2208
STANLEY CANTOR
be hoped that in the future measurements of integrated intensities may be made up to very high temperatures. Acknowledgments.-The author is deeply indebted to Prof. M. L. Josien for her hospitality
Vol. 65
and her contagious enthusiasm. He also would like to thank Pierre Saumagne and Jean Lascombe for the interest they have taken in this work. The French Atomic Energy Commission very kindly provided support for the cell construction.
FREEZING POINT DEPRESSIONS I N SODIUM FLUORIDE. EFFECT OF ALKALINE EARTH FLUORIDES BY STANLEY CANTOR Oak Ridge National Laboratory,2 P. 0. Box X , Oak Ridge, Tennessee Received July ‘7, 1961
Measurements were made of the freezing point depressions of NaF caused by the addition of up to 0.25 mole fraction alkaline earth fluorides. At a fixed concentration the smaller the alkaline earth cation radius, the greater were the deviations from ideal solution behavior. The excess partial molal free energies of solution of NaF, ( P - FO)EN,F evaluated from_the measurements were all negative and approached zero asymptotically as the mole fraction of NaF approached unity. ( F FO)EN.F a t fixed concentration was empirically related to U nI2 where U is the alkaline earth fluoride lattice energy, n is an arbitrary constant, and I z is the second ionization potential of the alkaline earth.
-
+
Introduction Understanding the effects of structural parameters, such as radius, charge and polarizability, on thermodynamic properties in fused salt solutions is a large general problem. One approach t,o solving this problem is to investigate a thermodynamic property of a solvent in which the type and concentration of solutes can be systematically altered, and then relate variations in this property to structural parameters of the pure solutes. The object of this particular investigation was to measure the depressions of freezing point of the solvent, NaF, and correlate the derived thermodynamic information with the structure of the solutes, the alkaline earth fluorides. The choices of freezing point depression as t,he measurement and NaF as the solvent were made of solid-liquid phase after reviewing collecti0ns~~4 diagrams of fluorides. Where NaF was a component, the high NaF end of the diagram indicated the absence of solid solutions. In other words, pure crystalline NaF was the primary phase on cooling from the liquid state. Furthermore, t’he activit.y of NaF could be accurately evaluated from freezing point data because the heat of fusion and heat capacit.ies of NaF are known.6 Some information on the desired freezing points is available from the NaF-BeF2,6-MgF2,’,9 -CaF2,* (1) Presented, in part, before the Division of Physical Chemistry, American Chemical Society, 138th National Meeting, New York, N. Y., Sept., 1960. (2) Operated for the United States Atomic Energy Commission by the Union Carbide Corporation. (3) E. M. Levin, H. F. McCurdie and F. P. Hall, Phaee Diagrams ~ O T Ceramlste, Part I (1956). Part I1 (1959), American Ceramic Society, Columbus, Ohio. (4) R. E. Thoma (ed.), ”Phase Diagrams of Nuclear Reactor Materials,” ORNL-2548, Nov. 6, 1959. (5) C. J. O’Brien and K. K. Kelley, J . A m . Chem. Soc., 79, 5616 (1957). (6) E. Thilo and H. Schroder, Z . physib. Chem., 197, 41 (1951); A. V. Novoselova, M. E. Levina, K. P. Semanov and A. G . Zhasmen, J . Gen. Chem. U.S.B.R., 14,385 (1944); D. M. Roy, R. Roy and E. F. Osborn. J . A m . CeTaa. Sac., SB, 185 (1953) (7) A. G. Bergman and E. P. Dergunov, Compt. rend. acad. sci. U.R.S.S., 81, 755 (1941).
