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The solid-state diffusion of plutonium in uranium dioxide
Journal of Nuclear Materials 78 (1978) 0 North-IIolland Publishing Company
THE SOLID-STATE
182--191
DIFFUSION OF PLUTONIUM IN URANIUM DIOXIDE
G.R. CHILTON and J. EDWARDS UKAEA, WindscaleNuclear Power Development Laboratories, WindscaleWorks,Sellafield, Seascale, Cumberland CA.20 IPF, UK Received
16 I:ebruary
1978
Lattice and inter-diffusion coefficients of plutonium in uranium dioxide have been calculated from electron microprobe analysis of the interface of diffusion couples annealed at 2023, 2123 and 2223 K. The results show that grain-boundary diffusion predominates in the overall diffusion process. The inter-diffusion coefficient follows a trough-like function with stoichiometry, a minimum occurring at an oxygen-to-metal ratio around 1.97.
2. Experimental
1. Introduction
2.1. Preparation and annealing of diffusion couples
In the fast reactor fuel cycle based on uranium-
The pellets used in this work were manufactured by granulation of the powder with an organic binder prior to cold pressing and debonding. The pellets were sintered at 1873 K in an argon-4% hydrogen atmosphere. Co-precipitated mixed oxide powder was used to manufacture the Ue.7ePue.302 pellets, the UO.ss Pue.r sOa pellets being prepared from physically blended material. Diffusion couples consisting of a UOa pellet bonded to a U0.,Pue.302 pellet were prepared by hot-pressing the two pellets at 1573 K. Prior to hotpressing the contact surfaces of the two pellets were coated with a thick slurry of finely ground Ue.,Pu,,s Oz. This resulted in a 5 pm thick film of mixed oxide at the interface. To retain the stoichiometry of the couples during the annealing process the diffusion couples and monitor pellets were doubly contained in molybdenum capsules. These capsules were annealed in flowing argon in a graphite resistance furnace for 30 h. Three annealing temperatures were adopted - 2023,2123 and 2223 K - with a heating and cooling rate of 300 K/h.
plutonium mixed oxide, quantitative knowledge of the diffusion rates of plutonium in uranium dioxide is required. Such information is particularly useful in understanding the rates of homogenisation, during sintering, of fuel prepared by physically mixing uranium dioxide and plutonium dioxide and also the mechanisms for the redistribution of plutonium and uranium during irradiation. Previous data reported on the diffusion of plutonium into UOa [l-6] cover a wide range of variables. The experiments reported in this work were designed to obtain diffusion coefficients at 2023, 2 123 and 2223 K as well as a range of stoichiometries and plutonium concentrations. A series of diffusion couples (produced by hot-pressing a UO? and a Ue.7Pue.302 pellet) were annealed for 30 h at constant temperature in molybdenum capsules. The oxygen potential in each capsule was monitored by the inclusion of a UO~ss~o~rsOz pellet. The annealed specimens were subjected to micrographic examination prior to the determination of uranium and plutonium concentrations across the interface of the diffusion couple by electron probe microanalysis (EPMA). 182
G.R. Chilton, J. Edwards /Solid-state
diffusion of plutonium
in uranium dioxide
183
2.2. B-eparation of couples for microscopic examination Photomicrographs were obtained from diametral cross-sections. The structure of the UOZ was revealed by etching the surface with hydrogen peroxide (fig. 1). Although the etchant clearly outlines the grains in the UO?, the effect on mixed oxide depended on the plutonium content. The higher the plutonium content, the less rapid the rate of attack by the etchant. 2.3. EPMA microscanning techniques 2.3.1. The network method This technique was developed to produce data from which the inter-diffusion coefficients (Or) could be calculated. The plutonium and uranium concentrations were measured from the plutonium-Mp and uranium& X-radiation. Concentrations were determined along lines parallel to the original interface in 500 pm sections (fig. 2). Close to the interface the lines were separated by 25 pm, further from the interface 100 pm separations were adequate. The outer 1000 pm of the couple was ignored because of the effects of surface diffusion and vapour transport processes. The instrument was calibrated by measuring the plutonium and uranium concentrations at the extremities of the UO? and U0.,Pu0.302 pellets. 2.3.2. The single grain scan method The uranium and plutonium concentration was measured within a single grain of UOZ close to the interface. The grain was selected from an X-ray image of the interface (fig. 3), the electron image (fig. 4) being used to verify the absence of porosity that would invalidate the data. Using a point source, the uranium and plutonium concentrations were measured at 0.5 pm intervals from a position on a grain boundary rich in plutonium (shown as a white area in fig. 3) to the centre of the UOZ grain. The instrument was calibrated as described above.
3. Calculation method 3. I. Techniques to establish the inter-diffusion coefficien ts The most common treatment for the analysis of metallurgical diffusion processes is the Boltzmann-
Fig. 1. PIlotomicrograph of a diffusion couple that had been etched u!sing hydrogen peroxide. The light areas repres :nt the grain boundary phases, X400. The arrow indicates Ithe interface of the two pellets.
Matano method. This technique allows the inter -diffusion toe :fficient to be evaluated from a concentr, ation gradient : curve produced by plotting the Pu/(U t .Pu)
G.R. Chilton, J. Edwards /Solid-state
184
diffusion of plutonium
in uranium dioxide
INTERFACE
Uo., Pu~.~ 0,
--
I
OUTER IOOOwm
lJ0, PELLET
PELLET
1
r
OF PELLET
---
t-
1
u LL
w
IOOpm
0
v m
-
‘--1-
I
1
OUTER
8 SEGMENTL< A-H -----
-
---
lOOO/um
-
I
I--- -4m Fig. 2. Schematic
/-
representation
-+
8CQrn
of the EPMA scanning
ratio (c), versus the distance (x) perpendicular to the contact plane between the UOZ and U0.7Pu0,302 pellets. By differentiating, the value of x can be derive d when dc/dx (the concentration gradient of a component in the x direction) is zero at c = ce, The diffusion coefficient at a specific concentration (D&) was eval-
Fig. 3. The U-M, X-ray image of a UO, grain surrounded by plutonium-rich grain boundaries, shown by their light coloration.
