NOTES
3354
visible transition and only 1.6in the second-order transition. Simpson6 has identified second-order peaks in the spectra of a series of two polymethine dyes. We have presented here a more extensive series; furthermore, the second-order bands are very well isolated in all but the first member of this series. The transitions An = 2 are forbidden in molecules with a center of symmetry. It seems that in the ground and excited electronic states there is sufficient rotation about double bonds, or asymmetric vibration, so that the symmetry restriction is lifted and the “forbidden” transitions appear. This explanation is consistent with the reduced linear dichroism in the eecond-order spectra, as well as the poor fit of relative intensities to calculations based on the particle-in-a-box model. However, that model can still he used as a good first approximation in predicting the wavelengths of the second-order spectra of symmetric cyanine dyes. Acknowledgment. This work was supported in part by a grant to M’ashington University from the Xational Aeronautics and Space Administration and by a grant from the Research Corporation. (6) W. T. Simlison, J . Chem. Phys., 16, 1124 (1948).
The Vaporization of Cadmium Phosphide’
by Richard Schoonmaker and Kenneth Rubinson Department of C‘hemtstry, Oberlzn College, Oberlzn, Ohto (Receized Aprzl 19, 1987)
Metal phosphides are attractive compounds for studies of the kinetics of retarded vaporization since they Vaporize by decomposition to relatively simple gaseous species with well-known structures and thermodynamic properties. As a class, they have been the obiect of increasing interest in recent vears as a result of their senliconductiIlg properties. At the present time there is remarkably little available information about the thermal stabilities of phosphides. Shchukarev and co-workers2reDorted a heat of formation for ZnaPz(c)of -9s kcal/m& while in subsequent work3 a heat of formation of -27 kcal/mole was reported for CdaPz(c). The large difference between Shchukarev’s heats of formation for zinc and cadmium phosphides, which have the Same crystal StrUcture,4 is unexpected since a drastic change in bonding would
-
The Journal of Physical Chemistry
not be predicted when zinc is replaced by cadmium in the crystal. Schoonmaker, Venkitaraman, and Lee,5 hereafter referred to as SVL, have reported AHt” 298[Zn,P,(c)] = -39.5 kcal/mole. In addition, they found evidence for a low coefficient for vaporization from ZnsPz(c) and concluded that an enthalpy barrier to activation for vaporization was at least partially responsible for deviation of the vaporization coefficient from unity. The present work was undertaken to determine the thermal stability of cadmium phosphide and t,o investigate the extent of analogy between the processes of vaporization from crystalline zinc and cadmium phosphides.
Experimental Section The torsion effusion and mass spectrometric apparatus and experimental techniques used in this work are similar to those previously d e ~ c r i b e d . ~Finely ,~ divided, polycrystalline Cd3Pz was prepared by direct union of the elements at 450-500” in an evacuated, sealed tube. A sample of the product was analyzed for cadmium by electrodeposition and gave 84.48% compared to a theoretical value of 84.49. X-Ray diffraction spectra of the phosphide provided no evidence for uncombined cadmium metal. On solution of the finely powdered phosphide in dilute acid there was either no residue or only a faint trace of undissolved phosphorus. Three conventional, double-orifice torsion effusion cells were machined from high-density graphite. The torque cells were identical except for effective orifice areas which were in the ratio 9.1:2.7: 1 for cells 1, 2, and 3, respectively. For each cell, several runs were made with torsion fibers of 0.0025- and 0.0051-cm diameters. Mass spectrometric analyses were made on a molecular beam generated by vaporization of Cd3Pz(c)in a Ihudsen cell with an orifice diameter of 0.140 cm.
Theory Detailed theory applicable to this work has been described by S V L . ~ A linear equation (1) has been llp,
=
Mmu)
+ WpJ
(1)
(1) This work was supported by grants from the U.S. Army Research Office (Durham) and the National Science Foundation. (2) s, A. Shchukarev, hf. p, Morozova, and G , Grossman, Zh. Obshch. K h i m . , 25, 633 (1955). (3) S. A. Shchukarev. M. P. Moroeova, and M. 11. Bortnikova, 28, 3289 (lg5’). (4) W. B. Pearson, “A Handbook of Lattice Spacings and Structures of Metals and Alloys,” Pergamon Press Ltd., London, 1958. (5) R. c. Schoonmaker, A. R. Venkitaraman. and P. K. Lee, J. P h m Chem., 71, 2676 (1967). (6) P. K. Lee and R. C. Schoonmaker, ”Condensation and Evaporation of Solids,” Gordon & Breach Publishing Co., New York, N. Y., 1965, 379.
