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Molar Gibbs energy formation of RbUO3(s)
ELSEVIER
Journal of NuclearMaterials 232 (1996) 233-239
Molar Gibbs energy formation of
RbUO3(s)
K. Jayanthi, V.S. Iyer, G.A. Rama Rao, V. Venugopal * Fuel Chemistry Division, Bhabha Atomic Research Centre, Trombay, Bombay 400 085, India
Received 27 November 1995; accepted 26 April 1996
Abstract The molar Gibbs energy of formation of RbUO3(s) was determined by measuring the oxygen pressure over the phase field, RbUO3(s) + Rb2U2OT(S)+ Rb2UOa(s), using a solid oxide electrolyte galvanic cell in the temperature range 920 to 1100 K and the partial pressure of rubidium using the Knudsen effusion mass loss method in the temperature range 1305 to 1459 K. The oxygen potential and the rubidium potential existing over the phase field can be respectively given by A/x(O2) + 0.4(kJ mol-]) = -531.6 + 0.2026T(K) and A/x(Rb) + 0.6(kJ mol-]) = - 152.7 + 0.018T(K).
1. Introduction Mixed (U, Pu)O 2 is a candidate fuel for a fast breeder reactor. The behaviour of the oxide fuel and the interaction of fission products with fuel, clad and coolant are being investigated in several laboratories. The fission products like Cs, Rb have been found to migrate axially leading to the formation of voluminous alkali metal uranates at the interface of the mixed oxide fuel and the uranium oxide axial blanket [1-3]. Though the fast fission yield of rubidium is small (20% of Cs fission yield) it has been found to be associated with Cs [4]. Thermodynamic properties of the ternary oxides in the R b - U - O system compared to oxides in the C s - U - O system [5-8] are not reported well in the literature. The thermodynamic properties of some of the rubidium uranates are discussed by O'Hare and Hoekstra [8]. The thermal and thermodynamic properties of Rb2U40 x where x = 11, 12 and 13 were studied in detail and reported earlier [9-11]. The compound with pentavalent uranium, RbUO3(s) has been prepared and identified [12,13]. The enthalpy and entropy of formation of the normal uranate, Rb2UO4(s) have been reported [14,15]. Lindemer et al. [16] have reported the thermodynamic properties of the uranates of rubidium using computational method. Cordfunke and
* Corresponding author.
Ouweltjes [17] have determined the enthalpies of solution of MUO 3 (M = Li, Na, K, Rb) by calorimetry. There is a paucity of information on the enthalpy or entropy values of ternary uranates. According to the revised phase diagram reported by Iyer et al. [9], RbUO3(s) coexists with Rb2U207(s) and Rb2UO4(s) up to 1100 K. In the present study the oxygen potential over the phase field Rb2U207(s) + RbzUO4(s) + RbUO3(s) were determined by measuring the emf using a solid oxide electrolyte galvanic cell. The Rb pressure in the phase field was measured using the Knudsen effusion mass loss method using a vacuum micro balance.
2. Experimental
2.1. Materials
Rb2U207(s) and Rb2UO4(s) were prepared by reacting high purity Rb2CO3(s) with U30 8 in air in 3:2 and 3:1 mole ratios respectively, in an alumina boat at 1000 K for 16 h. The product was exclusively identified as Rb2UzOT(S) and Rb2UO4(s). RbUO3(s) was prepared by reducing Rb2U207(s) in pure hydrogen at 1000 K in an alumina boat. The X-ray diffraction pattern obtained for the above compound was matching with the one reported for RbUO3(s) [18]. RbUO3(s), Rb2U2OT(s) and Rb2UOa(s) were mixed in 3:1:2 mole ratio and made in the form of
0022-3115/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0022-3115(96)00398-4
234
K. Jayanthi et al. / Journal o/" Nuclear Materials 232 (1996) 233-239
BEAM
I~,~
~
[
,,
2.2. E m f m e a s u r e m e n t s
A 15 mol% calcium oxide stabilized zirconia electrolyte (CSZ) in the form of a tube was used for the measurement of equilibrium emf over the phase field RbUO3(s) + Rb2UO4(s). The cell was tested by measuring the emf generated over the system Ni(s) + NiO(s) using air as a reference electrode. The cells used in the present study can be represented by
SAMPLEIN BORON NIT~IOE ~ A ~'~ KNUDSENCELL--k~q~L,I J~"~l
~
- -
FURNACE~--~~
-
-
T H E R M O W E L L
~'~'~KNUOSEN CELL
I III I
~
~_.s
~/'/j
~/7_/~
Cell I: PtJRbUO3(s ) + Rb2UO4(s )
WITH KNIFE EDGED
+ Rb2U207 (s)JCSZJair, Pt
O,,F,CE
Cell [I: PtjRbUO3(s ) + Rb2UO4(s )
THERMO-COUPLE ~
+ RbzU2Ov(s)lfSZlNi(s ) + NiO(s)lPt. High purity argon cover gas was used for the experiments. The temperature was measured accurately with in +1 K using a calibrated chromel-alumel thermocouple according to IPTS-68 [19]. The details of the experimental assembly and the method of measurement have been reported in an earlier publication [20]. The emf's were measured using two different pellets, both in the heating and cooling cycles
Fig. 1. Block diagram of the experimental set up for the Knudsen effusion mass loss assembly.
pellets of 6 mm diameter and 3 mm thickness by pressing at 100 MPa pressure. These pellets were degassed under vacuum and used for all measurements.
