THERMODYNAMIC REVIEW AND CALCULATIONS- .... actants of the standard Gibbs free energy (J/mol) at ...... For (A2 SeO,), these values were obtained.
178
Journal
of Nuclear Materrals 100 ( 19X1) 17X-226 North-Holland Puhlishmg Company
REVIEW ARTICLE THERMODYNAMIC REVIEW AND CALCULATIONSALKALI-METAL OXIDE SYSTEMS WITH NUCLEAR FUELS, FISSION PRODUCTS, AND STRUCTURAL MATERIALS * Terrence B. LINDEMER ChemicalTechnologyDivwon,
and Theodore
M. BESMANN
Oak Ridge National LaboratoT,
Oak Ridge. Tennessee 37830, USA
Carl E. JOHNSON Chemrcal Engineering Division, Argonne National L.aboratotyy. Argonne, Minors 60439, USA Received
4 November
This paper considers fuels, fission products,
1980; in revised form 19 March
1981
the phase equilibria of alkali metal oxides ‘and their combinations with other oxides relevant to nuclear and structural materials. The other oxides include those of the lanthanides, the actinides, iron, hickel,
aluminum, silicon, as well as those of periodic table groups IIA, IVB, VB, VIB, and VIA. The alkali metal halides, chalcogenides, and hydroxides are also included. Techniques are developed to permit calculation of phase equilibria and Ellingbam diagrams in ternary and higher-order systems. These techniques include values of the enthalpies of formation and the entropies of many compounds.
1. Introduction Knowledge of phase equilibria and other thermodynamic properties of the alkali metals (A) is necessary for the advancement of the technology of both fission- and fusion-based devices for energy production. Collectively, Cs and Rb are major fission products and are often particularly important in the interactions observed between actinide oxide nuclear fuels and either stainless steel or Zircaloy cladding. In the oxide-fueled hightemperature gas-cooled reactor (HTGR), Cs and Rb may form stable oxides at the lower fuel temperatures and thus affect the overall oxidation state of the fuel. The alkali metals, particularly Na, Cs, and Rb, may be significant components of the oxides used to immobilize radioactive waste. Both Na and K have been used as
coolant components in the liquid metal fast breeder reactor (LMFBR), with dissolved oxygen affecting the coolant-clad interactions. Similar effects may be found with Li and first-wall alloys used in fusion devices. These several applications collectively require a knowledge of alkali metal behavior with several other metals * Research sponsored by the Office
of Advanced Nuclear Systems and Projects, Gas-Cooled Reactor Programs Division, US Department of Energy under Contract W-7405-eng26 with the Union Carbide Corporation.
0022-3 115/8 1/OOOO-0000/$02.75 0 198 1 North-Holland
estimation
of previously
unknown
298.15 K
and nonmetals over a wide range of temperature and of the chemical potential of oxygen, or po,. [Here po, = RT ln(P, /PO”,), where R is the gas constant (J Ti s temperature (K), PO, is the pressure mol -‘KeT), of oxygen (MPa), and P& is the pressure of oxygen in the standard state (0.101 MPa).] Such knowledge is usually incomplete and reported fragmentarily. This paper represents an effort to systematize the relevant thermodynamic information, to estimate unknown but needed data, and to present all in a manner particularly useful for the engineering applications noted above. The literature review generally provided information in one or more of the following areas: the existence of compounds, their standard Gibbs free energy of formation at temperature, phase equilibria, and reactions of nonequilibrium phases. Consideration of the thermodynamic data for the entire alkali metal group revealed correlations’ that permitted estimation of unknown data. Additionally, a computer program was available that used the known and estimated thermodynamic data to calculate phase equilibrium diagrams and the po, versus T relationships (often called Ellingham diagrams or Richardson- Jeffes charts). Conversely, the program could be used to check the consistency of available thermodynamic information with experimentally determined phase equilibria. The final result of the present literature search, data analysis, and ensuing
T. B. Lindemer et u!. / Thermodynumzc review
calculations was an information base useful for identifying the conditions necessary for the stability of phases [e.g, in postirradiation examination (PIE) and in compatibility tests]. It should be noted, however, that a critical analysis of the large body of thermodynamical data considered here was beyond the scope of the present effort. Consequently, the most crucial applications may require such an evaluation of the data base reported here.
2. General calculational methods and data sources 2.1. Gibbs free energy The Gibbs free energy for chemical equilibria will be calculated using the approximation [l]
AG; = AH;.29s - TAS&,.
(1)
Here AGF is the difference between products and reactants of the standard Gibbs free energy (J/mol) at temperature T, A HFzYR is the difference in standard enthalpies of formation (J/mol) from the elements in their standard states at 298.15 K, and AS& is the difference in standard entropies, S” (J mol-’ K-‘) at 298.15 K. Since this approximation will be used throughout, all subsequent enthalpy and entropy values are defined to be at 298.15 K. Use of this approximation was necessitated by the lack of measured H;I - H& and S; - S&a values for most of the compounds to be considered here. These data are lacking even for (K,O) , (Rb,O), and (Cs,O) *. We have assessed the magnitude of the errors in AG; resulting from neglecting the Ht - H& and Sq - S&s terms for an equilibrium. These two terms for a given species are obtained by the appropriate integration of the heat capacity, Ct, and adding the enthalpy and entropy contributions of any phase transitions. Consider first the Cl contributions. For species in an equilibrium, the usual product-reactant differences, A( Hf - H&) and A(S; - S&s), can be obtained by the appropriate integration of the difference, AC;, of the C’; values of the products and reactants [1,2]. Products and reactants typical of those to be considered in this paper appear in the equilibrium 2(MoO,) + (0,) + 2(A,Mo,O,,) it 2(A,Mo,O,,). In the case of the two complex oxides, and in the usual absence of mea* The following notation is used throughout this paper: ( ) pure element or compound in solid state; [ ] solid solution (subscript denotes solvent); { state.
] liquid state; (
) gaseous
und
culculurions
179
sured high-temperature Ci- data, the Ct contributions to H; - H& and SF - S&s for each are commonly set equal to the appropriate sum of these enthalpy and entropy increments for the component simple oxides. This method is used, for example, in the JANAF tables [2] for a number of complex oxides; errors in AC; resulting from this “additive oxide” assumption will be examined later. The consequence of this “additive oxide” assumption in the case of the above complex equilibrium is that the A( H;I - H&) and A( SF - S&s) values are identical to those for the simple equilibrium 2(M00,) + (0,) F+2(MoO,). This generally applicable result greatly simplifies the assessment of the error in AG; resulting from neglecting the AC; contribution to the A( HF - H&) and A(SF - S&) terms. Values for the errors in AG; were computed at 500, 1000, and 1500 K by using JANAF data [2] for species having measured high-temperature values. In addition to the (MOO,) + (MOO,) equilibrium, the {Li} + (Li,O), {Na} + (Na,O), (MO) + (MOO,), (Ti) + (TiO,), (Nb) + (NbO), (NbO) + (NbO, ), (Cr) + (Cr,O, ), and (Fe) + (FeO) equilibria were considered, with each involving one mole of (0,). The above species are representative of those appearing in the complex oxides to be considered in this paper. Upon defining the error in AGF as being the difference between the actual value and that found using eq. (l), the average errors were calculated to equal -0.49, -5.76, and - 11.52 kJ/mol at 500, 1000, and 1500 K, respectively. (The range of the errors at the same temperatures was 0.84 to - 1.47, 4.50 to - 19.39, and 3.17 to -22.66 kJ/mol, respectively.) The absolute values of the average errors are nearly identical to those calculated by Lindemer [3] for several gas-solid reactions involving fluorides, borides, oxides, carbides, and nitrides. Consider next the error in AG; resulting from the “additive oxide” assumption. Data for the heat-capacity differences between six alkali-metal complex oxides and their component oxides average - 2.35 J mol - ’ K - ’ at 300 G TG 1200 K [4]. The resulting error in AGj is - 2.35[ T - 298 - Tln( T/298)] kJ/mol, or 1.2 kJ/mol at 1000 K. A similar analysis of high-temperature thermodynamic data [5] for ten alkali-metal alumino-silicates and their component oxides demonstrates that the “additive oxide” assumption leads to an average error in AGF of -0.085, 2.5, and 8.1 kJ/mol at 500, 1000, and 1500 K, respectively. The range of the error at these temperatures was 1.26 to - 2.26, 9.93 to - 1.07, and 24.92 to -2.31 kJ/mol, respectively. These errors are generally of the same sign and magnitude for each of the compounds in a given alkali-metal system, and thus the errors may partially cancel when complex oxides of
the same system are both reactants and products. Errors in AC; also result from neglecting the thermodynamic values for phase transitions. Each transition contributes to AC; by AHp(l - TT,-‘) above the transition temperature, T; here, AH,” is the enthalpy of the phase transition. Values of AH; for solid-state phase transitions are small [2], but neglecting them could lead to a AC:, error of approximately d -5 kJ/mol. The AH: contribution to AC; from melting and vaporization of the elements will be included in the present calculations, while the enthalpy of melting of the compounds is not a factor because the AC; calculations generally will not be extended above the melting temperatures. Having stated the magnitude of these errors, there is no known general method for including them in the present AC; calculations. In addition, there are errors in the 298 K A HP and So values that contribute to the error in AC& However, current developments concerning the effects of the errors on the calculation of phase equilibria will be described in section 2.5. All calculations of the AC; values assume an activity of unity for each of the condensed species, unless noted specifically. Ideal behavior was assumed for the gases. The appropriate standard states for the elements at referenced to 298.15 K, are used temperature, throughout. 2.2. Estimation
of S” values
Methods for estimating S” values for crystalline compounds are discussed in the literature [6-81. One common method is the calculation of the average entropy of formation from the elements, AS,?, of compounds having known S” values and chemical similarities to the compound of interest. The average ASP value is then used to calculate the unknown S” value. A second method is useful for estimating So values for complex oxide compounds that can be considered to be formed from simple oxides. Here one calculates the average entropy of formation from the component oxides, AS&, for compounds that have known S” values and chemical similarities to the compound of interest. This average is subsequently used to calculate the unknown S” value. Specific applications of each of these two methods will be described later. A simple expression for the estimation of S” values is needed for complex gases. Kubaschewski and Alcock [l] present estimation equations for molecules containing up to five atoms and having molecular weights, M, up to 300 g/mol. Since many of the species to be considered here have larger molecular weights and num-
bers of atoms, a new numerical approximation has been derived. Consider a molecule having the general formula D,E=O,+=+, 7in which D and E are any elements other than oxygen or hydrogen. Here, x + z Gy and x and/or z can be zero (i.e., S” for ozone can be estimated). A molecule is considered to be composed of x (DO) molecules, z (EO) molecules, and y/2 (0,) molecules, all of which have S” data in the standard reference tables or in ref. [9]. The present analysis considers the 298 K entropy difference between the complex and its diatomic components. The S” equations on pages 9 and 10 of the JANAF tables [2] were used to compute this difference and lead to the following expression for the entropy for the complex, S”( cx): S”(cx)=1.5RlnM,,
+4ln298.15-2.349+k’
+x( S” - 27.253 - 1.5R In M)(,,, +z( So - 27.253 - 1.5R In M),,,, +0.5y(S”
- 27.253 - 1.5R In M)(oz,.
(2)
A numerical analysis was made for the value of k’ for JANAF data [2] for gases as light as (Be,O,) and as heavy as (W,O,). The value was found to be equivalent to - 1.5R In 298.15, with a standard deviation of 12 J mol-’ K-‘, which is thus the standard deviation of the estimated S” value. The only apparent restriction on eq. (2) is that it not be used for trimer or higher-order molecules such as (B%O,) or (W,O,). However, even these molecules can be treated. If one defines (W,O,) and (Be,O,) as third-order molecules, (Be,O,) as a fifth-order molecule, etc., then eq. (2) can be used by subtracting the factor 0.5R (order - 2) In 298.15, the only exceptions being (P406) and (P40,0). Examination of the entropy equations in the JANAF tables [2] reveals that the errors in the estimations from eq. (2) result from the differences between the complex and the diatomic molecules in their vibrational, electronic, and anharmonicity contributions, with anharmonicity contributions being neglected in the JANAF tables [2] for molecules containing three or more atoms. An adaptation of eq. (2) was extended to the analysis of gases in which (x + Z) > y. with similar results. The use of eq. (2) in the latter case is best illustrated with an example. Consider the species (F4WO) to be composed of two (F,) molecules and one (WO) molecule. Thus, in eq. (2), the first line remains the same, the second line is calculated at an x value of 2 with S” and M values for (F,), the third line is calculated for one (WO) molecule, and the fourth line is not needed. Another equally valid estimate of the S” value of (F4WO) could be calculated by assuming that it was composed of one (WF) mole-
181
T. B. Lindemer et ul. / Thermodynomrc review und culculutions
cule, one (FO) molecule, and one (Fz) molecule. In all, known S” data for 60 gases were analyzed in deterrnining the value of k’ given above. 2.3. Estimation
of AH/ values
2.3.1. First method
Consider the binary or pseudobinary A-B system, including compounds (A,B), (AB), and (AB,). One can write three reactions, (A) + (AB) --+(A,B), (A,B)+
(AB,)-
3(AB),
CAB) + (B) -+ CAB, >. Since AC; < 0 for each, one can write three inequalities AH;,
I -AH;
.,:, -T(S;.,-S,O-S;,)
107.7 153.6 102. I
89.16 160.2 95.56
AH; S” ASP
210.8 196.8 138.5
137.5 230 127.2
127 249.6 120.2
AH; S” ASP AH;
-417.1 75.06 - 130.3 44.26 1405
-361.4 94.13 - 137.7
TlIl
-598.7 37.9 - 122.7 45.89 1843
AH; S”
- 552.8 55.06
-372.8 91.60
AH; S”
- 166.9 228.9 84.09 210.8 79.24
83.67 229 49.94
AH; S” AS;
- 632.6 56.48 - 206.7 713
-511.7 94.80 -213.3 948
1241
AH; S” As; ” L AH; S” AS; =’ Trll
- 347.2 77.4 -115 1477
2.19 83.67 961
1032
[231
W] [44] WI
WI WI [44] [251
WI WI 1251
703
b) b)
- 338.9 132.6 - 122.3
I1481
673
I1501
66.94 248. I 69.03
b,
iI31 I1501
-471.9 134.7 - 223.7 844 762
b) b) b) b) b)
IlW
- 377.8 79.49 - 137.2 1223
-414.2 112.9 - 129.7 1221
WI WI
- 360.6 133.8 - 133 8
WI
- 342.6 92.04 - 135.5 1150
- 384.9 125.5 - 128.4 975
WI PI
- 330.5 149.7 - 129.7
b) b) b)
108.7 - 128.4 1225
WI WI WI w
- 334.7 131.7 - 131.7 1000
11471 [I491
-302 168.1
b, b,
I1511
62.75 255.4 67.56 -484 152.8 -222.5
b) b, b,
1241
- 140.5 825
- 334.7
- 345.9 146.8 - 125.9 43.93 753
-92.04 317.9
- 287.8 138 - 143.8 685
[44]
2.09 92.06 944 76.65 175.4 90.33
- 284.5 122.4 - 147.1 782
WI
Ref.
