A. S. DWORKIN AXD M. A. BREDIG
2340 The “fluctuating cage” model (not to be confused with the “flickering cluster” model) is being examined further in a number of w a p in our laboratory. We are attempting to describe quantitatively the ultrasonic absorption in the systems discussed in this paper in terms of the fluctuation approach. We are also examining solutions of nonelectrolytes that are known to form clathrates of different composition. Finally, we are looking at the scattering spectra of solutions of “cage” formers. We are extremely hopeful that pur-
suit of this line of research may lead to some quantitative information on the dynamics of hydrophobic interaction.
Acknowledgment. The authors would like to acknowledge the financial support of the Office of Saline Water, U. S. Department of the Interior, under Grant 14-01-0001-1656. They also thank Professor H. G. Hertz for stimulating conversations and access to data before publication.
Miscibility of Liquid Metals with Salts. X.
Various Studies in Alkaline
Earth Metal-Metal Fluoride and Rare Earth Metal-Metal Difluoride and Trifluoride Systems’ by A. S. Dworkin” and M. A. Bredig Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 87830
(Received January $5, 1071)
Publication costs borne completely by The Journal of Physical Chemistry
The phase diagrams Ba-BaFz, Sm-SmFz, and Yb-YbFz were determined. The Ba-BaFz and Yb-YbF, systems are similar to Ca-CaF2 in that they exhibit complete miscibility. In Sm-SmF2, at 1216’, a large miscibility gap extends from the liquid nionotectic, 32 mol %, to almost 100% Sm. The solubilities of Mg in hlgF2, of La, Ce, and n’d in their respective trifluorides and of Th in ThF4 were found to be very low, less than 0.5 mol %. Determination of the melting point depression of calcium metal caused by the dissolution of CaF, and of the solubility of CaFz in solid Ca metal yielded the not unexpected result that in the solution the fluoride ions form separate particles.
Introduction Lichter and Bredig2 have shown earlier that the original data3 on the phase relations in the calcium metal-calcium fluoride system required a reinterpretation in terms of complete miscibility of the metal with the salt in the liquid state. The CaFg-Ca system, then, was the first metal-metal halide system other than the alkali metal systems for which no monotectic reaction and no equilibria between two liquid phases were observed. This suggested that barium fluoride, because of its lower lattice energy compared with calcium fluoride, would be considerably more soluble in liquid barium metal than CaF2in Ca. Furthermore, it seemed likely that some of the rare earth metal-metal difluoride systems (Eu, Yb, and perhaps Sm) also might exhibit complete miscibility since the metals have similar heats of vaporization to calcium and barium. We therefore have measured and report here the phase diagrams of The Journal of Physical Chemistry, Vol. 75, N o . 15, 1971
the barium-barium fluoride, samarium-samarium difluoride, and ytterbium-ytterbium difluoride systems. This work is an extension of our previous measurements of the miscibility of the alkaline earth metals with their halide^.^ An application of the principles governing the miscibility of the most electropositive mono- and divalent metals, the alkali and alkaline earth metals, with their fluorides to the behavior of the trivalent rare earth (1) Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corp. (2) B. D. Lichter and M. A. Bredig, J . Electrochem. Soc., 112, 506 (1965). (3) P. S. Rogers, J. W. Tomlinson, and F. D. Richardson, “Proceedings of the International Symposium on the Physical Chemistry of Process Metallurgy, Pittsburgh, 1959,” G. R. St. Pierre, Ed., Interscience, New York, N. Y . , 1961, p 909. (4) A. S. Dworkin, H. R. Bronstein, and M. A . Bredig, J . Phgs. Chem., 72, 1892 (1968).
