NOTES Quadruply distilled mercury was used as a manometer fluid for the hydrocarbon measurements, and either g cmda) or Dow Apiezon B oil (dZ5 0.86993 f g em-3) was Corning, silicone 704 oil (dZ51.06201 f used for those with water. The oils were continuously stirred and degassed in a bulb fitted to the side of the manometer. After the sample and manometer had been degassed, the system was isolated from the pumps and placed in a large thermostat which had a glass window as one side. The menisci were separately illuminated by two fluorescent lamps fitted with shields and slits 1 cni in width. Reflected light effects were minimized by fitting the mercury manometer with similar slits. The distances between the menisci were measured with respect to a calibrated invar scale12situated in the plane of the manometer arms. To take readings a Gaertner telescope with a very small depth of focus was mounted on a cathetometer stand. Distances between the scale marks and the menisci were measured by means of a micrometer screw gauge attached to the telescope. The apparatus frame to which the invar scale was attached was kinematically suspended13 in the water bath and thus it was possible to adjust the male to a vertical position by means of a sensitive level. The telescope was set in a horizontal position using the artificial horizon produced by the two menisci in the manometer. The measured pressures were corrected to standard ~0nditions.l~ A freezing mixture of Dry Ice and ethanol was used for measurements with benzene and with aqueous solutions, and liquid nitrogen was used for all other compounds. It was found that with a liquid nitrogen freezing mixture it was impossible to degas water with a single sublimation. Acknowledgment. This project was supported by the Australian Research Grants Committee. C. N. P. is grateful to the Commonwealth Scholarship and Fellowship Plan for an award, during the tenure of which this work was done. (12) Calibrated by the Metrology Section, South Australian Railways, Islington. (13) J. Strong, “Procedures in Experimental Physics,” Prentice Hall, Inc., Englewood Cliffs, N. J., 1938,p 585. (14) G.K.Burgess, J. Res. Nat. Bur. Stand., 1, 635 (1928).
Phase Separation in the Palladium-Hydrogen System
by Y. Ebisuzaki and M. O’Keeffe Department of Chemistry, Arizona State University, Tempe, Arizona 86881 (Received J u l y I , 1968)
Phase equilibria in metal-hydrogen systems are very frequently described in terms of the model originally
4695 proposed by Lacher’ and its subsequent refinements.2pa The essential feature of this theory is that it is postulated that there are short-range (strictly nearest neighbor) attractive interactions between dissolved hydrogens. The heat of solution of x g-atom of hydrogen/mol of metal is then written
AH = A x
+ Bx2 + constant
(1)
where A and B are constants. 2B/x is the energy of interaction per pair of hydrogens, where, in turn, x is the number of nearest neighbor positions of a given hydrogen. In its simplest form, the theory now assumes an ideal entropy of mixing. It is then predicted that two solid phases of different compositions can coexist below a critical temperature, T, = B / 2 R , where R is the gas constant. If the critical temperature and composition are used as adjustable parameters, it is possible to describe adequately the composition of the hydride as a function of temperature and hydrogen pressure. However, as discussed below, there are physical reasons for rejecting this model of hydrogen in metals. It is our purpose here to outline an alternative approach to the description of such systems.
Hydrogen in Metals There are several features of hydrogen in metals that bear examination. (a) There is good evidence4 that hydrogen dissolves in transition metals as a proton, with the proton charge strongly screened by the conduction electrons of the metal. I n a first approximation, the screened potential of the proton a t a distance T may be taken to be the form4s5 V(T>= ( 4 / r ) exp(-W (2) where q is the proton charge, and the screening parameter, A, is given by
x
(3) where N is the density of electronic states at the Fermi energy. The interaction energy between two protons a distance Ar apart will then be5 = (47rqW)”2
A E = (q2/Ar) exp(-AAr) (4) For hydrogen in a metal such as palladium, one calculates, according to eq 3 and 4,that A E < l cal mol-’; this is several orders of magnitude smaller than the value of 2Blx necessary to explain the observed behavior of the palladium-hydrogen system. More im(1) J. R. Lacher, Proc. Roy. Soc., A l d l , 525 (1937). (2) G. G. Libowitz, “The Solid State Chemistry of Binary Metal Hydrides,” W. A. Benjamin, Inc., New York, N. Y., 1965. (3) F. A. Lewis, ”The Palladium-Hydrogen System,” Academic Press, New York, N. Y., 1967. (4) Y. Ebisunaki and M. O’Keeffe, Progr. Solid State Chem., 4, 187 (1967). (5) J. M. Ziman, Advan. Phys., 13, 89 (1964). Volume ‘78, Number 19 December 1968
NOTES
4696
portantly, AE has the wrong sign, that is to say, that eq 4 predicts that neighboring hydrogens will naturally repel each other. These conclusions remain generally valid even when a more sophisticated form of the screened potential, such as discussed by Blandin and D6plantB,e is used in place of eq 2. (b) A second point is that the heat of solution of hydrogen in a metal or alloy depends strongly on the density of states at the Fermi energy,"' a quantity that will, in turn, vary with the valence e1ectron:atom ratio of the alloy. Solution of hydrogen in palladium contributes one electron per hydrogen to the d band of the metal with a consequent change in the Fermi energy density of states, in a way strictly analogous to the effect of allowing palladium with silver. It is anticipated, therefore, that the heat of solution of hydrogen in palladium will be strongly composition dependent.
