Standard molar enthalpies of formation of PrO2and SrPrO3: the unusual thermodynamic stability of APrO3(A = Sr, Ba)

O-548 J. Chem. Thermodynamics 1995, 27, 551–560

Standard molar enthalpies of formation of PrO2 and SrPrO3 : the unusual thermodynamic stability of APrO3 (A=Sr, Ba) S. A. Gramscha and L. R. Morssb Chemistry Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439 , U.S.A.

(Received 12 April 1994; in final form 5 December 1994) The standard molar enthalpies of formation Df H°m of the fluorite oxide PrO2 and the perovskite oxide SrPrO3 have been determined by solution calorimetry. A combination of appropriate thermodynamic cycles leads to the values Df H°m(PrO2 , 298.15 K)=−(959.824.1) kJ·mol−1 and Df H°m(SrPrO3 , 298.15 K)=−(1588.424.1) kJ·mol−1 . Unusual stability is found for SrPrO3 in terms of the enthalpy of reaction of the binary oxides to form the ternary oxide: Dr H°m{SrO(cr)+PrO2(cr)=SrPrO3(cr)}=−39 kJ·mol−1 . This stability of SrPrO3 is consistent with earlier thermochemical work on BaPrO3 . The Pr members of the series of perovskite oxides AMO3 (A=Sr, Ba; M=transition elements: Ce, Pr, Tb, actinides) are substantially more stable than expected from the trend established by the other members of the series, in which the enthalpy of reaction of the binary oxides to form the ternary oxide becomes less negative as the perovskite becomes more distorted. Electronic stabilization of the perovskite (PrO3 )2− framework in these 4f 1 compounds is proposed as the origin of the additional thermodynamic stability of the perovskite oxides of Pr4+ .

1. Introduction The perovskite structure ABO3 effectively stabilizes high oxidation states of the transition metal, lanthanide, and actinide elements by oxide coordination in the ‘‘B’’ site of the structure. This stabilization is unusual for the lanthanide elements, which usually occupy the twelvefold coordinate ‘‘A’’ site as trivalent cations in oxide perovskites A3+B3+(O2− )3 , since the trivalent rare-earth cations are too large to occupy the sixfold B sites. Trivalent Ce3+ , Pr3+ , and Tb3+ can be oxidized to tetravalent Ce4+ , Pr4+ , and Tb4+ , which are too small to occupy the A sites in oxide perovskites but are large enough to occupy the B sites. The perovskites A2+Ln4+(O2− )3 (A=Sr, Ba; Ln=Ce, Pr, Tb) thus offer a unique set of compounds with which to study the thermodynamic stability of the tetravalent rare earths in ternary oxides. Significant effort has gone into understanding the structural, magnetic, and thermodynamic

a b

Current address: Department of Chemistry, Augustana College, Rock Island, IL 61201, U.S.A. To whom inquiries should be sent.

0021–9614/95/050551+10 $08.00/0

7 1995 Academic Press Limited

552

S. A. Gramsch and L. R. Morss

properties of the BaLnO3 systems, in particular BaPrO3 .(1–4) More recently, the thermodynamic properties of SrLnO3 (Ln=Ce, Tb) have been determined,(5) but SrPrO3 was not included in the study because of synthesis difficulties.(6) For nearly all A2+M4+(O2− )3 perovskites, where M is one of many transition metals, lanthanides, and actinides, a linear relation exists between the enthalpy of the reaction of the binary oxides AO and MO2 to form the ternary oxide AMO3 : AO(cr)+MO2(cr)=AMO3(cr),

(1)

and the Goldschmidt tolerance factor(7) associated with the structure of the perovskite, t=d(A–O)/{21/2d(M–O)},

(2)

where bond lengths d are calculated using the effective ionic radii compiled by Shannon(8) for the appropriate cation coordination numbers (A2+ , 12; M4+ , 6). As the perovskite becomes more distorted from the ideal cubic structure, where t=1, the enthalpy of reaction (1) becomes less negative, so that more distortion corresponds to decreased stability. Because Pr4+ is a large ion, BaPrO3 is a highly distorted perovskite, but reaction (1) for BaPrO3 has been found to be unusually exothermic(3,5) so that BaPrO3 appears to be inexplicably stable. The objective of this research was to establish whether the unusual stability of Pr4+ perovskites is real. The enthalpy of reaction (1) for BaPrO3 rests partially on the thermochemistry of PrO2 , which was studied over 40 years ago. Therefore, we synthesized PrO2 and redetermined its enthalpy of formation. If there indeed exists an enhanced stability for BaPrO3 beyond what is predicted on the basis of the aforementioned crystal-chemical trends, then there should also be an enhanced stability for SrPrO3 . Therefore we synthesized and determined the enthalpy of formation of SrPrO3 .