106.2 283.9 113.6
71.12 237.9 70.70 -495.8 112.9 -221.3 763
CS
85.14 307
80.87 169.9 93.21
1154
- 264.4 115.8
-401.6 71.12 -117.1 1575
Ref.
76.77 312
2.28 71.45
I241
AH; S” AS;
-446.4 58.57 - 112.9 1645
Rb
- 50.20
AH; so AS;
AH; S” AS; c’
Ref.
64.68 336
159.1 138.6 109.5
Gl
CA 76
K
AH; S” AS;
cl
(We>
Ref.
51.46 371
Tm
(A#,)
(A&
Na
2.41 51.85 1156
Tn
CA%
Ref.
2.38 33.94 1615
Tb
G42Q)
Li
temperatures
11521 bl b) v41
775
1241
- 294.9
11521 b, b,
146.4 - 143.8 705 - 342.2
146.4 -138
[241 WI WI
PI
WI WI WI
-301.2 157.7 - 129.7
I1531
b) b) bl
-313.7 166.5 - 129.7 933
b, b, b,
-284.5 174.4 - 129.7 953
b’ b, b’ I221
WI
As;
69.70
64.68
60.45
58.7
56.60
@Cl)
AS;
72.25
66.77
62 80
61.12
59.32
P21
184 Table 1 (continued) Species
Quantity a’
WW
As;
72.46
66.98
63.05
61.63
59.95
[47]
(AI)
AS;
72.71
67.19
63.22
61 92
58.61
[47]
(A,F,)
AH; S” AS;
- 942.7 258.5 -2.34
- 846.4 287.2 - 18.37
- 862.7 319.8 - 12.22
- 853.5 339.7 - 16.52
b’ b,
-890.1 352.2 - 20.78
(A&I,)
AH; S” AS;
-598 5 288.6 7.55
- 566 325.3 -0.55
-617.6 352.7 0.42
-627.5 371.7 -4.77
b, b’
-659.8 383.3 -9.94
(A2Br2)
AH; S” AS;
-5008 314.4 10.88
-486.3 348.8 0.57
- 540.5 376. I 1.40
-557.7 395.9 -3.01
h’ b’ h,
-581.5 408.2 -743
b, b, h,
(A,&)
AH;
-361.9 330.5 11 78
-347.2 368.6 5.17
-422. I 395.6 5.68
-447.6 416 1.88
b’
[481 1481
b,
-461 428.9 - 1.93
-484.9
78.90 - 153.5 679 11.94
-418 I 90.79 - 153.9
b, b,
S” AS;
Li
Ref.
Na
Ref.
b, b, b,
K
Ref
Tl AH;
-154.1 744.3 IO.48
- 425.6 64.43 - 154.8 596 8.71
{AOH)
AH; S” AS;
- 474.4 48.07 - 148.7
-416.8 75.85 - 143.3
-412.7 96.56 - 135.8
(AOH)
AH; So AS;
- 234.3 210.5 13.63
- 197.7 228.3 9.08
- 232.6 236.2 3.81
(AOH),
AH; S” AS;
-711.2 269.6 -124
- 647.6 307.2 - 131.2
- 654.7 327 8 -137
(A,CrOd
AH; S” AS;
- 1394 145.7 -346 35.48
- 1342 [IO11 170.2 [1011 11011 - 366.2 22.84
- 1403 200. I - 362.8 33.59
-1518 129.7 - 366.9 14.01
iI61 -1468
- 1498 189.7 -379.2 1767
WH)
AH; S” AS;
A S&x AH; S” AS; A S&x
(A,WW
11561
- 1548 161 1004
AH; S” A Sk
(A,Cr,O,)
- 1999 248.9 -619.2 30
AH; S” AS; A S&x
(A,Mo,%)
AH; S” AS;
159.4 -382.5 6.59
-2280 223.4 -609.6 30
b, b’ b, b)
- 2245 250.6 -627 20.04
- 1682 190 20 bl
b’ b,
Ref.
b)
CS
Ref
-416.7 98.74 - 154.20 588 IO 72 -406 118.4 - 134.4
- 238.4 247.4 2.72
b’ b’
- 259.4 254.6 1.74 -687.8 360.6 - 145.1
- 1414 217.5 - 369.6 12.55 [I561
b;61 b)
-2061 291.2 -601.6 52.29 - 2397 279.4 -624.6 30
Rb
b)
” b’ h,
[I541
- 1430 228 5 - 375.3 9.33
11011 [I541
- 1493 234.3 - 357.8 23.89
11481 [I481
- 1514 248.3 -3605 23.74
[I551 [I571
- 1682 228.4 20
[b’,61
- 1682 242.6 20
i;61
-2062 306.6 -612.1 30
b)
-2091 330 - 605 38.40
G31 II581
- 2302 339.7 -605.2 37.36
[I591 [I591
- 2280 3179 -610.4 30
b)
b, b, b, bl b’ b’ b)
b)
T.B. Lindemer et al. / Thermodynamic review and culculatmns
185
Table 1 (continued) Species
Quantity a)
643CrO4
AH,” S” AS;
>
A S&X
Li
- 1669 130.2 - 390.7 15.02
Ref.
b’ b) bl
b)
AH,”
(A4CrO4)
A S&x
1
(A 2WO4
(AVO3
)
>
b) b)
b’ b)
b)
(ANbO2
>
(A2Seo3)
(A
2TeO3
(A2SO4)
>
20
iI61 b)
- 1201 422.5
AH,” S”
-1165 94.13 889
b’
-1145 113.8 911
-1154 122.1 793
b’
AH; S”
-1340 97.48 1523
- 1076 402
b’
[271 b) b) 1281
- 1877 133.4 1425 - 2052 136.8 1681
b) b’
691
i;91
- 1038 422.5
[791
-1128
I791
-1145
- 1317 116.3 1685
b)
[281 b) b) 1261
b)
S”
- 932.6 74.05
AH; S”
- 967.3 84.09
b) b) II611 [I621 I1631
As,0
-1150 -1164 105.8 -291.6
AH; SO d)
- 1058 110.8
b'
AH; SO d)
- 1092 118.4
- 1434 AH? 113.9 S” 23.76 A SlYOX -386 AS; T -m
1133
b’ b’
b’
[81
[I501
413.7
- I333 125.6 1312
-2918 318.4
-2951 348.5 I183
- 1757 189.5
- 1775 221.3 i573
1271 b)
I281 b) b)
AH; AH; S”
(A2SO3)
bl
-1164 418.3
AH;
>
b’
- 1552 330 -410.8
-II48 407. I
Tm (AVOZ
b)
[791 b)
Trn >
b’
-391.6 15.02
- 1010 382.8
AH; S”
CA,=04
b’
- 1021 418.3
Tn >
b’
AH; S”
T,
CAY04
- 1585 253 -493.3 20
-1518 272.3
I1601 691
- 979.4 406.6
AH; S”
(A4W,)
b)
- 1548 214.5 -413.1 15.02
Rb
- 1030 - 988.6 376.9
AH; S”
>
b’
Ref.
AH; AH; S”
Tm (AN’@
b’
K
1791
S” (A 2 Moo,
Ret.
-881.1 381.1
AH;
1
- 1531 185.9 -402 15.02 - 1623 214.8 - 424.6 20
S” AS;
(A,Cfl,
Na
- 1933 192.8 1265
b’ b)
WI
- 886. I 92.46
b)
- 920.4 102.9
b’
- 1090 146 - 296.2 -959.8 155.6 - 966.5 163.1 - 1386 149.6 22.25 -395.1 II57
b)
- 1949 225 1260 887.4 102
b’
417.9
I291
-1158 141.5 823
b) b)
- 1343 145.1
I261 b) b)
- 2943 425.5
b)
b' [261 'a b)
- 1767 279
- 1941 282.4
Ref.
b) b’ b)
b) b’ bb b’
b)
1791 b’
[791 b) b) b) v91 b)
b’
b) b) b’
b)
b’
CS
Ref.
- 1542 296.2 - 392.8 17.57
I731
- 1587 361.9 -412.1 23.43
[731 I731
-1047 435.1
!791
- 1207 -1154 431.3
1801 [791 I801
- 1210 435.1
I791 b)
-1187 148.6 913 - 1361 152.2 II30 - 2986 453.9 II65 - 1796 300 1473
b) b) 1291 b) b)
1271 bb bb i271 b) b) 1271
- 1970 303.7
b) b)
-II29 - 1096 212.5 - 297
[I611 I1621 b) b)
I281 b) bl
b)
1131 1131
b’
[;641
[I501
-III6
1131
166.1 - 302.9
II631
- 966.5 182.4
b’
- 962.3 189.5
b’
- 1437 175.5 29.12 - 395.6 1342
b' b’
[891
-1125 - II03 191.6 -297 -944.3 206.2 - 949.7 213.8 - 1435 197.4 12.55 - 397.9 1333
[I611 [I621 b)
b’ b) b’
P91
- 949.7 223
b) b)
- 945.5 230.5
b) b)
-1419 211.9 12.76 -400.1 1283
[I31 PI
II501
T.B. Lmdemer et ui. / Thermodpnumrc reviru und culculutron.~
186 Table
I (continued) QlUUltity a’
Species
(A,SiO,OS)
(AAISiO,)
- 1020
[b1,651
S” e) A SF,, AH‘P AH;
114.3 13.72 -1138 -1142
b) b)
AH; g= e)
- 1213 121.7
AH,” AH; S” S” T*
- 1649 - 1631 80.29 83.67 1474
AH; AH; S” S”
- 2560 -2520 125.5 125.5 1307
b)
-962.3 159.1 21 33 - 1080
-
1121 166.5
-1561 [1661 - 1556 113.8 11661 i 13.8 I362
[I661
[1661
-1189 53.34 1883
A H,O S”
-2123 103.8 >I600
[51 151 [51
- 3053 129.2 >I700
151 [51
A HP S”
Na
Ref
- 2470 - 2474 164 164.8 1147
Ret.
-1010 185.6 28.70 -1128 -ml133
it651
b)
-1146 192.8
bl
[I661
[1661
-1548 -1558 146 I 138 1249
-2493 [I661 -2483 182.4 11661 182 1310 -1133 8075
-1133 70.41 1923 -2092 124.3 1800
[51 [51 [261
-2121 133.2 2025 -3038 200.2 1965
1550
a) Temperatures in kelvin, enthalpy values in kJ/mol, entropy unless referenced specifically. b’ Estimated by authors, see text. ‘) AS/ from (A) and either (&), (Se,), or (Tez). d, From ASP =-296 J mol -’ K-‘, see section 4.10.2. e, From ASP = -396 J mot-’ K-‘, see section 4.10.2.
3.2.1.
K
I1651 b) b) b)
I1611 b)
A H,O S”
7, (AISi,O,)
Ref.
AGP
Cl (AAIO,)
LI
values in J mol _
A-O
Some data were estimated here for oxide species. For (RbO), A HP is the average of these values for (KO) and (CsO), while S” values for (RbrOr) and (Cs,Or) were calculated from the average of AS; for (Na,Oz) and (K,O,). The A HP value for (Cs,O,) is the average of those for (K202) and (Rb,O,); the AH; and S” values for (Cs,O,) and (Rb,O,) give AC; < 0 for the reaction (A,O) + (AO,) --t l.S(A,O,). The existence of (A,O,) compounds is referenced in table I, and melting temperatures are given there for the K, Rb, and Cs species; they have not been reported in the Li and Na systems. No thermodynamic values are available for
Rb
Ref.
cs
[1631 h) b) b)
[I611
-1004 209.6 14.22 -1122 -1114
-1002 226 5 16.90 -1120 -1138
b) b)
-1133 217
bt bl
-1129 233 8
hJ
-1581 -1529 191.2 184
n) b)
[I661 [I661 bi
I
-1556 -1532 176.9 151.4 1143
[261
-2481 -2458 220.9 213.3 1365
b) h)
-1128 100
g661
[I661
[51
[51
!;661 I1661 1271 h) 11661 h) [I661 [271 b)
h)
- 2497 -2454 235.1 2259 1343 -1135 107.1
-2121 159.4
Ref.
61651 hl b) I1611 h) ht hl ii661 I1661
L',661 [I661 [271 bl bl
b) b)
(261 [51 (51
- 3045 1979
bl h)
’ K - ’ Data from refs. [ 11, [ 121, [ 14). [ 151, and [ 17-2 I]
the (A,O,) compounds. The So values for (RbO,) and (CsO,) were calculated from the average of the ASP values for (NaO,) and (KO,). Compounds of the type (AO,) are known [23,24], but are stable only at positive values and thus cannot form in nupo, clear fuel systems. Compounds lying between.(A) and (A,O) are also known in the Cs and Rb systems [23,37] but these have melting temperatures < 445 K, no available thermodynamic data, and are not of interest here. Information on oxygen solubility in liquid alkali metals is available for all but {Rb}. The liquid alkali metals exhibit substantial, but widely differing, solubilities. Noden [38] has critically assessed 12 sets of mea-
T. B. Lindemer et (11./ Thermodynamic
187
review and culculuiions
surements and recommends the expression log(wppm O)mnx = 6.2571 - (2444.5/T)
(3)
for the maximum solubility by weight [(wppm O),,] in {Na). Adamson and Aitken [39] derived the pLo,-Toxygen content (wppm 0) relationship in {Na} by setting activity coefficients equal to the reciprocal of the solubility. Thus, clo,
(J/m4 = 2W,TWa20)
700
+ 38.2~ [lodwppm0) - log(wppm O),,,ax], (4) where AC& is the standard free energy of formation at temperature T. We used eqs(3) and (4), and AC;,,, (Na,O) from table 1 to obtain po, (J/mol)
= - 1086500 - 22.323 log(wppm 0).
Similarly, using the expression for the maximum solubility of oxygen in {K) quoted by Sreedharan and Gnanamoorthy [42] of log(wppm O),, = 5.3015876/T and the thermodynamic values for (K,O) in table 1 yields po, (J/mol)
= 689300 + 72.41T+ 38.29Tlog(wppm
0).