4 method
across a couple.
uated by application
of eq. (1):
(1) where f = time (s), dx/dc = the reciprocal of the concentration gradient, and Jx dc = the area enclosed by
Fig. 4. The electron image of the area shown coloured areas represent holes in the surface.
in fig. 3. Dark
G.R. Chilton, J. Edwards /Solid-state diffusion of plutonium in uranium dioxide
the concentration curve and the Matano interface. The Matano interface is defined as a pfane such that the areas enclosed by the concentration curve and the plane are equal. The network method was used to obtain a series of plutonium and uranium concentration curves. Eight concentration curves were produced, covering the central 4 mm of each diffusion couple. In order to
0.6
correct for misalignment of the couple interface, each curve was then superimposed on the preceding one. By measuring the displacement of the final curve (which represented the segment 4500-5000 pm from the edge of the pellet) from that of the initial curve (covering the 1000-l 500 pm region), the value of x was corrected for any errors due to misalignnlent of the couple. A final total concentration curve was then
O-220
t
TANGENT TO POINT IL%---o-3..0.112 4 A
0.
CONCENTRATION
C’
,
I to.022
“0.7
P”Q.3
INTERFACE
*2
DISTANCE
uo2
FROM THE INTERFACE (pm)
Fig. 5. The plutonium concentration
185
gradient across the couple.
186
G.R. Chilton, J. Edwards /Solid-state
diffitsion of plutonium in uranium dioxide
constructed using all the corrected values ofx and their respective plutonium-Mvlp uranium-M, ratios (fig. 5). Using the calibration data, points on the curve were translated into Pu/(U t h) ratios: for various values ofx. These data were used as the input for a computer program which calculated diffusion coefficients by application of eq. (1). To reduce the errors involved in finding the exact position of the Matano interface, the computer program fixed the position of the interface and evaluated the area under the curve on either side of the plane. This process was repeated, moving the interface in 0.1 ,um steps, until both the areas calculated were equal. When the exact position of this interface had been obtained (fig. 5) a concentration (c’) was selected and a horizontal line (AB) taken from they axis to a point which crossed the concentration gradient curve. The slope (dx/dc) of a line (CD), drawn tangentially to such a point (B), and the area (fx de), enclosed by the horizontal line, were used in conjunction with the Matano interface to calculate the inter-diffusion coefficients. 3.2. Determination of lattice diffusion coej&ients (DL)
The uranium and plutonium concentrations produced by scanning single grains were converted to Pu/(U + Pu) concentrations. A concentration gradient curve across a grain was then constructed in terms of Pu/(U + Pu) and x and the curve analysed by the Boltzmann-Matano method. It was assumed that only lattice diffusion occurred within a grain.
rity and remain intact to the end of the experiment. In several cases fractures occurred during the annealing process, probably resulting from an inability of the interface to accommodate the stresses caused by the different expansion properties of the two oxides making up the diffusion couple. 4.1.2. Inadequacies of the EPMA network method Inaccurate measurement of uranium and plutonium concentrations resulted when the scanning line traversed a pore. These effects were minimised by averaging the concentration gradients. Si~ificant errors were produced in the calculated diffusion coefficients if the scanning line was not parallel to the couple interface. These errors were minimised by the use of the graphical method to correct for misalignment. 4.2. The significance of microstructural observations The concentration of plutonium in the UOa could not be assessed quantitatively by microscopic examination of the diffusion couple but the following qualitative observations were made using this technique. (1) Most plutonium diffusion occurred along grain boundaries (fig. I) and outer surfaces of the UOa pellets were enriched in plutonium. This surface enrichment was probably caused by surface diffusion and vapour phase transport. In addition the porosity of the U0~,Pu0.302 pellet after annealing had increased, although the cause of this is not understood. (2) Any defects affecting the integrity of the interfacial bond were readily distinguishable from the photomicrographs.
