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Phase equilibria in the Cs-Cr-O system
Journal of Nuclear Materials 84 (1979) 286-294 0 North-Holland Publishing Company
PHASE EQUILIBRIA IN THE Cs-Cc-0
SYSTEM *
D.C. FEE, K.Y. KIM and C.E. JOHNSON chemical Engineering Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, USA Received 19 October 1978, in revised form 30 March 1979
Phase and thermodynamic data have been used to construct a self-consistent Cs-Cr-0 phase diagram. The cesium chromate which probably forms on the cladding inner surface in uranium-plutonium oxide fast reactor fuel pins is CssCrO4.
1. Introduction The lifetime of mixed uranium-plutonium oxide fuel pins may be limited by reaction of the stainlesssteel cladding with fuel containing fission products. Post-irradiation examinations show two types of reaction: the first type is the uniform oxidation (matrix attack) of the stainless steel, which results in a general decrease in the thickness of the cladding; the second type involves the intergranular penetration by oxygen and fission products along the grain boundaries in the cladding. Matrix attack rarely exceeds a depth of 50 urn; intergranular attack, on the other hand, may penetrate the entire thickness of the cladding. Intergranular attack is generally nonuniform in depth and sporadic in occurrence. Fission products play important roles in fuel-cladding inreractions. Cesium is always observed in the regions of attack and is usually associated with chromium from the cladding [l-l]. However, the identity of this Cs-Cr-0 phase has not been determined in post-irradiation examinations of mixed uraniumplutonium oxide fuel pins. Nevertheless, the formation of a Cs-Cr-0 phase is postulated to break up the protective Cra03 layer and open the way to cladding attack [5,6]. Bmakup of the protective CrsOs layer is an essential feature of fuel-cladding chemical
* Work performed under the auspices fo the US Department of Energy.
interaction that has been incorporated into various models of cladding attack [l-3]. In order to define the conditions required for the formation of a Cs-Cr-0 phase in stainless steel-clad fast-reactor fuel pins, we have used thermodynamic data and results of phaseequilibrium experiments to construct a self-consistent Cs-Cr-0 phase diagram.
2. Laboratory experiments
Experiments were conducted to determine the phases present at selected locations in the Cs-Cr-0 phase diagram. In these experiments, various cesium-, chromium-, and oxygen-containing mixtures were placed in sealed nickel capsules (7.9 mm I.D., 7 cm long) and heated isothermally at (923 f 5) K for 12 to 76 days. All of the sample preparations were performed in a high purity helium atmosphere [7] except for the heat treatment of the sealed capsules which was performed in air. During an experiment, the capsules were positioned vertically to ensure that liquid cesium (if present) was in contact with the solid reactant. To ensure intimate contact of the reactants, the capsules were inverted daily. Further, when liquid cesium was not a reactant, the powdered starting materials were pressed into a pellet (capsule F, table 1). At the end of each heat treatment, the capsules were quickly quenched (15 s) and any elemental cesium present was removed by vacuum distillation at 573 K before analysis of the capsule contents. The initial
D.C. Fee et al. /Phase equilibria in Cs-#-0 Table 1 Summary of conditions and results for isothermal Capsule
Reactants a)
Heating time (days)
system
phasestudiesat 923 K Products In reaction mixture b,
On cladding inner surface ‘)
Cs + CrOs (16, 10) Cs + Cr03 (21, 10)
43
Cs$rO4
Cr (trace)
14 23 76
Cs$rO4 + Cs&rO4 C&r04 Cs3CrO4
Cr (trace) Cr (trace) N.A. d,
Cs + CrO3 (22, 3.9)
23 56
Cs + Cr203 (6.4, 1.2)
19 19 19
f) f)
N.A. Cr e)
0
Cr e)
12
Cr, Cs-Cr-0
Cs + Cr203 (3.1, 1.2) Cs&rO4 + Cr (0.63, 0.66)
287
Cr e, N.A.
$4Cr04
‘*g)
N.A.
a) Values in parentheses are the quantity of each reactant in milimoles in the order shown; for replicate experiments the average composition is given. b, From X-ray diffraction analysis, unless otherwise noted. ‘) From electron microprobe analysis. d, Not analyzed. e, Thick Cr layer which contained no measurable Cs or 0. f) No Cs-Cr-0 or Cr-0 compounds could beidentified. g) Pure Cr phase and a phase containing Cs, Cr and 0.
composition of each mixture, the experimental cbnditions, and results of the experiments are summarized in table 1 and fig. 1. Also shown in the figure are the tie lines that were determined our analytical data; X-ray diffraction analysis of the reaction mixtures and electron microprobe analysis of the inner surface of the nickel capsules. The X-ray spectra obtained were characterized by weak and diffuse lines which
Fig. 1. Selected portions of the cesium-chromium-oxygen phase-diagram, isothermal section, 298-1100 K. The compounds CsCraOa, Cs#raO1o and probably Cs2Cr4013 exist only below 674 K. The compound G&20, melts at 658 K. The existence of Cs@O4 is tentative, see Appendix. T’he letter designations refer to sample compdsitions given in table 1.
288
D.C. Fee et al. /Phase equilibria in Cs-Cr-0
made unequivocal identification difficult. This may have resulted from the extremely hygroscopic nature of Cs&r04.
3. Results and discussion The principle result of our experiments was to establish a Cs4Cr04-Cr tie line in fig. 1. In addition,
our results confirmed the work of Knights and Nips [8] who report tie lines going from Crz03 to CszCr04, CssCr04 and Cs&r04. In our work, the existence of a Cr-Cs4Cr04 tie line is supported by the absence of evidence for the formation of Cs(Q) in capsule F and by the presence of extensive chromium deposits (which contained no measurable cesium or oxygen) on the inner surface of capsules C, D and E but not A and B. These chromium deposits suggest that chromium metal is an equilibrium phase and are the basis for the Cr-Cs4Cr04 tie line that is shown in fig. 1. The location of the chromium deposits on the capsule inner surface rather than along the grain boundaries of the product is consistent with chromium metal being an equilibrium phase at 923 K rather than a phase formed during quenching of the sample. However, the results do not rule out the possibility that chromium metal was an intermediate reaction product rather than an equilibrium phase. The existence of a Cr-Cs4Cr04 tie line is also supported by experimental work of Aitken et al. [9]. In their studies, a nickel capsule was loaded with 16.4 mmol Cr*Os and 37.6 mm01 cesium, welded closed, and heat treated for 100 h at 1073 K. The reactant composition in thsi capsule is nearly identical to that of capsule E in fig. 1 and table 1. A major phase of chromium metal, together with an unidentifiable minor phase were reported based on X-ray diffraction analysis of the products [9]. In contrast to the Cr-Cs&r04 tie line that we propose, Knights and Phillips [8] reported a Cs(Q)-CrzOJ tie line based on results of emf measurements (12-48 h, 923 K) and on a lack of a visually observable reaction between liquid cesium and CrzOs in an experiment for 16 h at 873 K. We have drawn a Cr-Cs&r04 tie line based on results of microprobe examination and X-ray diffraction analysis. Further, we have drawn a Cs&r04-Cr tie line because the emf measurements
system
were not sufficiently accurate to decide between a Cr-Cs&r04 or Cs(Q)-Cr303 tie line and because the equilibrium phases in the emf cell (other than Cs(Q)] were not determined at the end of the experiment. The emf cell measurements resulted in a typical uncertainty in the oxygen potential (A?&, = RT In poz) of +30 kJ/mol 02, while from thermochemical data an uncertainty of less than +7 kJ/mol O2 at 923 K is required to distinguish between a Cr-Cs4Cr04 or Cs(P)-CrzOS tie line. Fig. 2 shows a calculated Cs-Cr-0 phase diagram based on the thermodynamic data given in table 2. The calculational method is described in detail in Appen-
7007
700
900
II00
TK Fig. 2. Oxygen potentials in the cesium-chromium-oxygen system from 700 to 1100 K. The dashed lines are cesium isobars (in Pa). If a CssCr04-Cr tie line exists, the lowest solid line represents a region containing Cs(Q) and Cr in equilibrium with CssCrO4 instead of Cs&rO+ Also shown is the oxygen potential of (U~$u~~o) O~.noo.