In the oxygen-containing {Cs} system, the only measurements of oxygen potential are the recent results of Knights and Phillips [43]. They report that their data are well-fitted by the Henry’s law expression po, (J/mol)
-2 6
800
vwm
IO1 In
-
LI
--K
F
i
(5)
from which the values in fig. 2 were obtained. Mainwood and Stoneham [40] have theoretically derived excess enthalpies and entropies of solution for (Na,O) in {Na} which agree reasonably well with those derived from Noden’s solubility expression [38]. In the Li-0 system, Yonco et al. [41] represent the maximum solubility of oxygen in {Li} by the expression log(wppm O),, = 6.992 - 2896/T. Using this expression with the thermodynamic values for (Li,O) in table 1, a Henry’s law expression for oxygen potential can be obtained in a fashion analogous to that used for the Na system,
+38.29T
1
= -740600 + 21.02T
+ 38.293 log(wppm 0)
po, (J/mol)
k
z
= -583800 + 156T +38.29T( X log
F-3)
(wPpm 0) (6) 120300 + 0.8797(wppm 0) I ’
!200
1
I 400
I
1
I
I
800
600 TEMPERATURE,
I
I 1000
K
Fig. 2. Ellingham diagram for the Li, K, and Rb systems at equilibrium between the liquid metals and the oxides. Also displayed are oxygen isopleths for oxygen concentrations in (Li} and (K). Melting temperatures are indicated along the top of the diagram.
The various expressions for the oxygen potential as a function of temperature and concentration of oxygen in the liquid alkali metal are presented graphically in figs. 2 and 3. There is an obvious trend towards greater oxygen solubility and potential with increasing atomic weight of the metal. No solubility data are available for the Rb system; however, the equilibrium between the metal and (Rb,O) is plotted in fig. 2. From the observed trends, one might expect behavior which lies between that exhibited by the K and Cs systems, although the position of the Rb equilibrium line is at slightly greater oxygen potentials than those for the analogous Cs system. 3.2.2. A-(S,Se,Te) Phase diagrams are given by Moffatt [25] for the Li- S, Li-Se, Li-Te, and K-Se systems. The compounds (A*S), (A,Se), and (A,Te) are the most alkali-metal-rich and have the highest melting temperatures in a given binary. Compounds that contain higher ratios of the group VIA elements are reported, but these will not be considered further.
T. B. Lmdemer et al. / Thermodynomrc review und culculutrons
188
0, 3
AH;
,
kcallmol
-150
wppm[O]
t
tA’ 800
-
-100
m
Na
0.t
I’ I 400
I
I
I
I
800
600 TEMPERATURE,
I too0
K
Fig. 3. Ellingham diagram for the Na and Cs systems at equilibrium between the liquid metals and the oxides. Also displayed are oxygen isopleths for oxygen concentrations in the liquid metals. Melting temperatures are indicated along the top of the diagram.
0, 0
X s
0 -600
Te I
-400 AH; ,
Thermodynamic values for the most A-rich compounds in the A-(S,Se,Te) system are given in table 1. The AH; values for (Rb,Se), (Rb,Te), (Cs,Se), and (Cs,Te) were estimated from fig. 4, which was suggested by .similar plots used by Anderson and Parlee [IO]. In fig.4, AH; values for (A2X) or (A2X) are plotted versus the A HP values for (Li,X) , where X is either 0, S, Se, or Te and the definition of A is extended to include hydrogen-containing compounds. The two dashed lines in fig. 4 originating at the A HP values for (Cs,S) and (Rb,S) have slopes approximating those for the data sets for (Li,X) and (Na,X), with X being S, Se, and Te. The estimated AH; values for (Rb,Se), (RbaTe), (CsaSe), and (Cs,Te), as obtained from these dashed lines, are given in table 1. Values of S” for these 0, S, Se, and Te compounds are based on heat capacity measurements from 0 < T < 298K solely for (Li,O), (Na,O), and (Cs,O). Thus, So values listed in table 1 for the other compounds in this family may have relatively large uncertainties. The So values estimated in the present paper were calculated from an average ASP value derived from the S” values for the five (A,O) species and (Na,S). In this instance, the ASP value of -130Jmol-‘K-l was calculated by using S” values for (A), (0,) and (S,), and then applied to the Se- and Te-containing species by
Se
1
L
kJ/mol
Fig. 4. Values of A Hfq& of several alkali metal and hydrogen compounds containing oxygen, sulfur, selenium, and tellurium versus the values of AHt,, for lithium oxide, sulfide. selenide. and telluride.
using the S” values for (Se,) and (Te,). The S” values estimated by Mills [44], table 1, are reasonably consistent with the AS,? values used here. A comparison is also available for (CsrTe). Gotzman [45] lists an estimated AC& = - 3 14000 + 59T and Adamson et al. [46] estimated AC;, = -293000 + 59T, while the estimates here led to AC;, = -284500 + 43.3T J/mol. 3.3. The alkali metal halides Thermodynamic values for the (AX) and (AX) species, where X is either F, Cl, Br, or I, can be found in the standard reference tables, except for the (NaI), Cs-Br, and Cs-I systems. For (CsBr), AH: = -395 kJ/mol and S” = 113 J mol- ’ K-’ [ 11,while for (CsBr), S” = 268 J mol - ’ K- ’ [47]. Feber [48] has recently reviewed the data for cesium iodides. For (CsI) and (CsI), respectively, he lists A HP = -351 and - 157 k.I/mol and So = 122 and 275 J mol-’ K-t. For (NaI), So = 249 J mol-’ K-’ [47]. The values of AH; for (NaI) and (CsBr) were estimated from fig. 5, which shows
T. B. Lindemer et al. / Thermodynamic review and culcuhtrons
100 -
0
LI+
0
No+
0
Rb+
A
cs+
189
and (AOH), were generally available from the standard reference tables and are given in table 1 of this paper. The value of S” = 91.2 3 mol-’ K-’ for (RbOH) was calculated from the average of AS/ values for (CsOH) and (KOH); an analogous procedure was used to calculate S” = 248 J mol - ’ K - ’ for (Rb0I-I). 4.2. A-(group
IIA)-0
No solid solutions or complex oxide compounds are known to be formed from the simple oxides in the A-(Be,Mg,Ca,Sr,Ba)-0 system. 300
-
4.3. A-(SC, Y,lanthanide)-0
Cl-
FI
400 400
t
BrI 200
300 -AH;(Kx~,
i
I 100
kJ/mol
Fig. 5. Values of AH&z98 for gaseous alkali metal halides vs A H&T for the gaseous potassium halides.
linear plots suggested by Anderson and Parlee [lo]; the values are - 98 and -208 kJ/mol, respectively. The melting temperature of (CsI) is 899 K [48]. Many of the thermodynamic values for the (A2XZ) species, table 1, required estimation. The estimated A HP values were obtained from a plot similar to fig. 5. In this case, known AH,0 values for the (K,X,) species, table 1, were used along the abscissa and the resulting plots of the AH; data for Li, Na, Rb, and Cs were nearly linear. These plots were used to interpolate the estimated A HP values given in table 1. The estimated S” values were calculated from an analysis of known ASP values, the latter being calculated from S” values for (A) and (X,). A plot of AS,? values similar to that in fig. 5 was used, with the ASP values for (K2XZ) plotted on the abscissa. These plots were reasonably linear, and estimated So values for (Cs,Br,) and (Na,I,) were obtained. For the (Rb,X,) species, examination of the AS: values for the (AX) species suggested that the AS; values for (Rb,X,) could be set equal to the average of the ASP values for (K2XZ) and (Cs,X,) for each halide.
4. Ternary systems 4.1. A-O-H
Thermodynamic
values for (AOH),
AOH, (AOH),
The compounds (A,0 . Ln,O, ) have been reported, where Ln represents Sc, Y, La, and the lanthanides. Examples of these species exist in the Li [49,50], Na [51], K [52], Rb [53,54], and Cs [55] systems for all the elements except Pm. No thermodynamic values or phase diagrams are available for these systems. 4.4. A-(group
VIB)-0
4.4. I. Compounds
Many compounds are formed from the simple oxides in the A, Cr, MO, and W systems. (Let Cr, MO, and W = Me.) Compilations published by the American Ceramic Society [26-281 contain approximately 20 phase diagrams for these A-(group VIB)-0 systems, while table 2 lists those diagrams published since the compilations. Several papers have reported phases resulting from the reaction of elements and simple oxides in this system, particularly with stainless steel and other alloys [56-651. All of these references were used to compile table3, which lists the phases common to most of the ternary systems. Also given, when available, is the maximum temperature (congruent melting, peritectic, peritectoid) for the existence of the solid compound. More specific unique to specify A-Me-O systems have been reported and thus are not listed in table 3. Consider first the compositions lying between A,0 and MeO, in the A-Me-O ternary. Here (A4Cr0,,) exists for Na [63,66,67] (up to at least 925 [66]), for K [67], and for Cs [66], but not for Li [63]. In the Li-MO-0 system, (Li,Mo,O,,), (LizMoO,), and (Li,Mo,O,) are shown in figure 4276 of ref. [28] but are not reported in the other A systems. The compounds (K,MoO,) and (K2W03) are stable below 575 to 675 K [68], but are not found as equilibrium phases in the Li, Na, and K systems at 835 K [69]. Second, for compositions lying between A,0 and Cr,O,, the compound (LiCrO,) has
190
T. 19. Lmdemer
et of. / Thermo&numrc
Table 2 Phase diagram reported since the Americal Ceramic Society compilations [26-281 a) -
Li ,O-Fe20,
-Fe
Li ,O-MgO-Crz03 -Fe,O, Li ,O-Cr,O, -SiO, Li,MoO,-Np(MoO,), LizMoOd-Cs,Mo04-MOO, Li 2MOO, - Moo3 Li-W-O Li,O-WO,-MOO, LizWO,-WO, Li,O-WOs-UO, Li zO-V,O, -V,O, Li ,0-&O, -v*o, LiV,O, -v,o, Li-Fe-O LiV,O,-V,O, Li ,O-Fe,O, -Fe Li 20-Mg0-Crz0, -Fe,Os Li *O-Al 20, (NaNbO,),-BaNb,O,-(WO,) Na-MO-0 Na z MOO.,-UO, Na,MoO,-Np(MoO,), Na ,O-MoO, 40, Na,MoO.,-Cs,MoO, Na 2MOO, - WMo,Os Na,O-V,O,-UO, NaNd(WO,),-SrWO, Na-W-O Na,WO,-Na,Th(WO.,), NaVO, -V,O, NaVO, -V,O, -V,O, Na,O-VzO,-SiO, Na,O-NbO NaAIO, -A1203 Na,O-Fe,03 -V,Os K-MO-O K-W-O K,W,O,-KY(WO,), K,O-WO, -40, K ,o-KAlO, KZO-Fe,O, -SiO, K20-Al,O,-SiO, Rb,MoO.,-La,(MoO,), Rb,MoO,-Sm,(MoO& RbZMoO,-Kb2W0, RbV,O, -V,O, RbV,O, -V,O, Cs-Cr-0 CQMOO, -MoO, Cs,MoO,-V,O, Cs, MOO, -Cs,WO, Cs, MOO, -ThMo,O,
I1671 [711 [971 [I681 [I691 [170,171] I691 ~721 iI711 I1731 [I121 11881 [I881 [I971 11921 [I671 I711 [I931 (1741 I691 (175) [I681 I1761 I1771 [I781 [I791 [1801 1691 I1811 [I901 [19(I I1911 [I 191 [I981 [I961 [691 C691 [I821 WI [I981 [I941 [I951 [I831 [I831 I1841 u921
I1891 [56,66,73] WI II851 [I841 [I861
reuew und cuicukutrons
Table 2 (continued) Terminal compositions
Reference
Cs 2MOO, -V,O,
I1871 P.801 [I921 [I201
csv*o,-v*o, csv,o, v-o
-v,o,
a) The latest volume in this series will be issued in mid- 1981 by the American Ceramic Society, Columbus, OH, USA.
been observed at TG 1275 K [70], while (NaCrO,) has been observed in experiments where TG’1063 K [66], but (CsCrO,) could not be formed [66]. The compound (LiCr,O,) has also been reported [71]. Third, species found by reacting either Na, K, Rb, or Cs with either MOO, or WO, are solid solutions having the compositions(A,,+,MeO,),withOdx~0.7atT~675K[68]. Later investigations in the Na and K systems by the same authors ]72] at 573 d T d 873 K aad in the same composition ranges did not detect the (A,MeO,) compounds, nor did Reau et al. [69] at 835 K. Thus, they will not be considered further. Also, bronzes of the type (A,MeO,) (0 GxG 1) are found for A = Na, K, Rb, and Cs and Me = MO and W [69,73-761. These bronzes exist in equilibrium with (WO,) and (W) at 1025 K for the Na and K systems, but not with (MOO,) and (MO) in the Na and K systems at 825 K [69]. Fourth, Kessler et al, [72] have reported (NaMoO,), (Na,WO,,), (Na,MoO,), (LiWO,), and (Na,Mo,06). 4.4.2. Thermodynamic o&es The standard thermodynamics reference tables provided sufficient known AH; data to permit estimation of unknown AH; values. ln the present work, these values were +estimated from fig. 6 for (A,MeO, ), (A*Me*O,), (A,CrQ)V and (A4Cr04). On the abscissa are plotted the heats of formation from the oxides, A %X 9of (A,MoO,) from (A20) and (MOO,) for Li, Na, K, Rb, and Cs. The AH& values for other compounds, such as (A&-O, >, are plotted along the ordinate, with the ordinate value for (Li,CrO, } plotted above the abscissa value for (Li,MoO, ) , etc. (see section 2.3.3). As can be seen from fig. 6, a straight line can be passed near the five values and through the origin. Many other AH&,, values were plotted along the ordinate with similar results. These included (AOH) (from (A,O) and (H,O)), (AVO,), (A,Mo,O,) p (A ,WO, ) , and (A&JO, ) . Only the tungsten set of compounds exhibited a distinctly nonlinear behavior.
