98.2 0.37-5 1511 190 93.7 1.1 1410 27.59 98.4 0. 6
10-6 1511 190 94.9 1.1 1410 3.45 97.4 0.810-1 1511 190 95.1 0.9 1410 27.59 98.8 0.510-4 1511 190 95.2 0.9 1410 .14 96.5 0.7
10-5 1511 190 95.2 0.7 1353 20.69 98.4 0.310-2 1511 190 94.9 1.0 1460 20 69 95.9 0.4
10-7 1511 190 94.6 1.4 1460 20.69 99.6 0.3
7-1 1511 190 95.0 1.0 1410 3.45 96.5 0. 3
* T is a variable temperature test .'.
*t.P is a variaule pressure test.
-17-
Table 3. U0 Parameters from Ref. 162
-29 3Atceic Vol. E O = 4.09 x 10 m
-52D for volume diffusion E D = 1.2 x 10 m /secg gy
6D for boundary Diffusion E 6D = 2.0 x 10-15 3m /secg ob
Act:vation Energy,'
boundry diffusion E Q = 293 kJ/ moleb
Activation Energybulk diffusion E Q = 452 kJ/ moley
-18-
Footnotes
*Furnished through the courtesy of Exxon Nuclear Corporation
+0ak Ridge National Laboratory
'Usi. j ASTM #132**
Plastimet, Buehler Corp., 2120 Greenwood St., Evanston, IL 60204***
Iveron Pacific Corporation, Model 2100A,1152 Morena Blvd. ,San Diego, CA 92110
++Sensotec Corporation, Model TJE, 1200 Chesapeake Avenue,Columbus, OH 43212
Acknowledgement
The authors would like to express their appreciation to the NuclearRegulatory Commission for support under Contract #478231.
-19-
References
(1) S. F. Kaufman, "The Hot-Pressing Behavior of Sintered Low-DensityPellets of UO , 7r0 -UO , Th0 nd Th0 -UO " WAPD-Tm 751, (May 1969).
2 2 2 2 2 2
(2) A. A. Solomon and F. Hsu, pp 485-502 in Sintering Processes, Ed. byG. C. Kuczynski, Plenum, New York, (1980).
~
(3) P. E. Hart, " Fabrication of High-Density UO and (V Pu0.25) 022 O.75by Hot Pressing," J. Nucl. Mater., 51 (1974) 199-202.
(4) B. Schaner, in: Uranuim 0xide: Properties and Nuclear Applica-tions, ed. J. Belle (USAEC,1961) p. 30.
(5) 1. Amato, R. Colombo ad A. Balzari, J. Nucl . Mater. , 20 (1966) 210.
(6) I. H. Warren and A. C. D. Cnaklader, " Reactive Hot Pressing of Non-stoichiometric Uranium Dioxide." Mct Trans., 1 (1970) 199-205.
(7) J. L. Routbort, J. C. Voglewede and D. S. Wilkinson, " Final StageDensification of Mixed 0xide Fuels _ " J. Nucl . Mater. , 80(1979)348-355.
(8) R. C. Abbott and A. A. Solomon, "A New Technique to Study Effectsof Internal and External Pressure in Ceramics", Am. Ceram. Soc.Bull. , 58 (4) 470-72 (1979).
(9) C. E. McNeilly and T. D. Chikalla, " Determination of Oxygen / MetalRatios for Uranium, Plutonium, and (U, Pu) Mixed Oxides," J. Nucl.Mater., 39 (1971) 77-83.
(10) Contributions to the Data on Theoretical Metallurgy, XIV Entropiesof the Elements and Inorganic Compounds, by K. K. Kelley and E. G.King, Bureau oi " ire 3, Bull . 592, (1961).
(31) M.1. Mendelson, " Average Grain Size in Polycrystalline Ceramics,"J. Amer. Ceram. Soc., 52 (8) 443-46 (1969).
-20-
(12) M. S. Seltzer, A. H. Clauer and B. A. Wilcox, "The Influence ofStoichiometry on Compression Creep of Uranium Dioxide SingleCrystals," J. Nucl Mater., 44 (1972'. 43-56.
(13) M. S. Seltzer, A. H. Clauer and B. A. Wilcox, "The Influence ofStoichiometry on Compression Creep of Polycrystalline U0 "b24'Nucl. Mater., 44 (1972) 331-336.
(14) M. S. Seltzer, J. S. Perrin, A. H. Clauer, and B. A. Wilcox," Review of Out-of-Pile and In-pile Creep of Ceramic Nuclear Fuels,"Battelle Memorial Institute Report #BMI-1906, (July 1971).