4. Discussion 4.3. fn ter~retation of diffusion resu2ts 4.1. Sources of error Although the data reported were produced using precise analytical techniques, there were a number of unavoidable sources of error. The significance of these is discussed below. 4. I. 1. F7re integrity of the bond Incomplete bonding interfered with the solid-state diffusion processes and this resulted in a non-uniform diffusion front. It was essential that the bond between the pellets forming the couple should be of high integ-
The values of inter-diffusion coefficients and lattice diffusion coefficients obtained in this work are shown in table 1 and 2, respectively. Only a small amount of data has been produced at 2023 and 2123 K and any assessment of the results obtained at these temperatures must therefore be tentative. The discussion is therefore mainly concerned with results obtained at 2223 K. An activation energy of -lo4 kcal was obtained using data at all three temperatures at an oxygen/metal (O/M) ratio of 1.985. The variation of interdiffusion coefficients with O/M ratio for’a U0.8Pu0.2
G.R. Chiiton, .I. Edwards /Solid-state
187
diffusion of plutonium in uranium dioxide
Table 1 The variation of inter-diffusion Temperature (K>
O/M ratio
coefficients with temperature,
Pu valency
plutonium concentration
and stoichiometry
@(cm* /s) at Pu/(U + Pu) 24% X
lo-“ x lo-‘* X lo--l3 x 10-g x lo-‘0 x lO-“O x lo-” x lo-”
2223 2223 2223 2223 2223 2223 2223 2223
1.973 1.973 1.975 1.982 1.984 1.986 1.992 1.996
3.64 3.64 3.67 3.76 3.79 3.81 3.89 3.95
2.60 5.19 5.64 1.01 5.54 1.03 2.07 1.49
2123 2123 2123
1.980 1.981 1.986
3.73 3.74 3.81
1.30 x lo-‘0 2.32 X lo-‘” 6.34 X lo-”
8.70 x lo-” 7.93 x lo-” 2.59 X lo-”
5.30 x 10-l 8.53 X IO-” 2.65 X lo-”
4.60 X lo-” 2.30 X lo--” 2.64 X lo-”
2023 2023
1.989 2.00
3.85 4.00
3.90 x 1o-‘2 5.00 x lo-‘2
6.20 X IO-” 6.20 x lo-‘*
1.10 x lo-” 1.10 x lo-”
1.20 x lo-” 1.20 x lo-”
O,_, composition at the three annealing temperatures is shown in fig. 6. The calculated lattice diffusion coefficients are about three orders of magnitude smaller than coeffcients for the inter-diffusion process. This confirms the microscopic evidence of the minor role of lattice diffusion in the overall diffusion process. Although Lundy and Federer [7] have evaluated some lattice diffusion coefficients by graphical extrapolation of inter-diffusion data, our attempts to do this were unsuccessful because of the uncertainty in determining the point at which lattice diffusion was negligible. The results in fig. 6 show that differences of an order of ma~itude occurred in nominaliy identical
Table 2 Lattice diffusion data (cml/s) produced by the single scan method from specimens annealed at 2223 K OtM
Pu valency
1.982 1.984 1.986 1.992 1.996
3.76 3.79 3.81 3.89 3.95
8.4 X lo-” 6.4 X lo-” 4.7 x lo-‘4 1.0 x lo--l4 8.0 x lo-l5
3.40 5.59 5.29 2.95 1.44 1.27 2.19 1.28
12%
16%
20% x lo-” x lo-‘S x 1O-‘3 X lo--” x 1o-‘o x lo-” x lo-’ ’ x lo-”
3.70 5.57 4.14 2.33 1.59 2.31 1.54 7.97
x lo-” x lo-‘* x lo-l3 X lo-” x lo-‘0 X lo-” x 1o-L’ x lo-l2
4.40 5.30 3.97 3.14 8.50 2.13 1.70 8.58
X x x x
lo-” 1o-‘2 10F3 1o-‘o
X lo-’
’
X lo-” x lo-” x lo-”
specimens. These differences are unlikely to be caused by the quality of either the specimen or the bond forming the couple. Errors produced in fitting a curve to the plutonium concentration data are small (less than half an order of ma~itude) and cannot account for the observed variations, It should be noted, however, that similar variations are common for diffusion data reported on similar systems (fig. 7). It is unfortunate that these variations may mask the changes in the values of diffusion coefficients that occurred with a change in stoichiometry. The results in fig. 6, however, show a real difference in the magnitude of the ~ter-diffusion coefficients produced at 2223 K between O/M ratios above and below 1.97. Points above 1.97 show a systematic decrease in diffusion coefficient as the O/M ratio increases. It is clear from fig. 8 that the calculated diffusion coefficients reported in this work are in reasonable agreement with those suggested by other authors. Results published to date [I ,6,8-IO] suggest that a variation of diffusion coefficients with O/M ratio should follow a trough-like function similar to that shown in fig. 7. However, the position of the minimum has been a matter of some discussion [8]. The data reported in fig. 6 at 2223 K suggest that a minimum lies between O/M ratios of 1.967 and 1.975.
G.R. Chilton, J. Edwards / Solid-state diffusion of plutonium
188
in uranium dioxide
x at 2223K o at Zl23K
l aL2OaK
\
x
Id3
3-b
.
l
I.97
i-98
1.99
2-W
3.7
38
39
4-O
Fig. 6. Variation of inter-diffusion
The spar&y of data in this region precludes the con~rmation of the existence of the trough. Although other authors [ 1 ] have suggested that the minimum lies at an O/M ratio of around 1.98, all previous data have been obtained at lower temperatures. Matzke [ 111 suggested that the position of the minimum is dependent upon temperature. At higher temperatures the amount of lattice disorder will increase and the position of the trough is likely to shift towards greater hypostoichiomet~. The variation of inter-diffusion coefficients with stoichiometry has been explained in terms of a change in diffusion mechanism. Some early theoretical work [ 121 on the self diffusion of uranium in UOZ suggested that the mechanism could be explained in terms of various point defects present in the UO1 lattice and concluded that in hyperstoic~ometric UOZ the diffusion occurred via a vacancy mechanism whilst an interstitial diffusion mechanism was responsible for diffusion in hypostoichiometric oxide. Experimental evidence supporting these types of mechanisms has been obtained. Matzke [ 131 found that when U02 was
%I
ratio in ~e~20,
Pu valcncy
coefficients with stoichiometry.
Table 3 Analytical data for the UO, and U,,,,Pu,.,O, Element U(wt.%) Pu(wt.%) Pu/Pu + U(wt.%) Cl F MO co CU Fe Ni Cr Al ca Mg Cd B Ti Si C
UO, 88.12
>I0 >10 >20 8 1.5 170 110 15 >15 20 45 0.7 75 >20 _ 55
pellets U,.,Pu,.,O, 60.59 27.61 31.30 >lO >lO >20 8 15 830 70 65 >15 20 25 0.7 75 100 25 _
NB. Ail figures refer to ppm unless otherwise stated.