Table 2
573 [lo] b)
~2~3010
Not indexed [ 8,273
2603 [28]
No transitions [ 281
CsscTo4
Cr203
Hexagonal [ 291
1135 + 8 [28]
1587.6 * 3$ [26] 1606 f,
1542.7 f 2.6 [26]
i74 g)
429
411
393
375
605
2091.1 * 2.8 [ 171 1430.0 k 1.9 [22]
-
-
-A$,w (J/m01 - K)
-
-
-A%,, OEJ/moU
a) Standard entropies, &g {J/m01 - K) from ref. [ 191: Cs(c), 85.1 f 0.4; Cr, 23.6 f 0.2;02(g), 205.0 f 0.04. ‘) f)ecomPo=s by 2 CsCr&&) + Cq$r20#2) + 2 Cr203(c) + $Oz(g, 0.2 atm)at temperature indicated. c, Unknown. d, Decomposes by 4 CszCraOro(c) + 3 Cs2Cr207(c) + 2 CsCraOs + 3 02(g, ft.2 atm). e, C&O4 has also been identified by chemical analysis, see ref. ]25?. f, Estimated, see Appendix. Efforts to measure the entropy of Cs3CrO4 have been initiated at this laboratory. g) Additional data: AGp(Cs, g) = 71000 - 75.3 T J/mol [ 281.
-
No data
No data
CWfl4
[ 211
Cubic (241 e, Not indexed [ 8,271
Orthorhombic >1273 K [8]
cs3cro4
1293 [15]
CS2CrO4
cs2fi207
or618* 13 [14-171 P OL1070 [15] P No data 658 f 10 [14-171
-
No data
c32~4013
Monoclinic [ 121 a! - orthorhombic [ 121 13- rhombohedral [ 12,131 Not indexed [ 181
Orthorhombic [ 111 Monoclinic [ 10)
- c)
(L674 [lo] b, p 505 [lo] b)
C&r308
X-ray diffraction pattern
properties of c&urn chromates Melting point o<)
Transition temperature (K)
thermodynamic
Compound
physicaland
81.2 f 1.2 ]28]
430 f)
362f)
296 f,
228.59 f 0.23 [23]
330.06 f 0.33 [20]
-
-
-
@,,I3 a) (J/mol - K)
3 ?I
+ z
$ -. a a
g
9 n ?I 1 % x % L? 2
290
D.C. Fee et al. /Phase equilibria in Cs-G-0
dix I. The dashed lines in fig. 2 show the calculated cesium isobars (in Pa) in the two-phase regions. The accuracy of the calculated cesium isobars and the oxygen potential are discussed in Appendix II. Not shown in fig. 2 is the CssCrsO,--Css CrOo -Crz03\ region which exists only at oxygen potentials which are too positive to be encountered in nuclear fuels (for example, -50 kJ/mol at 600 K). Fig. 2 shows that the oxygen potential of the threephase region containing Cr t CrsOs is close (15 kJ/mol at 923 K) to the oxygen potential of a three-phase region containing liquid cesium. To resolve these two regions requires an emf cell technique with an uncertainty of less than 7 kJ/mol in the resultant oxygen potential. Because the choice of a Cr-Cs&r04 versus Cs@)-CrzOs tie line depends on resolving these two regions, the emf cell technique of Knights and Phillips [8], with a typical uncertainty in oxygen potentials of +30 kJ/mol, is too inaccurate to decide between a Cr-Cs&r04 or Cs(P)-CrsOs tie line.
4. Application to uranium-plutonium oxide fastreactor fuel pins In a fast-reactor fuel pin, the oxygen potential at the cladding inner surface is expected to be fixed by the initial O/M (M = U + Pu) and U/m! ratios of the fuel. At start-of-life, the O/M ratio of the fuel at the fuel-cladding gap is estimated to be slightly below 2.00 [l-3]. As shown in fig. 2, CssCrO,ois the Cs-Cr-0 equilibrium species expected to be found between the oxygen potential for stoichiometric fuel [3,30] and oxygen potentials about 150 kJ/mol more negative. The compound Cs&r04 is formed only at oxygen potentials nearly as negative as that of the Cr-Cr,Os equilibria. The compound Cs,Cr04 is formed only at oxygen potentials more positive than that of (Ue.s,-,Puo.,o) Oz.ooo. However, due to the uncertainties in the estimation of the &.!&a8 values in table 2, the possibility exists, that CszCr04 may be the Cs-Cr-0 phase present at the oxygen potential of (Ue.8ePue.2e) Oz_eoo.Nonetheless this possibility is remote because the O/M ratio is estimated to be slightly below 2.000 [l-3] and because the oxygen potential line for (Ue_aePue.~o)02+eeoin fig. 2 represents the upper limit of the range of oxygen potentials calculated for stoichiometric fuel f3 11.
system
Consequently, CssCrOI1is the cesium-chromiumoxygen species most likely to be formed on the stainless steel cladding of mixed uranium-plutonium oxide fast-reactor fuel pins. The conclusion that CssCrOe forms on the cladding inner surface in equilibrium with CrzOs is not in conflict with recent analysis of the composition of fuel-cladding reaction products in the gaps of several irradiated fuel pins [4]. Although the concentrations of elements determined in this analysis contains significant uncertainty (rtr20%),the results, when combined with reasonable assumptions concerning the phases other than cesium chromate and Cr?Os which are present [l-3], yield a range of Cs-Cr-0 compositions which bracket those along the Cs3Cr04-Cr203 tie line. Because of this uncertainty, the Cs&r04/ CrsOs molar ratios consistent with these post-irradiation results vary from 0 to 0.1. The calculated cesium pressures required for the formation of CssCr04 in fast-reactor fuel pins appears to be readily attainable from cesium-fuel equilibria [5,6,32]. Hence, the calculated cesium
5. Summary
Phase and thermodynamic data have been used to construct a self-consistent Cs-Cr-0 phase diagram. The cesium chromate which probably forms on the cladding inner surface in uranium-plutonium oxide fast-reactor pins is CssCr04.