A:
BEFORE
B : AFTER
EXPT. EXPT.
%
10
20
30
40
50
60
2o
Fig. 2. XRD pattern of the sample pellet of the mixture: RbUO3(s) + Rb2UO4(s) + Rb2U207(s) belore and alter the experiment.
235
K. Jayanthi et al. / Journal of Nuclear Materials 232 (1996) 233-239
with a precision + 2 mV. The pellets after experiment were subjected to X-ray powder diffraction analysis (XRD). 2.3. Knudsen effusion mass loss method
The rubidium pressure is generated from the coexisting phases, RbUO3(s) + RbzUO4(s) + RbaU2Ov(s) from the following reaction: RbaUOn(s ) + 3rbUO3(s ) + ½02(g) = 2rbaUzOv(s ) + Rb(g). The rubidium pressure was obtained by measuring the mass loss of Rb from a Knudsen effusion cell using a Cahn vacuum microbalance capable of detecting 1 /zg. The block diagram showing the experimental setup is shown in Fig. 1. The performance of the microbalance was tested by measuring the tellurium vapour pressure over tellurium(s) in the temperature range 614 to 713 K. High purity tellurium was contained in a graphite Knudsen cell of 14 mm height and 8 mm width with a central orifice of 1 mm on the lid. The cell had a Clausing factor of 0.694 [21]. The cell was heated in an isothermal zone of a resistance furnace and the temperature was maintained within + 1 K. A chromel-alumel thermocouple was positioned just near the Knudsen cell. The thermocouples used for the measurement of temperature were calibrated by
measuring the melting temperatures of ice, antimony and silver [19]. Using the partial pressure values of Tea(g) obtained from the graphite cell and the mass loss of Te 2 from the boron nitride Knudsen cell the Clausing factor of boron nitride cell was determined. This Clausing factor was subsequently used for the evaluation of rubidium pressures. A mixture of RbUO3(s) + RbaUaO7(s) + RbaUO4(s) along with Ni(s) + NiO(s) in the form of a small pellet was used in the experiments. The pellet approximately weighing 50 mg was loaded in the calibrated boron nitride Knudsen cell. The mass loss was monitored in a strip chart recorder with 1 mg at full scale in the temperature range 1305 to 1459 K. The XRD pattern before and after the experiment remained same indicating the absence of any reaction between the compounds used in the study.
3. Results and discussion 3.1. E m f studies
Fig. 2 shows the XRD pattern taken for the samples before and after experiments. It can be seen that there was no additional line, indicating the absence of any reaction between the compounds. Hence it confirms the coexistence of the compounds up to 1400 K.
870
'~
0
: PELLET
1
860 -
850 -
>
E
o
840 -
830
820
810
800
I
900
1000
110q
T(K) Fig. 3. Dependence of emf (mV) on temperature T (K) for the cell: PtlRbUO~(s) + RbaUO4(s) + RbaUaOT(s)lCSZlair(p(O 2) = 21.21 kPa)lPt.
236
K. Jayanthi et al. / Journal qf Nuclear Materials 232 (1996) 233-239
Table 1 Dependence of emf (mV) on temperature T (K) for cell I: PtlRbUO3(s) + Rb2UO4(s) + RbzU2OT(s)JCSZlair(p(O 2 ) = 21.21 kPa), Pt T(K)
Emf(mV)
T(K)
Emf(mV)
T (K)
Emf(mV)
864 855 854
t010 1022 1026 1037
847 840 838 834
1056 1062 1078 1091
824 821 810 806
1019 1032 1042
843 835 832
1048 1056 1066 1090
828 824 820 805
Table 2 Dependence of emf (mV) on temperature T (K) for cell lh PtJRbUO3(s) + RbzUO4(s)+ Rb2U20 7(s)JCSZINi(s) + NiO(s)JPt T (K) 974 983 989
Pel~tI
981 993 998
858 851 846
T (K)
Emf (mV)
125.0 122.0 121.0
1010 1040 1073 1100
120 ll7 113 107
127.0 124.0 120.0 118.0
1073 1020 1035 1055 1090
111 118 116 115 109
Pelletll
920 971 1002 11)15
Pellet 11
990 1005 1015
Emf (mV)
Pelletl
The respective reactions for cell I and II can be written
experimental temperatures. The emf values were least squares fitted against temperatures and can be given by
as
E~ ( m V ) 4- 1.0 = 1377 - 0.525T ( K ) ,
981-1091 K,
3RbUO3(s ) + RbzUOa(s ) + ½02(8)
3RbUO3(s )
(3) I)
= 2RbzUzOv(s) + R b ( g ) ,
+ Rb2UO4(s ) + NiO(s)
= 2RbzUzOv(s) + Ni(s) + Rb(g).
E,, ( m V ) 4- 0.9 = 234 - 0.114T ( K ) ,
920-1100 K,
(4) (2)
Tables 1 and 2 give the emf values of cell I and II at the
respectively. The emf's for a cell of Ni(s) + NiO(s) against air can be obtained from the subtraction of E . from E~.
130
~'~
0
: PELLET
I
120-
>
E
o
110-
100
[
900
1000
1100
T(K} Fig. 4. Dependence of emf (mV) on temperature T (K) for the cell: PtJRbUQ(s) + Rb2UO4(s) + Rb2U2OT(s)ICSZrNi(s) + NiO(s)lPt.