-BaF29 phase diagrams. But these data are not sufficiently precise and consistent to show the relationship between solute structural parameters and the freezing point depression of NaF. Experimental Chemicals.-NaF (Mallinckrodt A. R.) was purified by recrystallizing from slowly cooled melts and selecting only clear crystal fragments from the cooled ingot. These melts were contained in graphite or nickel crucibles and were protected by a helium atmosphere. Analyses showed the only impurities exceeding 100 parts per million were Ca, 400 p.p.m,.; Al, 300 p.p.m.; 0, 300 p.p.m. Commercial CaF2 (Mallinckrodt A. R.) and BaF, (Fisher “Certified”) were oven dried a t 150’ to constant weight before use. Commercial MgF, (Baker and Adamson “Purified”) and SrFz (Baker and Adamson Reagent Grade) were purified in graphite crucibles by first treating with NHBHFza t 250’ and then heating to 600” while flushing with a helium stream. Analyses for impurities in MgF, in weight per cent. were: Ca, 0.1; Fe, 0.2; Si 0.05; 0, 0.11; for SrF,; Ba, 1.0; Ca, 0.2; K, 0.01; Li, 0.005; Na, 0.02; 0.0.28. BeF2(Brush Beryllium) was purified by hydrofluorination a t 500”. Impurities in weight per cent. were: 0 , 0.38; Mg, 0.01; Fe, 0.005; S, 0.058. Apparatus and Procedures .-The cryoscopic vessel, welded from nickel, provided a cylindrical melt reservoir 6.35 cm. high and 4.8 em. in diameter, and contained a thermocouple well of 0.64 cm. diameter tubing extending to within 0.64 cm. of the bottom. A vertical tube, 1.3 cm. in diameter and 20.3 cm. high, welded to the top plate of the reservoir, had a side arm through which the vesssl could bc evacuated. Stirring was accomplished by bubbling argon gas through the melt via a long 0.65 cm. diameter tube which passed through the 1.3-cm. vertical tube and was sealed to it by a gas tight Swagelok fitting. The bubbling rate was measured by merely observing the number of bounces per unit time made by the ball float of a sensitive flow meter (Fischer & Porter Flowrator Model 10A1735). The sample sizes (approximately 1.5 moles of NaF) and low vapor pressure ensured that changes in melt composition due to transpiration were negligible. The vesEel was immersed in a Hevi-Duty 5-cm. tube furnace to a depth of 20.3 em., to prevent appreciable heat loss from the melt reservoir and thermocouple wires. Vessels, after being charged within a dry box, were evacuated for approximately one hr. while the temperature was raised to 700’. Argon then was passed through at the desired rate. ( 8 ) P. P. Fedotieff and W. P. Iljinskii, Z . anorg. 129, 101 (1923). (9) G. Grube, Z. Elektrochem., 35, 481 (1927).
u.
allgem. Chem.,
FREEZING POINT DEPRESSIONS IN SODIUM FLUORIDE
Dec., 1961
The absence of stolid solubility in NaF was confirmed by X-ray diffraction and microscopic examination of the cooled melt. Temperature Measurements and Manipulation.-Temperatures were measured with Pt us. Pt-lO% Rh thermocouples in a thermowell extending about 5 cm. into the melt. Periodic calibrations were made against thermocou les calibrated by the National Bureau of Standards. $he standard thermocouples were stated to be accurate within 1 0 . 5 " up to l l O O o . The e.m.f.'s were measured with a Leeds and Northrup Speedomax G recorder with a full chart range of 1 mv. The recorder contained a circuit by which thermocouple outputs could be suppressed in mv steps. The recording unit was calibrated a t frequent intervals by means of a Rubicon High Precision type B Potentiometer. Freezing temperatures with a precision of 0.3' were obtained from cooling curves. The cooling rates of the liquid ranged from 0.3-0.7' per minute. Supercooling, which occurred with most of the samples but seldom exceeded lo, was easily corrected for by extrapolating the crystallization temperature-time curve back to the liquid curve. Furnace tempera tures were controlled manually by means of a Powerstat.