191
T. B. Lindemer et ul. / Thermodynamic review and calculations
To the extent that A Htox values for hydrogen-containing species can be considered to behave like the alkali-metal -containing species, AH&, values for (HzMeO,) are within -t 10 kJ/mol of zero. The assumption that the fits are linear and pass through the origin thus seems reasonable. Consequently, the A Hto, values for (Cs,CrO,) and (Cs,CrO,) [77] and (K,CrO~) [78] are plotted on fig. 6 and connected with straight lines to the origin. Finally, this procedure led to the estimated A HP values shown in table 1 for the A-Me-O solid compounds. The A Hp values for (AzWzO, ) and (A,W,O,,) were not estimated here, but the critically evaluated value [16] of -2406 kJ/mol for (NazWzO,) and -4158 kJ/mol for (Na,W,O,,) could be used to estimate the others. Entropy values of many of the A-Me-O solid compounds listed in table 1 were also estimated. The critically evaluated S” values reported in the literature for the double oxides formed from (A,O) and one transition-metal oxide are for (NazCrO,), (K2Cr04), (NazMoO,), (NazWO,), and (NaVO,) (considered as (NazO . VzO,)). They have an average AS&, value of = 20 J mol - ’ K - ‘, with a standard deviation of 1I J mol - ’ K - ‘. Compounds considered to be composed of three or more simple oxides are (K,Cr,O,) (considered as (K,O . 2Cr0, )h (Na,Mo,O, ), (Na,V,O, ), (NarVO., ) (considered as (3Na,O .2V,O, )), and (Na,W,O,). Here the average AS&, value was = 30 J mol - ’ K- ‘, with a standard deviation of 13 J mol-’ K-‘. The required So value for (CrO,) is 72 J mol-’ [I]. Alternatively, average values of ASi’ for the two oxide groups considered above were evaluated, but the standard deviations were equal to those given above. Use of the average ASP values would thus not improve the accuracy of any estimated So values. Values of AH; estimated by Choudary, Gingerich, and Kingcade [79] for the (A,MeO,) and (A,SO,) species are listed in table 1. Comparison of these estimated values with the measured values for (LiZMoO,), (CszMoO,), and (KzWO,) indicates that the measured values are 17 to 50 kJ/mol more negative, which is within the stated error band of the estimated values. Eq (2) was used to calculate the So values for (AzMeO,)
in table 1. Rather interestingly, the S” values for (CszMoO.,) estimated by Johnson [80] and by using eq. (2) differ by only 0.74 J mol-’ K-l. Sokolova et al. [81] measured the pressure of (CszCrO~) over (Cs,CrO~) and determined that log PCs,Cro, (atm) = 6.98 14200/T at 977.4 4 T 4 115 1.OK. They noted that their results were in agreement with another study in the USSR. Their pressure data and the thermodynamic values for (Cs,CrO,) lead to a A HP value for
I
600
-
-
Z E .
4oo
-
0
A2Cr207
0
b&04
A
A4004
0
A3004
0
A$+07
b
A#04
v
AVO3
A
AOH
0
A2CrO4
I
I
I
2 0-
K RbCs
200
0 -A*;
,0x
tA2M0041,
-
400 kJ/mol
Fig. 6. Values of A H&x,298 (per mole of (A,O)) for several complex oxides vs analogous values for (A,MoO,).
(Cs,CrO,)
of 73T- 1158000 J/mol. Thermodynamic data have been reported for a few additional species. Wagman et al. [21] have reported a
A HP value of - 2544 kJ/mol for (K&O,). Data for (NaCrO, ) have been measured [8,83] and will be discussed in section 4.4.5. Solution of {MOO,} in (Na,MoO,} has been studied [84,85]. Frederickson and Chasanov [86] have measured the heat capacity of (Cs zMoO, ) , and Johnson [87] reports an enthalpy of melting of 43.1 Id/m01 at the melting temperature, 1215 K. The A HP values for three potassium tungstates have been estimated [88] but were not used here. 4.4.3. es-MO-O A ternary equilibrium diagram and Ellinham diagrams were calculated for the Cs-MO-O system because of its importance in fission-product behavior. The only known ternary compounds that occur in the composition field bounded by MO, Cs, Cs,O, and MOO, he between (Cs,O) and (MoO,). The values for AH; and So for the ternary compounds are known only for (Cs,MoO,) and (Cs,Mo,O,), table 1, thus requiring estimates for the compounds having Cs,O : MOO, ratios
192 Table 3 Partial listing (Cr,Mo,W)-0
T. B. Lmdemer
of composition systems a)
and
maximum
et (11./ Thermo&umrc
temperature
Alkali metal
Transition metal
Ratio, A,O/MeO,
(A)
(Me)
3/’
Ll
Cr
Na
(K) of the solid phase
2/’
for ternary
312
‘/I
_ Cl I573
1891 1623
[I731
[1731
1023 [691
_ C) ~721
MO W
1015
1018
[2001
12001
1066
633
958
885
970
1019
[691
[2001
12001
1245
671 768
833
_ C)
1200
1691 1023
[72,1 I I] _ =)
1185
957
[72,891
[2001
[2001
1263
665
C)
1208
753
1891 - C)
1225
970
[891
[2001
12001
1225
660
=)
1215
740
[891 - C)
1235
WI 1011
[2001
[2001
[691 Cr
-
MO
3625
~625
W
[891 2625
[891 z=-625
[891
1891
Cr
_ d)
MO W
803
[691 1023
Cr
cs
2/5
>625 [891
-
817 [I701
833
MO
Rb
in the (alkali-metal)-
l/2
978
1373
Cr
W
compounds
789
MO W
revtew und culculutrons
[1111
‘) Unreferenced data are from ref. [26]-[28]. b, Reference designation.
of 3 : 2, 1 : 3, 1 : 5, and 1 : 7. Note, table 3, that Week et al. [89] synthesized the 3 : 2 compound at 625 K, but not the 2 : 1 compound. Unknown S” values for the compounds lying between (C&MOO,) and (NoO,) were calculated by again assuming AS& = 30 J mol -’ K -‘. Upon applying the methods described in section 2.3.1, the reactions to be considered in the determination of the unknown A HP values are thus
2AHP,, .z -2303000-8T-AH;,,:,+b=O, -AH;,., +32T+c=O, 2AH& 4 -AH&.,
(1:1)+(1:3)-2(1:2),
3AHPl5
2(1:4)+
(1:7)-,
3(1 :S),
(1:5)+2(MoO,)+
(1:7).
One then obtains from the AC; expressions -3090000-227’-AH&.,
-2AHHp,:,
+a=O,
-AH;,
, -33T+d=O,
-2AH~~,,,+e=O,
(1:2)+(1:4)-2(1:3),
AH,?,z,=AHp,,5
(1:3)+(1:5)-2(1:4),
2a+2b+2c+e+d=82000+29T
T. B. Lmdemer et (11./ Thermodynamic review and calculations
193
A2°/Cr205
l/3
l/4
‘/5
l/6
‘/7
‘/8
3/l
IO23 [98] b’ 818
850 [171,199] 1078
1100
WY
Ll7ll 1073 [58,2Ol]
814
813 II08
1186 [2001
w31
-
C)
[201,202] 840
835
II15
1185
PW
PW
840 I211
1237 [2W
- C)
PO4 833
878
823
II41
1338
WI
1313
w31 923 [73,202]
823
778
823
WI
PI
PO,1991
850
PO,1991
1175
1319
VW
Pw
‘) Compound exists, but melting temperature not known. d, Did not form at 625 K [89].
in which the numerical subscripts denote the ratio Cs,O : MOO,. These relations were solved at 1000 K for a set of A HP values by iteration. Next, an adjustment to the S” value for (Cs,Mo,O,,) was made to accommodate the peritectoid decomposition Z(Cs,Mo,O,,) + (Cs,Mo,O,,) + (Cs,Mo,O,,) at 780 K [90], where AC;,,, = 0. This was done by reducing AS&,X*,., to 14 Jmol-’ K-l. The resulting AH; values for the 1:3, 1:4, 1: 5, and 1:7 compounds, respectively, are -3100, -3883, -4640, and -6146 kJ/mol, while the S” values are 410,472, 566, and 721 Jmol-’ K-‘. The values of a, b, c, d, and e at 780K are 7.2, 20.2, 0, 33.7, and 15.6 kJ/mol, respectively.
The AH; and S” values for (Cs,Mo,O,) are also needed. For the So value, the assumption of AS&, = 30Jmol-‘K-’ gives 626Jmol-‘K-l. The value of A Hi’ was estimated. Since there is no evidence of another compound lying between (Cs,O) and (Cs,MoO,), one can write the reaction (Cs,O) + 2(Cs,MoO, ) -, (Cs,Mo,O,). Since AC& (0 for this reaction (see section 2.3.1), oneobtainsAH& < -3377000 - 18.4T, or -z - 3400 kJ/mol at 1200 K. The most analogous reported phase equilibria are those for the K-MO-O system [69], in which (K,MoO, ) + (MO), (K,MoO,) -t (K,MoO,) + (MO), and (K,MoOs) + (K,O) -t (MO) phase fields were found. The latter is
194
T. B. Ldemer
et (11./ Thermodynumrc
demonstrably impossible. At their temperature of 833 K, poz for the {K} + (K,O) + (0,) equilibrium is -480 kJ/mol. This has to be more negative than po for the 2 (K,O ) + (MO) + &O,) it indicated equilibrium (K,MoO,), for which AC& = AHTz,, + 913200 and These two considerations lead to AH& , Ilo, = 5 AC&, . > - 1631 kJ/mol. On the other hand, their results indicate the equilibrium (K,MoO,) + (MO) + $(O,) P 2(K,MoO, ). Here, AC&, = -AHFz, - 666000, and the requirement that po, be greater = 5 AC;,,, , PO2 than that for the {K} + (K,MoO,) + (MO) equilibrium leads to AH& , < -2066. The two inequalities for AH& , have no solution. This impasse can be resolved by assuming that Reau et al. [69] had a {K) + (K,MoO,)+ (MO) equilibrium and that the (K) at room temperature was oxidized before examination. The phase equilibria in the K-MO-O system thus suggest the equilibrium {Cs} + (MO) + (Cs,Mo,O,), rather than {Cs} + (MO) + (Cs,MoO,), in the Cs-MO-O is more system. Since po, for the former equilibrium negative than that for the latter, then AC; for the equilibrium $(Cs,Mo,O,)* ${Cs} + $(Mo) + (0,) is less than that for +(Cs,MoO,)= {Cs} + ;(Mo)+ (0,). This inequality in the two AC; expressions leads to AH;,, < -3407000 - 72T, or - 3493 kJ/mol at value of -3500 kJ/mol is used here. 1200 K: A AH& The A HP and S” values given for the Cs-MO-O system in table 1 and in the above discussions were used to calculate the ternary equilibrium diagram shown in fig. 7. Two Ellingham diagrams were also calculated (figs. 8 and 9). Fig. 8 is for compositions lying between
rewew und culculurrons
Cs and MOO,, while fig. 9 is for compositions lying between Cs and all compositions with 0: MO > 9: 2. The maximum temperatures for the existence of the solid compounds are indicated along the top of figs. 8 and 9, and the thermodynamic data are given to the melting temperature of the lowest-melting compound involved in each two-phase equilibrium. The po, - T dependence of the isobars of (Cs) in the two-phase fields were also calculated and are given to 10 -_” MPa (N 10 _ I5 atm) in figs. 8 and 9. Takahashi [91] presents another approach to the representation of the Cs-MO-O system. He shows the phases present at 1000 K as a function of po, and pc,. He has treated the Cs-Cr-0 and Cs-U-O systems in a similar manner. Results indicate that (Cs,MoO,) is the predominant oxygen-containing gaseous species in the Cs-MO-O
400
600
800
TEMPERATURE,
Fig. 7. Cs-MO-O ternary equihbrium diagram for T;s730 K; the (Cs,MoO,) -(CslMozO,) eutectic occurs at 730 K [90].
1000 K
Fig. 8. Ellingham diagram for the Cs-MO-O system for compositions lying between Cs and MOO,. The melting, peritectic, and peritectoid temperatures of the solids are indicated at the top of the figure. Isobars (dashed hnes) for (Cs) pressure are also shown.
T. B. Lmdemer et ~11./ Thermodynumrc revrew and culculairons
I 200
I
195
I
I
I
I
I
I
Liz-
300
400 1 3 P i I
500
-I,-
‘;-
_--------------
600
700
It
I 600
I
I
600
I
I
1000
TEMPERATURE,
400
600
600 TEMPERATURE,
IO00 K
Fig. 9. Ellingham diagram for the Cs-MO-O system for compositions lying between Cs and 0: Mo19: 2. The melting, peritectic, and peritectoid temperatures of the solids are indicated at the top of the figure. Isobars for (Cs) pressure are also shown.
system. The isobars for (Cs,MoO,) are shown on the Ellingham diagram of fig. 10. Other calculations have demonstrated that pressures of (CsO), (Cs,O), (MOO), (MOO,), and (MOO,) are orders of magnitude lower than those for (Cs,MoO,) at the given po, and T conditions for each of these isobars. 4.4.4. Cs-Cr-0 The Cs-Cr-0 system may be an important participant in the corrosion of stainless steel cladding for oxide nuclear fuel. Thermodynamic values for the ternary compounds in this system are given in table 1. In addition, the compound (Cs,CrO,) has been tentatively identified, and the values AH: = - 1606 kJ/mol and So =430Jmol-‘K-’ have been estimated [73]. However, because of the uncertainties associated with this compound, it will not be considered further. Melt-
Fig. 10. Ellingham diagram (Cs,MoO,) pressure.
I
1200
K
of fig. 8 showing
the isobars
for
ing temperatures for (Cs,CrO,) and (Cs,Cr,O,) are given in table 3, while that for (Cs,Cr04) is > 1275 K [66]. The melting temperature of (Cs,CrO,) is unknown, but experimental work with this compound at 975 K is reported [66]. Enthalpy increments for (Cs,CrO,) and {Cs,CrO,} have been measured to 1324 K [92]. The phase diagram and Ellinghaus diagrams were calculated for the Cs-Cr-0 system (figs. 11 and 12). In fig. 11, there was some question as to whether the (Cr) + (Cs,CrO,) or the {Cs} + (Cr,O,) equilibrium was correct [66], but later work established the former [73]. The former is also calculated here. The calculated phase diagram agrees with the experimental results. The pressure isobars for (Cs,CQ) were calculated for the phase fields lying between {Cs} and (CrO,). They were always less than 0.1 of the pressure of (Cs,MoO,) at any given conditions of po, and T. 4.4.5. Na-Cr-0 Equilibrium behavior of the Na-Cr-0 system is relevant to the understanding of stainless steel corrosion by Na-containing species. The thermodynamic data for
196
CS
I
I
I
I
I
Fig. 1 I. Cs-0-O ternary equilibrium (CsJr,O,) melts at 660 K.