2. Experimental Sr(OH)2 (Johnson-Matthey, mass fraction 0.9999) and Pr6 O11 (Aldrich, mass fraction 0.999) were each stored in a desiccator under N2 and assayed before use by t.g.a. (Mettler TA-2 Thermobalance) to determine the metal contents. Sr(OH)2 was heated in dry nitrogen to give SrO, and Pr6 O11 was reduced in (0.04H2+0.96Ar) to Pr2 O3 . The powder X-ray diffraction pattern (Philips diffractometer, nickel-filtered Cu Ka radiation) of the reduction product of Pr6 O11 showed no lines other than those of hexagonal Pr2 O3 . Stoichiometric amounts of Sr(OH)2 and Pr6 O11 were then thoroughly mixed together and pressed into discs. These were fired in an alumina boat at T=1273 K under flowing O2 (mole fraction, 0.996, X-Dry, AGA Gas) for 72 h with two intermediate grindings. An X-ray powder-diffraction pattern (table 1) of the product SrPrO3 was indexed on a primitive orthorhombic unit cell with lattice constants a=0.597(1) nm, b=1.221(1) nm, and c=0.853(1) nm, and showed no evidence of any secondary phase, including unreacted SrO or Pr6 O11 . The structure of SrPrO3 is not the same as that of BaPrO3 , although both are distorted perovskites. BaPrO3 is a GdFeO3-type perovskite which is characterized by a simple (2)1/2a ·(2)1/2b ·2c

553

Molar enthalpies of formation of PrO2 and SrPrO3

TABLE 1. X-ray powder diffraction pattern of SrPrO3 {orthorhombic, a=0.597(1) nm; b=1.222(1) nm; c=0.853(1) nm} Cu Ka, l=0.15419 nm hkl

2u ·180/p obs. calc.

110 002 121 122 200 032 103 123 150 240 241 160 124 161

17.04 20.90 23.40 29.70 29.73 30.30 35.06 38.08 39.86 42.42 43.46 47.13 47.68 48.47

16.53 20.81 23.29 29.59 29.94 30.32 34.93 38.00 39.82 42.32 43.69 47.11 47.63 48.37

100·Ihkl /I122

hkl

2u ·180/p obs. calc.

7 14 6 100 51 32 6 7 10 50 6 14 11 6

044 252 071 234 080 270 045 421 280 362 281 305 216

52.31 52.91 53.62 57.82 60.45 61.48 62.18 65.28 69.08 69.67 69.85 72.98 74.13

52.27 52.94 53.53 57.72 60.56 61.49 62.28 65.29 69.02 69.61 70.01 73.03 74.25

100·Ihkl /I122

32 44 20 6 7 24 10 7 7 25 12 4 4

distortion of the primitive cubic ideal perovskite,(9) while SrPrO3 has a unit cell characterized by a (2)1/2a ·2(2)1/2b ·2c distortion. This is a GdFeO3-type perovskite which has a unit cell approximately doubled along the b direction, as seen for the isostructural SrCeO3 .(10) The problem of unresolved splittings in the low-angle reflections in the X-ray diffraction patterns of orthorhombically distorted perovskites, alluded to in reference 1, precluded a more precise determination of the lattice parameters. T.g.a. reduction of the product phase in (0.04H2+0.96Ar) gave an oxygen content consistent with a chemical formula SrPrO2.9720.03 . Pr2 O3 was prepared in the t.g.a. apparatus as described above in sufficient quantity for calorimetric measurements. The starting Pr6 O11 was heated in flowing (0.04H2+0.96Ar) to T=1373 K over a period of several hours, and heating was continued for 2 h after the sample had stopped losing mass. An X-ray diffraction pattern of the light-green product showed only the lines of the high-temperature hexagonal form of Pr2 O3 , with refined lattice parameters a=0.3840(2) nm and c=0.5996(4) nm determined by least-squares fitting, as compared with the literature values a=0.38577(3) nm and c=0.60090(6) nm, determined in a single-crystal diffraction study.(11) PrO2 was prepared for calorimetric experiments by heating Pr6 O11 (Alfa, mass fraction 0.996) in a Parr bomb under a pressure of 5500 kPa of high-purity O2 . The reaction was carried out at T=553 K for 24 h, followed by 3 h at T=608 K, and finally at T=568 K for 60 h. The bomb was then slowly cooled to room temperature. An X-ray powder diffraction pattern of the product PrO2 showed only the lines of the face-centered cubic fluorite structure, with a lattice parameter a0=0.53906(6) nm. The best available literature value for comparison is a0=0.5392 nm,(12) and the noticeably lower value for the lattice parameter of our material suggests that it is closer to true PrO2 stoichiometry than the material used in

