NOTES
Sept., 1963
1919
NEW HIGH PRESSURE FORM OF CALCIUM
PARTIAL MOLAL VOLUMES OF SULFUR HEXAFLUORIDE
DISILICIDE BYM. S. SILVERMAN AND J. R. SOULEN
BY H. HIRAOKA AND J. H. HILDEBRAND Department of Chemistry, University of California, Berlceleg, (lalifornia Received March 16, 1965
Research and Deuelopment Laboratories, Pennsalt Chemicals Corporation, Wyndmoor, Pennsylvania Received Awril 86. 196s
Several of our recent investigations have served to emphasize the fact that in regular solutions the partial molal entropy of solution at constant pressure includes, in addition to the entropy of dilution, a significant increment of entropy of expansion. This was brought out strikingly in the cases of solutions of iodine1 and stannic iodide,2 and of gases in various solvents.a It was evident, therefore, that measurements of the partial molal volume of SFBin several solvents were necessary in order to interpret its unusual solubility relations as reported by Archer and H i l d e b r a ~ ~ d . ~ The dilatometer was of the type devised by Horiuti5 and used by Jolley and Hildebrand3 with the improvement in technique adopted to main constant pressure described by Walkley and Hildebrand.6 From 4 to 6 additions of gas mere made to each solvent and the total volume increment was plotted against the mole6 of gas added. The points fell on straight lines with very small scatter. Different runs for the same system agreed closely. We estimate the probable error as 0.8%, except in the case of CS2, where it is a little larger because of low solubility. The mole fraction of dissolved gas was so small in each case that the partial molal volumes given in Table I are virtually the limiting values at infinite dilution. TABLE I SFe A S D E N T R O P Y O F SO&UTION SAMEMOLEFRACTION, AT 25"
P A R T I A L M O L A L FrOLUMES O F FROM
1 ATMOSPHERE TO Solvent
CJ%iCzFs CClzF'CClFz i-C*H,,
n-CJLs cc1, C6H6 CS,
-
-
61
6.1 73 6 9 74 8 6 9 2 10 0
v2,
00.
94.0 101.4 104.2 105.5 104.0 105.5 I26
S2(10-4) atm.)
&(l
... 1.0 1 7 2.0 2 5 3.8 4.1
Included in Table I are figures for the entropy of transferring SF6 from gas a t 1 atm. to solutions at the same mole fraction, calculated as described by Jolley and Hildebrand.3 The strong increases in both V2 and As, in descending the table contrast with the reverse trend in both quantities in solutions of argon, indicating, as does the excess over unity of the slope of the SFa line in Fig. 2 of the paper by Archer and Hildebrand, departures of SF6 from the geometric mean relation in mixtures with nonfluoride solvents. Theoretical treatment of these results in terms of intermolecular forces will be undertaken in a later paper. Acknowledgments.-This research was supported by the Atomic Energy Commission. We are indebted to the Minnesota Mining and Manufacturing Co. for the supply of C ~ F I I C ~ H S . (1) J. H. Hildehrand, J . P h y s . Chem., 64, 370 (1960). (2) E. B. Smith and J. Walkley, Trans. Faraday Soc., 66, 1276 (1960). (3) J. E. Jolley and J. H. Hildebrand, J . Am. Chem. Soo., 80, 1050 (1958). See also J. H. Hildebrand and R. L. Scott, "Regular Solutions," PrenticeHall, Inc., New York, N. Y., 1962, PP. 34 ff,, 44, 45, Chapter 8, p. 153. (4) G. Archer and J. H. Hildebrand, J. Phys. Chem., 67, 1830 (1963). (6) J. Horiuti, Sei. P a p e r s l n s t . Phys. Chem.. Res. (Tokyo), 17, 126 (1931). (6) 5 . Walkley and J. HaHildebrand, J . Am. Chem. Soc., 81,4439 (1859).