0.1
0.2
0.4
0.3 x
Figure 1. The heat of solution per gram-atom of hydrogen in the alloys Pd,-,Ag, (data of Brodowsky and Paeschelo).
The Palladim-Hydrogen System The two observations made above lead to the following considerations with respect to the palladium-hydrogen and related system?. (a) As the energy of interaction between two hydrogens is expected to be much less than RT (at or above room temperature), the configuration entropy of the solution is expected to be close to the ideal-solution value. (b) The heat of solution of hydrogen will be composition dependent. We write, therefore, the partial molar free energy of hydrogen in the solution PdH, =
RH- TSH = AI%x)
+ RT In I x / ( l - x)1 +
'/2po(&)
(5)
where the constant term '/zpo(H2)depends on the choice of standard state for hydrogen and is of no consequence in this context. AR(z) is the composition-dependent heat of solution of 1 g-atom of hydrogen in PdH,. In order to estimate A R ( x ) we make use of the obs e ~ a t i o n ' ,that ~ to a good approximation the heat of solution of hydrogen in an alloy depends only on the valence e1ectron:atom ratio of the alloy and not on the chemical identity of its minor constituent. Brodowsky and Poeschels have made very accurate measurements of the heat of solution in a series of alloys, Pd,-,Ag,, with the results shown in Figure 1. For the reasons just given we use these data as a measure of A R ( x ) . From eq 5 and the condition for a critical point a t xc, 02z.
=
d p / b x = b2#/bX== 0 ;
x
=
x.
=
(1 - 2 x ) / z ( x - 1); The Journal o/ Phy-1
Chemistry
*
=
RT,/x(x
-
1);
x
= X,
(8)
Using the critical composition already determined, one finds in this way that T , = 680 100"K, in fair enough
*
(6)
one readily derives (bzA~/bxz)/(b&/bx)
In Figure 2 we have plotted separately as a function of x the left-hand side of eq 7 as derived from the data of Figure 1 by graphical differentiation and the righthand side of the same equation. I t may be seen that, although there is considerable error in obtaining b 2 A R / b x a from the experimental data, it is nevertheless possible to locate fairly precisely the critical composition at x, = 0.24 0.02, in very good agreement with the experimental v a l ~ eof~ za . ~= 0.27. The critical temperature, T,, may likewise be evaluated from eq 5 and 6 as
bAR/&
Evaluation of the Critical Constants 2
Figure 2. Curve A: ( a l A H / a z a ) / ( P A H / P z ) ; curve B: (1 - 22)/2(2 - 1) BS a function of z in PdH.. The intersection of the two curves is the solution of eq 7.
x = xo (7)
(6) A. Blandin and . I . L. D&plant&. J . Phys. Radium, 23, 609 (1962). (7) H. Schnabl. Be. Bunsenws. Phya. Chem., 68, 549 (1964). (8) Y. Ebisuzaki and M. O'KeeKe, Phil. Mw.,14, 867 (1966). (9) H. Brodowsky and E. Poesehel, Z . Phys. Chem. (Frankfurt ~ r n Main). 44, 143 (1'365).
