1084
E. A. AITKEN,J. A. EDWARDS, AND R. A. JOSEPH
Thermodynamic Study of Solid Solutions of Uranium Oxide.
I.
Uranium Oxide-Thorium Oxide1
E. A. Aitken, J. A. Edwards, and R. A. Joseph Generat Electric Company, Nuclear Mate&& (Received September 20,1966)
and Propulsion Operation, Cincinnati, Ohio
The activity of uranium dioxide in solid solutions of U,Thl-,Oz+z was measured by the transpiration method. The partial pressure of UOOgas in a carrier gas of dry air was obtained and related to the thermodynamic activity of UOz in the solution according to the equation UOz(in solid soln)
+ l/zOz(g)
UOa(g)
The activity of UOz was found to decrease with an increase in thorium oxide content. The decrease was much greater if the solid solution contained interstitial oxygen. By means of an integral method for three-component systems, the UOz activity was calculated at the stoichiometric composition from published oxygen activity data and the measured U 0 2 activity of a nonstoichiometric composition. The stoichiometric solid solution was found to be ideal in the region of 1300”. The effect of interstitial oxygen which caused negative departure from ideality was explained in terms of localized interaction of the interstitial oxygen with the uranium ion. The free energy of formation data gave a predicted composition, consistent with X-ray diffraction results, for precipitation of U308 phase from the solid solution a t 0.2 atm of oxygen.
Introduction Uranium dioxide dissolves appreciable amounts of the group I11 and group IV oxides if the solute cation radius is similar to that of the uranium ion. Among the group IV oxides, T h o z and stoichiometric U022-4form a complete series of solid solutions which obey Vegard’s law. Solid solutions5 of urania-thoria also may take up oxygen interstitially. This first decreases the lattice parameter until the oxidation number of the uranium reaches about 5.0 and then increases it at higher oxidation numbers. The composition containing interstitial oxygen is limited to the region below i’110~.~~ regardless of the U/Th ratio. For uranium cation fractions above 0.59, the solid solution precipitates UaOs when it is heated in air above 1000°.6 Other than the diffraction results and some oxygen activity data5J-9 on selected compositions, little else is known about the thermodynamic behavior of urania-thoria solid solutions. Since Vegard’s law is obeyed and there is mutual solubility, we might expect
stoichiometric solid solutions to be nearly ideal. Vapor pressure measurements of the uranium dioxide component provide a direct means of determining its (1) This paper originated from work sponsored by the Fuels and Materials Development Branch, Atomic Energy Commission, under Contract AT(40-1)-2847. (2) W. Trezebiatowsky and P. W. Selwood, J . A m . Chem. Soc., 7 2 , 4504 (1950). (3) E. Slowinski and E. Elliot, Acta Cryst., 5 , 768 (1952). (4) W. Lambertson, M. Mueller, and F. Gunzel, J . A m . Ceram. Sac., 36, 397 (1953). (5) L. E. J. Roberts, “Nonstoichiometric Compounds,” Advances in Chemistry Series, No. 39, American Chemical Society, Washington, D. C., 1963, p 69. (6) (a) F. Hund and G. Niessen, 2. Elektrochem.. 56. 972 (1952): (b) J. Handwerk, L. Ahernathy, and R. Bach, A m . Ceram. Sac. Bull., 36, 99 (1957). (7) S.Aronson and J. Clayton, J . Chem. Phys., 3 2 , 1749 (1960). (8) “Uranium Dioxide: Its Properties and Applications,” J. Belle, Ed., U. S. Government Printing Office, Washington, D. C., 1961, p 293. (9) L. E . J. Roberts, L. E. Russell, A. G. Adwick, A. J. Welter, and M. H. Rand, P/26 UK Geneva Conference of Peaceful Uses of Atomic Energy, Vol. 28, 1958, p 215.