~IISCIBILITY OF LIQUID METALSWITH SALTS metals which form many subhalides with the other halogens5 seemed to be somewhat uncertain. Therefore we have made some qualitative measurements of the solubility of lanthanum, cerium, and neodymium in their respective molten fluorides. We also measured the solubility of magnesium in molten magnesium fluoride and of thorium in molten thorium tetrafluoride. A determination of the freezing point depression of calcium metal produced by dissolving CaF2 and of the solubility of CaFpin solid Ca was made to examine the hitherto little-explored mechanism of the dissolution of a salt in a liquid metal or the "structure" of that solution. Experimental Section (a) The phase diagrams were delineated by the method of thermal analysis (heating and cooling curves). It was necessary to modify the apparatus used for our previous measurement^.^ A platinum-wound Marshall tube furnace 40 cm in length with a 6.3-cm bore was employed to attain the necessary high temperatures. The salts and metals were loaded into tantalum capsules in a drybox under a helium atmosphere. The capsules were then sealed by welding in a drybox. The capsules were mounted on a tantalum frame in a 5-cm 0.d. Morganite impervious recrystallized alumina tube, 45 cm in length. The top of the tube, 15 cm above the top of the furnace, was fitted with a water-cooled stainless steel head which also sealed the tube with a silicone rubber gasket. Fittings in the head made it possible to pump a vacuum of a few microns in the tube or alternatively to perform the experiment in an inert atmosphere of argon. Special fittings in the head allowed for the entrance of a PtPt-lO% R h thermocouple which was placed in a well extending about 1.5 cm into the tantalum capsule from the bottom. The entire furnace assembly could be rocked about the horizontal position to obtain mixing. The apparatus used to obtain the freezing point depression of calcium metal produced by dissolving CaF2 was essentially the same as that described above except that a regular nichrome-wound Marshall furnace was used and the outer tube and mount were constructed of stainless steel. (b) The solid solubility of calcium fluoride in calcium metal was obtained as follows. Calcium was melted in an inert atmosphere in a tantalum capsule similar to those used for the thermal analysis experiments. Upon solidification, the surface of the calcium was machined flat. A crystal of CaF2with a flat surface was placed on the calcium and a molybdenum weight was used to press the crystal against the metal. The capsule was then sealed by welding under helium, placed in the apparatus described above, and equilibrated for approximately 1 week at 815 f I", ie., a few degrees below the eutectic temperature. The capsule was then cooled, opened, and the calcium cut into several sec-
2341 tions. The calcium was dissolved in a dilute HC1 solution and the insoluble calcium fluoride was filtered and weighed. The filtrate was also analyzed for the small amount of soluble fluoride. The calcium fluoride crystal was also weighed for loss as an extra check. (c) The rare earth trifluorides were prepared by gradually heating an intimate mixture of the rare earth oxide (Lindsay Chemical, 99.9%) with ammonium hydrogen fluoride in a platinum dish under an inert atmosphere to a temperature of 500". The samarium and ytterbium difluorides were prepared by heating to a temperature of 1000" a stoichiometric mixture of the trifluoride and 200-mesh metal (Lindsay Chemical, 99.9%). The difluorides analyzed 79.8% Sm (theoretical 79.82%) and 82.0% Yb (theoretical 82.0%). Their X-ray patterns agreed with the literatures as did their melting points (see Table
Table I : Melting Points of Fluorides and Metals -----Melting Measured
MgFz CaFz BaFz SmFz YbFz LaFa CeFa NdFI ThF4 Ca
Ba Sm Yb
1256 1416 1354 1425 1407 1495 1429 1372 1110 839 731 1086 843
point, C ' -Literature
1261, 1263 1423, 1418 1355, 1354 1417 1407 1493, 1490 1430, 1437 1374 1110, 1102 836 729 1072 824
Ref
7, 8 7, 8 7, 9 10 10 10, 9 10, 9 10 11, 9 12 12, 13 10 10
Calcium fluoride and barium fluoride were Harshaw optical grade single crystals and were used without further purification. Calcium and barium metal were purified by vacuum distillation a t 900" under dynamic vacuum. The metal was distilled from a molybdenum cup and collected on a stainless steel cold finger. Melting points of 731" for barium and 839" for calcium are in good agreement with the literature (see Table I). (5) E.o., J. D. Corbett, "Fused Salts," B. Sundheim, Ed., McGrawHill, New York, N. Y . , 1964. (6) (a) E. Catalano, R. G. Bedford, V. G. Silveira, and H. H. Wickman, J . Phys. Chem. Solids, 30, 1613 (1969); (b) J. J. Steaowaki and H. A. Eick, Inorg. Chem., 9, 1102 (1970). (7) H. Kojima, S. G. Whiteway, and C. R. Masson, Can. J . Chem., 46, 2968 (1968). (8) B. F. Kaylor, J . Amer. Chem. Soc., 67, 160 (1945). (9) B. Porter and E. A. Brown, J. Amer. Ceram. SOC., 45, 49 (1962). (10) F. H. Spedding and A. H. Daane, Met. Rep., 5 , 297 (1960). (11) R. E. Thoma, H. Insley, B. S. Landau, H. A . Friedman, and W. R. Grimes, J. Phys. Chem., 63, 1266 (1959). (12) D. T. Peterson and J. A. Hinkebein, ibid., 63, 1360 (1959). (13) D. T. Peterson and M . Indig, J. Amer. Chem. SOC.,82, 5645 (1960). The Journal of Physical Chemistry, Vol. 76, N o . 16, 1971