Calcium disilicide is known to have a hexagonal layer type structu:re,l as do graphite and boron nitride. At very high pressures and temperatures the latter compounds form the more dense cubic polymorphs, diamond2 and borazon.3 CaSiz has now been transformed at high pressures to a new, more dense modification which appears to be tetragonal. Commercial grade CaSi2 obtained from K and K Laboratories was used as one starting material. This contained several per cent iron as an impurity. Mixtures of semiconductor grade silicon, spectroscopic grade graphite, and CaO prepared by heating 99.9% CaC03 were also used. The apparatus was of the tetrahedral anvil type developed at the National Bureau of standard^.^ The sample holder, heating assembly, and calibration techniques were similar to those described previ~usly,~ except that a boron nitride insulating capsule was used between the graphite heater and the sample. I n carrying out the runs, CaSi2 or a CaO Si C mixture was first compressed to the desired pressure between 8 and 87 kilobars; temperature then was raised and held at the desired level, which ranged up to 1800". After 2 to 10 min. the electrical power was shut off and the sample was; decompressed after the product had reached ambient temperature. With CaSiz as th.e starting material, striking changes were noted in the solid resulting from a number of runs. Under microscopic examination it appeared that essentially 100% conversion to a reflective, coral material had occurred from the original gray form. In concentrated HC1 the latter reacted with vigorous effervescence whereas the new form, even when finely ground, underwent only slight reaction. Density of the hexagonal starting maLerial was 2.47 f 0.02 g . / ~ m . ~in, good agreement with 2.46 g./cm. reported previously.1 Measured densities of the high pressure form ranged from 2.60 to 2.76 :k 0.02 g . / ~ m . ~ The . highest value was obtained from a product formed under the most severe combination of condit'ions, 87 kilobars and 1500*, and thus must be closest to correct for the new form. XRay diffraction films of many of the samples gave a n identical powder paittern which is characteristic of the new form and is completely different from that of the original material. The strongest lines are listed in Table I. These can be indexed on the basis of a tetragonal structure with a = 6.23 A. and c = 4.52 8. Density calculated from these constants, assuming 3 CaSi2 per unit cell, is 2.73 g./cm.a, compared with 2.76 for the highest density product. Taking the iron impurity into account, produlct analysis showed about 2.6% Fe and a compositioii approximately Ca~,~~Feo.o&3i2.00.
+ +
(1) J. Bohm and 0. Hassel, 2. anoro. allgem. Chem., 160, 152 (1927). (2) F. P. Bundy, H. T. Hall, H. M. Strong, and R. H. Wentorf, Jr., n'ature, 176, 51 (1955). (3) R. H. Wentorf, Jr., J Chem. Phys., 26, 956 (1957). (4) E. C. Lloyd, U.0. Hutton, and D. P. Johnson, J . Res. Nut?. B u r . Std., 6aC, 59 (1858). (6) J, R d Soulen and M. $3, Silverman, J . Polymer ,%..,. Ly 823 (1963).
NOTES
1920
TABLE I X-RAYPOWDER DIFFRACTIOK PATTERN OF HIGHPRESSURE FORM OF CaLcImr DISILICIDE A.“
2.77 2.28 2.14 1.76
I 100 80 55 55
1.56
50
d,
hkl
210 002 102 212 222
-------sinz Obsd.
0.0774 ,1143 ,1297 ,1918
0.0766 .1164 .1317 .1929 .2388
30
.2450 .2542 .2599
410 213 1.326
Calcd.*
,2442 400 302
1.512
e-.
.2603 ,3387
30
.3380 .3353 42 1 1.235 25 .3843 223 .a896 a Copper K, radiation takgn as 1.5418 A. Assuming tetragonal structure with a = 6.23 A. and c = 4.52 A.