THERMODYNAMIC STUDY OF SOLID SOLUTIONS OF URANIUM OXIDE
activity since gaseous UOS volatilizes from the solution in oxidizing atmospheres above 1000".lo The vaporization process may be visualized from eq 1. U,Thi-,02+z
+ 36502(g) e 6uoa(g)
+ U,-,Thi-&h+z
(1)
If 6 is small, the amount of gas removed does not significantly change the composition of the solution, and the uranium dioxide activity may be determined from the partial pressures of UOS and 0 2 gas in equilibrium with the solution. Since a fixed oxygen pressure is required to maintain the U03 pressure constant, the transpiration method is a convenient one in that air can be used as the carrier gas. High oxygen pressures, however, result in excess oxygen in the solid solution and the activity of U02 cannot be determined directly a t the stoichiometric composition U,Thl_,O2. Fortunately, we know, approximately, the variation of the oxygen activity as a function of excess oxygen, which allows us to calculate the uranium dioxide activity at the stoichiometric composition. Using the activity measurements of two of the components in the system we can delineate more clearly the mixing behavior of the urania-thoria solid solution.
Experimental Section The transpiration apparatus used for measuring the U03 partial pressure consisted of a dense, gas-tight muffle of Alz03 (Morganite) in a Pt-Rh wire-wound furnace capable of achieving temperatures of 1600". A rhodium boat containing a powder (- 325 mesh) of the solid solution was placed in the hot zone of the muffle and dry carrier gas was passed over the boat and exhausted through a small hole in a platinum condenser, The carrier gas saturated with uranium oxide vapors passed 1hrough the platinum condenser where the uranium oxide vapor condensed and then through a flowmeter. The platinum collector was leached after the run (1-100 hr) and the number of moles of uranium collected was determined fluorometrically. The UOa partid pressure was determined from the ratio of the moles of uranium collected to the moles of air multiplied by the absolute pressure which in all cases was 1 atm. The technique and system were calibrated by measuring the vapor pressure over us08 powder at 1300" in air. The results were within 20% of the work reported by others;lo,l1 the relative standard deviation mas about 50%. The flow rate was varied between 50 and 200 cc/min for several of the solid solutions studied. I n all cases the UOS partial
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pressure was insensitive to the flow rate, an indication that the carrier gas was saturated. Most measurements were taken at flow rates between 90 and 130 cc/min. The temperature was measured with an optical pyrometer sighted on the sample and the end of the collector tube. Thermocouples placed in the charge gave readings which differed by less than 5" from the temperatures read optically. The solid solutions were prepared by blending the oxide powders (-325 mesh), heating the blended powders in air a t 1850", and then impact-milling the product to -325 mesh powder. About 10 g of charge was used and the net loss of uranium determined by chemical analysis was 0.20 and for all values of x except possibly near the limit of the integration, x = 0. The limit, x = 0, corresponds to U(1V) and xo corresponds to approximately U(V) over most values of y. Over 0 I x 5 xo,BO?, Ro,, and SO, may be represented as nearly linear functions of 5 or x' for a given y as shown in Table 111. These relationships were obtained by plotting the available data as a function of x' and drawing the best straight line. Since the data were obtained at temperatures a few hundred degrees below 1300", B o z and Soz were assumed to be temperature independent and GO, mas estimated at 1300" by adding a correction term of -ATSO,. These functions were selected at values of y near the compositions used in the transpiration study. The functions at y = 0.06 are approximate since data existed for only two values of 2'. -4s x' approaches zero, it is expected that the partial molar free energy will become rapidly more negative at all values of y similar to observations made by Markin and Roberts" for UOZ. Since this change occurs over narrow ranges of x' (-0.002) the contribution to the integral should be small and nearly equivalent for all y. Thus, it seems reasonable to evaluate eq 9 using linear relations of Go1, and So, as a function of x'.