189
G.R. Chilton, J. Edwards f Solid-state diffusion of plutonium in uranium dioxide -I
1873K
T= -
0 8 J
KEY 0 Schmitz l
Matzke
& Marajofsky
(ref. 8)
(ref. 14)
x Marin & Contamen
(ref. 10)
+ Hawkins
(ref. 91
& Alcock
-I 3.0
3-5 URANIUM
Fig. 7. Dependence
of diffusion
of uranium
4’0 OR PLUTONIUM
in UO,
and plutonium
doped with Nba 0s) an oxygen-rich compound (U, Nb) Oz+r was formed, and self-diffusion coefficients were enhanced when compared with those for pure stoichiometric UOa. On the other hand, diffusion rates in oxygen-deficient compounds produced by doping UOz with either lanthanum or yttrium oxide, were lower
4.5
VALENCY
in (UPu) 0~~
on the valence
of the metal ions.
than for pure UOa. These results were interpreted in terms of the number of Frenkel defects. In hyperstoichiometric oxide the number of such defects is high and hence the uranium (4+) ions will diffuse via a vacancy mechanism whilst in the hypostoichiometric material diffusion will most likely occur via uranium
G.R. Chilton, J. Edwards / Soiid-state diffusion of plutonium in uranium dioxide
190
I200
0 -
1400 t
MATZKE 8 BUTLER
0 x
LAMBERT 8
b=
I800
1
2000
I
(REF (REF
Ij 2)
R I&
IN
2200 1
2600 2400 2800
UPu02_
8 3 5%
T(K)
,,I,
,,
b. UP
MATZKE (REF 3) U in UO2+” DAVIES D NOVAK (REF 4 ) Pu IN m,
-_SCHMITZ -_____ RIEMER 63
MEYER
1600
THIS
& LINDNER a SCHERFF
(REF (REF
5)
Pu IN uo,
6) PU IN UPUO~+~
WORK
BURN UP
I.76
3
3.74
2-
4_
IO-
16
1
9
3
7
L
1
8
t
I
6
5
4
3
2
tO4/
T(K”I)
Fig. 8. Diffusion coefficients obtained by other authors studying plutonium diffusion into UO, (some of the results reported in this work are shown)..
G.R. Chilton, J. Edwards /Solid-state
(4t) interstitial sites. Although these results are based on self-diffusion in a UOZ system, it is likely that such mechanisms are responsible for the variation of interdiffusion coefficients reported in this work. Schmitz [8] has suggested that diffusion depends on the value of x/y in compounds of the type Ur __,, PLI,,O~_~ and that a defect ring-type structure exists, consisting of two plutonium atoms and one oxygen vacancy, stabilised by localising electrons that ensure covalent bonding. The presence of these defects causes considerable deformation of the oxide lattice and an interstitial ring-type mechanism could operate in this deformed lattice that would cause an exchange of plutonium and uranium atoms. The concentration of these defect ring structures decreases as stoichiometry is approached and as a result diffusion coefficients are reduced. In an ideal mixed oxide, a minimum in the diffusion rate would occur at an O/M ratio of 2.00. The analysis of the pellets used to form the couples (table 3) shows that most impurities have a valency of less than 4.00. The presence of these impurities in the lattice could be expected to cause the position of the minimum to shift towards hypostoichiometry and the exact position of the minimum will be strongly dependent on the purity of the mixed oxide. 5. Conclusions (a) Grain-boundary diffusion processes predominate in the diffusion of plutonium in UOa. (b) The variation of inter-diffusion coefficients at 2223 K with stoichiometry suggest that the rate of
diffusion of plutonium
in uranium dioxide
191
diffusion decreases as the O/M ratio of the mixed oxide increases from 1.975 to 1.996. (c) The size of the lattice diffusion coefficients suggest that this process is about three orders of magnitude slower than the inter-diffusion process. Acknowledgements The authors would like to thank Messrs J.H. Pearce, J.A.M. Douglas and G. James for their assistance. We are also grateful to Dr. P.E. Potter and Mr. H.J. Hedger of AERE, Harwell, for discussion and helpful advice throughout the work.
References [l] Hj. Matzke and R.A. Lambert, J. Nucl. Mat. 49 (1973) 32.5. (21 E.M. Butler and R.O. Meyer, J. Nucl. Mat. 47 (1973) 229. [ 31 Hj. Matzke, J. Nucl. Mat. 30 (1969) 26. [4] J.H. Davies and P.E. Novak, Trans. Amer. Nucl. Sot. 7 (1964) 393. [5] F. Schmotz and R. Lindner, J. Nucl. Mat. 17 (1965) 259. [6] G. Riemer and H.L. Scherff, J. Nucl. Mat. 39 (1971) 183. [7] T.S. Lundy and J.I. Federer, Trans. Met. Sot. AIME 224 (1962) 1285. [S] F. Schmitz and A. Marajofsky, IAEA-SM-190/22 (1974). [9] R.J. Hawkins and C.B. Alcock, J. Nucl. Mat. 26 (1968) 112. [lo] J.F. Marin and P. Contamin, J. Nucl. Mat. 30 (1969) 16. [ 1 l] Hj. Matzke, unpublished work. [ 121 A.B. Lidiard, J. Nucl. Mat. 19 (1966) 106. [ 131 Hj. Matzke, Trans. Amer. Nucl. Sot. 8 (1965) 26. [14] Hj. Matzke, J. Phys. 349 (1973) 317.