(15) M. F. Ashby, C. Gandhi and D. M. R. Taplin, Acta Met, 27,(1979)699.
(16) D. S. Wilkinson, Ph.D. Thesis, University of Cambridge (1978).
(17) R. L. Coble, " Diffusion Models for Hot Pressing with Surface Energyand Pressure Effects as Driving Forces," J. Appl . Phys. , 41 (12)(1970) 4798-4807.
(18) D. S. Wilkinson and M. F. Ashby, " Pressure Sintering by Power LawCreep," Acta Met, 23 (1975) 1277-1285.
(19) P. Murray, D. T. Livey, and J. Williams, "The Hot Pressing ofCeramics," in Ceramic Fabrication Processes, W. D. Kingery, Ed. ,pp.147-171, lhe M.1. T. Press, Cambridge Mass. (19581
(20) A. A. Solomon and F. Hsu, " Swelling and Gas Release in Zno," J.-/mer. Ceram. Soc., 63 (7-8) (1980) 467-474.
(21) MATPRO - Version 11 (Revision 1). A Handbook of Materials Proper-ties for Use in the Analysis of Light Water Reactor Fuel Rod Be-havior, NUREG/CR-0497 TREE-1280, Rev.1 (Feb.1980).*
*Available for purchase from the NRC/GPO Sales Program, U.S. Nucir iRegulatory Commission, Washington, DC 20555, and the National TerinicalInformation Service, Springfield, VA 22161.
-21-
evac / pressure 4
'
i
LVDT -
JLVDT core r--
nut -
water jackc*- =
gas seal e cover, .
-,
,
V//2 /'
:extension rod
W/pressure vessel =
Y, f'
,gas jocket :
!.
/
MoSi2
furnace eleme/nt ///
\samole, j j, g
Y //'thermocouple well R !:
./ \ dgas
fig. 1. Isostatic pressurization system
-23-
14 i j j ji i :|
i j j ii j i
- _
OPEN2 - _
, o A CLOSED_ _
OPEN _10 -
np A- ~
5 e - -
0 Ay tu- -
e o /~g6g e- -
,
E A A- -o/4 A A A- -
Ao kNA CLOSED jA_
4-
2 4- -
/ es eo e o A -
'I fl I I I 'I' ' ' ' " * a' 'O #84 86 88 90 92 94 96 98 100
PERCENT OF THEORETICAL DENSITY
Fig. 2. Pore closure in UO fr m immersion density2
&. i
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As-Sintered - 96.8% TD
Fig. 4. SEM photograph of sintered 00 .7
-26-
1.75 -
,i ; ; ,,y , ,
n_
h UO2 HOT PRESS1410 DEG Ct. 1.25 - _
I x
~
g 0.75 - _
,
/ww j &>
_ -
e' g4#6& 0.25 PRESINTER s-. ,_
,
h U yo_ _
e o o
$ -0.25 *- _
e %o - _oJ
I I I I | l.-' ' ' ' '-0.75 ' '
93 94 95 96 97 98 99 100
PERCENT OF THEORETICAL DENSITY
Fig. 5. Hot-pressing of UG t various pressures2
25 i i i| | ji
/-
_
20 --
E^ n 95 X TDT A 96 --
mL o 97
_c
15 --y1
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v _ _
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EXTERNAL APPLIED PRESSURE (MPa)
Fig. 6. Hot-pressing rates at constant derisity and 1410 L
-28-
6 i i g ;i i i i
- -
5 - -
R PRESSURE CYCLINGaS EXTRAPOLATION- -
9 4 - -
o_r e --
v
o. 3 - -
I
~
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? N6 2 --- -
N- _
1 - -
- _
I I ! ('
' ' ' ' '092 93 94 95 96 97 98
PERCENT OF THEORETICAL DENSITY
Fia. 7. Variation in surface tension and internal pressurewith density at 1410 C
1.5 ; i , , , , ,i ,
_ _
1.25 UO2 HOT PRESS __-
1410 DEG C- 4
'0 1e, _-
i Am _
_
/L /C0.75 -
-
Y @u -_
o p- x 9C3 0.5 / --
/W __
F-< &x 0.25 --
? oz _ c _
q/$ 0 --
F- N,-
D - p __
a Co -0.25 -
-
J B 95% TD~
A 96% TD-
j- oO 97% TD-0.5 _
-
__
I I I' ' ' ' ' '' '-0.75O.4 07 1 1 3 1 6
LOG F CMPa)
Fig. 8. Dependence of strain-rate on driving force
-30-
'.,djW:::." hj~% dh?1gb~iS*|$;;5.1- fi&Q%.--%|;2 :; c. ::c. v._rga#n;|;QfQ. ) -1=.;||;. . , . . .- . -5 .L ..9.-.. : 2 ::. . :. :in =;. . . s, ,, x;
.ng::.: ?ms .. ;; .. . n . :... ..:~ .. .: ...