I
I
diagram
I
for TC660
CI
K;
the ternary compounds are listed in table I for all species except (NaCrO,), for which AH; and AH&, are -879.9 and - 101.4 kJ/mol, respectively [16,82]. The S” value of 88 J mol - ’ K - ’ was estimated by again assuming AS&, =20Jmol-‘K-’ from (NazO) and (Cr,O,). These data lead to AC&,,., = - 101400 - IOT J/mol, which can be compared with AC&,,, = - 102 800 + 11.1T, as determined from emf data at 824 G T C 1020 K by Shaiu et al. [83]. If one applied the “additive oxide” method, section 2.1, to estimate the unknown high-temperature thermodynamic properties of (NaCrO,), then the two coefficients in the latter AC”f,ox,Texpression are identical to AH&,, and AS&, for (NaCrO,) at 298.15 K, as noted by Shaiu et al. [83]. Therefore, the data of Shaiu et al. [83] indicate AS&, = -11.1 Jmol-‘K-‘. Since all of the other AS&,, data for the A-Cr-0 compounds are positive, table 1, the data of Shaiu et al. [83] may be in error, and is not used in the present analysis. Knights and Phillips [66] have made mass spectrometric measurements for specific equilibria in the Na-Cr-0 system and have derived co, values. Values for AC&, obtained from and AG;,ooo the data given here fall within their stated error bands. Melting temperatures for (Na,CrO,) and (Na,Cr,O,) are given in table 1. The maximum experimental temperatures of Knights and Phillips [66] suggest that (NaCrO,) and (Na,CrO,) are solids to at least 1063 K and that (Na,CrO,) is a solid to at least 940K. The thermodynamic data were used to calculate the equilibrium phase diagram shown in fig. 13. This calculated diagram agrees with previous experimental dia-
L
I 400
I
I
I
600
I
I
600 TEMPERATURE,
I
I
1000 K
Fig. 12. Ellingham diagram for the Cs-Cr-0 system for compositions lying between Cs and CrOz. The melting temperatures of the solids are indicated at the top of the figure. Isobars for (Cs) pressure are also shown.
grams. The Ellingham diagrams of figs. 14 and 15 were also calculated. It is important to note that the poz values for the three-phase equilibria involving more than one Na-Cr-0 compound (figs. 14 and 15) may be shifted substantially as more precise measurements of AH; and S” become available for the ternary compounds. Also shown in fig. 14 is the [0] content in {Na} from fig. 2. The oxygen content of {Na} at&e {Na} + (Cr) + (NaCrO, ) equilibrium is consistent with some of the information [93,94] on the appearance of the corrosion product (NaCrO, ) during the exposure of stainless steel to {Na} containing given concentrations of [0], but below that in other experimental work reviewed by Wu [95]. Shaiu et al. [83] have reviewed emf data for this equilibtium; the resulting po, values are scattered on either side of those shown in fig. 14.
T. B. Lmdemer et (11./ Thermodynumic
review und culcuhtions
Fig. 13. Na-Cr-0 ternary equilibrium diagram for T 1 and O/Me > 1. Table 2 lists several equilibrium diagrams for this composition range that have been published since the American Ceramic Society compilations [26 - 281. These compositions include several semiconducting solid solutions and glasses. However, such systems exist at oxygen potentials higher than those of interest here. 4.6.2. Thermodynamic values The thermodynamic values of AH: and S” for the vanadium and niobium oxides are needed. Values from the JANAF tables [ 151 were used for the Nb-0 compounds while a recent critical evaluation of the V-O system by Smith [ 1201 was the source of the A HP values for the vanadium oxides. The A HP values for (VO) , (V,O,), (VO,), and (V,O,) are -431.8, - 1219,
- 714, and - 1550.5 kJ/mol, respectively; the corresponding S” values are 33.93, 47.1, and 130.3 J mol - ’ K- ‘, respectively. Smith [ 1201 cites Morozova and Eger [ 1211 for AH; values for the lower vanadium oxides, all of which exhibit a range of composition. Their data tabulations give A Hp values of -232.6, - 101.6, and - 54.4 kJ/mol, respectively, for (VO, s0s), (VO, 206)r and (VO, , ,). The S” values for these compounds were estimated here and found to be 26.72, 28.93, and 28.76 J mol _ ’ K ‘, respectively. These values and the values of S” for the higher oxides lead to a smoothly varying plot of ASP (in J g-atom-’ K-- ‘) versus x in VO,, with ASP = 0 when x = 0. They also satisfy AC; = 0 for the peritectoid decomposition of (VO, , ,) to (V) and (VO,,,) at 783 K and the peritectoid decomposition of (VO, 505) to (VO, 206) and (VO) at 1458 K [ 1201. Unknown values of AH; for compounds lying between (A,O) and (Me,O,) were estimated with the aid of fig. 16. The AH; values for (NaVO,), (Na,V,O,), (NayO,), and (KVO,) [21], given in table 1, were used to calculate the A Hi& values plotted in fig. 16. Khodos et al. [ 121 have determined A HP values for several K-V-O compounds, but they were not used because the (KVO,) value was 13 kJ/mol more stable than the critically assessed value [21]. The AC; value for (RbNbO,) is known [21], and by again assuming that AS&, ~20 Jmol-’ K-’ from (Rb,O) and (Nb,O,), the values of S”, AS;, AH;, and AH&, were successively calculated for (RbNbO,). As can be seen in fig. 16, the AH&,, values for the analogous (AVO,) and (ANbO,) species are essentially identical. Thus, it was assumed that the AH;“, values for the (A,NbO,) species were identical to those for the vanadium analogs. Fig. 16 was then used to estimate the values shown in table 1 for A H&X and the AH: (AMeO,) and (A,MeO,). The AH; values for (LiNbO,) and (NaNbO,) were also estimated previously [123], but they were not used here because some of the known AH; data used in that evaluation are in considerable disagreement with presently accepted values. Unknown values of S” for the compounds lying between (A,O) and (Me,O,) were estimated by values of 20Jmol-’ K-’ again assuming AS&, for(A,O. Me,O,) and 30 J mol-’ K-‘for (2A,O. Me,O,) and (3A,O. Me,05). The A HP and S” values for the (AMeO,) compounds were estimated. The So values shown in table 1 were obtained by assuming AS&, = 30 J Mol - ’ K - ’ from (A,O), (MeO), and (MeO,). (Although (V,O,) exists, (Nb,O,) does not, and use of AS&, and AH&
from (A,O), (MeO), and (MeO,) permits the thermodynamic values for the V and Nb compounds to be estimated similarly.) The most positive A HP values possible for the (AMeO-,) compounds result from requiring AC; = 0 for the reactions (A3Me0,) + 2(MeO) 3(AMeO,). These values lead to the most positive A H,Poxvalues shown in fig. 16. The most negative values of AH: for (AMeO,) were calculated by requiring AC; = 0 for the reaction (LiVO, ) + 2(LiVO, ) + (LiYO,)+ (V,O,); the latter two phases are in equilibrium at 853 K [ 1121. This reaction was also assumed for the Na and K systems and led to the most negative A H& values shown in fig. 16. Several other possible reactions involving (AVO,) and (ANb02) were considered, but none gave more positive values for the most negative limit for A H&, . Thus, the permissible range of AH&, for (AMeO,) shown in fig. 16 is believed to be as narrow as possible. The line through this range, arbitrarily chosen, was used to calculate the,A HP values given in table 1. The S” and AH,? values for (Na2Nbz05) were estimated. The value of S”, 214 J mol-’ Km-‘, is 30 J mol-’ K-’ plus the sum of the S” values for the component oxides. The most positive possible value of A HP can be calculated by setting AC; = 0 for the (NaNbO, ) + (NaNbO, ) - (Na,Nb?O, ), reaction while the most negative value can be similarly calculated for the reaction (Na,Nb,O,) + (Nb) - (NbO) + 2(NaNbO,). (The literature always indicates equilibrium between (MeO) and (AMe02).) These calculations result in - 226 1 < A HP < - 2242 kJ/mol; thus a value of -2250 kJ/mol was used. For (Na,VO,), the S” value of 227 J mol.~ ’ K _’ was estimated in the usual way. The most positive A HP value can be calculated from AC; = 0 for the reaction {Na} + (NayO,) + (Na,VO,). The most negative value can be calculated similarly for the reaction (NayO,) - (Na;VO,) + (Na), which was observed at 563 K in a vacuum of = 0.001 Pa [ 1181. These calculations gave - 1767 < A HP < - 1800 kJ/mol at 0.001 Pa and 563 K; therefore, a value of - 1785 kJ/mol was used. 4.6.3. Ll-v-o The calculated Li-V-O equilibrium diagram is shown in fig. 19. The Ellingham diagram is shown in fig. 20 for compositions lying along an imaginary line between Li and the V,O,-rich side of the (Li,VO,) + (V,O,) + (LiVO,) phase field. The latter phase field exists at 853 K [112]. The (Li,CO,)-(V,O,) quasi-binary characteristics are known (figure 2282 in ref. [27]). There are no other known experimental phase equilibria for this system at the poI values shown in fig. 20.
T. B. Lindemer et ul. / Thermodynumic review and calculations
201
observed by Hooper and Trevillion [ 124] upon reacting {V} wire with (Na} between 16 and 23 wppm [O)NJ. This indicates that the present estimated values of AH: and So for (NaVO,) are in close agreement with the actual values. However, earlier work [ 1253is somewhat inconsistent with this; (Na,VO, >, not (NaVO,), was identified upon reacting (V) with (Na} at 873 K and 100 G [O]Na G 3O00 wppm. It can be seen from fig. 24 that {salvos} might exist under these [OjNa conditions, and the {Na) + (Na,VO,) twophase equilibrium may have been established at the liquid-solid interface of the reacting system. However, (NaVO,) could have been present as the next phase in the reaction deposit, although not in sufficient quantity for detection, and could have been followed by the several observed v~d~urn oxide phases.
0
Fig. 23. Na-V-Q equilibrium diagram, The shaded areas are two-phase equilibria with V-O phases having variable stoichiometry. This diagram is applicable from 783 K, where (VO, II > decomposes [ 120], to at least 1023 K, the highest reported temperature for experiments involving (NaVC&) [SS].
T. B. Ltndemer et ul. / Thermo+numrc
203
review und culculuttons
4.6.6. Na-Nb-0 The Na-Nb-0 equilibrium diagram and the Ellingham diagram are shown in figs. 25 and 26, respectively. The only experimental studies of the reactions of chemical species in this system verify the calculated (Na) + (Na,NbO,) equilibrium [57,110,115] and the (Nb) + (Na,NbO,) + (NaNbO,) equilibrium [ 1151 at 650 to 975 K. 4.6.7. (Rb,Cs)-(
4000 400
600 TEMPERATURE
a00
1000
(K)
Fig. 24. Ellingham diagram for the Na-V-O system for compositions lying between the Na-V binary and V,O,. The melting and peritectoid temperatures of the solids are indicated along the top of the diagram. Concentrations of [O],, (dashed lines) are from fig. 2.
There are inconsistencies between the calculated [O] Na values at the (V) - (VO, 2 ) equilibrium (fig. 24) and the results of Smith et al. [107,108] and Hooper and Trevillion [ 1241. The values of (01 Na at the (V)-(VO,,,) equilibrium as determined by Smith et al. [ 107,108] at 873 4 T G 973 are = 1000 times higher than those shown in fig. 24. Hooper and Trevillion [ 1241 concluded that the results of Smith et al. [ 107,108] were nonequilibrium, that accurate determination of [0] Na by reaction with (V) wire was dependent upon control of several kinetic and other experimental factors involving formation of vanadium oxides on the wire surface, and that (V) is not an equilibrium phase at 1023 K and [O],, > 1 wppm. This [O],, value would have been 10 wppm if Hooper and Trevillion [ 1241 had used the present po,-T-[O],, values (fig. 3) and again would be 1000 times higher than that shown in fig. 24. The primary difference between the earlier results and the present calculated results is not the [O],, relationship, however, but the po, values for the (V)-(VO,,,) equilibrium, as well as those for the higher vanadium oxide equilibria. The value for the (V)-(VO,,) equilibrium is based on a well-founded and critically assessed A HP value 11201 for (VO,,) and a So value estimated by standard techniques. It would thus appear that solution of oxygen in (V) wire at equilibrium cannot be used for determining practically important [O],, levels, e.g., in LMFBR coolant or coolant-fuel systems.
V,Nb)-0
Addition of (Nb) and (V) to the LMFBR oxide fuel system has been considered as a method of controlling poz during burnup [46]. Formation of the simple oxides in the V-O and Nb-0 systems would getter oxygen, and possibly buffer the po, value. In addition, formation of Cs- and Rb-containing ternary oxides in this system would provide additional oxygen-gettering capability for a given Nb or V addition [46]. As noted in section 4.6.1, (Rb,O) and (Cs,O) form compounds with (V,O,) and (Nb,O,). Experiments by Adamson et al. [46] suggest additional compounds with lower-valent Nb and V oxides, and po, values have been measured for equilibria involving undefined Cs-Me-O compounds. It would appear that further experiments are needed to demonstrate, in particular, the possible existence and thermodynamic values of the (AMeO,) compounds. With this information and the estimated thermodynamic values, table 1, for the (A,O)-(Me,O,) compounds, Ellingham diagrams could be calculated and the results used for this particular LMFBR application.
0
2460K
No
Fig. 25. Na-Nb-0 480 K, (NaNbO,)
Nb
equilibrium diagram for Ta480 K. Below is calculated to be unstable.
204
T. B. Ldemer
et (II. / Thermo+uzmrc revrew und colculutrons
searched specifically for (A,FeO,) and (A,FeO,). Melting temperatures or maximum reported preparation temperatures are also listed in table4. The compound (NaFe,O,) was prepared at 1275 K [ 1261 but will not be considered further. Solutions in (Fe,O,) are reported for (Li,O) (figure 62, ref. [26]) and (Na,O) (figure 2160, ref. [27]). The former diagram shows (LiFe,O,) and (LiFeO,) in equilibrium, indicating that the lithium analogs of the intervening 17:4, 4: 1, and 3 : 1 compounds shown in table 4 for the Na-Fe-O system do not exist. The compound (AFe,O, ,) has been reported in the systems containing K, Rb, and Cs [ 1271.