THE SOLID-STATE
182--191
DIFFUSION OF PLUTONIUM IN URANIUM DIOXIDE
G.R. CHILTON and J. EDWARDS UKAEA, WindscaleNuclear Power Development Laboratories, WindscaleWorks,Sellafield, Seascale, Cumberland CA.20 IPF, UK Received
16 I:ebruary
1978
Lattice and inter-diffusion coefficients of plutonium in uranium dioxide have been calculated from electron microprobe analysis of the interface of diffusion couples annealed at 2023, 2123 and 2223 K. The results show that grain-boundary diffusion predominates in the overall diffusion process. The inter-diffusion coefficient follows a trough-like function with stoichiometry, a minimum occurring at an oxygen-to-metal ratio around 1.97.
2. Experimental
1. Introduction
2.1. Preparation and annealing of diffusion couples
In the fast reactor fuel cycle based on uranium-
The pellets used in this work were manufactured by granulation of the powder with an organic binder prior to cold pressing and debonding. The pellets were sintered at 1873 K in an argon-4% hydrogen atmosphere. Co-precipitated mixed oxide powder was used to manufacture the Ue.7ePue.302 pellets, the UO.ss Pue.r sOa pellets being prepared from physically blended material. Diffusion couples consisting of a UOa pellet bonded to a U0.,Pue.302 pellet were prepared by hot-pressing the two pellets at 1573 K. Prior to hotpressing the contact surfaces of the two pellets were coated with a thick slurry of finely ground Ue.,Pu,,s Oz. This resulted in a 5 pm thick film of mixed oxide at the interface. To retain the stoichiometry of the couples during the annealing process the diffusion couples and monitor pellets were doubly contained in molybdenum capsules. These capsules were annealed in flowing argon in a graphite resistance furnace for 30 h. Three annealing temperatures were adopted - 2023,2123 and 2223 K - with a heating and cooling rate of 300 K/h.
plutonium mixed oxide, quantitative knowledge of the diffusion rates of plutonium in uranium dioxide is required. Such information is particularly useful in understanding the rates of homogenisation, during sintering, of fuel prepared by physically mixing uranium dioxide and plutonium dioxide and also the mechanisms for the redistribution of plutonium and uranium during irradiation. Previous data reported on the diffusion of plutonium into UOa [l-6] cover a wide range of variables. The experiments reported in this work were designed to obtain diffusion coefficients at 2023, 2 123 and 2223 K as well as a range of stoichiometries and plutonium concentrations. A series of diffusion couples (produced by hot-pressing a UO? and a Ue.7Pue.302 pellet) were annealed for 30 h at constant temperature in molybdenum capsules. The oxygen potential in each capsule was monitored by the inclusion of a UO~ss~o~rsOz pellet. The annealed specimens were subjected to micrographic examination prior to the determination of uranium and plutonium concentrations across the interface of the diffusion couple by electron probe microanalysis (EPMA). 182
G.R. Chilton, J. Edwards /Solid-state
diffusion of plutonium
in uranium dioxide
183
2.2. B-eparation of couples for microscopic examination Photomicrographs were obtained from diametral cross-sections. The structure of the UOZ was revealed by etching the surface with hydrogen peroxide (fig. 1). Although the etchant clearly outlines the grains in the UO?, the effect on mixed oxide depended on the plutonium content. The higher the plutonium content, the less rapid the rate of attack by the etchant. 2.3. EPMA microscanning techniques 2.3.1. The network method This technique was developed to produce data from which the inter-diffusion coefficients (Or) could be calculated. The plutonium and uranium concentrations were measured from the plutonium-Mp and uranium& X-radiation. Concentrations were determined along lines parallel to the original interface in 500 pm sections (fig. 2). Close to the interface the lines were separated by 25 pm, further from the interface 100 pm separations were adequate. The outer 1000 pm of the couple was ignored because of the effects of surface diffusion and vapour transport processes. The instrument was calibrated by measuring the plutonium and uranium concentrations at the extremities of the UO? and U0.,Pu0.302 pellets. 2.3.2. The single grain scan method The uranium and plutonium concentration was measured within a single grain of UOZ close to the interface. The grain was selected from an X-ray image of the interface (fig. 3), the electron image (fig. 4) being used to verify the absence of porosity that would invalidate the data. Using a point source, the uranium and plutonium concentrations were measured at 0.5 pm intervals from a position on a grain boundary rich in plutonium (shown as a white area in fig. 3) to the centre of the UOZ grain. The instrument was calibrated as described above.
3. Calculation method 3. I. Techniques to establish the inter-diffusion coefficien ts The most common treatment for the analysis of metallurgical diffusion processes is the Boltzmann-
Fig. 1. PIlotomicrograph of a diffusion couple that had been etched u!sing hydrogen peroxide. The light areas repres :nt the grain boundary phases, X400. The arrow indicates Ithe interface of the two pellets.
Matano method. This technique allows the inter -diffusion toe :fficient to be evaluated from a concentr, ation gradient : curve produced by plotting the Pu/(U t .Pu)
G.R. Chilton, J. Edwards /Solid-state
184
diffusion of plutonium
in uranium dioxide
INTERFACE
Uo., Pu~.~ 0,
--
I
OUTER IOOOwm
lJ0, PELLET
PELLET
1
r
OF PELLET
---
t-
1
u LL
w
IOOpm
0
v m
-
‘--1-
I
1
OUTER
8 SEGMENTL< A-H -----
-
---
lOOO/um
-
I
I--- -4m Fig. 2. Schematic
/-
representation
-+
8CQrn
of the EPMA scanning
ratio (c), versus the distance (x) perpendicular to the contact plane between the UOZ and U0.7Pu0,302 pellets. By differentiating, the value of x can be derive d when dc/dx (the concentration gradient of a component in the x direction) is zero at c = ce, The diffusion coefficient at a specific concentration (D&) was eval-
Fig. 3. The U-M, X-ray image of a UO, grain surrounded by plutonium-rich grain boundaries, shown by their light coloration.