Appendix I: Thermocttemicalcalculations To serve a basis for constructing the Cs-Cr-0 phase diagram, thermodynamic functions for the cesium chromates were estimated in a self-consistent manner from the measured values of the enthalpies and entropies of formation given in table 2. Thermodynamic data were estimated for CssCr04, whose existence has been tentatively deduced 1331, although a unique X-ray pattern has not been reported for this
D.C. Fee et al. /Phase equilibria in Cs-Cr-0
compound. Thermodynamic data were not estimated for CssCrsOs, CszCr301e and CszCr40rs even though unique.X-ray patterns have been reported for these compounds [ 10-131, because these compounds presumably decompose (even in air) to CssCr20, below 770 K, the temperature at which cladding attack begins. The standard enthalpy of formation of CssCr04 was estimated by extrapolating the measured trend [22,26] toward a more negative AH,, in the series of reactions Cs(c) + Cs,_ 1CrOe(c) 5
Cs,CQ
,
(A.11
where n = 3-5. The standard entropies of formation of Cs3Cr04, Cs&r04 and Cs&r04 were estimated from the measured standard entropy of formation [23] of Cs2Cr04 by assuming a constant entropy increment for each additional cesium atom in the series Cs,Cr04 (n = 2-5). This approach proved to be self-consistent in that each cesium chromate was stable with respect to disproportionation to the adjacent compounds. That is, the disproportionation reaction (reaction A.2, for example) 2 Cs3Cr04 + C&r04
+ CsaCr04
291
system
the data in table 2 is that the uncertainty in the latter is greatly reduced, particularly for the A@ values. Therefore, it appears that table 2 contains the most accurate available 298 K data which together with the data of Knights and Phillips can be used with some confidence as the basis for construction of the Cs-Cr-0 phase diagram shown in fig. 2. The Cs-Cr-0 phase diagram shown in fig. 2 was constructed in the following manner. By application of the phase rule, it can be shown that in the threephase regions of fig. 1 (e.g., CszCr04-CssCr0,+-Cr203), there is one degree of freedom. Therefore, setting the temperature futes the cesium partial pressure and the oxygen partial pressure of the system. The resultant temperature dependency of the oxygen potential (A&, a RT In po2) can be calculated from the thermodynamic properties of the phases present. For example, the oxygen potential of the CszCr04-Cs3Cr04-Crz03 region may be calculated from the equilibrium 4 Cs&r04 + CrzOs + 3 O2 + 6 CszCr04 ,
(A-3)
by using the corresponding free energy relationship 4 AGf(CssCr04, c) + AG$‘(Cr20s, c)’
(A.2)
exhibited a positive free energy change. Further, the ~;2!W values derived in this manner and shown in table 2, compare favorably with values derived by Knights and Phillips [8] from emf-cell measurements. (Comparison between calculated cesium pressures and measured values from Knudsen effusion experiments by Knights and Phillips are made in Appendix II.) The AS& values (T= 500-I 100 K) of Knights and Phillips are (-398 + 130), (-430 f 140) and (-440 + 140) J/mole K for Cs&Q, CssCr04 and CsqCr04, respectively. Similarly, derived AH& values (T = 500-l 100 K) from Knights and Phillips are (-1410 * 120) (-1510 f 130) and (-1550 f 140) kJ/mol for CszCr04, CssCr04 and Cs&r04, respectively. Knights and Phillips corrected their AH& and A$,T values (T= 500-I 100 K) to AH&as and Al!?f,298 values [27]. This results in better agreement between emf cell [8] and calorimetric values (table 2). For example, temperature corrected emf cell results for C&r04 are @,298 = (-1422 f 120) kJ/mol and A$,298 = (378 f 130) J/mol * K [27]. As a result, the principle difference between the emf cell data [8] and
+ $RTlnpo,
= 6 AGi(CssCr04, c) .
(A-4)
Similarly, in the two phase regions (e.g., Cs2Cr04Crz03) there are two degrees of freedom. Therefore, at a given temperature, the cesium partial pressure depends on the oxygen partial pressure in the system. This dependency can also be calculated from the thermodynamic properties of the phases that are present. Consider the equilibrium 6 Cs(g) + Cr&(c)
+ $ Os(g) + 2 CssCrOI)(c) . (A.5)
The corresponding free energy relationship may be written as: 6 AGi(Cs, g) + 6 RT In pi + AGfo(CrzOJ,C) + $
RT
inpoz
= 2 AGfO(Cs&r04, C)
.
64.6)
cesium pressure and the oxygen potential are related by
The
In PCs = [2 AG~(CssCrO,, c) - 6 AGp(Cs, g) - AGfO(CrsOs,c) - 3 A&,,]/6 RT.
292
D.C. Fee et al. /Phase equilibria in Cs-Cr-0
The calculated oxygen potentials and cesium pressures in the Cs-Cr-0 system that are shown in fig. 2 are based on the thermodynamic data of table 2, with the assumption that AH&as and AS&as are independent of temperature. This approach has been shown to be valid in the Cs-U-O system [34-361. Further, the effect on the thermodynamic properties of the cu+ fl phase transition in CssCrsO, at 618 K (table 2) and in CszCr04 at 1070 K is assumed to be small and therefore has been neglected. This assumption has been shown to be valid in other ternary oxide systems [28]. In calculating the cesium pressures shown in fig. 2, we have also assumed that the solubility of cesium in CrsOs or in the cesium chromates is very low and does not significantly affect the thermodynamic properties shown in table 2. The requisite solubility data are not available to test this assumption.
Appendix
II: Accuracy of calculated equilibria
Although the data in fig. 2 are in accord with the experimental phase diagram shown in fig. 1, the set of thermodynamic data which predicts the observed tie lines is not unique. A slightly different estimated asor,ass values would have led to identical tie lines. Therefore, while it appears that the estimated thermodynamic data in table 2 are qualitatively correct, the quantitative accuracy of the data in table 2 is uncertain and requires further experimentation. A rough estimate of the quantitative accuracy of the data in table 2 and fig. 2 can be obtained by comparing the calculated results with the experimental emf cell results and Knudsen effusion results of Knights and Phillips [8]. This comparison is shown in table Al where the experimental data are extrapolated to the range of interest. The comparison is made for three regions. In each region, the oxygenpotential values calculated with the data in table 2 (lines 1,5 and 8) fall within the large uncertainty bands of the experimental emf cell results (lines 2, 6 and 9). Similarly, the calculated cesium pressures in phase field C (CsJCr04--Cs4Cr04-CraOs) fall well within the uncertainty bands of the experimental Knudsen cell-mass spectrometer results. In phase field B (CszCr04-Cs3Cr04--CrzOs), the calculated cesium pressures fall at slightly lower pressures than the lower limit of the uncertainty band in the
system