K. Jayanthi et al. / Journal of Nuclear Materials 232 (1996) 233-239 Table 3 Dependence of p(Te2)(g) over Te(s) on temperature T (K) for graphite Knudsen cell T (K) 614 622 634 645 658 669 679
dw/dt (g s-1 )
p (kPa)
p (kPa) [22]
10 7
10 4
10 4
1.097 1.778 2.820 4.800 8.080 13.20 20.53
2.087 3.121 4.995 8.600 14.590 24.010 36.610
2.023 3.040 5.490 9.150 16.730 27.133 38.510
237
Table 4 Dependence of p(Tez)(g) over Te(s) on temperature T (K) for boron nitride Knudsen cell T (K)
d w / d t (g s t ) 106
p(Te 2) (kPa) 103
k (Clausing factor)
622 634 647 661 675 694
0.621 1.148 2.065 3.796 7.500 7.530
0.304 0.548 1.015 1.913 3.506 3.566
0.91 0.94 0.92 0.92 0.99 0.99
mental set up. Table 4 gives the mass loss of Te2(g) from the boron nitride Knudsen cell from 614 to 713 K along with the vapour pressure of Te2(g) over Te(s) from Ref. [21 ]. The Clausing factor of the Knudsen cell was obtained from the mass loss and the p(Te 2) from Ref. [21] using the equation
These emf's agree excellently with the values obtained in the previous study [20]. This indicates the reliability of the present measurements. Hence all the subsequent calculations were carried out based on cell reaction (1) using air as a standard reference. Figs. 3 and 4 show the comparison of the experimental emf values with the fit values for cells I and II.
p (kPa) = ( d w / d t ) ( l O 1 . 3 2 5 / 4 4 . 3 3 )
× (1/a)(1/k)(~/T/M),
3.2. Knudsen effusion mass loss studies
(5)
where p is the pressure in kPa of Tez(g) from Refs. [22,23], d w / d t is the mass loss in g s - I , T is the temperature in K, M was taken as 0.2552 kg mol-~, a is the area of cross-section of the orifice which is assumed constant throughout the experiment, and k is the Clausing factor of the cell. The calculated value of k = 0.945.
Table 3 gives the comparison of tellurium pressure over Te(s) obtained in the present experiment with the literature values. It is seen from the table that the present values are in good agreement indicating the reliability of the experi-
-4.5
-4.6
-4.7 O E
0.
-4.8
-4.9
0
0
-5.0
-5.1
-5.2 6.8
,
,
6.9
7.0
l 7.1
, 7.2
,
~
7.3
7.4
, 7.5
, 7.6
7.7
1/T(K)
Fig. 5. Variation of log p(Rb) with 1/T for the reaction: RbUO3(s) + Rb2UO4(s) + 1/202(g) = 2Rb2U2OT(S) + Rb(g).
238
K. Jayanthi et al. / Journal ()f Nuclear Materials 232 (1996) 233-239
Table 5 Dependence of p(Rb) (kPa) on temperature T (K) for the reaction: 3RbUO3(s) + Rb_,UO4(s) + 1/2 O2(g) = 2Rb~U~OT(s) + Rb(g) T(K) 1305 1332 1344 1373 1396 1418 1459
dw/dt(gs
I)
sal gas constant and the standard state of Rb is taken as Rb(g) at 101.325 kPa and the Gibbs energy is zero at all temperatures. The Gibbs free energy of reaction (1) is given by
p(kPa)
10 6
10 5
a , G ° + 0.7 (kJ) = - 113.08 + 0.0830T ( K ) .
0.599 0.666 0.725 1.320 1.500 1.607 2.254
0.750 0.842 0.921 1.395 1.803 2.099 2.985
The molar Gibbs energy of formation of Rb2UO4(s) and Rb2U2OT(S) were calculated from the enthalpy and entropy of formation at 298 K from literature [16,24] and can be given by ~rG°(Rb2UO4) _+ 1.4 kJ mol -
1913 + 0.425T ( K )
i ( 9 2 0 - 1 4 5 9 K),
~ f G ° ( R b 2 U 2 0 7 ) + 3.0 kJ mol Table 5 gives the mass loss of Rb at each isothermal temperature over the co-existing phase and the corresponding pressures. The rubidium pressure in the reaction (1) was calculated using Eq. (5). The molar mass of Rb was taken as 85.47. The rubidium pressures were least squares fitted with temperature and can be given by log p (kPa) _+ 0.33 = ( - 7 9 7 7 / T
( K ) ) + 2.95.
= - 3232 + 0.674T ( K )
A/x(O 2) _+ 0.4 (kJ m o l - ' ) (920-1091 K).
(7)
The rubidium potential over the phase field: RbUO3(s) + Rb2U207(s) + Rb2UO4(s), can be defined as ~/x(Rb) = R T In PRb" The dependence of rubidium potential on temperature can be represented by ')
= - 152.7 + 0.018T ( K )
/ ( 9 2 0 - 1 4 5 9 K).
( 1 3 0 5 - 1 4 5 9 K).
(8)
The Gibbs energy changes for the cell reaction (1) can be given by A~G = - 2 F E = - R T In K where K is the equilibrium constant ( K = [ p ( R b ) / p ( O 2) and R is the univer-
~ G ° ( R b U O 3 ) + 3.4 (kJ m o l - ' ) ( 9 2 0 - 1 4 5 9 K).