554

S. A. Gramsch and L. R. Morss

TABLE 2. Molar enthalpy of solution at T=298.15 K for Pr2 O3(cr) in HClO4(aq, c=4 mol·dm−3 ) Sample no. 1 2 3 4

a b

m/mg

DH/J

70.63 −90.51 30.36 −38.47 56.73 −72.77 36.05 −46.48 Dsol Hm =−(423.024.3) kJ·mol−1

a

Dsol Hm /(kJ·mol−1 ) −422.6 −417.9 −422.9 −428.4 b

For the reaction: Pr2 O3(cr)+6H+(aq)=2Pr3+(aq)+3H2 O(l). The uncertainty is twice the standard deviation of the mean.

the earlier study. Results of the t.g.a. reduction of the PrO2 in (0.1H2+0.9N2 ) indicated an oxygen content consistent with the formula PrO2.0020.03 . The binary oxides Pr2 O3 and PrO2 were loaded into ampoules for the calorimetric experiments in a nitrogen atmosphere and sealed therein with glass plugs and Apiezon W black wax to avoid spontaneous air oxidation or reduction to PrO1.5+x . A small amount of the Pr2 O3 sample left open to the ambient atmosphere showed no discoloration over a period of two weeks. Although CO2 and H2 O were certainly absorbed from the air, no significant oxidation took place over this period, as the color of the material would have changed to brown or grey had it been oxidized to PrO1.5+x . The color of PrO2 appeared unchanged from its black color upon lengthy exposure to air. Similar care was taken in the preparation of SrPrO3 calorimetric samples. Enthalpy-of-solution measurements were carried out on the SrPrO3 , PrO2 , and Pr2 O3 products in an isoperibol solution calorimeter equipped with an automated data-acquisition and analysis routine which was described in detail.(13,14) The calorimeter was calibrated and the data-acquisition algorithm verified with NBS standard reference material SRM-724 tris(hydroxymethyl)aminomethane (‘‘TRIS’’). Two samples gave values for Dh of −(235.7420.58) J·g−1 and −(235.5120.58) J·g−1 for dissolution of the material in HCl(aq, c=0.100 mol dm−3 ), where c denotes concentration. These are in excellent agreement with the literature value of −(235.8020.23) J·g−1 .(15) During the experiments, chemical-dissolution events were alternated with electrical-heating calibration events TABLE 3. Molar enthalpy of solution at T=298.15 K for PrO2(cr) in {HNO3(c=6.00 mol·dm−3 )+ NaBF4(c=0.10 mol·dm−3 )}(aq) a Sample no. 1 2 3 4

a b

m/mg

DH/J

46.6 −45.19 48.4 −47.39 49.4 −47.55 62.5 −60.41 Dsol Hm =−(167.621.2) kJ·mol−1

Dsol Hm /(kJ·mol−1 ) −167.7 −169.3 −166.4 −167.1 b

For the reaction: PrO2(cr)+3H+(aq)=Pr3+(aq)+(3/2)H2 O(l)+(1/4)O2(g). The uncertainty is twice the standard deviation of the mean.