Results Melting Point and Thermochemical Properties of Pure NaF.--Pure NaF was found to melt at 1268.0 1 0.5"B;. This temperature agrees with the results of Bredig, et al.1° O'Brien and Kelley,s who were primarily interested in high temperature enthalpies, report 1285°K. These authors also give 1300°K. as the melting point of cryolite for which Grjotheimll obtained 1282°K. O'Brien and Kelley probably got higher results because their thermocouple, not in contact with the sample container, reflected in part furnace wall temperatures. In this and the imo other investigationsl0?l1cited, thermocouples we1e in contact with thermowells which were immersed in the samples. Accordingly, if it is assumed that O'Brien and Kelley have a systematic error of plus 17" and no error in their heat contents, then the recalculated heat of fusion of XaF is 8017 cal., as compared to 8030 cal. When the temperature dependence of the heat of fusion is taken into account the relation between the activity of S ~ F ( ~ N and , F ) the temperature, T , at which KaF crystallizes out of solution, is Lu
-
)(&$J+
AUTM- A2b TM'
Tg Ab Auln T f -2-(TM
- T)
(1)
where LM is the heat of fusion of pure XaF at the melting point ( 2 ' ~ ) ; Aa and Ab are constants from the heat capacity-temperature equations.6 Freezing Points of NaF Solutions.-The temperatures a t which NaF began crystallizing out of solutions containing an alkaline earth fluoride are given in Table I. From these temperatures, values of In UN,F were calculated using equation 1 with LM = 8,017, T M = 1268, Aa = 6.00 and Ab = -3.88 x 10-5. For each value of In a N a F , ln.yNaF was obtained ( Y N ~ F is the activity coefficient). The excess partial molal free energy of solution of NaF, (I' - F o ) E h : a ~ , then was calculated from the equation ( P - F o ) E a ,~ RT In
YN~F
(2)
(IO) &I. A . Bredig, J. W. Johnson and Wm. T. Smith, Jr., J . Am. Chem. SOC.,11, 307 (195,s). (11) K.Grjotheim, Norske Videnskaps Selskabs Skrifter, No. 5 (1956).
2209
0
- 50 - 100 -150
--.
-200
0
I
kg
-___-
-250
0-
k
-500
'
0
y
I
I
I
I
0.01
0.02
0.03 (t
0.04
0.05
0.06
0.07
-
Fig. 1.-Excess partial molal free energy of solution of NaF us. mole fraction squared of the alkaline earth fluoride solute.
Discussion For the same solute concentrations, lower liquidus temperatures of NaF are found with solutes whose cation sizes are smaller. If the forces in solution are preponderantly coulombic, the higher the electric field strength of the solute cation the more difficult it is for NaF to crystallize out of solution. The thermodynamic quantity, obtained from freezing point depressions, which is the measure of this relative difficulty is the partial molal free energy of solution of NaF. For all the solutions studied, the partial molal free energy of mixing at the freezing temperatures was always less than RT In N N ~ Fie., , the excess ptrtial molal free energy of solution of NaF, (F - F o ) , E ~was . ~ , always negative. But as the mole fraction of NaF approached unity, the excess partial molal free energy of mixing approached zero (see Fig. 1). TABLEI
OBSERVEDFREEZING POINTSOF NAF CONTAINING MF2 SOLUTES Mo!e fraction
NsF
BeFz
Freezing point of NaF, "C. solute MgFe CaFz SrFz
995.0 986.2 971.4 939.9
.880
...
995.0 986.9 971.9 941.7
.850 ,825 .8218 .goo .777r ,750
897.3
904.0 880.8
1.000 0.980 .950 .goo
... ...
...
...
995.0 986.9 973.9 949.8 939.1 924.0
995.0 986.9 973.9 951.8
...
914.4 903.7 892.5 878.0
...
839.7 ...
854.5
895.1
...
...
859.3
...
...
BaFz
995.0 986.8 974.2 952.8
...
...
927.8
930.7
...
... ...
907.3
...