measured data. It may be significant that the deviation between calculated and experimental results occurred in the phase field with the lowest (and, therefore, least accurate) experimentally determined cesium pressure. Fig. 2 is consistent with fig. 1 in that a CsqCr04Cr tie line is shown instead of a Cs(Q)-Cr,Os tie line. Our calculations show that a Cs4Cr04-Cr tie line results in the proper ordering of the oxygen potentials in this region of the phase diagram; namely the oxygen potential of the Cs(Q)-Cs4Cr04-Cr region is more negative than the oxygen potential of the Cs4C!r04Cra03--Cr region. The inclusion of a CssCr04--Cr tie line in the calculations also results in the proper ordering of oxygen potentials; namely, that the threephase region containing Cs(Q), Cs,Cr04 and Cr has the most negative oxygen potential of any three phase region in the system and that the oxygen potentials of the other three-phase regions are monotonically more positive with monotonically increasing oxygen content for a fmed Cs/U ratio. This is shown by the lowest dashed and solid lines in fig. 2. [If a CssCr04-Cr tie line exists, the lowest solid line in fig. 2 represents a region containing Cs(Q) and Cr equilibrium with CssCr04 instead of CsqCr04]. The important thing to note is that the proper ordering of oxygen potentials was not obtained with the data in table 2 when Cs(P)-CraOs tie was considered. In this case, the oxygen potential of the hypothetical Cs(Q)-Cs4Cr04-CrzOs [or Cs(Q)-CssCr04--Cr?Os region] was more negative than the oxygen potential of the hypothetical Cs(Q)-CraOs-Cr region. Further, indirect evidence supporting a Cs&r04Cr tie line was obtained by repeating the calculations with the AH&s value in table 2 but with alternative estimates of AS&ass values for CsqCr04 and CssCrO+ These alternative values are chosen to yield a Cs(Q)Crz03 tie line and the proper ordering of oxygen potentials associated with that tie line. The oxygen potentials and cesium pressures calculated with this alternative set of thermodynamic data are also shown in table Al (lines 4,7 and 10). The proper ordering of oxygen potentials with this alternative set of thermodynamic data is also shown in table Al (lines 3,4, 7 and 10). The alternative data set consistent with a Cs(P)-Cr20s tie line results in larger deviations between measured and calculated oxygen potentials (phase field B) and between measured and calculated
D.C. Fee et al. /Phase equilibria in Cs-Cr-0
293
system
Table Al Comparison of calculated and experimental oxygen pa;tentials (kJ/mol) and cesium pressures (Pa) at selected temperatures in selected three phase regions of the Cs-Cr-0 system Phase field
-._ A. Region with Cs(Q) + Cs4CrO4 b, 1. Calculated for Cs(Q)-Cs,CrO,-Cr, data from table 2 2. Measured: emf cell (890-990 K) d, 3. Calculated: Cs(Q)-Cs&r04-CraOa e, 4. Calculated Cs(Q)-CraOa-Cr B. CsaCr04-CsaCr04-CraOa 5. Calculated, data from table 2, Cr-Cs4Cr04 tie line 6. Measured: emf celJ (870-1100 K) Measured: Knudsen celJ (750-950 K) 7. Calculated - data consistent with a Cs(Q)-CraOa tie line e, C. CsaCr04--Cs&r04-Cr203 8. Calculated, data from table 2, Cr-Cs4Cr04 tie line 9. Derived from emf cell results (810-1100 K) Measured: Knudsen cell (500-680 K) 10. Calculated - data consistent with a Cs(Q)-Cr20a tie line e,
700 K
1100 K
900 K
log PCS
-AC%
- c) -
650 620 f 30 619 629 -
-log PCS
-A&
-log PCS
609 580 i 30 563 592 -
1.12 -0.83 364 396 390 f 30 350 f 30 -2.4 i 0.4 0.3 f 0.2 2.0 f 0.3 2.14 -0.91 460, 446 4.09
-A?&
568 550 f 30 506 556 331 310* 30
-3.88
1.16
562 520 f 60
4.39 497 529 470 f 60 490 f 60 3.18 f 0.6 4.3 i 0.6
564
4.22
1.4 i 0.6 2.31
432
3.17
532
5.43
500
a) The calculated data are from this work. The experimental data are from ref. [ 81. b, Ignoring the possibility of CssCrOg. The argument unchanged by this omission, see text. ‘) Because the cesium pressure in this three-phase region depends only on the Cs(Q) ++Cs(g) equilibria, all calculated cesium pressures are the same at each temperature and are not shown. Similarly, because the Cs(Q) f* C&g) equilibria was used to calibrate the Knudsen cell - mass spectrometer system, the cesium pressure was not measured independently in this region (line 2). d, The emf results are from a cell containing liquid cesium and other phase(s). The identity of the other phase(s) was not determined after the experiment. e, Using the data in table 2 except for CsaCrO4: A$QQg = 450 J/mole K, S&, = 239 J/m01. K; CsqCrO4: AS&Q8 = 488 J/mole K, S&g = 285 J/mol . K. These entropy values are c&sistent with a Cs(Q)-Cr20a tie line.
cesium pressures (phase fields B and C) than the thermodynamic data set (in table 2) consistent with a Cs4Cr04-Cr tie line (table Al, lines 1,s and 8). This analysis again supports a Cs4Cr04-Cr tie line. The foregoing comparison illustrates the sensitivity of the calculated results to large changes in A,!$$sa values, i.e., 57 and 77 kJ/mol * K for Cs3Cr04 and Cs4Cr04, respectively. These changes in A,.&, result in a change in the oxygen potential at 900 K of 82 kJ/mol for phase field B and 3 kJ/mol for phase field C, as shown in table Al. These changes in AS&as values also result in an increase in the calculated cesium equilibrium pressures over the Cs3Cr04-Cr203 and Cs4Cr04-Cr203 two-phase regions of one log pcs unit over the values shown in fig. 2. Assuming that
the estimated A&as values shown in table 2 are accurate to within +20 kJ/mol *K, a maximum uncertainty of zt20 kJ/mol in the oxygen potentials and an uncertainty of kO.3 in the log pcs value given in fig. 2 are calculated.
Acknowledgements
The authors would like to acknowledge a series of fruitful discussions with Dr. A.E. Martin. The assistance of B.S. Tani and W.A. Shinn in performing the analyses and L.O. Nippa in preparing the isothermal capsules is gratefully acknowledged.
294
D.C. Fee et al. /Phase equilibria in Cs-Cr-0
Note added in proof The entropy of Cs&rO,) has recently been determined experimentally [37]. The experimental value, $&(Cs3Cr04) = 296.2 f. 1.5 J/mol +K agrees well with the estimated value of 296 J/m01 - K used in this paper.
References [l] Fuel and Cladding Interaction, International Working Group on Fast Reactors, Tokyo, February 21-25, 1977, IWGFR-16 (CONF-770215,19X’). [ 21 Behaviour and Chemical State of Irradiated Ceramic Fuels (IAEA, Vienna, 1974). (31 D.C. Fee, I. Johnson and C.E. Johnson, ANL-75-53 (1975). [4] C.T. Walker, J. Nucl. Mater. 74 (1978) 358. [ 5] 0. Gatzmann, in: Proc. Int. Conf. Fast Breeder Reactor Fuel Performan~ Monterey, CA, March 5 -8,1979, p. 489. [6] D.C. Fee and C.E. Johnson, to be published. [ 71 C.E. Johnson, M.S. Foster and M.L. Kyle, Nucl. Appl. 3 (1967) 563. [ 81 C.F. Knights and B.A. Phillips, Chem. Sot. Special Publication 30 (1977) 134. 191 E.A. Aitken, M.G. Adamson, D. Dutina, S.K. Evan and T.E. Ludlow, GEAP-12418 (1973). [ 101 J.J. Foster and A.N. Hambly, Austr. J. Chem. 29 (1976) 2137. [ 111 K.A. Wilhelmi, Arkiv for Kemi 26 (1966) 141. [12] R. Mattes, 2. Anorg. Allg. Chem. 382 (1971) 163. [13] R. Mattes and W. Meschede, 2. Anorg. Allg. Chem. 395 (1973) 216. [ 141 R.G. Samuseva, I.F. Pole&v and V.E. Plyushchev, Zh. Neorg. Khim. 7 (1962) 1146 [Russian J. Inorg. Chem. 7 (1962) 5891. [ 151 L. Erdey, C. Liptay and S. Gal, Talanta 12 (1965) 257. [ 161 Y.I. Vesnin and L.A. Khripin, Zh. Neorg. Khim. 11 (1966) 2216 [Russian J. Inorg.Chem. ll(1966) 11881. (171 P.A.G. O’Hare, J. Boerio and K. Jensen, J. Chem. Thermodyn. 8 (1976) 381. [ 181 S.M. Arkipov, P.D. Komissarova and N.A. Druz, Zh.