2342
A. S. DWORKIN AND M. A. BREDIG
All the fluorides and metals used were analyzed spectrographically and were found to have only trace amounts of foreign cations. A comparison of our melting points ( f3 ” ) with the “best” literature values is given in Table I. Our melting point of MgFz is low because of the presence of about 1 mol yooxygen. Our values for the melting points of ytterbium and samarium metals are somewhat higher than those found in the literature (Table I). This may be caused by small quantities of oxygen and/or hydrogen in the metals forming solid solutions with melting points higher than the pure metal. Such behavior is known in the systems barium-barium hydride, l 3 neodymium-neodymium hydride,14and yttrium-yttrium oxide.15
Results and Discussion The phase equilibria data are given in Table I1 and illustrated in Figure 1. As expected, barium fluoride is considerably more soluble in liquid barium metal than calcium fluoride in calcium by as much as a factor of 4. Furthermore, ytterbium also exhibits complete miscibility in the liquid state with ytterbium difluoride, the extent of the solubility being between that for the calcium and barium cases. There is a large monotectic solubility of samarium in samarium difluoride (32%) but from that concentration to almost 100% samarium, a large miscibility gap exists. The dotted solid solution lines are estimated except for the calcium case which was measured previously.2 The estimations were made on the basis of (1) ideal activity for MFz in the solid phase, ( 2 ) a two-particle effect, Le., dissociation according to 31 --t ;\I2+ 2e- in both the liquid and solid phases, and ( 3 ) an average literature value16 for the entropy of fusion of BaFz of 3.3 eu and a value for the rare earth difluorides of 4 eu. This latter figure is based on our assumption that the rare earth difluorides, having the fluorite type of structure, are similar to the alkaline earth fluorides in that they have a diffuse transition in the solid and a low entropy of fusion. l7 Corbett and coworkersls have correlated the solubilities of the rare earth metals in their respective trichlorides with the sum of the sublimation energy and ionization energies of the metals. They found that the sublimation energies appear primarily responsible for the observed trends while the ionization energies and the other terms in the complete Born-Fajans-Haber cycle’g had only relatively small effects. A similar scheme with vapor pressure as the prime factor was proposed by TopoLZ0 The overall effect is that of increasing solubility with decreasing sublimation energy of the metals. This correlation also seems to apply to the metal-difluoride systems with the sublimation energy of samarium being about 12 to 14 kcal higher than the other three metals. We would then predict that the europium-europium difluoride system is somewhat similar t o the calcium-calcium fluoride system and that, if thulium difluoride is stable, the solubility
+
The Journal of Physical Chemistry, Val. 76, N o . 16, 2971
Table I1 : Equilibrium Phase Compositions in the Ba-BaFz, Sm-SmFz, and Yb-YbFt Systems Composition, mol % metal
Liquidus, OC
Monoteotia, OC
Euteatia, OC
Ba-13aFz
0 3.9 9.4 19.6 27.5 35.1 55.3 69.6 85.0 91.9 100
1354 1321 1282 1231 1192 1166 1098 1045 948 862
724 729 728 728 729 730 730
731 Sm-SmF2
0 5.2 10.3 24.4 48.7 68.7 85.5 95.3 100.0
1425 1375 1332 1253
1212 1216 1217 1214 1211 1211
1080 1080 1083 1085 1087
1086 Yb-YbFt
0 9.4 25.3 49.9 73.0 90.5 100
1407 1347 1282 1244 1186 1029 843
810 820 827 832 837
of thulium metal in liquid thulium difluoride is less than that of samarium in samarium difluoride, since the heat of sublimation of thulium exceeds that of samarium by 8 kcal/mol. Figure 2 is a (nonisothermal) plot of the partial molar excess free energy or excess chemical potential of BaFz, A p E ( ~ & *us. % )the , square of the barium metal mole fraction, N B ~ .I n this test of the most simple form of the dependence of the activity coefficient on concentration according to regular solution theory, the experimental (14) D. T. Peterson, T. J. Poskie, and J. A. Straatmann, J. LessCommon Metals, 23, 177 (1971). (15) R.C.Tucker, Jr., E. D. Gibson, and 0. N. Carlson, Nucl. Met., 10, 315 (1964). (16) (a) G. Petit and F. Delbove, C. R. Acad. Sci. Paris, 254, 1388 (1960); (b) D. F. Smith, University of Alabama, private communication, 1969; (c) R. I. Efremova and E. V. Matizen, Izv. Sib. Otd. Akad. Nauk SSSR, Ser. K h i m . Nauk, (l),3 (1970). (17) A. S. Dworkin and M. A. Bredig, J . Phys. Chem., 72, 1277 (1968). (18) J. D. Corbett, D. L. Pollard, and J. E. Mee, I n o r g . Chem., 5 , 761 (1966). (19) D. F.C.Morris and E. L. Short, Nature, 224, 950 (1969). (20) L. Topol, J . Phys. Chem., 69, 11 (1965).
2343
MISCIBILITY OF LIQUID METALSWITH SALTS 1
I
I
I
I
I
I
I
I
I
-
”
1200-
I
I
x
I
I
20
0
40 6C 80 100 0 MOLE % Sm
20
x
X
x
I
.n
I
t
60 80 I00 0 MOLE % Y b 40
20
40
60
80 100
MOLE % M
Figure 1. Equilibrium phase diagrams of metal fluoride-metal systems, MFt-M (M = Sm, Yb, Ca, or Ba).