+
noz,
b (1 - Y>-
Bo,
pGoz(at Po) 1-P
(8)
po represents the mole fraction of excess molecular oxygen at the oxygen pressure of 0.2 atm. Since p = (x/2)/[1 (x/2)], eq 8 transforms to (9). The limit of
+
RT In
integration, xo, is the amount of excess oxygen per mole of cation in equilibrium with 0.2 atm of oxygen gas at 1300". GO, (at xo) is RT In (0.2) or -5.0 kcal/mole of 0 2 for all values of y. The integral is evaluated for a constant value of y. If Gozis known as a function of x for particular values of y, the U02 activity change can be determined; the attainable accuracy, however, is limited somewhat because of the difficulty of evaluating derivatives of the partial molar functions.
Table 111: Partial Molar Free Energy, Enthalpy, and Entropy Relations as a Function of Excess Oxygen at 1300' Compn Y
0.52' 0 29' 0.065
BOl,
kcallmole
862'
742' 192'
- 49 - 42 - 13
S'OZI
GO?, kcal/mole
eu
-54 62' - 70 -24 h' 67 CU. -44
-78.5,' - 14 -862' - 13 Ca. -22
-
Roberts5 has shown for constant x' = 0.175 that the partial molar enthalpy exhibits only small variations with y until y < 0.20 and the entropy changes sharply only when y < 0.05. He attributes this behavior to local trapping of the excess oxygen because strong reaction occurs with uranium ion neighbors nearby. (16) C. Wagner, "Thermodynamics of Alloys." Addison-Wesley Publishing Co., Reading, Mass., 1952, p 19. (17) T . L. Markin and L. E. J. Roberts, Symposium on Thermodynamics of Nuclear Materials, May 1962, International Atomic Energy Agency, Vienna, 1962, p 701.
Volume 70,Number 4
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E. A. AITKEN,J. A. EDWARDS, AND R. A. JOSEPH
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If this is so, then the partial molar quantities to a first approximation would be determined uniquely by x' and not x. The empirical equations in Table I11 for a given region of y would vary with y only as x' varies with y. Therefore, c o n = C(x/y) D and &o,/ dy = -Cx/yz, where C and D are the coefficients to the linear equation in Table 111. If we replace; co2and dGo,/dy (in eq 9) wit,h these algebraic expressions and evaluate, the right-hand side reduces t'o -Cxoz/4y2. The coefficient, C, will be different for various values of y o Dividing -Cxo2/ 4y2 by RT and solving, we get
+
the enthalpy of sublimation from a particular solid solution shown in Table I. AHlois obtained from the int egra1
{JRO2$}
y
-
constant
where the algebraic expression for Ro, is listed in Table 111. A H 1 2 is obtained from the sum of enthalpy of sublimation of UOa from U02.e1 and the enthalpy of oxidation of 1 mole of UOz.ooto UOz.61,which was listed earlier as -22.5 kcal/gfw of U. The enthalpy of 2 kcal/ sublimation for UOz.61 from Table I is 84.3 gfw of U, making AHlz = 61.8 i 2 kcal/gfw of U. Table IV compares the calculated sum of AH10 and AH11 with AHlz, and it is apparent that there is reasonable agreement over the range of y. The deviation is largest at y = 0.06 but within experimental error.