system
Neog. Khim. 9 (1964) 498 [Russian J. Inorg. Chem. 9 (1964) 275. [ 191 R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser, K.K. Kelley and D.S. Wayman, Selected Values of the Thermodynamic Properties of the Elements (American Society for Metals, Metals Park, OH, 1973). 1201 W.G. Lyon, D.W. Osborne and H.E. Flotow, J. Chem. Thermodyn. 8 (1976) 373. 1211 H.E. Swanson, M.C. Morris, E.H. Evans and L. Uhner, United States National Bureau of Standard Monograph 25, Section 3 (1964) p. 25. [ 221 P.A.G. O’Hare and J. Boexio, J. Chem. Thermodyn. 7 (1975) 1195. [23] W.G. Lyon, D.W. Osborne and H.E. Flotow, J. Chem. Thermodyn. 7 (1975) 1189. [ 241 G. Meyer and R. Hoppe, Rev. Chhn. Miner. 12 (1975) 454. [ 2.51 R. &holder, F. Schwochow and H. Schwarz, Z. Anorg. Allg. Chem. 363 (1968) 10. [26] K.Y. Kim, G.K. Johnson, C.E. Johnson, H.E. Floton, E.H. Appelman and P.A.G. O’Hare, (Argonne National Laboratory) and B.A. Phillips (HarwelI), to be published. [ 271 C.F. Knights (Harwell) private communication (1978). [ 281 J ANAF Thermochemical Tables, NSRD-NBS-37. [ 291 H.E. Swanson, N.T. Gilfrich and GM. Ugrinic, United States National Bureau of Standard Circular 539, Vol. 5 (1955) p. 22. [ 301 P.E. Blackburn and C.E. Johnson, in: Thermodynamics of Nuctear Materials Vol. I (IAEA, Vienna 1975) p. 17. 1311 R.E. Woodley and M.G. Adamson, in: Proc. Symp. Thermodynamics of Nuclear Materials, Julich, January 29-February 2, 1979 (IAEA-SM-236162). 1321 D.C. Fee and C.E. Johnson, in: Proc. Int. Conf. Fast Breeder Reactor Fuel Performance, Monetrey, CA, March 5-8, 1979, p. 372. [ 331 J.E. Antill, K.A. PeakaIl and E.F. Smart, J. Nud. Mater. 56 (1975) 47. f34) D.C. Fee and C.E. Johnson, J. Inorg. Nucl. Chem. 40 (1978) 1375. [35] D.C. Fee and C.E. Johnson, J. Nucl. Mater. 78 (1978) 219. [36] D.C. Fee, I. Johnson, S.A. Davis, W.A. Shinn, G. Staahl and C.E. Johnson, Argonne National Laboratory Report ANL-76-126 (1977). [ 371 H.E. Floton, Argonne National Laboratory, private communication, 1979.
PHASE EQUILIBRIA IN THE Cs-Cc-0
SYSTEM *
D.C. FEE, K.Y. KIM and C.E. JOHNSON chemical Engineering Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, USA Received 19 October 1978, in revised form 30 March 1979
Phase and thermodynamic data have been used to construct a self-consistent Cs-Cr-0 phase diagram. The cesium chromate which probably forms on the cladding inner surface in uranium-plutonium oxide fast reactor fuel pins is CssCrO4.
1. Introduction The lifetime of mixed uranium-plutonium oxide fuel pins may be limited by reaction of the stainlesssteel cladding with fuel containing fission products. Post-irradiation examinations show two types of reaction: the first type is the uniform oxidation (matrix attack) of the stainless steel, which results in a general decrease in the thickness of the cladding; the second type involves the intergranular penetration by oxygen and fission products along the grain boundaries in the cladding. Matrix attack rarely exceeds a depth of 50 urn; intergranular attack, on the other hand, may penetrate the entire thickness of the cladding. Intergranular attack is generally nonuniform in depth and sporadic in occurrence. Fission products play important roles in fuel-cladding inreractions. Cesium is always observed in the regions of attack and is usually associated with chromium from the cladding [l-l]. However, the identity of this Cs-Cr-0 phase has not been determined in post-irradiation examinations of mixed uraniumplutonium oxide fuel pins. Nevertheless, the formation of a Cs-Cr-0 phase is postulated to break up the protective Cra03 layer and open the way to cladding attack [5,6]. Bmakup of the protective CrsOs layer is an essential feature of fuel-cladding chemical
* Work performed under the auspices fo the US Department of Energy.
interaction that has been incorporated into various models of cladding attack [l-3]. In order to define the conditions required for the formation of a Cs-Cr-0 phase in stainless steel-clad fast-reactor fuel pins, we have used thermodynamic data and results of phaseequilibrium experiments to construct a self-consistent Cs-Cr-0 phase diagram.
2. Laboratory experiments
Experiments were conducted to determine the phases present at selected locations in the Cs-Cr-0 phase diagram. In these experiments, various cesium-, chromium-, and oxygen-containing mixtures were placed in sealed nickel capsules (7.9 mm I.D., 7 cm long) and heated isothermally at (923 f 5) K for 12 to 76 days. All of the sample preparations were performed in a high purity helium atmosphere [7] except for the heat treatment of the sealed capsules which was performed in air. During an experiment, the capsules were positioned vertically to ensure that liquid cesium (if present) was in contact with the solid reactant. To ensure intimate contact of the reactants, the capsules were inverted daily. Further, when liquid cesium was not a reactant, the powdered starting materials were pressed into a pellet (capsule F, table 1). At the end of each heat treatment, the capsules were quickly quenched (15 s) and any elemental cesium present was removed by vacuum distillation at 573 K before analysis of the capsule contents. The initial
D.C. Fee et al. /Phase equilibria in Cs-#-0 Table 1 Summary of conditions and results for isothermal Capsule
Reactants a)
Heating time (days)
system
phasestudiesat 923 K Products In reaction mixture b,
On cladding inner surface ‘)
Cs + CrOs (16, 10) Cs + Cr03 (21, 10)
43
Cs$rO4
Cr (trace)
14 23 76
Cs$rO4 + Cs&rO4 C&r04 Cs3CrO4
Cr (trace) Cr (trace) N.A. d,
Cs + CrO3 (22, 3.9)
23 56
Cs + Cr203 (6.4, 1.2)
19 19 19
f) f)
N.A. Cr e)
0
Cr e)
12
Cr, Cs-Cr-0
Cs + Cr203 (3.1, 1.2) Cs&rO4 + Cr (0.63, 0.66)
287
Cr e, N.A.
$4Cr04
‘*g)
N.A.
a) Values in parentheses are the quantity of each reactant in milimoles in the order shown; for replicate experiments the average composition is given. b, From X-ray diffraction analysis, unless otherwise noted. ‘) From electron microprobe analysis. d, Not analyzed. e, Thick Cr layer which contained no measurable Cs or 0. f) No Cs-Cr-0 or Cr-0 compounds could beidentified. g) Pure Cr phase and a phase containing Cs, Cr and 0.
composition of each mixture, the experimental cbnditions, and results of the experiments are summarized in table 1 and fig. 1. Also shown in the figure are the tie lines that were determined our analytical data; X-ray diffraction analysis of the reaction mixtures and electron microprobe analysis of the inner surface of the nickel capsules. The X-ray spectra obtained were characterized by weak and diffuse lines which
Fig. 1. Selected portions of the cesium-chromium-oxygen phase-diagram, isothermal section, 298-1100 K. The compounds CsCraOa, Cs#raO1o and probably Cs2Cr4013 exist only below 674 K. The compound G&20, melts at 658 K. The existence of Cs@O4 is tentative, see Appendix. T’he letter designations refer to sample compdsitions given in table 1.