600
4.7.1. Na-Fe-O The experimental evidence for the Na-Fe-O compounds listed in table 4 is reviewed more fully here so that phase equilibria can be calculated. The compounds can be considered to be formed from (Na,O) and (FeO), as based on interplanar spacings published for (Na,FeO,) [128,129] and (Na,FeO,) [129]. Gross and Wilson [128] and Horsley [ 1301 demonstrated by weight loss measurements that evacuation of mixtures with Fe: Na, 2 1 carried out at 873 K removed (Na) and resulted in weight losses that were consistent with the formation of (Na,FeO, ) and (Na,FeO, ) . ‘The latter compound was formed only after prolonged evacuation [128]. However, in less iron-rich formulations, Gross and Wilson [128], Tschudy et al. [ 1311, and Knights and Philips [66] did not observe (Na,FeO,), even though the compositions in their experiments could have led to the presence of this compound along with other phases. Possibly a large excess of (Fe) is neces-
900 1000
800
600
400
TEMPERATURE
(K)
Fig. 26. Ellingham diagram for the Na-Nb-0 system for compositions lying between the Na-Nb binary and NbO,. The binary (NbO,) + (Nb,Os) equilibrium is also shown. 4.7. A -Fe-O
Compounds to be considered here lie within the composition field bounded by A, Fe, A,O, and Fe,O,. If these compounds were considered to be formed from (A,O) and either (FeO) or (Fe,O,), then they could be listed as shown in table 4. In addition to the general literature searches performed for this paper, all decennial formula indexes of Chemical Abstracts were
Table 4 Partial listing of composition and maximum reported preparation temperature (K) of the solid phases formed in the (alkali-metal)-Fe -0 systems Alkali Metal (A)
Ratio, A *O/Fe0 2/l
A,O/FezO, I/’
Li
5/l
11/4
4/’
3/’
1875
1890
P61
P61
Na
-loo0 [128,129]
K
[1281
11321
l/l
(1321
[I331
=‘925 [1321
1620 [I261
>875 [2031
[ 127,204]
Rb
[ i27,204] cs
_ 11271
205
T. B. Lmdemer et ul. / Thermo&numrc reorew und culculutions sary for (Na,FeO,) formation in all these non-steadystate experiments. Formation of (Na,FeO,) is assumed here primarily on the basis of the X-ray data of Wu et al. [129]. Both (Na,FeO,) and (Na,FeO,) may exhibit nonstoichiometry [57,128,130]. For the compounds lying between (Na,O) and (Fe,O,), (Na,,Fe,O,,) [ 1321 and (Na,Fe,O,) [I331 will be considered here to be a single compound having the latter composition. Knights and Phillips [66] note the existence of (Na,F%O,,) and (Na,Fe,O,), while figure 2160 of ref. [27] shows only (Na,,Fe,,O,,) lie between (NaFeO, ) and (Fe,o, ). Since all three are very close in overall composition, and the first two bracket the third, only the first two will be considered here for the sake of simplicity. Thermodynamic data for the A-Fe-O ternary compound exist only for the Li and Na systems. Table 5 lists data either reported in the literature or derived as described below. The A HP value for (Na,FeO,) was calculated from AH&,, = - 104.9 kJ/mol reported by Gross and Wilson [ 1281. The invariant equilibrium 2{Na) + (Na,FeO,) P (Na,O) + (Fe) is indicated at - 675 K [66,134], where AC:,, = 0. Of all the enthalpy and entropy values for the species in the A H605 expression, only the S” value for (Na,FeO,) was unknown: it was thus calculated to be 203 J mole’ K ~ ‘. Both AH; and S” were estimated for (Na,FeO,). Since the S” value shown for AS:“, = 0 for (Na,FeO,),
Table 5 Thermodynamic data for the A-Fe-O Compound
system at 298.15 K
AH; (kJ/mol)
Ref.
(NaFeO,) (NajFcO,) (Na,F%O,,) (Na,Fe,O,) (LiFeO,)
-1211 a) - 780 -1596 - 2746 - 697.5 -1155 - 3665 -2890 - 766
b) b) b) [I331 [I351 b) b) b) [I351
(LiJFeO,) (CsFeO,) (Ca,FcO,) (CszFcO,)
- 1950 -700 - 1109 -743.5
\;051
(NahFeO3) (Na,FcO,) (NaSFeO,) WPW,)
(Na,FeO,) in table 5 is the sum of the So values for (Na,O) and (FeO). Another invariant equilibrium, 2(Na,FeO,) + (Fe) P 3(Na,FeO,) + 2{Na}, can be inferred from the work of Horsley [130]. When pure (Fe) wqs exposed to oxygen-contaminated {Na), only (Na,FeO,) formed at 1073 K. Thus, (Na,FeO,) would be in equilibrium with (Fe) and {Na) only at Ta 1073 K. Since AC; = 0 for the above invariant equilibrium at Ta - I 150 K, one can calculate that A HP (kJ/mol) = - 808.9 + 0.0246T for (Na,FeO,). One can also reasonably assume the occurrence of the reaction 2(Na,Fe,,O,) + Z(NaFe0,) + 3(Fe) * 9(Na,FeO,), for which AC; (0 (see section 2.3.2). This leads to A HP (kJ/mol) < -765 + 0.010T for (Na,FeO,) and establishes an upper limit; a value of -780 kJ/mol was assumed. Shaiu et al. [83] have reported thermodynamic data for these two compounds, but their data are believed to be erroneous for reasons to be discussed later. Values of A HP and S” were estimated for the compounds having Na,O:Fe,O, ratios of 5: 1, 3: 1, 2:3, and 3 : 5. The estimated entropy values given in table 5 are the sum of those for the (Na,O) and (Fe,O,) components, plus 30 J mol - ’ K ’ (e.g., AS&, values of 15 J mol - ’ K ~ ’ in the table result from S” for (Na,FeO,) being equal to half of the sum of five times the S” value for (Na,O) plus the So value for (Fe,O,) plus30Jmol-‘K-l). ValuesofAHP for the 5:l and 3 : 1 compounds were estimated by the method of sec-
b) b)
S” (J mol-’
Ref. K-‘)
203 136 246.3 438.1 88.3 172 442 346 75
b)
117 354 209
b) b) b)
‘) Calculated from AH&, = - 104.9 kJ/mol reported in ref. [ 1281. b, Estimated by authors, see text. c, 30 J mol-’ K-’ from the appropriate integer numbers of moles of (Na,O)
b)
A To, (Jmol-’ -8 0
bl
15 =’
[I331 11351 b) b) b) 11351
50.42 7.07 15 ,=’ 30 15 c’ 12.5
and (Fe,O,).
0 0 0
Km’)
206
T. B. Lwuiemer et ul. / Thermo+namrc
tion 2.3.1,
which
gives
the reactions
(Na,O)+(4:1)-+(5:1), 2(4:1)+(1:1)+3(3:1), (5:1)+(3:1)+2(4:1). The arbitrary positive constants e, a, and f were added, respectively, to the AGF t0 inequality for the first, second, and third reactions to obtain AGF = 0 for each. Since the A HP value for the 1 : 1 compound and the S” values for all the compounds are known or estimated, one can then manipulate the three equations to obtain AH;,,,, = - (3 163000 + 20.4T+ e), AH:,
I = -0.33(6887000
+ 23.6T+a),
AHHp.3I + AH& , =f- 5492000 - 40.3T. 0.33~ + e+f12T= 33300 J/mol
revtew and cukulutrons
A% 5 value shown in table5 was then estimated and was found to be consistent with the relevant equations given above. Phase equilibria and an Ellingham diagram were calculated by using the data in table5. The Ellingham diagram, shown in fig. 27, is for phase fields crossed by an imaginary line lying between Na and Fe,O,. Also shown are the concentrations of oxygen dissolved in {Na} (eq. (3)) and the isobars for (Na). A phase diagram is shown in fig. 28; this is applicable over the range 720 < T < 880 K. The phase equilibria shown on fig. 28 that lie within the composition field bounded by remain un(Na,O), (NaFeO, >, and (Na,FeO,) changed for 400 < TG 1400 K. Phase diagrams at other temperatures can be constructed from the two-phase and three-phase equilibria indicated in fig. 27.
in which the subscripts on A HP indicate the Na,O/Fe,O, ratio. The A Hf” values given in table 5 for the 5 : 1 and 3 : 1 compounds are consistent with the above equations and were selected to result in compound stability over the maximum possible temperature range. Similarly, for the 2 : 3 and 3 : 5 compounds, one considers the reactions (3:1)+2(2:3)+7(1:1),
A Fe203+Na3Fe309 0
B Fe304tNo3Fe30g C FeOt
Na3Fe309
200 K Fe t Na4Fa03
(1:1)+(3:5)+2(2:3), 3(2:3)+(Fe,0,)+2(3:5). The positive constants b, c, and d were added to obtain AC; = 0 for each of the three reactions. The AC; equations were manipulated to give AH:,,,
= 0.56 - 3 728000 - 4.6T,
2AH&,
-AH;s
2AH;?,
-3AH&,
0.5b+2c+d=
s = -1395000+
15.4T-c,
= -824000-29.4T-d,
114000+6TJ/mo1. 600
An additional reaction was considered to help termine the AH& 3 value. Knights and Philips observed that the 2: 3 compound was apparently equilibrium with (Fe) to at least 875 K. By using second method for determining A HP (section 2.3.2), writes the reaction
de[66] in the one 400
600 TEMPERATURE,
2(1:1)+3(FeO)-+(Fe)+(2:3), and derives A Hp2 3 < - 3 606 000 - 66.2 T. Agreement with Knights and' Philips’ [66] observation requires that the most positive possible value of AH& be -3665 kJ/mol, which was chosen for the present work. The
1200 K
Fig. 27. EIIingham diagram for the Na-Fe-O system for compositions lying between the Na-Fe binary and Fe,O,. The two-phase fields are identified in the key; the three-phase equilibria (solid lines) involve the phases common to adjacent two-phase fields. Isobars for (Na) pressures are shown, as are I"lN, values from fig. 2.
T. B. Lindemer et ul. / Thermodynumic review and
Fig. 28. Na- Fe- 0 equilibrium
diagram for 720 < TC 880 K.
The work of Shaiu, Wu, and Chiotti [83] will now be discussed. They determined AC; for (Na,FeO,) in emf cells from 795 to 1048 K. In their cell V they proposed the reaction (Ca) + 2(NaF) + 2(FeO) -) (Na,FeO,) + (CaF,) + (Fe); the resulting emf versus T data were presented in both numerical and graphical form. They reported AC;’ = -776600 + 208T J/mol. In their cell VI they proposed the reaction (Na,FeO,)+ (FeO)+ (Cu,O) - Z(NaFe0,) + I, but no thermodynamic analysis was given. However, the AC& data of Koehler et al. [135] for (NaFeO,) permit one to derive AC& = -710600+258T J/mol for (Na,FeO,). The discrepancy between the two AC;, expressions and the calculated results in fig. 27 suggests that (FeO) is not part of the two equilibria, as was also concluded by Knight and Philips [66]. An additional check of the validity of the (Na,FeO,) data of Shaiu et al. [83] was made. The results from cells V and VI were averaged to give AC;, = -734600 + 233T. The AH;, and AS& data were converted from 900K to 298K by using H; - H&a and SF - S,O,, data [2]; for (Na,FeO,), these two quantities were set equal to the sum of the like quantities for (Na,O) and (FeO). These calculations resulted in A HP = -747.7 kJ/mol and S” = 101.5 Jmol-’ K-l. The latter value results in AS&, = - 34.3 J mol - ’ K-l, which is atypical when compared with other experimental AS& values in table 1. A computer analysis of the Na-Fe-O system with the above 298 K values for (Na,FeO,) showed that it was never a stable phase. Thus, the phases in cells V and VI were apparently not at equilibrium, and this nonequilibrium led to incorrect thermodynamic values.
calculations
201
Thermogravimetric experiments performed by Tschudy et al. [131] provided results that are inconsistent with the calculated data shown in fig. 27. In these experiments, {Na} was held at 600 K in one end of a closed glass tube and the (Na) was allowed to react with either (Fe,O, ) or (NaFeO, ) held at higher temperatures in the other end. They assumed that the pressure of (Na) was that over {Na) at 600 K. Several invariant equilibria could be deduced from their experiments, but none of these was consistent with the calculated results shown in fig. 27. Furthermore, they were not in agreement with another Ellingham diagram,of the Na- Fe- 0 system calculated by assuming that (Na,FeO,) was not present. Instead, pressures of (Na) much lower than those assumed by Tschudy et al. [ 13 l] were indicated in both cases. Clearly, the Na-Fe-O system needs to be studied further. Isothermal, closed-system experiments that could permit attainment of true equilibrium would be preferable to most of the experiments reported above. 4.7.2. G-Fe-0 This system could be important to oxide fuel and cladding interactions in the LMFBR system [136]. The compound (CsFeO, ) exists, but no reference to (Cs,FeO,) and (Cs,FeO,) could be found. For the sake of illustration, the latter compounds are also assumed to exist. Fig. 16 yielded AH,P,, values of - 115, - 145.2, and - 125.6 kJ/mol, respectively, for and (Cs,FeO,). The esti(CsFeO,), (Cs&03), mated AH; values are shown in table 5. The value for (CsFeO,) is 120 kJ/mol more negative than that estimated by Fitts et al. [36]. Values of S” were calculated by assuming that AS&, - 0, which is consistent with the behavior for the Na-Fe-O analogs. These values, which are given in table 5, were used to calculate the phase diagram of fig. 29 and the Ellingham diagram shown in fig. 30. 4.8. A-Ni-0 Several compounds and solid solutions are reported in the A-Ni-0 system. For A = Li, two different (Li,Ni,_,O) solid-solution regions are reported in an atmosphere of pure oxygen at 625 < T < 975 K [137,138]. One exists with a NaCl structure for x GO.28 and the other with an a-NaFeO, structure from 0.38 ( x < 0.6 1. The compound (Li,NiO, ) , which has the monoclinic NaFeO, structure, also exists [ 1371; in addition, (LiNiO?) has been found [139]. For A = Na, Addison and Pulham [ 1401 studied the reaction 2{Na} + at 395 < T Q 450 K and (NiO) + (Na,O) + (Ni)
208 0
T>46OK
Both sets of investigators postulated the existence of the compound (Na z NiOz ) , discovered by Wol tersdorf [ 1411, which can be found in the systems containing Li. K, and Cs [ 142,143]. The existence of (NaNiO,) is well established [129, 144, 1451, and (Na,Ni?O,) has been rep o rted [I 441. For A = K. (K,NiO,), (K,NiO,), and (KzNizO,) have been reported [146]. For A = Rb, (Rb,Ni,O,), (Rb,NiO,), and (Rb,NiO,) have been reported [137,144], For A = Cs, (Cs2Ni0456) and (Cs,NiO,,,) were prepared [137,144]. Little thermodynamic data exist for these compounds. Sham et al. [83] have emf data for equilibria possibly involving (Na,NiO,) and (NaNiO,), but they consider it to be unreliable. Their data suggest AH&, =
/I
0.
Fig. 29. G-Fe-0
4.9. A-U-O
equilibrium diagram.
found no ternary compounds. Addison et al. [ 1341 reacted (Ni) and (Na,O) in a vacuum at T> 755 K and obtained an unknown ternary phase; Gross and Wilson [ 1281 observed the same reaction at 775 G TG 875 K.