Phase fields
T(K) 1000
Rb2U4Otl + Rb2U4Oi2 [ 2 3 ] RbUO~ + Rb2U207+ Rb2UO~ ' Rb2U4OI2 + Rb2U4013 [23] ~ Present study.
~(O~)
356 329 95
(12)
The molar Gibbs energy of Rb2UO 4 and Rb2U20 7 were calculated from the enthalpy of formation at 298 K and entropy of formation (calculated from ~98K (16) values) at 298 K using the relation: AfGT= AfH;98KTAfS;98K. In the absence of reliable Ct, values, it is assumed that the enthalpy and entropy changes due to variation of Ct, with temperature are negligible. An error of 3.4 kJ mol ~ shown in the molar Gibbs energy of formation of RbUO3(s) is mainly attributed to the error approximation made in the molar Gibbs energy formation values of Rb2UO4(s) and Rb2U207(s). The enthalpy of tbrmation at 298 K of RbUO 3 is reported to be - 1520.9 + 1.7 kJ tool- t [24]. The present value ( - 1479 kJ mol ~), from Eq. (12) is less negative as expected. The oxygen potential existing over the coexisting phase fields in the R b - U - O system along with the rubidium pressure in the temperature range 1000 to 1450 K are shown in Table 6.
Table 6 The oxygen potential [ - ~/x(O 2)] and the rubidium potential [ - ~ / x ( R b ) = RT In PRb] at 1000, 1100 and 1200 K
-
(11)
Using the molar Gibbs energy formation of Rb2UO4(s) and Rb2U2Ov(s) and the Gibbs molar free energy change for reaction (2), the molar Gibbs energy formation of RbUO3(s) is calculated and can be given by
= - 1479 + 0.278T ( K )
A/x(Rb) + 0.6 (kJ mol
(10)
(6)
The pressure values at the experimental temperatures are compared with the fit values in Fig. 5. The oxygen potential existing over the system R b U O 3 ( s ) + R b 2 U 2 0 7 ( s ) + Rb2UOn(s) for cell I after correction of 0 2 to 101.325 kPa can be represented by
= -531.6+0.2026T(K)
(9)
It00
1200
- ~(Rb)
- A~(O 2 ) (kJ mol i)
-A~(Rb)
- ~ ( O 2)
- A~(Rb)
134.7 --
314 308 84
132.9 -
273 288 59
131.0 -
K. Jayanthi et al. / Journal of Nuclear Materials 232 (1996) 233-239
Acknowledgements The authors are thankful to Dr D.D. Sood, Director Radio Chemistry and Isotope Group, and Dr H.C. Jain, Head Fuel Chemistry Division, for their constant encouragement during the course of this work.
References [1] D.C. Fee, I. Johnson, S.A. Davis, G.A. Shinn, G. Staahl and C.E. Johnson, Oak Ridge National Laboratory Report, ANL76-126 (1977). [2] D.C. Fee and C.E. Johnson, J. Nucl. Mater. 96 (1981) 80. [3] G.S. Schumancher and S.A. Wright, J. Nucl. Mater. 21 (1985) 130. [4] M.E. Meek and B.F. Rider, General Electric Report No. APED-5398 (1968). [5] A.B. Van Egmond and E.H.P. Cordfunke, J. Inorg. Nucl. Chem. 38 (1976) 2245. [6] E.H.P. Cordfunke, A.B. Van Egmond and G. Van Voors, J. Inorg. Nucl. Chem. 37 (1975) 185. [7] E.H.P. Cordfunke, Proc. IAEA Symp. on Thermodynamics of Nuclear Materials 2 (1974) 185. [8] P.A.G. O'Hare and H.R. Hoekstra, J. Chem. Thermodyn. 7 (1975) 831. [9] V.S. Iyer, K. Jayanthi, S.K. Sali, S. Sampath and V. Venugopal, J. Alloys Compounds (1995), accepted. [10] V. Venugopal, V.S. Iyer and K. Jayanthi, J. Nucl. Mater. 199 (1992) 29.
239
[11] V.S. Iyer, V. Venugopal and D.D. Sood, J. Radio Anal. Nucl. Chem. 143 (1990) 157. [12] W. Ruedoff, S. Kemmeler Sack and H. Leutner, Angew. Chem. 74 (1962) 429. [13] S. Kemmler Sack and W. Ruedorff, Z. Anorg. Allg. Chem. 354 (1967) 255. [14] E.H.P. Cordfunke and P.A.G. O'Hare, eds., The Chemical Thermodyn. Actinide Elem. Comp., Part 3. Misc. Actinide Compounds (IAEA, Vienna, 1978). [15] E.A. Ippolotova, D.G. Faustova and V.I. Splitsyn, in: Proc. Symp. on Invest into the Field of Uranium Chem., Moscow Univ., ed. V.I. Spitsyn, 1961, Argonne National Lab. Report, ANL-Trans-33 (1964) 170. [16] T.B. Lindemer, T.M. Besmann and C.E. Johnson. J. Nucl. Mater. 100 (1981) 178. [17] E.H.P. Cordfunke and W. Ouweltjes, J. Chem. Thermodyn. 13 (1981) 187. [18] A. van Egmond, JCPDS Powder diflYaction file 2, 1-43 (1993). [19] International Practical Temperature Scale, 1968, Amended Edition 1975, HMSO London, 1976, Metrologia 12 (1976) 7. [20] V. Venugopal, V.S. lyer, V. Sunderesh, Z. Singh, R. Prasad and D.D. Sood, J. Chem. Thermodyn. 19 (1987) 19. [21] R.A. Rapp, ed., Physicochemical Measurements in Metal Research, Technique of Metal Research, Vol. 4, Part 1, series ed. R.F. Bunshah (Wiley, New York, 1970) ch. 2. [22] O. Kubeschewski and C.B. Alcock, Metallurgical Thermochemistry, 5th Ed. (Pergmon, Oxford, 1979). [23] K.C. Mills, Thermodynamic Data for Inorganic sulphides, Selenides and Tellurides (Butterworths, London, 1974). [24] J. Fuger, J. Nucl. Mater. 130 (1985) 253.