4 method
across a couple.
uated by application
of eq. (1):
(1) where f = time (s), dx/dc = the reciprocal of the concentration gradient, and Jx dc = the area enclosed by
Fig. 4. The electron image of the area shown coloured areas represent holes in the surface.
in fig. 3. Dark
G.R. Chilton, J. Edwards /Solid-state diffusion of plutonium in uranium dioxide
the concentration curve and the Matano interface. The Matano interface is defined as a pfane such that the areas enclosed by the concentration curve and the plane are equal. The network method was used to obtain a series of plutonium and uranium concentration curves. Eight concentration curves were produced, covering the central 4 mm of each diffusion couple. In order to
0.6
correct for misalignment of the couple interface, each curve was then superimposed on the preceding one. By measuring the displacement of the final curve (which represented the segment 4500-5000 pm from the edge of the pellet) from that of the initial curve (covering the 1000-l 500 pm region), the value of x was corrected for any errors due to misalignnlent of the couple. A final total concentration curve was then
O-220
t
TANGENT TO POINT IL%---o-3..0.112 4 A
0.
CONCENTRATION
C’
,
I to.022
“0.7
P”Q.3
INTERFACE
*2
DISTANCE
uo2
FROM THE INTERFACE (pm)
Fig. 5. The plutonium concentration
185
gradient across the couple.
186
G.R. Chilton, J. Edwards /Solid-state
diffitsion of plutonium in uranium dioxide
constructed using all the corrected values ofx and their respective plutonium-Mvlp uranium-M, ratios (fig. 5). Using the calibration data, points on the curve were translated into Pu/(U t h) ratios: for various values ofx. These data were used as the input for a computer program which calculated diffusion coefficients by application of eq. (1). To reduce the errors involved in finding the exact position of the Matano interface, the computer program fixed the position of the interface and evaluated the area under the curve on either side of the plane. This process was repeated, moving the interface in 0.1 ,um steps, until both the areas calculated were equal. When the exact position of this interface had been obtained (fig. 5) a concentration (c’) was selected and a horizontal line (AB) taken from they axis to a point which crossed the concentration gradient curve. The slope (dx/dc) of a line (CD), drawn tangentially to such a point (B), and the area (fx de), enclosed by the horizontal line, were used in conjunction with the Matano interface to calculate the inter-diffusion coefficients. 3.2. Determination of lattice diffusion coej&ients (DL)
The uranium and plutonium concentrations produced by scanning single grains were converted to Pu/(U + Pu) concentrations. A concentration gradient curve across a grain was then constructed in terms of Pu/(U + Pu) and x and the curve analysed by the Boltzmann-Matano method. It was assumed that only lattice diffusion occurred within a grain.
rity and remain intact to the end of the experiment. In several cases fractures occurred during the annealing process, probably resulting from an inability of the interface to accommodate the stresses caused by the different expansion properties of the two oxides making up the diffusion couple. 4.1.2. Inadequacies of the EPMA network method Inaccurate measurement of uranium and plutonium concentrations resulted when the scanning line traversed a pore. These effects were minimised by averaging the concentration gradients. Si~ificant errors were produced in the calculated diffusion coefficients if the scanning line was not parallel to the couple interface. These errors were minimised by the use of the graphical method to correct for misalignment. 4.2. The significance of microstructural observations The concentration of plutonium in the UOa could not be assessed quantitatively by microscopic examination of the diffusion couple but the following qualitative observations were made using this technique. (1) Most plutonium diffusion occurred along grain boundaries (fig. I) and outer surfaces of the UOa pellets were enriched in plutonium. This surface enrichment was probably caused by surface diffusion and vapour phase transport. In addition the porosity of the U0~,Pu0.302 pellet after annealing had increased, although the cause of this is not understood. (2) Any defects affecting the integrity of the interfacial bond were readily distinguishable from the photomicrographs.