NOTES
4697
agreement with the e ~ p e r i m e n t a l value ~ * ~ of T , = 570°K. A further check is possible on the validity of the assumption that AH is given accurately by the data of Figure 1. At room temperature the composition of the hydrogen-rich phase in equilibrium with the metal-rich phase is PdHo.e. The integral heat of formation, per gram-atom of hydrogen, of PdHo will be
AHI = ( l / 0 . 6 ) ~ 0 ' 6 A ~ (dx z)
Mass Spectra and Sublimation Pressures of IF7 and IOFj
by C. J. Schack, D. Pilipovich, S. K.Cohz, and D. F. Sheehan Research Division, Rocketdyne, a Division of North American Rockwell Corporation, Canoga Park, California 91304 (Received J u l y 6 , 1968)
(9)
Numerical integration of the area under the curve in Figure 1 gives AHt = -5.0 kcal, in very good agreement with the experimental (calorimetrii) value of AHr = -4.8 lical mol-'.lO
Concluding Remarks The excellent agreement with experiment of the approach to the palladium-hydrogen system outlined above leads us to believe that the basic assumptions are well founded. These assumptions are that the configurational entropy of the solution has the ideal value and that to an excellent approximation the heat of solution of hydrogen contains no contributions from the hydrogen-hydrogen interactions but depends only on the valence electron : atom ratio of the compound. Using these aosumptions, the critical constants for the Pd-H system can be predicted using only experimental data obtained with very dilute solutions of hydrogen in palladium-silver alloys. Finally, it is interesting to note that it is probable that hydrogen-hydrogen interactions, although weak, are repulsive. One would anticipate, therefore, that at a sufficiently low temperature there will be an orderdisorder transition in a hydride of suitable composition. It is tempting to interpret the specific heat anomaly observed1' in p-Pd-H a t 55°K in these terms. One might suppose that the vacant and ordered sites would order as in CuAu (L1, type) or CusAu (L12 type), although the establishment of long-range order would be hindered by the low mobility of hydrogen at these temperatures. In this connection, low-temperature neutron diffraction experiments with hydrides of the ideal composition PdHo.5 or PdH0.7j would be very interesting .
Acknowledgment. This work was supported by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under AFOSR Grant No. AF-AFOSR-68-1371.
(10) D. M. Nace and J. G. Aston, J . Amer. Chem. SOC.,79, 3619 (1957). (11) D. M. Nace and J. G. Aston, {bid., 79, 3623 (1957).
Several recent have dealt with the preparation and properties of IF7 and IOF5. While these articles have helped to clarify some of the earlier discrepancies with regard to the properties of IF7 and IOF5, some inaccuracies still persist. For example, the reported vapor pressuresa and/or sublimation pressures of these compounds are incorrect. The vapor pressure-temperature relationship of IF7 has been corrected' but that of IOFs has not. We wish to report the sublimation pressure-temperature data and also the characteristic mass spectra of IF?and IOF6. Experimental Section Materials. Iodine pentafluoride (Matheson Co.) and Fz were heated at 150" in monel or stainless steel cylinders for several hours. Partial purification of the IF7 was achieved by vacuum fractionation on a vacuum line constructed of stainless steel and equipped with Teflon U traps. Final purification of IF7 was accomplished by treatment with K F to remove H F and IF5, followed by additional fractional condensations. No H F was detectable by near-infrared ~pectroscopy.~ This method generally gave IF7 contaminated with 1-2% of IOFj. However, the product on occasion was found to be completely free of IOF5or any other detectable impurity and comprised the material used for the measurement,s. Iodine oxide pentafluoride m7as prepared by condensing IF7 over Si02 (Cab-0-Sil) at -196" in stainless steel cylinders, warming to ambient temperature over several hours, and allowing the reaction to proceed overnight. If the reaction cylinder was warmed too rapidly, sufficient heat was generated to decompose most of the IOFE to IF6 and 0 2 . Vacuum fractionation, treatment with KF, and an additional fractionation served to purify the product. No impurities were detected by gas chr~matography,~ infrared spectroscopy, and nearinfrared spectroscopy. Sublimation-Vapor Pressure Measurements. The pressures over solid or liquid IF, or IOFE were measured (1) H. Selig, C. W. Williams, and G. J. Moody, J . Phys. Chem., 71, 2739 (1967). (2) D. F. Smith and G. M.Begun, J . Chem. Phys., 43, 2001 (1965). (3) N . Bartlett and L. E. Levchuk, Proc. Chem. SOC.,342 (1963). (4) V. H. Dayan and B. C. Neale, Advances in Chemistry Series, No. 54, American Chemical Society, Washington, D. C., 1966, p 223. Volume 7.9, Number 1 3 December 1968