555

Molar enthalpies of formation of PrO2 and SrPrO3

TABLE 4. Molar enthalpy of solution at T=298.15 K for SrPrO3(cr) in HClO4(aq, c=4 mol·dm−3 ) DH/J

Sample no.

m/mg

1 2 3 4

71.4 −97.2 83.2 −114.7 128.7 −172.1 85.6 −117.4 Dsol Hm =−(377.224.8) kJ·mol−1 a b

Dsol Hm /(kJ·mol−1 )

a

−377.3 −382.3 −379.2 −369.8 b

For the reaction: SrPrO3(cr)+5H+(aq)=Pr3+(aq)+Sr2+(aq)+(5/2)H2 O(l)+(1/4)O2(g). The uncertainty is twice the standard deviation of the mean.

which allowed the heat capacity of the calorimeter to be determined. Corrected temperature changes were obtained using the method of Dickinson,(16) and this procedure was incorporated into the computer algorithm, so that analysis of the time-against-temperature curves for a given event (chemical or electrical) gave directly the corrected temperature change for that event. The solvent chosen for the solution reactions of SrPrO3 and Pr2 O3 was HClO4(aq, c=4 mol·dm−3 ), since it cannot be oxidized and {when pure, as confirmed by absence of reaction with MnO− 4 (aq)} also contains no reducing agents. Thus the dissolution reaction of SrPrO3 is simply SrPrO3(cr)+5H+(aq)=Sr2+(aq)+Pr3+(aq)+(5/2)H2 O(1)+(1/4)O2(g),

(3)

where the species designated (aq) refer to HClO4(aq, c=4 mol·dm−3 ). Enthalpy-of-solution measurements for PrO2 were also carried out, but with {HNO3(c=6 mol·dm−3 )+NaBF4(c=0.10 mol·dm−3 )}(aq) as the solvent. This change in solvent was necessary because PrO2 dissolves too slowly in HClO4(aq), and it also allowed a direct comparison with much earlier calorimetry of PrO2 .

3. Results and discussion Results for solution-calorimetric experiments at T=298.15 K on Pr2O3 , PrO2 , and SrPrO3 , respectively, appear in tables 2, 3, and 4. The results for PrO2 amd SrPrO3 were TABLE 5. Thermochemical cycle for the calculation of Dsol Hm(Sr, cr) in HClO4(aq, c=4 mol·dm−3 ) Reaction SrCO3(cr)+2H+(aq)=Sr2+(aq)+CO2(g)+H2 O(aq) Sr(cr)+C(cr)+(3/2)O2(g)=SrCO3(cr) CO2(g)=C(cr)+O2(g) H2 O(aq)=H2(g)+(1/2)O2(g) Sr(cr)+2H+(aq)=Sr2+(aq)+H2(g) a

Reference 18. b Reference 19. c Reference 20. d Reference 21.

DHm /(kJ·mol−1 ) −17.121.0a −1225.821.1b 393.520.1c 285.920.5d −563.521.6

556

S. A. Gramsch and L. R. Morss

TABLE 6. Thermochemical cycle for the calculation of Dsol Hm(Pr, cr) at T=298.15 K in HClO4(aq, c=4 mol·dm−3 ) Reaction

DHm /(kJ·mol−1 )

PrO1.5(cr)+3H+(aq)=Pr3+(aq)+(3/2)H2 O(aq) Pr(cr)+(3/4)O2(g)=PrO1.5(cr) (3/2)H2 O(aq)=(3/2)H2(g)+(3/4)O2(g)

−211.522.2 a −904.821.5 b 428.920.7 c

Pr(cr)+3H+(aq)=Pr3+(aq)+(3/2)H2(g)

−687.422.8

a

Table 2. b Reference 22. c Reference 21.