Journal of NuclearMaterials 232 (1996) 233-239
Molar Gibbs energy formation of
RbUO3(s)
K. Jayanthi, V.S. Iyer, G.A. Rama Rao, V. Venugopal * Fuel Chemistry Division, Bhabha Atomic Research Centre, Trombay, Bombay 400 085, India
Received 27 November 1995; accepted 26 April 1996
Abstract The molar Gibbs energy of formation of RbUO3(s) was determined by measuring the oxygen pressure over the phase field, RbUO3(s) + Rb2U2OT(S)+ Rb2UOa(s), using a solid oxide electrolyte galvanic cell in the temperature range 920 to 1100 K and the partial pressure of rubidium using the Knudsen effusion mass loss method in the temperature range 1305 to 1459 K. The oxygen potential and the rubidium potential existing over the phase field can be respectively given by A/x(O2) + 0.4(kJ mol-]) = -531.6 + 0.2026T(K) and A/x(Rb) + 0.6(kJ mol-]) = - 152.7 + 0.018T(K).
1. Introduction Mixed (U, Pu)O 2 is a candidate fuel for a fast breeder reactor. The behaviour of the oxide fuel and the interaction of fission products with fuel, clad and coolant are being investigated in several laboratories. The fission products like Cs, Rb have been found to migrate axially leading to the formation of voluminous alkali metal uranates at the interface of the mixed oxide fuel and the uranium oxide axial blanket [1-3]. Though the fast fission yield of rubidium is small (20% of Cs fission yield) it has been found to be associated with Cs [4]. Thermodynamic properties of the ternary oxides in the R b - U - O system compared to oxides in the C s - U - O system [5-8] are not reported well in the literature. The thermodynamic properties of some of the rubidium uranates are discussed by O'Hare and Hoekstra [8]. The thermal and thermodynamic properties of Rb2U40 x where x = 11, 12 and 13 were studied in detail and reported earlier [9-11]. The compound with pentavalent uranium, RbUO3(s) has been prepared and identified [12,13]. The enthalpy and entropy of formation of the normal uranate, Rb2UO4(s) have been reported [14,15]. Lindemer et al. [16] have reported the thermodynamic properties of the uranates of rubidium using computational method. Cordfunke and
* Corresponding author.
Ouweltjes [17] have determined the enthalpies of solution of MUO 3 (M = Li, Na, K, Rb) by calorimetry. There is a paucity of information on the enthalpy or entropy values of ternary uranates. According to the revised phase diagram reported by Iyer et al. [9], RbUO3(s) coexists with Rb2U207(s) and Rb2UO4(s) up to 1100 K. In the present study the oxygen potential over the phase field Rb2U207(s) + RbzUO4(s) + RbUO3(s) were determined by measuring the emf using a solid oxide electrolyte galvanic cell. The Rb pressure in the phase field was measured using the Knudsen effusion mass loss method using a vacuum micro balance.
2. Experimental
2.1. Materials
Rb2U207(s) and Rb2UO4(s) were prepared by reacting high purity Rb2CO3(s) with U30 8 in air in 3:2 and 3:1 mole ratios respectively, in an alumina boat at 1000 K for 16 h. The product was exclusively identified as Rb2UzOT(S) and Rb2UO4(s). RbUO3(s) was prepared by reducing Rb2U207(s) in pure hydrogen at 1000 K in an alumina boat. The X-ray diffraction pattern obtained for the above compound was matching with the one reported for RbUO3(s) [18]. RbUO3(s), Rb2U2OT(s) and Rb2UOa(s) were mixed in 3:1:2 mole ratio and made in the form of
0022-3115/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0022-3115(96)00398-4
234
K. Jayanthi et al. / Journal o/" Nuclear Materials 232 (1996) 233-239
BEAM
I~,~
~
[
,,
2.2. E m f m e a s u r e m e n t s
A 15 mol% calcium oxide stabilized zirconia electrolyte (CSZ) in the form of a tube was used for the measurement of equilibrium emf over the phase field RbUO3(s) + Rb2UO4(s). The cell was tested by measuring the emf generated over the system Ni(s) + NiO(s) using air as a reference electrode. The cells used in the present study can be represented by
SAMPLEIN BORON NIT~IOE ~ A ~'~ KNUDSENCELL--k~q~L,I J~"~l
~
- -
FURNACE~--~~
-
-
T H E R M O W E L L
~'~'~KNUOSEN CELL
I III I
~
~_.s
~/'/j
~/7_/~
Cell I: PtJRbUO3(s ) + Rb2UO4(s )
WITH KNIFE EDGED
+ Rb2U207 (s)JCSZJair, Pt
O,,F,CE
Cell [I: PtjRbUO3(s ) + Rb2UO4(s )
THERMO-COUPLE ~
+ RbzU2Ov(s)lfSZlNi(s ) + NiO(s)lPt. High purity argon cover gas was used for the experiments. The temperature was measured accurately with in +1 K using a calibrated chromel-alumel thermocouple according to IPTS-68 [19]. The details of the experimental assembly and the method of measurement have been reported in an earlier publication [20]. The emf's were measured using two different pellets, both in the heating and cooling cycles
Fig. 1. Block diagram of the experimental set up for the Knudsen effusion mass loss assembly.
pellets of 6 mm diameter and 3 mm thickness by pressing at 100 MPa pressure. These pellets were degassed under vacuum and used for all measurements.