*
The exponential term is listed in the fourth column of Table I1 as a correction factor. Evaluation of eq 9 by graphical determination of Boz and dcoz/by indicates that the correction factor at y = 0.06 is probably higher than the value of 1.3 obtained algebraically. Because of the paucity of Table IV : Enthalpy Comparison for Reactions data the correction factor at y = 0.06 is more uncer10, 11, and 12 (kcal)" tain. Graphical evaluation at other values of y give correction factors which are in reasonable agreement AHia AHii AHia f AHii AH12 with the values obtained algebraically. Y (12) (*3) (*2.0) The activity coefficient for UOZ listed in the last 0.52 ( -20.9) column of Table I1 is obtained by dividing a ~ 0 , ( ~ , 0 ) 0.50 -20.9 84.6 63.7 61.8 by y. The activity coefficients within experimental 0.29 (-18.2) 0.25 -17.3 79.1 61.8 61.8 error are essentially unity over the range of y which 0.20 -16.5 74.1 57.6 61.8 indicates that the stoichiometric solid solution is 0.06 (-9.5) nearly ideal. Nonideal behavior in the activity 0.06 --9.5 66.0 -56.5 61.8 of UOZ is attributed almost completely, therefore, to a Numbers in parentheses are calculated from data of ref 5 the excess oxygen. This is consistent with Roberts' and 7 ; intermediate values were estimated by interpolation. suggestion that the excess oxygen atoms interact strongly with the uranium ions in the solid solution, while the thorium ions are principally a diluent. The entropy relations between reactions 10, 11, and Enthalpy and Entropy of Mixing. Some indication 12 should be similar to the enthalpy relation except of solid solution behavior can be obtained from the for an added configurational term because of the enthalpy and entropy of sublimation but with less random distribution of thorium and uranium atoms. accuracy than from the activity data. Ideal solutions Again, if the entropy change upon adding excess oxyhave no enthalpy of mixing and the entropy of mixing gen occurs because of its localization with uranium is random. If the heats of mixing are caused only by ASlo ASl, = ASl2 R In y. Evaluating ions, then reactions between uranium ions and excess oxygen, these terms in a similar manner as the enthalpy terms, then the presence of T h o z is secondary and the partial we compare the last two columns in Table V. Again reactions 10 and 11 should be equivalent to the total there is substantial agreement within experimental AH11. AH11 is reaction 12. Thus, AHlz = AH10 error except at y = 0.06. These arguments based on enthalpy and entropy considerations are not inconsistent with the activity results, which together with the knowledge that the stoichiometric solid solution obeys Vegard's law indicates that the solution is ideal at 1300" when stoichio-
+
+
The Journal of Physical Chemistry
+
THERMODYNAMIC STUDY OF SOLID SOLUTIONS OF URANIUM OXIDE
1089
Table V: Entropy Comparison for Reactions 10, 11, and 12 (entropy units)"
Y
0.52 0.50 0.29 0.25 0.20 0.06 0.06
+ AS11
AS12
+
R In u
ASIQ
ASii
(f1.0)
(f0.7)
(dz1.5)
(f2.0)
30.2
21.8
20.2
26.0 22.7
17.8 15.1
18.8 18.4
16.5
11.8
16.1
(-8.4) -8.4 (-8.6) -8.2 -7.6 (-4.7) -4.7
Aslo
Numbers in parentheses are calculated from data of ref 5 and 7; intermediate values were estimated by interpolation.
metric. When excess oxygen is present, negative departure from ideality occurs which is caused principally by the localized interaction of oxygen interstitials with the uranium ions. Total Free Energy us. Composition. Ackermann, et aZ.,l* list the standard free energy of formation of Th02(s) as follows.
+
AGr" (ThOz) = -296,000
46.38T(20W300OoK)cal/gfw of T h
Uranium c a t i o n fraction, y
Figure 1. Free energy of formation of U,Thl-,02 a t 1300".
function of composition, y, is shown in Figure 1. From the integral
Assuming that the free-energy equation is valid to 1573°K AGt"(ThO2 at 1573°K) = -223,040 cal/gfw of T h Alexanderll recently derived the standard free energy equation for uO2.61(s) as AGt"(U0z.a) = -279,700 f .~ ...., 48.48T(1300-18000K) cal/gfw of from which we obtain at 1573°K AGf"(UOz.6i at 1573°K)
=
-203,440 Cal/gfw
Of
u
Since AG for oxidation of UOz.o to UOz.t,l is -7620 cal/gfw of U at 1573"K, we get by subtraction
AGr" (UOz.oat 1573°K) = - 195,820 cal/gfw of U The standard free energies of formation have an absolute accuracy of only 2000 cal/mole. Assuming that the stoichiometric solid solution is ideal, the total free energy of formation of the solution is calculated from eq 13. The freeenergy curve as a
+ +
A G ~(y,O) " = y AGr" (UOz) (1 - y)AGr"(ThOz) R[y In Y (1 - Y) In (1 - Y)1
+
(13)
the free-energy change between AGf"(y,O) and AGf"(y,zo) is obtained for various values of y. If we use the equations for dol in Table 111, the free-energy change on oxidation to the nonstoichiometric solid solution in equilibrium with 0.2 atm of O2 at 1300" is, respectively, -6.9, -5.9, and -1.9 kcal/gfw of U for u values of 0.52, 0.29, and 0.06. Using- these values for the free energy of formation, we can draw a curve in Figure 1 for the nonstoichiometric solid solution. For u > 0.5 the curve must extend upward and approach AGf" (UOz.25) because no further oxygen can be added to the fluorite phase without precipitating uoz.6i.