Assuming simple substitution of Fe for Ca to this extent in the proposed CaSiz structure, calculated density is 2.76 g . / ~ m . ~in, excellent agreement with the measured value. To determine whether iron is a necessary constituent of the new structure, reaction of calcium oxide, silicon, and carbon was carried out under high pressure conditions using very pure reactants. Although conversions were poor, the X-ray diffraction powder pattern of Table I mas obtained from a number of the pressed pellets, showing formation of the new high pressure form from these entirely different reactants in which the impurity level is very low. The pattern must thus be characteristic of calcium disilicide itself, and the presence of iron in the products obtained from impure CaSiz is not essential to obtain it. The high pressure form was obtained from hexagonal CaSi2in varying amounts over the ranges 17 to 87 kilobars and 700 to 1800”. Below 17 kilobars no transformation occurred, even at temperatures up to 1500°. Besides thermodynamically favoring the reaction, pressure also favors formation of the new form kinetically. Thus in 10-min. runs a t 1250” and 17 and 42 kilobars. conversions to the high pressure form were less than 50 and loo%, respectively. At 1000” no new product was obtained after 10 min. a t 20 kilobars, whereas complete convel.sion resulted after 10 rnin. a t 50 kilobars and 3 min. at 83 kilobars, To obtain essentially complete conversion to the high pressure form in short periods of time, pressures above 40 kilobars and temperatures above 1000O are required simultaneously. Acknowledgment.-The authors wish to thank Dr. W. Clavan and Mr. R.Hamilton for obtaining the Xray diffraction patterns and the analytical and shop groups for their help in this work. It was supported in part by the Office of Naval Research.
A THEORY OF SURFACE REACTION CONTROLLED GROWTH BY A. G. WALTON Department of Chemzstrg, Case Instztute of Technology. Cleveland 6, OhzO Reeeaved March 8, 1953
The growth of precipitates or sols from supersaturated solutions has been investigated frequently by
Vol. 67
various techniques over the past few years, and the results derived from these experiments usually have been analyzed by use of the empirical equations developed by Nielsen.lJ It recently has become increasingly apparent that there are many inconsistencies associated with the published data3 and it seems worthwhile, therefore, to re-examine some of the basic postulates used in growth kinetics in an effort to provide a more substantial theoretical basis for this type of investigation. There is no doubt that most, if not all, sparingly soluble salts precipitate at a rate which is far too slow to be accounted for by the simple diffusion of ions from the bulk of ~ o l u t i o n . ~The importance of the surface of the sol has been convincingly demonstrateds-’ and hence the terminology “surface” or “interface” controlled growth has been introduced to describe the growth process. Doremus4 has related the growth rate to a reaction between surface adsorbed ions, and surface reaction or nucleation2 appears to be commonly accepted as a rate limiting process. The form of the empiricaI growth equations, however, has proved rather baffling from a mechanistic point of view. Davies and Jones6 have pointed out that the growth equation for silver chloride seed crystals de _ - -Ls(c - Cf)2 dt
where c = jAg+I = IC]-!, s = surface a r m of the seed crystals, and cf = the solubility concentration, is not representative of an equilibrium process tetween growth and dissolution and no convincing explanation of the form of this equation has yet been published. One of the assumptions of the surface reaction theory has been that the concentration of adsorbed ions is proportional to the bulk concentration in solution. For the salts most commonly investigated, Le., silver chloride and barium sulfate, this relation does not appear to be correct.8 The essence of the following treatment therefore is to revise the formulation of general growth equations based upon the surface reaction theory. Theory Experimental measurements upon the adsorption of ions upon sols of the same material frequently conform to isotherms of the typea$ and where F A + and r B - are the total concentration of adsorbed A+ and B- ions, respectively. These isotherms are of the same form as the approximate form of the Temkin isothermlO,ll (1) A. E. Nielsen, J . Colloid Sci., 10,576 (1955). (2) A. E. Nielsen, Acta Chem. Scand., 13, 784 (1959). (3) G. R. Weiss, Ph.D. Thesis. Columbia University, 1962. (4) R. If. Doremus, J . Phys. C‘hem., 62, 1068 (1958). (5) C. W. Davies and A. L. Jones, Trans. Faradag Sac., 61,812 (1955). (6) J. R. Howard and G. H. Naneollas, zbzd., 63, 1449 (1957). (7) D. Turnbull, Acta Met., 1, 684 (1953). (8) E. Lange and R. Berger, 2.Etektrochem., 36, 171,980 (1930). (9) E. J. W. Varwey and H. R. Kruyt, 2. physik. Chem., A167, 149 (1934). (IO) J. M. Parry and R. Parsons, Trans. Faraday Sac., 69, 241 (1963). (11) 8. J. Gregg, “The Surface Chemistry of Solids,” Reinhold Publ. Carp., New York, N. Y., 1961, p. 96.