A:
BEFORE
B : AFTER
EXPT. EXPT.
%
10
20
30
40
50
60
2o
Fig. 2. XRD pattern of the sample pellet of the mixture: RbUO3(s) + Rb2UO4(s) + Rb2U207(s) belore and alter the experiment.
235
K. Jayanthi et al. / Journal of Nuclear Materials 232 (1996) 233-239
with a precision + 2 mV. The pellets after experiment were subjected to X-ray powder diffraction analysis (XRD). 2.3. Knudsen effusion mass loss method
The rubidium pressure is generated from the coexisting phases, RbUO3(s) + RbzUO4(s) + RbaU2Ov(s) from the following reaction: RbaUOn(s ) + 3rbUO3(s ) + ½02(g) = 2rbaUzOv(s ) + Rb(g). The rubidium pressure was obtained by measuring the mass loss of Rb from a Knudsen effusion cell using a Cahn vacuum microbalance capable of detecting 1 /zg. The block diagram showing the experimental setup is shown in Fig. 1. The performance of the microbalance was tested by measuring the tellurium vapour pressure over tellurium(s) in the temperature range 614 to 713 K. High purity tellurium was contained in a graphite Knudsen cell of 14 mm height and 8 mm width with a central orifice of 1 mm on the lid. The cell had a Clausing factor of 0.694 [21]. The cell was heated in an isothermal zone of a resistance furnace and the temperature was maintained within + 1 K. A chromel-alumel thermocouple was positioned just near the Knudsen cell. The thermocouples used for the measurement of temperature were calibrated by
measuring the melting temperatures of ice, antimony and silver [19]. Using the partial pressure values of Tea(g) obtained from the graphite cell and the mass loss of Te 2 from the boron nitride Knudsen cell the Clausing factor of boron nitride cell was determined. This Clausing factor was subsequently used for the evaluation of rubidium pressures. A mixture of RbUO3(s) + RbaUaO7(s) + RbaUO4(s) along with Ni(s) + NiO(s) in the form of a small pellet was used in the experiments. The pellet approximately weighing 50 mg was loaded in the calibrated boron nitride Knudsen cell. The mass loss was monitored in a strip chart recorder with 1 mg at full scale in the temperature range 1305 to 1459 K. The XRD pattern before and after the experiment remained same indicating the absence of any reaction between the compounds used in the study.
3. Results and discussion 3.1. E m f studies
Fig. 2 shows the XRD pattern taken for the samples before and after experiments. It can be seen that there was no additional line, indicating the absence of any reaction between the compounds. Hence it confirms the coexistence of the compounds up to 1400 K.
870
'~
0
: PELLET
1
860 -
850 -
>
E
o
840 -
830
820
810
800
I
900
1000
110q
T(K) Fig. 3. Dependence of emf (mV) on temperature T (K) for the cell: PtlRbUO~(s) + RbaUO4(s) + RbaUaOT(s)lCSZlair(p(O 2) = 21.21 kPa)lPt.
236
K. Jayanthi et al. / Journal qf Nuclear Materials 232 (1996) 233-239
Table 1 Dependence of emf (mV) on temperature T (K) for cell I: PtlRbUO3(s) + Rb2UO4(s) + RbzU2OT(s)JCSZlair(p(O 2 ) = 21.21 kPa), Pt T(K)
Emf(mV)
T(K)
Emf(mV)
T (K)
Emf(mV)
864 855 854
t010 1022 1026 1037
847 840 838 834
1056 1062 1078 1091
824 821 810 806
1019 1032 1042
843 835 832
1048 1056 1066 1090
828 824 820 805
Table 2 Dependence of emf (mV) on temperature T (K) for cell lh PtJRbUO3(s) + RbzUO4(s)+ Rb2U20 7(s)JCSZINi(s) + NiO(s)JPt T (K) 974 983 989
Pel~tI
981 993 998
858 851 846
T (K)
Emf (mV)
125.0 122.0 121.0
1010 1040 1073 1100
120 ll7 113 107
127.0 124.0 120.0 118.0
1073 1020 1035 1055 1090
111 118 116 115 109
Pelletll
920 971 1002 11)15
Pellet 11
990 1005 1015
Emf (mV)
Pelletl
The respective reactions for cell I and II can be written
experimental temperatures. The emf values were least squares fitted against temperatures and can be given by
as
E~ ( m V ) 4- 1.0 = 1377 - 0.525T ( K ) ,
981-1091 K,
3RbUO3(s ) + RbzUOa(s ) + ½02(8)
3RbUO3(s )
(3) I)
= 2RbzUzOv(s) + R b ( g ) ,
+ Rb2UO4(s ) + NiO(s)
= 2RbzUzOv(s) + Ni(s) + Rb(g).