AGf"(UOz.61)and AGf"(UOz.25) are shown as points at the right-hand side of Figure 1. There is no known solubility of thorium oxide in U308--zphase; therefore, the minimum in the free energy us. composition for UOz.61occurs at y = 1. If we draw a dashed straight line from the value for U02.61and tangent to the nonstoichiometric curve, the point of tangency occurs in the vicinity of 0.5 > y > 0.6. For y larger than the (18) R. J. Ackermann, E. G. Rauh, R. J. Thorn, and M. C. Cannon, J . Phys. Chem., 67, 762 (1963).
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E. A. AITKENAND R. A. JOSEPH
1090
point of tangency, precipitation of U02.s1would occur. This is in agreement with the results obtained from Xray diffraction measurements.6
Acknowledgment. The authors wish to acknowledge the technical contributions of S. F. Bartram, K. M. Bohlander, H. S. Edwards, and E. A. Schaefer.
Thermodynamic Study of Solid Solutions of Uranium Oxide. 11. Uranium Oxide-Y ttrium Oxide1
by E. A. Aitken and R. A. Joseph General Electric Company, Nuclear Materials and Propulsion Operation, Cincinnati, Ohio (Received September 20, 1966)
The activity of uranium dioxide in solid solutions of U,Y1-,02-, along a selected composition line was measured by the transpiration method. The partial pressure of UOs gas in a carrier gas of air (0.2 atm of 02)or C02-CO mixture was obtained between 1200 and 1700" and related to the U 0 2 activity of the solid solution according to the equation UOz(in solid soln)
+ 1/202(g)
UOa(g)
A large negative departure from Raoult's law was obtained a t 1300". The U02 activity measured a t two different oxygen partial pressures differed significantly. However, if the solid solution was visualized as a pseudobinary mixture of UO2+,t and YO1.5, the effect of oxygen pressure on the activity could be largely eliminated. The results could then be expressed according to a binary regular solution model with an at,tractive interaction energy term of about 41 kcal. The linear relation between log activity coefficient and (1 - y ) 2 appeared to be independent of the average valence and the degree of anion deficiency. Examination of the enthalpy and entropy of vaporization indicated that the regular solution model did not properly describe the enthalpy and entropy changes on mixing; however, qualitatively these differences were largely the result of volume changes on mixing, which the regular solution model ignores. Additions of Zr02 to solid solutions of uranium oxide-yttrium oxide caused an increase in U02 activity but no change was observed with T h o 2 additions.
Introduction A previous study2& of U02-Th02 solid solutions showed that the U02 activity followed Raoult's law provided the compound was stoichiometric with respect to oxygen to metal ratio [constant U(IV)]. If the average uranium valence was increased by accommodating excess oxygen, interstitially, a negative departure from ideal behavior was observed. To understand The Journal of Phusicd Chemistry
further the effect of valence changes on TJOz activity, solid solutions of U0z+z-Y203 were studied. These two oxides are not completely miscible but there is (1) This paper originated from work sponsored by the Fuels and Materials Development Branch, Atomic Energy Commission, under Contract AT(40-1)-2847. (2) (a) E. A. Aitken, J. A. Edwards, and R. A. Joseph, J . Phys. Chem., 70, 1084 (1966); (b) 9.F. Bartram, E. F. Juenke, and E. A. Aitken, J . A m . Ceram. SOC.,47, 171 (1964).