I
1 Y
I .I
I
I
.2
.3
I .4
I
I
.5
.6
I .7
I .8
i
.9
t i
2 NBaArne+ol
Figure 2. Excess chemical potential of BaFz as a function of concentration.
points should have fallen on a straight line. Its slope and intercept at N B =~ 1 would equal the parameter B in In Y B ~ F=~ ( B / R T ) N B , ~ .This plot for the BaFz-Ba solutions (the Ca and Yb solutions are slightly higher but similar) greatly resembles earlier plots for several alkali metal-metal halide systems, Rb-RbBr, Cs-CsI,
and the other cesium systems.21 The actual nonlinear character of the curve indicates considerable deviation from simple regular solution behavior,22Le., nonideal entropy of mixing and very likely also a temperature dependence of this entropy. The value of B from an approximate straight line through the experimental points, -6 kea1 per equivalent of BaF2, compares with the 3.5 to 4.5 kcal/mole for the alkali metal systems above. A qualitative determination of the solubilities of Mg in MgFz, La, Ce, and Nd in their respective trifluorides, and T h in ThF4 was made by determining the melting point depression of the fluoride produced by dissolving the metal. The measurements were qualitative because the melting points were depressed only a few degrees in all the above cases despite additions of up t o more than 20 mol % metal. The maximum lowering 3” for the rare earth triwas 3 f 1’ for l/IgFz, 4 fluorides, and 2 i 1’ for ThF4. Assuming the metal dissolves as A4 = M”+ ne-, a monotectic solubility of 0.3 to 0.6 mol % for R4g (n = 2 ) in MgFz, 0.1 to 0.5 mol % for La, Ce, and Nd (n = 3) in their trifluorides, and 0.1 to 0.3 mol % for T h (n = 4) in ThF4,is calculated from the melting point depression equation AT/N = nRT/ AS,. These low solubilities indicate that there is essentially no tendency toward formation of lower valent fluorides in any of the above systems.
*
+
(21) M. A. Bredig, “Molten Salt Chemistry,” M. Blander, Ed., Interscience, New York, N. Y . , 1964. (22) K. S. Pitzer, J . Amer. Chem. Soc., 84, 2026 (1962).
The Journal of Physical Chemistry, Vol. 76, N o . 16,1971
2344
A. S. DWORKIN AND IM.A. BREDIG
"
O
i
erties of the solution. Figure 3 shows both the meltingpoint depression of calcium metal produced by dissolving CaFz and the solubility of CaFz in solid Ca metal. The latter is shown as an estimated dotted line since the solid solution determination was made at only one temperature. The observed solid solubility of 1.1 f 0.1 mol % Ca comes from three determinations at 815 f 1" and permits the estimate of the solidus curve which brings the melting point depression in agreement with an AT A S = R T ( N C a F , ( i n liq)
Phase diagram, vapor pressure, and electrical conductance data for solutions of alkali metal halides in liquid alkali metals were interpreted2lSz2in terms of substitution of electrons by single halide ions. I n these cases, colligative properties would not allow distinction between dissociation of 1IX into Mf and X- and dissolution as MX molecules, since the RI + ions introduced by the salt would be indistinguishable from those of the metal. On the other hand, in R!I-XXn systems with n > 1, dissociation into individual AT"+ cations and n X - anions could be reflected into the colligative prop-
The Journal of Physical Chemistry, Vol, 76, N o . 16,1071
-
= 2
NCaFi(in solid))
corresponding to the expected separation of the F- ions. Without the solid solubility, the limiting slope for the melting point depression would suggest the highly unlikely occurrence of association rather than dissociation of the CaFz. I n the BaFz-Ba system a relatively high solubility of BaFz in solid Ba metal, N B a F l ( i n s o l i d ) , of approximately 2.5 mol % is estimated from the above equation. N B ~ F liquid) ~ ( ~ is ~ the intercept of the liquidus with the eutectic horizontal at -2.5 mol %, AT is the difference of -1' between the eutectic temperature and the melting point of pure barium, A S is the entropy of fusion of Ba metal, 1.86 cal deg-' mol-', and the number of particles, n, is taken as 2 in the CaFz-Ca system. The high solubility as compared with the calcium system is ascribed to the lower lattice energies of the components in the barium system (CaF2, 617; Ca, 456; BaFz, 547; Ba, 393 kcal mol-').23
Acknowledgment. We wish to acknowledge the valuable contribution of D. E. LaValle who prepared the rare earth fluorides used in this work. (23) "Gmelins Handbuch Der Anorganische Chemie," 8th ed, 1957, 1960.