E,, ( m V ) 4- 0.9 = 234 - 0.114T ( K ) ,
920-1100 K,
(4) (2)
Tables 1 and 2 give the emf values of cell I and II at the
respectively. The emf's for a cell of Ni(s) + NiO(s) against air can be obtained from the subtraction of E . from E~.
130
~'~
0
: PELLET
I
120-
>
E
o
110-
100
[
900
1000
1100
T(K} Fig. 4. Dependence of emf (mV) on temperature T (K) for the cell: PtJRbUQ(s) + Rb2UO4(s) + Rb2U2OT(s)ICSZrNi(s) + NiO(s)lPt.
K. Jayanthi et al. / Journal of Nuclear Materials 232 (1996) 233-239 Table 3 Dependence of p(Te2)(g) over Te(s) on temperature T (K) for graphite Knudsen cell T (K) 614 622 634 645 658 669 679
dw/dt (g s-1 )
p (kPa)
p (kPa) [22]
10 7
10 4
10 4
1.097 1.778 2.820 4.800 8.080 13.20 20.53
2.087 3.121 4.995 8.600 14.590 24.010 36.610
2.023 3.040 5.490 9.150 16.730 27.133 38.510
237
Table 4 Dependence of p(Tez)(g) over Te(s) on temperature T (K) for boron nitride Knudsen cell T (K)
d w / d t (g s t ) 106
p(Te 2) (kPa) 103
k (Clausing factor)
622 634 647 661 675 694
0.621 1.148 2.065 3.796 7.500 7.530
0.304 0.548 1.015 1.913 3.506 3.566
0.91 0.94 0.92 0.92 0.99 0.99
mental set up. Table 4 gives the mass loss of Te2(g) from the boron nitride Knudsen cell from 614 to 713 K along with the vapour pressure of Te2(g) over Te(s) from Ref. [21 ]. The Clausing factor of the Knudsen cell was obtained from the mass loss and the p(Te 2) from Ref. [21] using the equation
These emf's agree excellently with the values obtained in the previous study [20]. This indicates the reliability of the present measurements. Hence all the subsequent calculations were carried out based on cell reaction (1) using air as a standard reference. Figs. 3 and 4 show the comparison of the experimental emf values with the fit values for cells I and II.
p (kPa) = ( d w / d t ) ( l O 1 . 3 2 5 / 4 4 . 3 3 )
× (1/a)(1/k)(~/T/M),
3.2. Knudsen effusion mass loss studies
(5)
where p is the pressure in kPa of Tez(g) from Refs. [22,23], d w / d t is the mass loss in g s - I , T is the temperature in K, M was taken as 0.2552 kg mol-~, a is the area of cross-section of the orifice which is assumed constant throughout the experiment, and k is the Clausing factor of the cell. The calculated value of k = 0.945.
Table 3 gives the comparison of tellurium pressure over Te(s) obtained in the present experiment with the literature values. It is seen from the table that the present values are in good agreement indicating the reliability of the experi-
-4.5
-4.6
-4.7 O E
0.
-4.8
-4.9
0
0
-5.0
-5.1
-5.2 6.8
,
,
6.9
7.0
l 7.1
, 7.2
,
~
7.3
7.4
, 7.5
, 7.6
7.7
1/T(K)
Fig. 5. Variation of log p(Rb) with 1/T for the reaction: RbUO3(s) + Rb2UO4(s) + 1/202(g) = 2Rb2U2OT(S) + Rb(g).
238
K. Jayanthi et al. / Journal ()f Nuclear Materials 232 (1996) 233-239
Table 5 Dependence of p(Rb) (kPa) on temperature T (K) for the reaction: 3RbUO3(s) + Rb_,UO4(s) + 1/2 O2(g) = 2Rb~U~OT(s) + Rb(g) T(K) 1305 1332 1344 1373 1396 1418 1459
dw/dt(gs
I)
sal gas constant and the standard state of Rb is taken as Rb(g) at 101.325 kPa and the Gibbs energy is zero at all temperatures. The Gibbs free energy of reaction (1) is given by
p(kPa)
10 6
10 5
a , G ° + 0.7 (kJ) = - 113.08 + 0.0830T ( K ) .
0.599 0.666 0.725 1.320 1.500 1.607 2.254
0.750 0.842 0.921 1.395 1.803 2.099 2.985
The molar Gibbs energy of formation of Rb2UO4(s) and Rb2U2OT(S) were calculated from the enthalpy and entropy of formation at 298 K from literature [16,24] and can be given by ~rG°(Rb2UO4) _+ 1.4 kJ mol -
1913 + 0.425T ( K )
i ( 9 2 0 - 1 4 5 9 K),
~ f G ° ( R b 2 U 2 0 7 ) + 3.0 kJ mol Table 5 gives the mass loss of Rb at each isothermal temperature over the co-existing phase and the corresponding pressures. The rubidium pressure in the reaction (1) was calculated using Eq. (5). The molar mass of Rb was taken as 85.47. The rubidium pressures were least squares fitted with temperature and can be given by log p (kPa) _+ 0.33 = ( - 7 9 7 7 / T
( K ) ) + 2.95.
= - 3232 + 0.674T ( K )
A/x(O 2) _+ 0.4 (kJ m o l - ' ) (920-1091 K).