4. Discussion 4.3. fn ter~retation of diffusion resu2ts 4.1. Sources of error Although the data reported were produced using precise analytical techniques, there were a number of unavoidable sources of error. The significance of these is discussed below. 4. I. 1. F7re integrity of the bond Incomplete bonding interfered with the solid-state diffusion processes and this resulted in a non-uniform diffusion front. It was essential that the bond between the pellets forming the couple should be of high integ-
The values of inter-diffusion coefficients and lattice diffusion coefficients obtained in this work are shown in table 1 and 2, respectively. Only a small amount of data has been produced at 2023 and 2123 K and any assessment of the results obtained at these temperatures must therefore be tentative. The discussion is therefore mainly concerned with results obtained at 2223 K. An activation energy of -lo4 kcal was obtained using data at all three temperatures at an oxygen/metal (O/M) ratio of 1.985. The variation of interdiffusion coefficients with O/M ratio for’a U0.8Pu0.2
G.R. Chiiton, .I. Edwards /Solid-state
187
diffusion of plutonium in uranium dioxide
Table 1 The variation of inter-diffusion Temperature (K>
O/M ratio
coefficients with temperature,
Pu valency
plutonium concentration
and stoichiometry
@(cm* /s) at Pu/(U + Pu) 24% X
lo-“ x lo-‘* X lo--l3 x 10-g x lo-‘0 x lO-“O x lo-” x lo-”
2223 2223 2223 2223 2223 2223 2223 2223
1.973 1.973 1.975 1.982 1.984 1.986 1.992 1.996
3.64 3.64 3.67 3.76 3.79 3.81 3.89 3.95
2.60 5.19 5.64 1.01 5.54 1.03 2.07 1.49
2123 2123 2123
1.980 1.981 1.986
3.73 3.74 3.81
1.30 x lo-‘0 2.32 X lo-‘” 6.34 X lo-”
8.70 x lo-” 7.93 x lo-” 2.59 X lo-”
5.30 x 10-l 8.53 X IO-” 2.65 X lo-”
4.60 X lo-” 2.30 X lo--” 2.64 X lo-”
2023 2023
1.989 2.00
3.85 4.00
3.90 x 1o-‘2 5.00 x lo-‘2
6.20 X IO-” 6.20 x lo-‘*
1.10 x lo-” 1.10 x lo-”
1.20 x lo-” 1.20 x lo-”
O,_, composition at the three annealing temperatures is shown in fig. 6. The calculated lattice diffusion coefficients are about three orders of magnitude smaller than coeffcients for the inter-diffusion process. This confirms the microscopic evidence of the minor role of lattice diffusion in the overall diffusion process. Although Lundy and Federer [7] have evaluated some lattice diffusion coefficients by graphical extrapolation of inter-diffusion data, our attempts to do this were unsuccessful because of the uncertainty in determining the point at which lattice diffusion was negligible. The results in fig. 6 show that differences of an order of ma~itude occurred in nominaliy identical
Table 2 Lattice diffusion data (cml/s) produced by the single scan method from specimens annealed at 2223 K OtM
Pu valency
1.982 1.984 1.986 1.992 1.996
3.76 3.79 3.81 3.89 3.95
8.4 X lo-” 6.4 X lo-” 4.7 x lo-‘4 1.0 x lo--l4 8.0 x lo-l5
3.40 5.59 5.29 2.95 1.44 1.27 2.19 1.28
12%
16%
20% x lo-” x lo-‘S x 1O-‘3 X lo--” x 1o-‘o x lo-” x lo-’ ’ x lo-”
3.70 5.57 4.14 2.33 1.59 2.31 1.54 7.97
x lo-” x lo-‘* x lo-l3 X lo-” x lo-‘0 X lo-” x 1o-L’ x lo-l2
4.40 5.30 3.97 3.14 8.50 2.13 1.70 8.58
X x x x
lo-” 1o-‘2 10F3 1o-‘o
X lo-’
’
X lo-” x lo-” x lo-”
specimens. These differences are unlikely to be caused by the quality of either the specimen or the bond forming the couple. Errors produced in fitting a curve to the plutonium concentration data are small (less than half an order of ma~itude) and cannot account for the observed variations, It should be noted, however, that similar variations are common for diffusion data reported on similar systems (fig. 7). It is unfortunate that these variations may mask the changes in the values of diffusion coefficients that occurred with a change in stoichiometry. The results in fig. 6, however, show a real difference in the magnitude of the ~ter-diffusion coefficients produced at 2223 K between O/M ratios above and below 1.97. Points above 1.97 show a systematic decrease in diffusion coefficient as the O/M ratio increases. It is clear from fig. 8 that the calculated diffusion coefficients reported in this work are in reasonable agreement with those suggested by other authors. Results published to date [I ,6,8-IO] suggest that a variation of diffusion coefficients with O/M ratio should follow a trough-like function similar to that shown in fig. 7. However, the position of the minimum has been a matter of some discussion [8]. The data reported in fig. 6 at 2223 K suggest that a minimum lies between O/M ratios of 1.967 and 1.975.
G.R. Chilton, J. Edwards / Solid-state diffusion of plutonium
188
in uranium dioxide
x at 2223K o at Zl23K
l aL2OaK
\
x
Id3
3-b
.
l
I.97
i-98
1.99
2-W
3.7
38
39
4-O
Fig. 6. Variation of inter-diffusion
The spar&y of data in this region precludes the con~rmation of the existence of the trough. Although other authors [ 1 ] have suggested that the minimum lies at an O/M ratio of around 1.98, all previous data have been obtained at lower temperatures. Matzke [ 111 suggested that the position of the minimum is dependent upon temperature. At higher temperatures the amount of lattice disorder will increase and the position of the trough is likely to shift towards greater hypostoichiomet~. The variation of inter-diffusion coefficients with stoichiometry has been explained in terms of a change in diffusion mechanism. Some early theoretical work [ 121 on the self diffusion of uranium in UOZ suggested that the mechanism could be explained in terms of various point defects present in the UO1 lattice and concluded that in hyperstoic~ometric UOZ the diffusion occurred via a vacancy mechanism whilst an interstitial diffusion mechanism was responsible for diffusion in hypostoichiometric oxide. Experimental evidence supporting these types of mechanisms has been obtained. Matzke [ 131 found that when U02 was
%I
ratio in ~e~20,
Pu valcncy
coefficients with stoichiometry.
Table 3 Analytical data for the UO, and U,,,,Pu,.,O, Element U(wt.%) Pu(wt.%) Pu/Pu + U(wt.%) Cl F MO co CU Fe Ni Cr Al ca Mg Cd B Ti Si C
UO, 88.12
>I0 >10 >20 8 1.5 170 110 15 >15 20 45 0.7 75 >20 _ 55
pellets U,.,Pu,.,O, 60.59 27.61 31.30 >lO >lO >20 8 15 830 70 65 >15 20 25 0.7 75 100 25 _
NB. Ail figures refer to ppm unless otherwise stated.