882.4
22 10
STANLEY CANTOR
Vol. 65
[TVIF~]-~, [MzF7]-3, IMR1-2, [MZ[MFB]-4. If only a single complex species was used over the entire experimental concentration range, the calculated temperatures compared poorly with the temperatures in any of the columns of Table I. It was possible to "fit" the observed liquidus temperatures by postulating the presence of two or more complex ions in solution. However, these data are insufficient to establish the equilibria between the complex species that do "fit." The stringent condition of ideality is the main drawback to the use of complex ion models in trying to calculate freezing points. It is doubtful that effects related to the enthalpy of solution are absent. An empirical method of treating the data is suggested by a relation given in the monograph of Yatsimirskii and Vasilev. l 3 These authors show that the free energy of complex formation is equal to the sum of two quantities. The first quantity depends on the volume and charge of the central metal ion. The second quantity is the product of three terms which represent the number of ligands, the polarizability of the ligand and the polarizing effectof the cation. By analogy, it is assumed that ( F - FO)EN,F is a linear function of the lattice energy, U , plus the second ionization potential, 1 2 , of the alkaline earth metal multiplied by a constant, n. The purpose of using I 2 was to approximate the polarizing action. The constant, n is purely arcalculations:
0
Fs]-6,
- 50 - 100
-f50
-.
-200
..0
2;
-250
k
ti
-300
-350
-400
-450
-500 2250
2300
2350 2400 (U+nf2),(kcal),
2450
2500
Fig. 2.-Excess partial molal free energy of solution of NaF us. an empirical function of solute structural parameters.
TABLE I1 In considering the possibility of regular solution LATTICEENERGY ( U),SSCOND IONIZATION behavior the function ( F - F o ) E ~ a p / (-l N N ~ F )BORN-HABER ~ C0NSTAh.T ( n ) O F THE mas tested for constancy. These solutions did not POTENTI.4L (Iz), AND ADJUSTABLE ALEALINE EARTHFLUORIDES show regular solution behavior over the entire n1Fr U(kca1.) I, (kcalJa n concentration range. However, when this funcBcF~ 813 420 4 00 tion was plotted against (1 - N N ~ Fthe ) slopes of MgFL 69% 346.5 5 04 these plots were negative for solutions of BeF2 and CaFz 617 273 5 6 14 MgF2, close to zero for CaF2, and positive for SrFz Sr FL 583 254 6.62 and BaF2. The cation sizes of sodium and calcium BaFz 549 230 5 7.38 are about the same while sodium is smaller than b l l U l l L l C l l l l itllU
uallulll
UUL large1 Lllall
uelylllulll
and magnesium. The structural parameter that seems most significant in the interpretation of these data appears to be the ionic radius or interionic distance. However, no simple quantitative relationship between free energy and simple functions of ionic radii or interionic distances was found. - A better correlation was obtained by plotting ( F - FO)EN~F a t constant composition us. the lattice energies of the alkaline earth fluoridrs (the lattice energy is related to complicated functions of interionic distances). 13ut these plots did not give smooth curves. As an alternative approach, consideration was given to the possibility that the solute forms comMFz = plex ions by reactions of the type: zF[MF,+.)-x If these complex ions are in ideal solution thcri the temperature-composition curve for the Narc liquidus may be obtained by suitably alteying equation 1.12 The following complex ions mere postulated for the purpose of trial
+
(12) Reference 11 has several examples of this calculation carried o u t in the NaF-AIFa system.
a C. E. hloore, Atomic Energy Levels, Kational Bureau of Standards Circular 467 (1949-1958).
bitrary and for BcF2 solutes was set equal to 4.00 because this is, to a good approximation, the number of nearest neighbors coordinated around Be2+ in liquid BeF2.14 Since fluoride ions are the ligands throughout they were not put in the function. An excellent fit occurs when the values iven in Table I1 are used for plots of U n1221s. ( - F o ) E N a ~at constant composition (Fig. 2). It must be reiterated that the fit is empirical. Although structural parameters are used, no detailed relationship be~ molecular structure is intween ( F - F 0 ) x aand tended. Acknowledgments.-The author is indebted to Messrs. R. E. Thoma and C. F. Weaver for the Xray diffraction and petrographic analyses, and to Drs. R. F. Newton, M. Blander and J. Rraunstein for many valuable diwussionr.
+
8
(13) K. B. Yatsimirskii and Y. P Vnsilev, "Instability Constants of Complex Compounds." Pergamon Press, New York. N. Y., 1960, p. 70. (14) B. E. Warren and C. F. Hill. Z. Kraut 89, 481 (1834)