600
I
I
I
I
I
I
I
I
I
I
’ 400
I 600
I
600 TEMPERATURE,
I
In this section we shall focus on the alkali metal uranates, a class of compounds that are extremely important to nuclear fuels. This is especially true for the cesium- and sodium-uranates; the former in relation to internal fuel rod chemistry and the latter in relation to the chemistry surrounding cladding breach fuel-coolant interaction problems in LMFBRs. In keeping with the scope of this manuscript, this section will deal solely with phase equilibria and thermodynamics for the various compound, leaving it to the reader to pursue, through the indicated references, further literature on kinetic behavior and more detailed thermodynamics. There are many publications covering this field; it is appropriate to cite several that can be used both for more detailed information and for the references contained therein. Such publications include the IAEA symposia on nuclear fuels that have been held about every three years [219-2231, the Montery symposium covering fast reactor fuels [224], and the treatise by Keller [225]. The recent publication by Cordfunke and O’Hare [ 1I] is invaluable in providing assessment and recommendation of thermodynamic data. In spite of all the scientific effort, differences do exist between that reported here and other literature because not all data have been rigorously assessed to ensure self-consistency: we believe this manuscript to be the first publication to deal with self-consistent data assessment in so comprehensive a fashion.
I
IO00 K
Fig. 30. FUingbam diagram for the C&Fe-O system for compositions lying between Cs and FezO, and at 7’>480 K. The compound (FeO) is never stable below 480 K.
4.9.1. Li-U-O The lithium uranate system is more complicated than had been assumed for some time [226]. Recently, Hauck [ 1731 has reinvestigated the Li-U-O system and
T.B. Lindemer et ul. / Thermodynumtc revtew und calculutions
surveyed its literature. For the pseudobinary system Li 20-UOs, Hauck [ 1731 suggests the following uranates are likely to be found: (Li6U06)cr,B, (Li,UO,), (Li&JO, ), (Li&O1s )a.~.r~ (Li&sO1a )* and (Liz&O,,). Upon reduction of the lithium uranates (VI), Kemmler-Sack [227] found a number of lowervalent uranates, (Li,UO,), (Li,UO,), (LiUO,), and (Li,U,O, ,). Fig. 31 shows a phase diagram including all of the above compounds. Phase fields were selected by self-consistent assessment of .available thermodynamic data for the lithium uranates and by analogy to other alkali metal uranate systems. There is a paucity of data describing the thermochemical characteristics of the Li-U-O system. O’Hara and Hoekstra [99] give a AH; value for (Li,UO,) of - 1961 kJ/mol. This value is in agreement with an older value of - 1954 kJ/mol given by Ippolitova et al. [228]. The standard entropy of (Li,UO,) was estimated [99] to be 133 f6.3 Jmol-’ K-‘, from which ASP is calculated to be - 385 * 8.2 J mol - ’ K - ’ and AS&,, is -3.6 J mol-’ K-‘. From this datum, the assumed phase equilibria of fig. 3 1, and the techniques of sections 2.3.1 and 2.3.2, the thermodynamic properties were estimated for the other uranates of this group (table 6). 4.9.2. Na-U-O Due to its greater importance to LMFBRs, much prork has been and continues to be done on the Na-U-O system. Several compounds in the Na,O-UO, system have been well characterized. These include (Na&JO,), (Na&O,), (Na&JO,), (NaUO,),
Fig. 3 1. Li-U-O
ternary equilibrium diagram for T w4w
o-J308 >
PO, > (Li4JOd W&JW W4UW
WJJ04 > (LlAJO4) (LiUO,) (L&%3)
(Li 2U&M (Lj,U,OI,) (Li&%) (Li&O& Wa2UO4h Wa2u04
)@
Wa2U2W (Na4W
>
WG-J7024
>
WPO4) WW
>
W4W) WW4) 62U207
>
WP4Od @2U7022) P-JO,
>
W4W
)
W2U04
>
QWJ207
)
@b,U40,,) W2U7022 WUO, P
w3
> > 56)
PwJO4) PP20,> P4U5%) ?w-!4012) FwJ40,3~ @29%?> (CS2U6W Fs2wh2) 0
2tl,o2,
(Cs2U,A6)
a) b, ‘) d, e, 0
>
ef d. / Thermo@umrc
data at 298.15 K for the alkali-metal
revrew and culculut~ons
uranates
AH; a) (kJ/mol)
Reference
- 1084.3 -4510 -3574 - 1228 - 3402 ” - 3279 - 2640 d, -2192 d, - 1961 - 1536 d’ - 8420 -4481 - 5440 - 5722 -8193 - 1889.5 - 1879 -3194.5 - 2430 - 10870 - 2022. I - 1506.2 -2419d’ - 1911 -3200e’ - 5690 ” -9405 0 -1517d’ - 2429 d, - 1913.3 -3199e’ - 5686 fl -9417 0 - 1516 d, - 1739.7 - 1926.3 -3199 - 7667 - 5573.9 -5713 -6957 - 8086 - 9434 --1l810 - 19280
PO61 PO81 PC’81
So b) (J mol-’
Reference K-’
)
77.0 336.0 282.0 98.7
[2091
12071 I2081
PO81 PO81
219.3 211.3 173.8 1442 [99]
[210,21 I] [210,213]
12101 11II 1111 [III
IllI
[I 1,215,216] 12181
Unreferenced values were estimated, see text. Calculated from AS”I,0X=O, except for reference values. -203~AHf’o,~-127.3 kJ/mol; AH:,,=150 kJ/mol Calculated from A Hof,ox interpolated from the Na analogs Calculated from AH&, interpolated from the Na and Cs Calculated from AH&, interpolated from the Cs analogs
132.6 106.6 607.7 333.4 388.9 432. I 629.3 166.0 166.1 275.9 248.9 916.3 198.2 125.5 286.9 180.3 291.4 486.7 784.5 134.9 327.8 202.9 311 8 509.1 804.9 145. I 239.0 219.7 332.0 777.0 526.43 536.0 636.0 703 0 834.0 998 0 1627.0
used h&e. on a graph similar to fig. 6. analogs on a graph similar to fig. 6 on a graph similar to fig. 6.
[991
I2121
12141
[991
t991
T. B. Lindemer et (11./ Thermodynamic rewew
I
und culcuhtions
I
I
’
211
I
I
r,/
/’ ,I
t
,g&
lo-3 / 5 ,’ Jo-’
,
Fig. 32. Na-U-O
No,u05’
I
I
/I
/’
/ 1’
IO'
,/
PN,.103P0
/
:/
N!Y&b
ternary equilibrium diagram for T 8) as mentioned by Anderson [240]. The phase region (K,O . nU0,) (3 d n 4 6) has been a source of much confusion with each researcher interpreting his crystallographic data in a slightly different fashion. We have followed the lead of Van Egmond and Cordfunke [239] in that, besides (K2U7022)r the only stable potassium polyuranate we have found is (K&O , 3) . Thus, the “intermediate” polyuranates (K&O,,), (K2U50i6), and (K&O,,) are not co*-
’
/ I
I
I
600
600
1000
TEMPERATURE,
1200
K
Fig. 33. Ellingham diagram for the Na-U-O system for compositions lying between Na and Na,U,O,,. The melting temperatures of the solids are indicated at the top of the figure and isobars for sodium pressure (in Pa) are shown as dashed lines.
sidered further. Therefore, recognizing the confusion that still exists for this system, a simplified approach was taken to constructing the phase diagram given in fig. 34. The only potassium uranate for which reliable thermodynamic data are given is (K2U04). Cordfunke and O’Hare[ll]reportaAH~valueof -1911*1.7kJmol. This value is preferred to older work by Ippolitova [228] because of the chosen thermochemical cycle. The standard entropy has been estimated by O’Hara and Hoekstra [99] as 180.3 * 6.3 J mol-’ K-‘, from which a value of AS&, has been calculated to be - 12.5 J mol - ’ K - ’ . From this datum, and using techniques described before, thermodynamic properties were estimated for the other uranates of this group. The thermochemical data are given in table 6. 4.9.4. Rb-U-O This system is very similar to the potassium
uranate
T. B. Lmdemer
212
Fig. 34. K-U-
0 ternary
equilibrium
diagram
ef u/. / Thermo&numrc
for T< 950 K.
system. Thus, the uranates (VI) (Rb,UO,), (RbsUO,), (Rb,U,O,), (Rb,U,O,,), and (Rb,U,O,,) have been found to exist [239]. From the X-ray powder diffraction patterns [239], it is evident that all the rubidium uranates are isostructural with the corresponding potassium uranates. Rlidorff et al. [241,227] have reported the preparation of (RbUO,) along with structural data. Workers in the USSR [242] have reported the existence of a compound (Rb,U,O,,); however, we can find no other work supporting this finding and have therefore not included it in this discussion. The phase diagram shown in fig. 35 has been constructed from the above information. Very little has been done regarding the determination of enthalpy or entropy data for these compounds. It is only for the normal uranate, (Rb,UO,), that data are reported [ 11,228]. Calculations have been made for the other compounds using the property of additive oxides and elements to obtain the requisite data. These data are given in table 6. 4.9.5. cs-u-o Because of its important role in irradiated nuclear fuels, especially to Urania-plutonia mixed oxide fast reactor fuels, the cesium-uranaium-oxygen system is by far the most thoroughly studied. Fission-product cesium has been observed to migrate both radially and axially within the fuel pin and high concentrations of cesium have been associated with a “two phase” region of undefined composition.
revrew und culculutrons
Fig. 35. Rb-U-O
ternary
equilibrium
diagram
for TC950
K.
Probably the earliest reported effort in organizing the structural chemistry of the cesium uranates is that of Kovba [243]. Ippolitova et al. [228] reported on extensive studies of the alkali-metal uranates, indicating the existence of a number of cesium polyuranates. More recently the work of Cordfunke et al. [244,245], Van Egmond [246-2491, and, in particular, Fee and Johnson [250-2521 have done much to put the phase equilibria of this polyuranate system in some semblance of order. These works have identified the following hexavalent uranates: (Cs,UO,>, (Cs*UrO,>, (Cs&O,,)* and (Cs&J,O,, >, (Cs&JsO,, >, (Cs$J,O,s >, (Cs,U,,O,). Cesium uranates with uranium in other than the hexavalent state include (Cs,UO,,,), (Cs,U,O,,>, (Cs,U,O,s>, and (Cs&O,,>. The data in fig. 36 are consistent with the phase data of Cordfunke et al. [218] and Lorenzelli et al. [253], but differ slightly from earlier work of Fee and Johnson [250,251]. There exists a z phase, (Cs,UO,~,,), with an O/(U + Cs) atom ratio less than that encountered in (Cs,UO, ) . This phase exists in equilibrium with {Cs} and (UO, ) . Also, there is no tie line between (UO, ) and (Cs,UsO, ) . Such a tie line had been considered in earlier work based on the observations of a (C&O,) -(UO, ) equilibrium mixture in work of Aubert et al. [254]. However, the recently measured thermodynamic properties of (Cs,U,O,,) [218] now eliminate the previously considered narrow stability range for (C&O, > - (UO, >. The z phase, i.e.; (Cs&JO, se), is believed to exist in two forms, a and 8. However, because the z phase has
213
T. B. Lmdemer et ul. / Thermocjvnumlc review and culculutrons
0 cs2u15046 \
cs%s Fig 36. Selected portions of the Cs-U-O system; isothermal sections from 873 to 1273 K. The solid areas show the width of the two phase regions at 1000 K; some tie lines change slightly with temperature.
yet to be isolated in pure form, the exact transition between the a and /.I forms cannot be determined. Thus, the thermodynamic estimates include both phases together. Thermodynamic data are available for several of the cesium uranates. O’Hare and Hoekstra [215] and Cordfur&e [216] have measured AH! for (Cs,UO,) and the selected value is - 1926.3,kJ/mol. Similarly, the recommended value [ 1 I] for the AH,” value for (Cs,V,O, ) is - 3 199 f 4.1 kJ/mol. The low-temperature calorimeter study of Osborne et al. [217] yielded a standard entropy for (Cs,UO,,), So =219.7 J mol-’ K-‘. In constructing the Cs-U-O phase diagram, thermodynamic functions were estimated in a self-consistent manner (see section 2.3) from the measured values of AH; for (Cs,UO,), (Cs,U,O,), (Cs,O), and (UO,). The miasured data, along with the estimated data, are given in table 6; fig. 37 displays the data graphically in a plot of oxygen potential as a function of temperature with an overlay of cesium pressure to more rigorously define stability regions. Estimates of AH/ were made graphically by starting with measured data for (Cs,UO,) and (Cs&O,). The AH: value for the next compound, (Cs&O,,), was chosen so that it was about 3kJ per (mol Cs,O + mol UO,) less negative than that obtained from a linear extrapolation of the measured data. This choice, although arbitrary in magnitude, makes the compound (Cs,UrO,) stable with respect to decomposition into (Cs,UO,) and (Cs&O,,). In a similar way, AH; values were estimated for all other reported
0
1200 1,
1400
K 8
Fig. 37. Ellingham diagram for the Cs-U-O and UO,,, system for compositions between Cs and Cs,U,O,,. The cesium pressures (in Pa) in equilibrium with the various phases are shown as dashed lines.