(7)
The rubidium potential over the phase field: RbUO3(s) + Rb2U207(s) + Rb2UO4(s), can be defined as ~/x(Rb) = R T In PRb" The dependence of rubidium potential on temperature can be represented by ')
= - 152.7 + 0.018T ( K )
/ ( 9 2 0 - 1 4 5 9 K).
( 1 3 0 5 - 1 4 5 9 K).
(8)
The Gibbs energy changes for the cell reaction (1) can be given by A~G = - 2 F E = - R T In K where K is the equilibrium constant ( K = [ p ( R b ) / p ( O 2) and R is the univer-
~ G ° ( R b U O 3 ) + 3.4 (kJ m o l - ' ) ( 9 2 0 - 1 4 5 9 K).
Phase fields
T(K) 1000
Rb2U4Otl + Rb2U4Oi2 [ 2 3 ] RbUO~ + Rb2U207+ Rb2UO~ ' Rb2U4OI2 + Rb2U4013 [23] ~ Present study.
~(O~)
356 329 95
(12)
The molar Gibbs energy of Rb2UO 4 and Rb2U20 7 were calculated from the enthalpy of formation at 298 K and entropy of formation (calculated from ~98K (16) values) at 298 K using the relation: AfGT= AfH;98KTAfS;98K. In the absence of reliable Ct, values, it is assumed that the enthalpy and entropy changes due to variation of Ct, with temperature are negligible. An error of 3.4 kJ mol ~ shown in the molar Gibbs energy of formation of RbUO3(s) is mainly attributed to the error approximation made in the molar Gibbs energy formation values of Rb2UO4(s) and Rb2U207(s). The enthalpy of tbrmation at 298 K of RbUO 3 is reported to be - 1520.9 + 1.7 kJ tool- t [24]. The present value ( - 1479 kJ mol ~), from Eq. (12) is less negative as expected. The oxygen potential existing over the coexisting phase fields in the R b - U - O system along with the rubidium pressure in the temperature range 1000 to 1450 K are shown in Table 6.
Table 6 The oxygen potential [ - ~/x(O 2)] and the rubidium potential [ - ~ / x ( R b ) = RT In PRb] at 1000, 1100 and 1200 K
-
(11)
Using the molar Gibbs energy formation of Rb2UO4(s) and Rb2U2Ov(s) and the Gibbs molar free energy change for reaction (2), the molar Gibbs energy formation of RbUO3(s) is calculated and can be given by
= - 1479 + 0.278T ( K )
A/x(Rb) + 0.6 (kJ mol
(10)
(6)
The pressure values at the experimental temperatures are compared with the fit values in Fig. 5. The oxygen potential existing over the system R b U O 3 ( s ) + R b 2 U 2 0 7 ( s ) + Rb2UOn(s) for cell I after correction of 0 2 to 101.325 kPa can be represented by
= -531.6+0.2026T(K)
(9)
It00
1200
- ~(Rb)
- A~(O 2 ) (kJ mol i)
-A~(Rb)
- ~ ( O 2)
- A~(Rb)
134.7 --
314 308 84
132.9 -
273 288 59
131.0 -
K. Jayanthi et al. / Journal of Nuclear Materials 232 (1996) 233-239
Acknowledgements The authors are thankful to Dr D.D. Sood, Director Radio Chemistry and Isotope Group, and Dr H.C. Jain, Head Fuel Chemistry Division, for their constant encouragement during the course of this work.
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[11] V.S. Iyer, V. Venugopal and D.D. Sood, J. Radio Anal. Nucl. Chem. 143 (1990) 157. [12] W. Ruedoff, S. Kemmeler Sack and H. Leutner, Angew. Chem. 74 (1962) 429. [13] S. Kemmler Sack and W. Ruedorff, Z. Anorg. Allg. Chem. 354 (1967) 255. [14] E.H.P. Cordfunke and P.A.G. O'Hare, eds., The Chemical Thermodyn. Actinide Elem. Comp., Part 3. Misc. Actinide Compounds (IAEA, Vienna, 1978). [15] E.A. Ippolotova, D.G. Faustova and V.I. Splitsyn, in: Proc. Symp. on Invest into the Field of Uranium Chem., Moscow Univ., ed. V.I. Spitsyn, 1961, Argonne National Lab. Report, ANL-Trans-33 (1964) 170. [16] T.B. Lindemer, T.M. Besmann and C.E. Johnson. J. Nucl. Mater. 100 (1981) 178. [17] E.H.P. Cordfunke and W. Ouweltjes, J. Chem. Thermodyn. 13 (1981) 187. [18] A. van Egmond, JCPDS Powder diflYaction file 2, 1-43 (1993). [19] International Practical Temperature Scale, 1968, Amended Edition 1975, HMSO London, 1976, Metrologia 12 (1976) 7. [20] V. Venugopal, V.S. lyer, V. Sunderesh, Z. Singh, R. Prasad and D.D. Sood, J. Chem. Thermodyn. 19 (1987) 19. [21] R.A. Rapp, ed., Physicochemical Measurements in Metal Research, Technique of Metal Research, Vol. 4, Part 1, series ed. R.F. Bunshah (Wiley, New York, 1970) ch. 2. [22] O. Kubeschewski and C.B. Alcock, Metallurgical Thermochemistry, 5th Ed. (Pergmon, Oxford, 1979). [23] K.C. Mills, Thermodynamic Data for Inorganic sulphides, Selenides and Tellurides (Butterworths, London, 1974). [24] J. Fuger, J. Nucl. Mater. 130 (1985) 253.