uncorrected for the dissolution of O2 (g) in the HClO4 solvent, or the saturation of the evolved O2 (g) by the water vapor over the solvent, as these corrections amount to enthalpy effects well inside the uncertainties in the measured enthalpy-of-solution values.(17) Thermodynamic cycles for the calculation of enthalpies of solution for Sr(cr) and Pr(cr) are given in tables 5 and 6. No attempt was made to determine the enthalpy of solution of Pr(cr) directly because of the possibility of reduction of HClO4(aq). However, the derived value for the enthalpy of solution of Pr(cr) in HClO4(aq, c=4 mol·dm−3 ) (table 6) is in good agreement with a value of −692.16 kJ·mol−1 determined by Fitzgibbon et al.,(22) who employed direct dissolution of the metal in HCl(aq, c=2 mol·dm−3 ). Combination of this result with the enthalpy of solution of SrPrO3 then gives its enthalpy of formation, as calculated in table 7. The molar enthalpy of solution obtained in our measurements on PrO2 is in good agreement with, but differs slightly from, that determined previously by Eyring et al. [−177.4 kJ·mol−1 in HNO3(aq, c=6 mol·dm−3 ), and −(175.721.7) kJ·mol−1 in {HNO3(c=6 mol·dm−3 )+HBF4(c=0.1 mol·dm−3 )}(aq)].(23) As illustrated in figure 1, the molar enthalpy of solution becomes less negative in the LnO2-x systems as x 4 0.(23–25) A less negative molar enthalpy of solution for PrO2 in the present determination as compared with previous experiments is reasonable and expected in view of the fact that our material is most likely closer to stoichiometric PrO2 . Table 8 contains the appropriate thermodynamic cycle for the calculation of the standard TABLE 7. Thermochemical cycle for the calculation of Df H°m(SrPrO3 , cr) at T=298.15 K Reaction Sr2+(aq)+Pr3+(aq)+(5/2)H2 O(aq)+(1/4)O2(g)=SrPrO3(cr)+5H+(aq) Sr(cr)+2H+(aq)=Sr2+(aq)+H2(g) Pr(cr)+3H+(aq)=Pr3+(aq)+(3/2)H2(g) (5/2)H2(g)+(5/4)O2(g)=(5/2)H2 O(aq) Sr(cr)+Pr(cr)+(3/2)O2(g)=SrPrO3(cr) a

Table 4. b Table 5. c Table 6. d Reference 21.

DHm /(kJ·mol−1 ) 377.224.8 a −563.521.6 b −687.422.8 c −714.721.3 d −1588.424.1

557

Molar enthalpies of formation of PrO2 and SrPrO3

FIGURE 1. Molar enthalpy of solution Dsol Hm at T=298.15 K of TbOx and PrOx as a function of x along the sesquioxide-to-dioxide coordinate. W, PrOx (23,24); Q, TbOx (25). The point corresponding to the present determination is marked with an asterisk (*).

molar enthalpy of formation of PrO2 , a result we believe to be more accurate than that published previously. Enthalpies of formation for all ALnO3 perovskites are presented in table 9. When combined with enthalpies of formation for SrO and BaO,(26) and the rare-earth dioxides CeO2 , TbO2 ,(20) and PrO2 (present work), the molar enthalpy of formation of the complex perovskite oxide from the binary oxides is calculated according to equation (1). These results are presented graphically as a function of the tolerance factor in figure 2. For all ALnO3 perovskites, except those with Ln=Pr, the value of Dr H°m appears to correlate directly with the tolerance factor. Since both SrPrO3 and BaPrO3 show additional thermodynamic stabilization upon complexation of the binary oxides, the effect appears to be real and due to the Pr(IV). Of special note is that the molar enthalpy of complexation for the formation of SrPrO3 deviates less from the value TABLE 8. Thermochemical cycle for the calculation of Df H°m(PrO2 , cr) at T=298.15 K Reaction

DHm /(kJ·mol−1 )

Pr(cr)+(3/4)O2(g)=PrO1.5(hex) PrO1.5(hex)+3H+(aq)=Pr3+(aq)+(3/2)H2 O(aq) Pr3+(aq)+(3/2)H2 O(aq)+(1/4)O2(g)=PrO2(cr)+3H+(aq)

−904.821.5 a −222.621.0 a 167.621.2 b

Pr(cr)+O2(g)=PrO2(cr)

−959.822.2

a

Reference 22. b Table 3.