288
D.C. Fee et al. /Phase equilibria in Cs-Cr-0
made unequivocal identification difficult. This may have resulted from the extremely hygroscopic nature of Cs&r04.
3. Results and discussion The principle result of our experiments was to establish a Cs4Cr04-Cr tie line in fig. 1. In addition,
our results confirmed the work of Knights and Nips [8] who report tie lines going from Crz03 to CszCr04, CssCr04 and Cs&r04. In our work, the existence of a Cr-Cs4Cr04 tie line is supported by the absence of evidence for the formation of Cs(Q) in capsule F and by the presence of extensive chromium deposits (which contained no measurable cesium or oxygen) on the inner surface of capsules C, D and E but not A and B. These chromium deposits suggest that chromium metal is an equilibrium phase and are the basis for the Cr-Cs4Cr04 tie line that is shown in fig. 1. The location of the chromium deposits on the capsule inner surface rather than along the grain boundaries of the product is consistent with chromium metal being an equilibrium phase at 923 K rather than a phase formed during quenching of the sample. However, the results do not rule out the possibility that chromium metal was an intermediate reaction product rather than an equilibrium phase. The existence of a Cr-Cs4Cr04 tie line is also supported by experimental work of Aitken et al. [9]. In their studies, a nickel capsule was loaded with 16.4 mmol Cr*Os and 37.6 mm01 cesium, welded closed, and heat treated for 100 h at 1073 K. The reactant composition in thsi capsule is nearly identical to that of capsule E in fig. 1 and table 1. A major phase of chromium metal, together with an unidentifiable minor phase were reported based on X-ray diffraction analysis of the products [9]. In contrast to the Cr-Cs&r04 tie line that we propose, Knights and Phillips [8] reported a Cs(Q)-CrzOJ tie line based on results of emf measurements (12-48 h, 923 K) and on a lack of a visually observable reaction between liquid cesium and CrzOs in an experiment for 16 h at 873 K. We have drawn a Cr-Cs&r04 tie line based on results of microprobe examination and X-ray diffraction analysis. Further, we have drawn a Cs&r04-Cr tie line because the emf measurements
system
were not sufficiently accurate to decide between a Cr-Cs&r04 or Cs(Q)-Cr303 tie line and because the equilibrium phases in the emf cell (other than Cs(Q)] were not determined at the end of the experiment. The emf cell measurements resulted in a typical uncertainty in the oxygen potential (A?&, = RT In poz) of +30 kJ/mol 02, while from thermochemical data an uncertainty of less than +7 kJ/mol O2 at 923 K is required to distinguish between a Cr-Cs4Cr04 or Cs(P)-CrzOS tie line. Fig. 2 shows a calculated Cs-Cr-0 phase diagram based on the thermodynamic data given in table 2. The calculational method is described in detail in Appen-
7007
700
900
II00
TK Fig. 2. Oxygen potentials in the cesium-chromium-oxygen system from 700 to 1100 K. The dashed lines are cesium isobars (in Pa). If a CssCr04-Cr tie line exists, the lowest solid line represents a region containing Cs(Q) and Cr in equilibrium with CssCrO4 instead of Cs&rO+ Also shown is the oxygen potential of (U~$u~~o) O~.noo.
Table 2
573 [lo] b)
~2~3010
Not indexed [ 8,273
2603 [28]
No transitions [ 281
CsscTo4
Cr203
Hexagonal [ 291
1135 + 8 [28]
1587.6 * 3$ [26] 1606 f,
1542.7 f 2.6 [26]
i74 g)
429
411
393
375
605
2091.1 * 2.8 [ 171 1430.0 k 1.9 [22]
-
-
-A$,w (J/m01 - K)
-
-
-A%,, OEJ/moU
a) Standard entropies, &g {J/m01 - K) from ref. [ 191: Cs(c), 85.1 f 0.4; Cr, 23.6 f 0.2;02(g), 205.0 f 0.04. ‘) f)ecomPo=s by 2 CsCr&&) + Cq$r20#2) + 2 Cr203(c) + $Oz(g, 0.2 atm)at temperature indicated. c, Unknown. d, Decomposes by 4 CszCraOro(c) + 3 Cs2Cr207(c) + 2 CsCraOs + 3 02(g, ft.2 atm). e, C&O4 has also been identified by chemical analysis, see ref. ]25?. f, Estimated, see Appendix. Efforts to measure the entropy of Cs3CrO4 have been initiated at this laboratory. g) Additional data: AGp(Cs, g) = 71000 - 75.3 T J/mol [ 281.
-
No data
No data
CWfl4
[ 211
Cubic (241 e, Not indexed [ 8,271
Orthorhombic >1273 K [8]
cs3cro4
1293 [15]
CS2CrO4
cs2fi207
or618* 13 [14-171 P OL1070 [15] P No data 658 f 10 [14-171
-
No data
c32~4013
Monoclinic [ 121 a! - orthorhombic [ 121 13- rhombohedral [ 12,131 Not indexed [ 181
Orthorhombic [ 111 Monoclinic [ 10)
- c)
(L674 [lo] b, p 505 [lo] b)
C&r308
X-ray diffraction pattern
properties of c&urn chromates Melting point o<)
Transition temperature (K)
thermodynamic
Compound
physicaland
81.2 f 1.2 ]28]
430 f)
362f)
296 f,
228.59 f 0.23 [23]
330.06 f 0.33 [20]
-
-
-
@,,I3 a) (J/mol - K)
3 ?I
+ z
$ -. a a
g
9 n ?I 1 % x % L? 2
290
D.C. Fee et al. /Phase equilibria in Cs-G-0
dix I. The dashed lines in fig. 2 show the calculated cesium isobars (in Pa) in the two-phase regions. The accuracy of the calculated cesium isobars and the oxygen potential are discussed in Appendix II. Not shown in fig. 2 is the CssCrsO,--Css CrOo -Crz03\ region which exists only at oxygen potentials which are too positive to be encountered in nuclear fuels (for example, -50 kJ/mol at 600 K). Fig. 2 shows that the oxygen potential of the threephase region containing Cr t CrsOs is close (15 kJ/mol at 923 K) to the oxygen potential of a three-phase region containing liquid cesium. To resolve these two regions requires an emf cell technique with an uncertainty of less than 7 kJ/mol in the resultant oxygen potential. Because the choice of a Cr-Cs&r04 versus Cs@)-CrzOs tie line depends on resolving these two regions, the emf cell technique of Knights and Phillips [8], with a typical uncertainty in oxygen potentials of +30 kJ/mol, is too inaccurate to decide between a Cr-Cs&r04 or Cs(P)-CrsOs tie line.