polyuranates. This graphical technique is equivalent in approach to the mathematical one of section 2.3.1. 4.10. A-(S,Se,
Te)-0
Only a portion of the ternary system will be considered here. Let X represent S, Se, and Te. The overall composition limits relevant to nuclear fuel studies are delineated by A, A,O,, A,XO,, and A,X because the fission product yields have (Rb + Cs) B (Se + Te). Also, po, values for this portion of the system include those for oxide nuclear fuels; their possible stability in nuclear oxide fuels will be considered in section6. Sulfur is included in this analysis in order to permit better estimation of thermodynamic data. 4.10.1. Compoundr
The ternary compounds are (A,XO, ) and (ArXO.,); the existence of the sulfites and sulfates is well established. The X-ray powder diffraction data for the selenates and tellurates are reported for all the alkali metals except Na [255]; (Na,TeO,) does exist [256,257]. All of the alkali metal telhuites exist [255,258], as do the selenites of Na and K [255]. The compounds (A,Te,O,)
214
T.B. Lmdemer ef 01. / Thermohnamlc reorew unJ c~lculutrons
also exist for Li, Na, and K [258]. Melting temperatures for (A,SO, ) are given in table 1, while those for (K,SeO,) and (Na,TeO,) are 875 [13] and 900K [257], respectively. No additional melting temperatures could be found, but experiments with these Se and Te double oxides are usually performed at TS 700 K. 4.10.2. Thermodynamic values The thermodynamic data
for these systems were developed next. Table 1 lists the AH,0 and S” values available from the literature. The S” value for (Na,SO,) led to ASP = -296 J mall’ K-‘, which was used to calculate S” values for all the other (A,XO,) species. The A$’ values for the Na, K, and Rb sulfates were averaged to give A&“ = - 396 J mol - ’ K-‘, which was used to calculate unknown values of S” for the remaining (A,XO,) species. It is probably significant to note that the difference in the AS,!’ values for the (A,XO,) and (A,XO,) species is essentially half the S” value for (0,). Earlier estimates of S” values for (A2Se0,) [259] were -37 J mol-’ K-’ less than those given in table 1. The several values of A HP estimated here are listed in table 1. For (A2 SeO,), these values were obtained through the use of fig. 38, where all the known AH&, 0 I
0
I
I
I
I
I
A2S03
600
0
400
200 -9,
ox
+ a-CO,, +$(Al,Si,O,,) +y(SiO,). Also assume that the (0,) pressures for the mass spectrometric measurements were equal, although undefined, for both. If one takes the ratio of the two equilibrium constants, Poz5 cancels,
211
T. B. Lmdemer et ul. / Thermodynumic review and culculatlons
leaving the ratio of the two cesium pressures. This ratio can be calculated from the results of Odoj et al. [271], who give log P, (Torr) = -21828/T + 10.3 for the decomposition of synthetic (CsAlSi,O,) and log P2 (Torr) - 26 850/T + 12.4 for the decomposition of (csAlSi,O,,). Furthermore, RT ln(P,/P,) = -AC;, + AC;.,. Substitution of known AH; and So val&s into the pressure ratio equation leads to A HP = - 5840 +O.O2468TkJ/mol for (CsAlSi,O,,). At lOOOK, AH; = - 58 16 kJ/mol and AH&, = - 250 kJ/mol, while at 2OOOK, AHi’ = -5791 kJ/mol and AH&, = -225 kJ/mol. A AH&, value of -240 kJ/mol, which is reasonably consistent with the work of Odoj et al. [271], was used here; it also falls within the limits of -213 to -259 kJ/mol derived above. Thus, A HP = - 5805 kJ/mol for (CsAlSi,O,,). A calculated Cs,O-Al,O, -SiO, phase diagram is shown in fig. 42. An Ellingham diagram (fig. 43) was calculated for elemental Cs-Al-Si-0 compositions lying between (CsAlSi,O,), (CsAlSi,O,,), and (Al ,Si 20, 3) . These would include the maximum cesium concentrations to be expected in nuclear fuel or nuclear waste applications. The calculations included the thermodynamic data for (Cs), (CsO), (Cs,O), (Al,O,), (SiO,), (Cs,O), {Cs}, (Cs,SiO,), (Cs,Si,O,), (Al,Si,O,,) (mullite), (Si), {Al}, (CsAlO,), and the three cesium aluminosilicates. The isobars for the pressure of (Cs) are also plotted in fig. 43. The po, values derived from fig. 43 at the temperatures and cesium
I I
600
I 1000
I
I
I
1400 TEMPERATURE.
I
I
1600 K
Fig. 43. FUingham diagram for the Cs-Al-Si-0
system for compositions lying within those for the (CsAlSi,06 ) (CsAlSis0,2) -(Al,Si,O,j) phase field. Isobars for (Cs) pressures are shown as dashed lines. The melting temperatures of the solids are indicated at the top of the figure.
pressures obtained by Odoj et al. [271] over (CsAlSi,O,) lead to PO, = 0.01 Pa for the atmosphere in the Knudsen cell of their mass spectrometer, a fairly reasonable value for high-vacuum equipment. Also, the pressures of (CsO) and (Cs,O) were always orders of magnitude lower than that for (Cs) at any given po, and T. Comparison of the po, -T range in which the cesium aluminosilicates are stable with the range for the other cesium oxide compounds considered in this paper demonstrates that the cesium aluminosilicates are the most stable.
6. The system U-Mo-Cs-Te-&Fe-H-O Fig. 42. Cs,O-Al 203 -&O, equilibrium diagram at T= 1 I50 K. This is the lowest temperature for stability of (Al,Si,O,,) relative to (A1203) and (SiO,), and for the three eutectics lying between (Cs,SiO,) and (SiO,).
The calculational techniques used in this paper can be applied to multicomponent, multispecies systems of engineering interest. The present intent is to provide a fairly simple illustrative example. Thus, Ellingham dia-
grams were calculated for po, < -375 kJ/mol for isothermal equilibria in a nuclear fuel system composed of UO,, the fission products Cs, MO, and Te, and the stainless steel cladding components Fe and Cr. Approximately 10% burnup of the UO, was assumed. The numbers of moles of U, Cs, MO, Te, Fe, and Cr were, respectively, 90, 1.5,2.05, 0.25, 160, and 50. In addition, P,* = 10 Pa was assumed. Gaseous species considered here were (O,), (Cs), (Cs,), (Te), (Tel), (Cr), (U), (MO), (Fe), (Hz), (Fe(OH)& (CszMoO& (HIMoO,), (Cs,O). (CsO), (Cs,CrO,), (CsOH), the dimer (CsOH),, (MOO), (MOO,), (MOO,), (CrO), (Cr02), and (CrO,). The condensed species considered in the calculations were the elements, (Cs,Te) , (Cs,TeO, ) , (CsFeO, ) 1 (C@Q > , (C@+ > , (C@Q >, (Cs,CQ > , (Cs,CQ), (Cs,MoQ,), {Cs,MoQ,}, (Cs,Mo,O,), (GNo05), (Moo2 >, (W-JO4 > , (W >, (WA >, (FeCr,O,), (Co,U03,,), and {CsOH). An activity of unity was assumed for all condensed species. The results of the calculations for the entire system are shown in figs. 44 and 45. Either (CsI) or {&I) would also be present, but these compounds have been treated earlier [276]. Most of the equilibria illustrated in fig. 44 are self-explanatory, with the exception of the two in which (Cs,Te) decomposes. The equilibrium may (Cs,Te) + (MO) + 2(0,) P (Te) + (Cs,MoO,) occur if (MO) is present. However, in the fuel-clad gap, (MO) may not be present, and the other equilibrium would then be relevant. Formation of either Fe, Cr, or Ni tellurides, which are weakly stable [44,46], would change these po, values slightly. For example, formation of (FeTe, 9) instead of {Te} would add - 13000 4.6T J/mol to the po, values for the equilibrium involving (Cs,MoO,) and - 1500 + 16T J/mol to these values for the equilibrium involving (Cs,UO,) in the region where (FeO) is stable. Formation of (NiTe, ,) 1441 from (Ni) and (Te) or (Te} would add = -52 kJ/mol to both po, values. Isobars for the gaseous species having pressures > 10 lo MPa are shown in fig. 45. In addition, (Te) falls into this category but is always insignificant in comparison to (Te,), while (CsI), (Cs,I,), and (I) may have pressures > IO lo MPa [276]. All of the other gaseous species listed above had pressures C 10 _ lo MPa under all p + and T conditions. A relevant chemical subsystem of this set is Cs-CrFe-O, such as might exist on the stainless steel cladding in the absence of physical contact with the oxide fuel. The Ellingham diagram is shown in fig. 46 for a Fe : Cr : Cs proportion of 160 : 50 : 1.5. It is interesting to note the decomposition of the Cs-Cr-0 compounds by the Cs-Fe-O compounds as po, becomes more positive. The several calculated phase transitions at LMFBR
TEMPERATURE,
K
Fig. 44. Ellingham diagram for the U-Mo-Cs-Te-Cr-Fe-H0 system. The system composition is that for UO,, the chromium and Iron content of stainless steel, the f&on product concentration at 10% bumup, and P,,: = IO Pa. The meltmg temperatures for the solids are mdxated at the top of the figure. The condensed species were assumed to exist at an activity of unity.
cladding temperatures, - 800 K, may be important to the in-reactor cladding corrosion phenomena. As was noted in section 4.7.2. however, the occurrence of (Cs,FeO,) is assumed, the melting temperatures of the Cs-Fe-O compounds are unknown, and all the thermodynamic data for the compounds are estimated.
7. Discussion and recommendations The chemical systems considered in this paper have been examined to identify the more critical data needs. The primary criterion was applicability to conditions existing in nuclear fi$sion and fusion fuel Ad coolant systems, and their interactions with structural and containment metals. Values of A HP,So,and melting tem-
T. B. Lmdemer et ul. / Thermodynumic (Tep) I
revrew und cukulutrons
219
(CszMo04)
I
I
I
lo;‘0lo- Hf4 I ; I I
600
:C
-
/*
0 .E 2
-
800
-
,
I
7 I
(CsOH) I
I
;
I I
’
I
1
’
-_-
I
ICE.1 I
I
I
I
I 500
IO00
1500 TEMPERATURE,
500 K
I 1000
1500
Fig. 45. Isobars (units of MPa) for the gaseous species having pressures > IO - lo MPa in the system of fig. 44. In addition, (CsI) is significant [276]. The lettered equilibria are also shown on fig. 44 and involve the following condensed phases: A, (Cs) + (UO,) + (Cs2U04); C, (CsJJO,) + (MO) + (Cs,MoO,) + (UO); E, (Cs,Te) + (MO) + (Te) or {Te) + (Cs,MoO,); F, (MO) + (MOO,); H, (Cs,Te)+(UO,)+(Te) or (Te)+(Cs,UO,). The pressures of the gases (Cs,O,H,), (Cs,), (Te), and (Cs212) are also >lO-‘” MPa, but are significantly less than those of (CsOH), (Cs), (Tez), and (CsI), respectively, at any p,,-T condition [276]. Either (CsOH) or (Cs,MoO,) is the primary oxygen-containing gas, depending upon the po,-T conditions,
peratures for specific compounds are generally the minimum required information, but the existence of some compounds requires demonstration. The recommendations from this overview are given in table 7. The recommendations for the cesium compounds also apply to the rubdium analogs. The properties of (CsrTe), (Rb,Te), and the Cr, Fe, and Ni tellurides may be particularly important to the performance of possible LMFBR (Th,U)O, fuels [46,277,278]. Unlike (U,pU)O,_, fuels, the (Th,U)O, fuels cannot be made substoichiometric. The initial fuel po, value would be 2 -420 kJ/mol, rather than the = -570 kJ/mol of U,sPu0,20, %. (The latter po, value is at w 1500 K and is temperature dependent.) In addition, po, increases with burnup. It can be seen in figs. 44 and 45 that the thermodynamic activity of tellurium
may be much higher in the (Th,U)O, fuel, and may lead to more tellurium interaction with the stainless steel cladding than has been observed in the plutoniumcontaining fuel. The thermodynamic effects of temperature gradients have been treated recently [45,46,252,278], thus they are not considered here. For example, Cs-Cr-0 compounds were not stable in the isothermal fuel-clad system shown in fig. 44; however, they could be stable on the cladding inner surface, where the temperature is lower than that of the fuel circumference. The equilibria of fig. 46 would thus be relevant. A computer program has been described for the prediction of fission product migration in a temperature gradient and in a concentration gradient [279]. Computer calculation of thermodynamic equilibria is
T. B. Lmdemer et 01. / Thermodynumtc revtew und culculurrons
220
1 A
FeaO,
I
1 +
Fe’&.O,
+
CsFeOz
B
Fe0
+
Fe’&O,
+
CsFeO,
C
Fe
+
Fe’&O,
+
CsFeOp
D
Fe
+
F&,0,
+
Cs,FeO,
E
Fe
+
FeCrzO,
+
Cs,CrO,
I
I 400
I 600
600
determination
Fig. 46. Ellingham diagram for the Cs-C&Fe-O system at a ratio of Fe : Cr : Cs of 160 : 50 : 1.5, which is used to represent that of stainless steel and fission-product cesium.
recommended as a powerful analytical tool. An analysis of the Na-V-O system, as shown in figs. 23 and 24, would have been invaluable to the earlier attempts to interpret the results of equilibration of [O],, with V wire and sheet; AH; data on the lower vanadium oxides did not exist at that time [121]. The Na-Fe-O system (fig. 27) is an example of extremely complex behavior, with at least seven ternary phase diagrams calculated to exist between 300 and 1400 K. Such behavior almost mandates computer assistance with intepretation of future experimental data in this system. The data generated for multielement systems (figs. 43-45) are most efficiently and accurately interpreted by computer. Many engineering systems containing numerous species probably cannot be interpreted as satisfactorily by other means.
I 1200
1000
TEMPERATURE.
Table 7 Species needing
I
K
of A HP, S”, and the maximum
temperature
for stability
of the crystalline
state
Species
Substantiation
Figure
P 3) WJ’e)
Important species in fuel-cladding interactions; for (Cs,Te), T, =953 K [22]; also see refs.
44.45
((Cr,Fe,Ni)Te,)
144,461
46
(CsFeOs )I (Cs,PeOz)
Proof of existence;
(Cs,Mo,O,)
Proof of equilibrium
(Cs,CrO,)
Conformation
(Na,CQ)
Substantiate
(NaCG
Confirm
)
LMFBR
AH&,
I. 8, 9 II, 12 6
of (Cs,CrO,)
Na conditions
for equilibrium
(Cs, ZrOs )
Proof of existence;
To confirm equilibria fusion device
with (Nb);
To confirm
with (“0,)
)
46
A HP known
with (Cr) and (Cs);
(LiNbO,) (LisNbO, (NaVOs
interactions
with {Cs) and (MO)
of equilibrium
T-[0]
fuel-cladding
with (Na} and (Cr):
species in LWR fuel-cladding
equilibria
confirm
contacting
Nb alloys for
Nn conditions
The suggested
(Cs,GJPu)O,-,)
Determination solution
PI,
General need for [O],-pot-T data below the saturation limit for all alkali metal systems
(CsAlSi,O,) (CsAlSisO,,)
Compounds
[I I] is apparently
21,22
23
(Na&O&
with (Fe) and (Na)
incorrect
of co, - T values for equilibrium
to nuclear
(Li,O)
compounds
(NasFeOs) (NadFeOs)
significant
14
interaction
for (Li,O,)-contaminated
Proof of existence;
data in ref.
T-[0]
A HP known
waste isolation
27
and needs redetermination.
with (Cs} and ((U, Pu)O,);
32,33 effect of Pu
2. 14, 24 27 technology
42,43
T. B. Ltndemer
et ul. / Thermodynamrc
Acknowledgements
221
Bailey and R.H. Schumm, U.S. Nat’]. Bur. Stand. Tech. Rep. 270-3 (1968).
One of the authors (T.B. Lindemer) is indebted to Drs. H. Nickel and A. Naoumidis of the Institute for Reactor Materials, Kemforschungsanlage Jtilich GmbH (KFA), J&h, Fed. Rep. Germany, for use of the KFA facilities during the author’s assignment there. Gratitude is also expressed to D.C. Fee, of ANL, for his critique of this manuscript; C. Ling, a co-op student at ORNL, for special assistance with data processing; and B. Drake of ORNL, for typing the manuscript.
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