189
G.R. Chilton, J. Edwards f Solid-state diffusion of plutonium in uranium dioxide -I
1873K
T= -
0 8 J
KEY 0 Schmitz l
Matzke
& Marajofsky
(ref. 8)
(ref. 14)
x Marin & Contamen
(ref. 10)
+ Hawkins
(ref. 91
& Alcock
-I 3.0
3-5 URANIUM
Fig. 7. Dependence
of diffusion
of uranium
4’0 OR PLUTONIUM
in UO,
and plutonium
doped with Nba 0s) an oxygen-rich compound (U, Nb) Oz+r was formed, and self-diffusion coefficients were enhanced when compared with those for pure stoichiometric UOa. On the other hand, diffusion rates in oxygen-deficient compounds produced by doping UOz with either lanthanum or yttrium oxide, were lower
4.5
VALENCY
in (UPu) 0~~
on the valence
of the metal ions.
than for pure UOa. These results were interpreted in terms of the number of Frenkel defects. In hyperstoichiometric oxide the number of such defects is high and hence the uranium (4+) ions will diffuse via a vacancy mechanism whilst in the hypostoichiometric material diffusion will most likely occur via uranium
G.R. Chilton, J. Edwards / Soiid-state diffusion of plutonium in uranium dioxide
190
I200
0 -
1400 t
MATZKE 8 BUTLER
0 x
LAMBERT 8
b=
I800
1
2000
I
(REF (REF
Ij 2)
R I&
IN
2200 1
2600 2400 2800
UPu02_
8 3 5%
T(K)
,,I,
,,
b. UP
MATZKE (REF 3) U in UO2+” DAVIES D NOVAK (REF 4 ) Pu IN m,
-_SCHMITZ -_____ RIEMER 63
MEYER
1600
THIS
& LINDNER a SCHERFF
(REF (REF
5)
Pu IN uo,
6) PU IN UPUO~+~
WORK
BURN UP
I.76
3
3.74
2-
4_
IO-
16
1
9
3
7
L
1
8
t
I
6
5
4
3
2
tO4/
T(K”I)
Fig. 8. Diffusion coefficients obtained by other authors studying plutonium diffusion into UO, (some of the results reported in this work are shown)..
G.R. Chilton, J. Edwards /Solid-state
(4t) interstitial sites. Although these results are based on self-diffusion in a UOZ system, it is likely that such mechanisms are responsible for the variation of interdiffusion coefficients reported in this work. Schmitz [8] has suggested that diffusion depends on the value of x/y in compounds of the type Ur __,, PLI,,O~_~ and that a defect ring-type structure exists, consisting of two plutonium atoms and one oxygen vacancy, stabilised by localising electrons that ensure covalent bonding. The presence of these defects causes considerable deformation of the oxide lattice and an interstitial ring-type mechanism could operate in this deformed lattice that would cause an exchange of plutonium and uranium atoms. The concentration of these defect ring structures decreases as stoichiometry is approached and as a result diffusion coefficients are reduced. In an ideal mixed oxide, a minimum in the diffusion rate would occur at an O/M ratio of 2.00. The analysis of the pellets used to form the couples (table 3) shows that most impurities have a valency of less than 4.00. The presence of these impurities in the lattice could be expected to cause the position of the minimum to shift towards hypostoichiometry and the exact position of the minimum will be strongly dependent on the purity of the mixed oxide. 5. Conclusions (a) Grain-boundary diffusion processes predominate in the diffusion of plutonium in UOa. (b) The variation of inter-diffusion coefficients at 2223 K with stoichiometry suggest that the rate of
diffusion of plutonium
in uranium dioxide
191
diffusion decreases as the O/M ratio of the mixed oxide increases from 1.975 to 1.996. (c) The size of the lattice diffusion coefficients suggest that this process is about three orders of magnitude slower than the inter-diffusion process. Acknowledgements The authors would like to thank Messrs J.H. Pearce, J.A.M. Douglas and G. James for their assistance. We are also grateful to Dr. P.E. Potter and Mr. H.J. Hedger of AERE, Harwell, for discussion and helpful advice throughout the work.
References [l] Hj. Matzke and R.A. Lambert, J. Nucl. Mat. 49 (1973) 32.5. (21 E.M. Butler and R.O. Meyer, J. Nucl. Mat. 47 (1973) 229. [ 31 Hj. Matzke, J. Nucl. Mat. 30 (1969) 26. [4] J.H. Davies and P.E. Novak, Trans. Amer. Nucl. Sot. 7 (1964) 393. [5] F. Schmotz and R. Lindner, J. Nucl. Mat. 17 (1965) 259. [6] G. Riemer and H.L. Scherff, J. Nucl. Mat. 39 (1971) 183. [7] T.S. Lundy and J.I. Federer, Trans. Met. Sot. AIME 224 (1962) 1285. [S] F. Schmitz and A. Marajofsky, IAEA-SM-190/22 (1974). [9] R.J. Hawkins and C.B. Alcock, J. Nucl. Mat. 26 (1968) 112. [lo] J.F. Marin and P. Contamin, J. Nucl. Mat. 30 (1969) 16. [ 1 l] Hj. Matzke, unpublished work. [ 121 A.B. Lidiard, J. Nucl. Mat. 19 (1966) 106. [ 131 Hj. Matzke, Trans. Amer. Nucl. Sot. 8 (1965) 26. [14] Hj. Matzke, J. Phys. 349 (1973) 317.