558

S. A. Gramsch and L. R. Morss

TABLE 9. Standard molar enthalpies of formation at T=298.15 K for ALnO3 perovskites (A=Sr, Ba; Ln=Ce, Pr, Tb) Compound BaTbO3 BaPrO3 BaCeO3 SrTbO3 SrPrO3 SrCeO3

c

Df H°m /(kJ·mol−1 ) −1607.626.4 c −1644.928.0 c −1688.624.6 c −1612.922.1 d −1588.424.1 e −1684.523.6 d

t

a

0.985 0.946 0.938 0.930 0.892 0.885

Dr H°m /(kJ·mol−1 )

b

−88 −137 −52 −49 −39 −4

a Goldschmidt tolerance factor (defined in text). b Reaction is AO(cr) + LnO2(cr) = ALnO3(cr). Reference 3. d Reference 5. e Table 7.

predicted by the linear relation of tolerance factor against molar enthalpy than the analogous value for BaPrO3 . The more distorted nature of SrPrO3 compared with BaPrO3 has offset at least part of the thermodynamic stabilization that appears to be inherent in these Pr(IV) compounds. Even so, the degree of stabilization is quite significant: about 20 kJ·mol−1 in SrPrO3 and 80 kJ·mol−1 in BaPrO3 . This linear molar-enthalpy-against-tolerance-factor relation may be extended to other AMO3 systems, where A is an alkaline-earth metal cation and M is a tetravalent cation, as shown previously by Fuger and co-workers.(5,17) Deviations from this linear behavior occur only for BaMoO3 (Mo4+ , 4d3 ) and the Pr4+ (4f 1 ) compounds discussed here. In contrast to the extra thermodynamic stability observed for SrPrO3 and BaPrO3 , BaMoO3 exhibits a decreased thermodynamic stability with respect to the

FIGURE 2. Standard molar enthalpy of reaction Dr H°m at T=298.15 K as a function of the perovskite tolerance factor t for the formation of ALnO3 perovskites from binary oxides. R, Ce, Tb compounds; W, Pr compounds.

Molar enthalpies of formation of PrO2 and SrPrO3

559

trend established by other perovskites, while the analogous SrMoO3 does not show any deviation. Other open-shell AMO3 systems with M4+ in octahedral coordination, such as those incorporating Tb4+ (4f 7 ), Pu4+ (5f 4 ), U4+ (5f 2 ), Am4+ (5f 5 ), and Cm4+ (5f 6) appear to fit the linear tolerance-factor relation quite well. However, it is clear that there may indeed be reasons for the deviation of 4f 1 from the expected behavior which could be elucidated by an investigation of the electronic structures of these compounds. A change from the cubic eightfold coordination of the fluorite dioxide to the octahedral coordination in the perovskite appears to be associated with an extra driving force in the case of the Pr compounds. Also, formation of delocalized orbitals between the 4f 1 levels of the Pr4+ cations and 2p orbitals on oxygen in the perovskite offers the possibility for electronic stabilization of the PrO2− framework. Even though the 3 energetic position of the 4f states may be more favorable for the formation of delocalized bond orbitals in ATbO3 as opposed to APrO3 , the smaller size of the Tb atom may preclude effective overlap with intervening 2p orbitals on oxygen in the perovskite framework. The 4f shell is half filled with 7 electrons for Tb4+ and thus the orbital set is symmetrically occupied. A combination of these two effects suggests that the electrons on Tb4+ are also highly localized and generate the same sort of electronic situation as that found in AMO3 systems incorporating closed-shell transition-metal ions. Both SrPrO3 and BaPrO3 appear to be unique among the AMO3 series with respect to the thermodynamic stabilization of the perovskite framework as compared with the component binary oxides. It is possible that an electronic stabilization of the perovskite framework in these materials is the cause of this extra stability. Calculations of the enthalpy of reaction (1) for the perovskite BaUO3 ,(27) are consistent with the observed enthalpy of reaction determined calorimetrically.(28) If the extra thermodynamic stability attributed to Pr4+ perovskites has no structural origin, similar calculations based on effective interatomic potentials, which include the polarizability of the non-spherical cations as well as Madelung energies and short-range repulsion effects, should be able to help determine the origin of the stabilization at the atomic level. We are currently using the aforementioned computational techniques to address this problem. In addition, a neutron powder-diffraction study of SrPrO3 is underway in an effort to determine its crystal structure and bond distances in comparison with BaPrO3 and other M4+ perovskites. This research has been supported in part by the United States Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, under contract W-31-109-ENG-38. We thank Ben Tani for help with the X-ray diffraction work. REFERENCES 1. Jacobson, A. J.; Tofield, B. C.; Fender, B. E. F. Acta Cryst. 1972, B28, 956. 2. Hinatsu, Y. J. Alloys and Compounds 1993, 193, 113. 3. Morss, L. R.; Mensi, N. The Rare Earths in Modern Science and Technology. McCarthy, G. J.; Silber, H. B.; Rhyne, J. J.: editors. Plenum: New York. 1982, p. 279. 4. Bickel, M.; Goodman, G. L.; Soderholm, L.; Kanellakopulos, B. J. Solid State Chem. 1988, 76, 178. 5. Goudiakas, J.; Haire, R. G.; Fuger, J. J. Chem. Thermodynamics 1990, 22, 577. 6. Fuger, J. Joint Research Center, Institute for Transuranium Elements, Karlsruhe, F.R.G. Personal communication.