4. Application to uranium-plutonium oxide fastreactor fuel pins In a fast-reactor fuel pin, the oxygen potential at the cladding inner surface is expected to be fixed by the initial O/M (M = U + Pu) and U/m! ratios of the fuel. At start-of-life, the O/M ratio of the fuel at the fuel-cladding gap is estimated to be slightly below 2.00 [l-3]. As shown in fig. 2, CssCrO,ois the Cs-Cr-0 equilibrium species expected to be found between the oxygen potential for stoichiometric fuel [3,30] and oxygen potentials about 150 kJ/mol more negative. The compound Cs&r04 is formed only at oxygen potentials nearly as negative as that of the Cr-Cr,Os equilibria. The compound Cs,Cr04 is formed only at oxygen potentials more positive than that of (Ue.s,-,Puo.,o) Oz.ooo. However, due to the uncertainties in the estimation of the &.!&a8 values in table 2, the possibility exists, that CszCr04 may be the Cs-Cr-0 phase present at the oxygen potential of (Ue.8ePue.2e) Oz_eoo.Nonetheless this possibility is remote because the O/M ratio is estimated to be slightly below 2.000 [l-3] and because the oxygen potential line for (Ue_aePue.~o)02+eeoin fig. 2 represents the upper limit of the range of oxygen potentials calculated for stoichiometric fuel f3 11.
system
Consequently, CssCrOI1is the cesium-chromiumoxygen species most likely to be formed on the stainless steel cladding of mixed uranium-plutonium oxide fast-reactor fuel pins. The conclusion that CssCrOe forms on the cladding inner surface in equilibrium with CrzOs is not in conflict with recent analysis of the composition of fuel-cladding reaction products in the gaps of several irradiated fuel pins [4]. Although the concentrations of elements determined in this analysis contains significant uncertainty (rtr20%),the results, when combined with reasonable assumptions concerning the phases other than cesium chromate and Cr?Os which are present [l-3], yield a range of Cs-Cr-0 compositions which bracket those along the Cs3Cr04-Cr203 tie line. Because of this uncertainty, the Cs&r04/ CrsOs molar ratios consistent with these post-irradiation results vary from 0 to 0.1. The calculated cesium pressures required for the formation of CssCr04 in fast-reactor fuel pins appears to be readily attainable from cesium-fuel equilibria [5,6,32]. Hence, the calculated cesium
5. Summary
Phase and thermodynamic data have been used to construct a self-consistent Cs-Cr-0 phase diagram. The cesium chromate which probably forms on the cladding inner surface in uranium-plutonium oxide fast-reactor pins is CssCr04.
Appendix I: Thermocttemicalcalculations To serve a basis for constructing the Cs-Cr-0 phase diagram, thermodynamic functions for the cesium chromates were estimated in a self-consistent manner from the measured values of the enthalpies and entropies of formation given in table 2. Thermodynamic data were estimated for CssCr04, whose existence has been tentatively deduced 1331, although a unique X-ray pattern has not been reported for this
D.C. Fee et al. /Phase equilibria in Cs-Cr-0
compound. Thermodynamic data were not estimated for CssCrsOs, CszCr301e and CszCr40rs even though unique.X-ray patterns have been reported for these compounds [ 10-131, because these compounds presumably decompose (even in air) to CssCr20, below 770 K, the temperature at which cladding attack begins. The standard enthalpy of formation of CssCr04 was estimated by extrapolating the measured trend [22,26] toward a more negative AH,, in the series of reactions Cs(c) + Cs,_ 1CrOe(c) 5
Cs,CQ
,
(A.11
where n = 3-5. The standard entropies of formation of Cs3Cr04, Cs&r04 and Cs&r04 were estimated from the measured standard entropy of formation [23] of Cs2Cr04 by assuming a constant entropy increment for each additional cesium atom in the series Cs,Cr04 (n = 2-5). This approach proved to be self-consistent in that each cesium chromate was stable with respect to disproportionation to the adjacent compounds. That is, the disproportionation reaction (reaction A.2, for example) 2 Cs3Cr04 + C&r04
+ CsaCr04
291
system
the data in table 2 is that the uncertainty in the latter is greatly reduced, particularly for the A@ values. Therefore, it appears that table 2 contains the most accurate available 298 K data which together with the data of Knights and Phillips can be used with some confidence as the basis for construction of the Cs-Cr-0 phase diagram shown in fig. 2. The Cs-Cr-0 phase diagram shown in fig. 2 was constructed in the following manner. By application of the phase rule, it can be shown that in the threephase regions of fig. 1 (e.g., CszCr04-CssCr0,+-Cr203), there is one degree of freedom. Therefore, setting the temperature futes the cesium partial pressure and the oxygen partial pressure of the system. The resultant temperature dependency of the oxygen potential (A&, a RT In po2) can be calculated from the thermodynamic properties of the phases present. For example, the oxygen potential of the CszCr04-Cs3Cr04-Crz03 region may be calculated from the equilibrium 4 Cs&r04 + CrzOs + 3 O2 + 6 CszCr04 ,
(A-3)
by using the corresponding free energy relationship 4 AGf(CssCr04, c) + AG$‘(Cr20s, c)’
(A.2)
exhibited a positive free energy change. Further, the ~;2!W values derived in this manner and shown in table 2, compare favorably with values derived by Knights and Phillips [8] from emf-cell measurements. (Comparison between calculated cesium pressures and measured values from Knudsen effusion experiments by Knights and Phillips are made in Appendix II.) The AS& values (T= 500-I 100 K) of Knights and Phillips are (-398 + 130), (-430 f 140) and (-440 + 140) J/mole K for Cs&Q, CssCr04 and CsqCr04, respectively. Similarly, derived AH& values (T = 500-l 100 K) from Knights and Phillips are (-1410 * 120) (-1510 f 130) and (-1550 f 140) kJ/mol for CszCr04, CssCr04 and Cs&r04, respectively. Knights and Phillips corrected their AH& and A$,T values (T= 500-I 100 K) to AH&as and Al!?f,298 values [27]. This results in better agreement between emf cell [8] and calorimetric values (table 2). For example, temperature corrected emf cell results for C&r04 are @,298 = (-1422 f 120) kJ/mol and A$,298 = (378 f 130) J/mol * K [27]. As a result, the principle difference between the emf cell data [8] and
+ $RTlnpo,
= 6 AGi(CssCr04, c) .
(A-4)
Similarly, in the two phase regions (e.g., Cs2Cr04Crz03) there are two degrees of freedom. Therefore, at a given temperature, the cesium partial pressure depends on the oxygen partial pressure in the system. This dependency can also be calculated from the thermodynamic properties of the phases that are present. Consider the equilibrium 6 Cs(g) + Cr&(c)
+ $ Os(g) + 2 CssCrOI)(c) . (A.5)
The corresponding free energy relationship may be written as: 6 AGi(Cs, g) + 6 RT In pi + AGfo(CrzOJ,C) + $
RT
inpoz
= 2 AGfO(Cs&r04, C)
.
64.6)
cesium pressure and the oxygen potential are related by
The
In PCs = [2 AG~(CssCrO,, c) - 6 AGp(Cs, g) - AGfO(CrsOs,c) - 3 A&,,]/6 RT.
292
D.C. Fee et al. /Phase equilibria in Cs-Cr-0
The calculated oxygen potentials and cesium pressures in the Cs-Cr-0 system that are shown in fig. 2 are based on the thermodynamic data of table 2, with the assumption that AH&as and AS&as are independent of temperature. This approach has been shown to be valid in the Cs-U-O system [34-361. Further, the effect on the thermodynamic properties of the cu+ fl phase transition in CssCrsO, at 618 K (table 2) and in CszCr04 at 1070 K is assumed to be small and therefore has been neglected. This assumption has been shown to be valid in other ternary oxide systems [28]. In calculating the cesium pressures shown in fig. 2, we have also assumed that the solubility of cesium in CrsOs or in the cesium chromates is very low and does not significantly affect the thermodynamic properties shown in table 2. The requisite solubility data are not available to test this assumption.