. . .
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n'
-_
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|| | |
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I 10.35 MPam 20.69L 1.25 - -
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>
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92 93 94 95 96 97 98
PERCENT OF THEORETICAL DENSITY
Fig. 9. Pre *sure cycling experiment
e i ; i ; i ; ; ;i i i
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LOG HOT-PRESSING TIME Cmin.)
Fig. 10. Hot-pressing of UO with temperature cycling.2
00-
_
- __ .
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o- i l l l l i I I Ii i i i i i i i i ig70 200 400 600 800 1000 1200 1400 1600 1800 2000
TIME AT TEMPERATURE Cmin)
Fig. 13. Hot-pressing and swelling in sintered U0 *2
@T.#s N @N_p@ 1;(fm$p< p sR 57p
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NRC eonu 2 1. P PORT NUMBE R MnN DOC)U.S. Nu:EEAR REcutAtoRY coMuimoNt' nt NUREG/CR-2023BIBLIOGRAPHIC DATA SHEET PUR-101
4 TSTLE AND SUBTITLE 4cc Vdame No.. o%prevona1 2. (Lean ble' Al
Modelling Hot-Pressing of UO2s. RECIPIENT s accession No.
7. AUTHOR (S) 6. DATE REPORT COMPLE TEDMONTH | YEARA. A. Solomon, K. M. Cochran, J. A. Habermeyer August 1980
,
9 PE RF ORMING ORGANIZATION NAME AND W AILING ADDRESS (tactum I,p Coor/ DNE REPORT ISSUED |MO.v 7 H | YEARSchool of Nuclear Engineering _l6t h lon1
Purdue University P (te.ve u u lWest La'ayette, Indiana 47907
8 (Leave Nash)
12. SPONSOR!fs i oRGANt2 ATION N AME AND M AILING ADDRE SS I/nctum Isp Coortgp g ggg
U.S. Nuclt tr Regulatory CommissionDivision o' Reactor Safety Research u. CONTRACT No.Office of Nuclear Regulatory ResearchWashington, D.C. 20555 FIN B6313
13 TYPE OF REPORT PE Rico covt RE O (tactus we 88821
Technical Report N/A,
1b. SUPPLEMENTARY NOTES 14. (Leave & seal
i
16. ABSTRACT 000 wcres or en/
Final state isostatic hot-pressing of nearly stoichimetric 002 was investigat Therate of hot-pressing is linearly dependent on the pressure driving force F=P+Jgd. p,-
where P and p are the external and internal pressures, respectively, y is the averagesurface energy and r is average pore radius. The apparent activation energy for hot-pressing agrees with that for U bulk diffusion. Grain growth during hot-pressingfollows d = tn, where d is the grain diameter, t is time and n = 0.2. Grain size isalso a function of temperature at constant density. The results indicate that Nabarro-Herring creep is the controlling mechanism of hot-pressing over the rar.ge of variablesinvestigated, although the applicability of this model is questioned. The restltsalso show that sintered U02 can entrap gas that can lead to swelling. For mod tilingpurposes, the isostatic hot-pressing of UO , under the conditions investigated, is2best described by, 1 dV
I dV_ = A_2 l-P where, V dt {s the volumetric strain-3(exp - Q/RT) F rate in sec , A=8x10 , d is in um, pV dt d p is the relative density, Q=480 kJ/g-
male, RT has its usual meaning, and F is in Pa cals.
17. KE Y WORDS AND DOCUMENT AN ALYsts 17a DESCRIPTORS
Hot-pressingSwelling
N/A002sintering
17b. IDE NTIF IE RSIOPEN-E.N DE D TE RMS
N/A
18. AVAILABILITY ST ATEMINT 19. SE CURITY CLASS (This reportl 21. N O. OF P A GE SUnclassified
Unlimited 20 SECURITY CLASS (ru,e,gl 22. price
Unci a s si fiM E
N Rc eoRu nas tv.rt