560

S. A. Gramsch and L. R. Morss

7. Goldschmidt, V. Skrifter Norsk Videnskaps-Acad. Oslo I. Mat. Naturv. Kl. 1926, 2, 1. See also Shannon, R. D. Inorg. Chem. 1967, 6, 1474, for a more recent review. 8. Shannon, R. D. Acta Crystallogr. 1976, A32, 751. 9. Muller, O.; Roy, R. The Major Ternary Structural Families. Springer: New York. 1974, pp. 187, 218. 10. Longo, V.; Ricciardiello, F.; Minichelli, D. J. Mater. Sci. 1981, 16, 3503. 11. Wolf, R.; Hoppe, R. Z. Anorg. Allg. Chem. 1985, 529, 61. 12. Joint Committee for Powder Diffraction Standards. Swarthmore, PA. Card 24-1006. 13. Nocera, D. G.; Morss, L. R.; Fahey, J. A. J. Inorg. Nucl. Chem. 1980, 42, 55. 14. Morss, L. R.; Day, P. P.; Felinto, C.; Brito, H. J. Chem. Thermodynamics 1993, 25, 415. 15. Kilday, M. V. J. Res. Natl. Bur. Stand. (U.S.) 1980, 85, 467. 16. Dickinson, H. C. Bull. Natl. Bur. Stand. (U.S.) 1914, 11, 189. 17. Fuger, J.; Haire, R. G.; Peterson, J. R. J. Alloys Compounds 1993, 200, 181. 18. Morss, L. R.; Sonnenberger, D. C.; Thorn, R. J. Inorg. Chem. 1988, 27, 2106. 19. Busenberg, E.; Plummer, L. N.; Parker, V. B. Geochim. Cosmochim. Acta 1984, 48, 2021. 20. Wagman, D. D.; Evans, W. H.; Parker, V. B.; Halow, I.; Bailey, S. M.; Churney, K. L.; Nuttall, R. L. J. Phys. Chem. Ref. Data 1982, 11 (Supplement 2). 21. The partial molar enthalpy of formation of H2 O in HClO4(aq, c=4.0 mol·dm−3 ) was calculated from the apparent molar enthalpy of formation of HClO4(aq). See Parker, V. B. Thermal Properties of Aqueous Univalent Electrolytes. U.S. Department of Commerce Publication NSRDS-NBS 2: Washington, D.C. 1965. For the standard state of infinite dilution, Df H°m(H2 O, l) is found in reference 20. Calculations were carried out according to the method described in Lewis, G. N.; Randall, M.; Pitzer, K. S.; Brewer, L. Thermodynamics, 2nd edition. McGraw-Hill: New York. 1961, Chap. 17, 23. 22. Fitzgibbon, G. C.; Huber, E. J.; Holley, C. E. Rev. Chim. Minerale 1973, 10, 29. 23. Eyring, H.; Lohr, R.; Cunningham, B. B. J. Am. Chem. Soc. 1952, 74, 1186. 24. Stubblefield, C. T.; Eick, H.; Eyring, L. J. Am. Chem. Soc. 1956, 78, 3018. 25. Fitzgibbon, G. C.; Holley, C. E. J. Chem. Eng. Data 1968, 13, 63. 26. Cordfunke, E. H. P.; Konings, R. J. M.; Ouweltjes, W. J. Chem. Thermodynamics 1990, 22, 991. 27. Ball, R. G. J. J. Mater. Chem. 1992, 2, 641. 28. Morss, L. R.; Williams, C. W.; Choi, I.-K. ACS Symposium Series No. 246 . American Chemical Society: Washington, D.C. 1984, p. 323.