Appendix
II: Accuracy of calculated equilibria
Although the data in fig. 2 are in accord with the experimental phase diagram shown in fig. 1, the set of thermodynamic data which predicts the observed tie lines is not unique. A slightly different estimated asor,ass values would have led to identical tie lines. Therefore, while it appears that the estimated thermodynamic data in table 2 are qualitatively correct, the quantitative accuracy of the data in table 2 is uncertain and requires further experimentation. A rough estimate of the quantitative accuracy of the data in table 2 and fig. 2 can be obtained by comparing the calculated results with the experimental emf cell results and Knudsen effusion results of Knights and Phillips [8]. This comparison is shown in table Al where the experimental data are extrapolated to the range of interest. The comparison is made for three regions. In each region, the oxygenpotential values calculated with the data in table 2 (lines 1,5 and 8) fall within the large uncertainty bands of the experimental emf cell results (lines 2, 6 and 9). Similarly, the calculated cesium pressures in phase field C (CsJCr04--Cs4Cr04-CraOs) fall well within the uncertainty bands of the experimental Knudsen cell-mass spectrometer results. In phase field B (CszCr04-Cs3Cr04--CrzOs), the calculated cesium pressures fall at slightly lower pressures than the lower limit of the uncertainty band in the
system
measured data. It may be significant that the deviation between calculated and experimental results occurred in the phase field with the lowest (and, therefore, least accurate) experimentally determined cesium pressure. Fig. 2 is consistent with fig. 1 in that a CsqCr04Cr tie line is shown instead of a Cs(Q)-Cr,Os tie line. Our calculations show that a Cs4Cr04-Cr tie line results in the proper ordering of the oxygen potentials in this region of the phase diagram; namely the oxygen potential of the Cs(Q)-Cs4Cr04-Cr region is more negative than the oxygen potential of the Cs4C!r04Cra03--Cr region. The inclusion of a CssCr04--Cr tie line in the calculations also results in the proper ordering of oxygen potentials; namely, that the threephase region containing Cs(Q), Cs,Cr04 and Cr has the most negative oxygen potential of any three phase region in the system and that the oxygen potentials of the other three-phase regions are monotonically more positive with monotonically increasing oxygen content for a fmed Cs/U ratio. This is shown by the lowest dashed and solid lines in fig. 2. [If a CssCr04-Cr tie line exists, the lowest solid line in fig. 2 represents a region containing Cs(Q) and Cr equilibrium with CssCr04 instead of CsqCr04]. The important thing to note is that the proper ordering of oxygen potentials was not obtained with the data in table 2 when Cs(P)-CraOs tie was considered. In this case, the oxygen potential of the hypothetical Cs(Q)-Cs4Cr04-CrzOs [or Cs(Q)-CssCr04--Cr?Os region] was more negative than the oxygen potential of the hypothetical Cs(Q)-CraOs-Cr region. Further, indirect evidence supporting a Cs&r04Cr tie line was obtained by repeating the calculations with the AH&s value in table 2 but with alternative estimates of AS&ass values for CsqCr04 and CssCrO+ These alternative values are chosen to yield a Cs(Q)Crz03 tie line and the proper ordering of oxygen potentials associated with that tie line. The oxygen potentials and cesium pressures calculated with this alternative set of thermodynamic data are also shown in table Al (lines 4,7 and 10). The proper ordering of oxygen potentials with this alternative set of thermodynamic data is also shown in table Al (lines 3,4, 7 and 10). The alternative data set consistent with a Cs(P)-Cr20s tie line results in larger deviations between measured and calculated oxygen potentials (phase field B) and between measured and calculated
D.C. Fee et al. /Phase equilibria in Cs-Cr-0
293
system
Table Al Comparison of calculated and experimental oxygen pa;tentials (kJ/mol) and cesium pressures (Pa) at selected temperatures in selected three phase regions of the Cs-Cr-0 system Phase field
-._ A. Region with Cs(Q) + Cs4CrO4 b, 1. Calculated for Cs(Q)-Cs,CrO,-Cr, data from table 2 2. Measured: emf cell (890-990 K) d, 3. Calculated: Cs(Q)-Cs&r04-CraOa e, 4. Calculated Cs(Q)-CraOa-Cr B. CsaCr04-CsaCr04-CraOa 5. Calculated, data from table 2, Cr-Cs4Cr04 tie line 6. Measured: emf celJ (870-1100 K) Measured: Knudsen celJ (750-950 K) 7. Calculated - data consistent with a Cs(Q)-CraOa tie line e, C. CsaCr04--Cs&r04-Cr203 8. Calculated, data from table 2, Cr-Cs4Cr04 tie line 9. Derived from emf cell results (810-1100 K) Measured: Knudsen cell (500-680 K) 10. Calculated - data consistent with a Cs(Q)-Cr20a tie line e,
700 K
1100 K
900 K
log PCS
-AC%
- c) -
650 620 f 30 619 629 -
-log PCS
-A&
-log PCS
609 580 i 30 563 592 -
1.12 -0.83 364 396 390 f 30 350 f 30 -2.4 i 0.4 0.3 f 0.2 2.0 f 0.3 2.14 -0.91 460, 446 4.09
-A?&
568 550 f 30 506 556 331 310* 30
-3.88
1.16
562 520 f 60
4.39 497 529 470 f 60 490 f 60 3.18 f 0.6 4.3 i 0.6
564
4.22
1.4 i 0.6 2.31
432
3.17
532
5.43
500
a) The calculated data are from this work. The experimental data are from ref. [ 81. b, Ignoring the possibility of CssCrOg. The argument unchanged by this omission, see text. ‘) Because the cesium pressure in this three-phase region depends only on the Cs(Q) ++Cs(g) equilibria, all calculated cesium pressures are the same at each temperature and are not shown. Similarly, because the Cs(Q) f* C&g) equilibria was used to calibrate the Knudsen cell - mass spectrometer system, the cesium pressure was not measured independently in this region (line 2). d, The emf results are from a cell containing liquid cesium and other phase(s). The identity of the other phase(s) was not determined after the experiment. e, Using the data in table 2 except for CsaCrO4: A$QQg = 450 J/mole K, S&, = 239 J/m01. K; CsqCrO4: AS&Q8 = 488 J/mole K, S&g = 285 J/mol . K. These entropy values are c&sistent with a Cs(Q)-Cr20a tie line.
cesium pressures (phase fields B and C) than the thermodynamic data set (in table 2) consistent with a Cs4Cr04-Cr tie line (table Al, lines 1,s and 8). This analysis again supports a Cs4Cr04-Cr tie line. The foregoing comparison illustrates the sensitivity of the calculated results to large changes in A,!$$sa values, i.e., 57 and 77 kJ/mol * K for Cs3Cr04 and Cs4Cr04, respectively. These changes in A,.&, result in a change in the oxygen potential at 900 K of 82 kJ/mol for phase field B and 3 kJ/mol for phase field C, as shown in table Al. These changes in AS&as values also result in an increase in the calculated cesium equilibrium pressures over the Cs3Cr04-Cr203 and Cs4Cr04-Cr203 two-phase regions of one log pcs unit over the values shown in fig. 2. Assuming that
the estimated A&as values shown in table 2 are accurate to within +20 kJ/mol *K, a maximum uncertainty of zt20 kJ/mol in the oxygen potentials and an uncertainty of kO.3 in the log pcs value given in fig. 2 are calculated.
Acknowledgements
The authors would like to acknowledge a series of fruitful discussions with Dr. A.E. Martin. The assistance of B.S. Tani and W.A. Shinn in performing the analyses and L.O. Nippa in preparing the isothermal capsules is gratefully acknowledged.
294
D.C. Fee et al. /Phase equilibria in Cs-Cr-0
Note added in proof The entropy of Cs&rO,) has recently been determined experimentally [37]. The experimental value, $&(Cs3Cr04) = 296.2 f. 1.5 J/mol +K agrees well with the estimated value of 296 J/m01 - K used in this paper.
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