NOTES
3355
used to extrapolate pressure in the effusion cells, pt, to zero effective orifice area, Wa, to obtain the total pressure, p,, of :dl gaseous species in equilibrium with solid cadmium phosphide. If the vaporization occurs by congruent decomposition according to ( 2 ) and if the CdJ'?(c)
3Cd(g)
+ '//zP4(g)
- 3.4 - 3.8 -4.2
(2)
I (dt
p 2
partial pressure of P2(g) is neglible compared to that of P4(g), the equilibrium constant for (3) and the partial pressures of P4(g) and Cd(g) may be related to the total equilibrium pressure by the equations: K , = 0.238~~"';pp, = 0.143pe; P C d = 0.85717,. CdJ'2(c)
3Cd(g)
+ '/'/zP4(g)
(3)
Results At the beginning of runs with fresh samples, torque cell deflection was larger than the steady-state value to which it declined after a period of time. The steady state was constant and reproducible for several hours. I n the earliest runs sample weights were recorded, but no precaution was taken to use identical quantities for different runs with a given cell with the consequence that while the data for any single run were reproducible, pressures with a given cell were not consistent when different runs were compared. When a large number of pressure measurements was available it was apparent that pressure in the torque cell varied with sample weight and it was concluded that sample surface area effects were important. This conclusion was verified by use of a differential torque cell7 which is, in effect, two identical conventional, double-orifice torque cells arranged in such a way that effusion from a set of orifices in one cell produces a torque couple which acts in opposition to the couple produced by effusion from he other cell. When one set of chambers contained approximately twice as much sample as the other set, the differential torque cell deflected in the direction which would be expected if the effusion rate was greater in the set which contained the larger weight of CdaPz(c). In all subsequent runs exactly the same weight of samples was used. Figure 1 shows the temperature and orifice area dependences of total pressure over Cd3P2(c)in three different torque cells. The line for each cell is a composite of data from several runs with both 0.0025- and 0.0051cm diameter torsion fibers. The data for each cell were smoothed by a least-squares procedure and total pressures were calculated for each cell a t 10" intervals over the temperature range 530-650°K. Figure 2 illustrates a typical linear extrapolation, eq 1, from
-4.6
-
-5.0
-
-5.4
-
h
3d
v
if
2 -5.8
-
J -6.2
-
-6.6
-
-7.0
-
-7.4
-
-7.8
1.55
1.59
1.63 1.67 1.71 1.75 (1/T) x 108,OK-'.
1.79
1.83
1.87
Figure 1. Logarithm of the total pressure in torsion effusion cells us. reciprocal temperature: 0, 0.0025-cm diameter torsion fiber; A and 0, 0.0051-cm diameter torsion fibers.
which the total pressure of all gaseous species in equilibrium with crystalline cadmium phosphide may be determined. The temperature dependence of the vapor pressure is well represented by log p, (atm) = (-7725.2/T) 8.4933. Visual observation, mass spectrometric analyses of effusing vapors, and comparison of X-ray diffraction spectra of fresh samples and residues after vaporization all provided strong evidence for vaporization of cadmium phosphide by congruent decomposition. The detailed reasoning is very similar to that previously presented for zinc p h ~ s p h i d e . ~For example, in the mass spectrometric studies no ions were detected which contained both cadmium and phosphorus, but, over a temperature range of 130°, the Cd+/P4+ratio remained essentially constant while the Cd+ intensity changed by a factor of more than lo3. I n the interest of brevity we do not reproduce further details of the argument. I n the congruent decomposition, equilibrium total pressures may be used to calculate the partial pressures and equilibrium constants listed in Table I. Even for
+
(7) R. C. Schoonmaker, A. Buhl, and J. Lemley, J . Phgs. Chem., 6 9 , 3455 (1965).
Volume 71,Number 10 September 1967
NOTES
3356
-12 -.
-1
a
-14
-20
2
6
10 14 18 ( F a ) x loa, cmt.
22
26
Figure 2. Linear extrapolation of l/po to zero effective orifice area at 540'K: 1?, A, 0, cells 1, 2, 3, respectively.
~~
~
Table I : Thermodynamic Data for the Decompositicin of CdaPz(c)" Kp =
530 540 550 560 570 580 590 600 610 620 630 640 650 a
7.06 x 10-7 1.32 x 10-6 2.41 4.26 7.52 1.29 X 2.15 3.54 5.82 9.25 1.47 X 2.29 3.51
1.18 2.20 4.01 7.10 1.26 2.14 3.58 5.90 9.96 1.54 2.44 3.81 5.84
x
10-7
x
x
10-6
''a
x 10-22 x x 10-21 x x 10-19 x 10-l8 1.88 x 10-17 1.07 x 10-16
1.20 1.07 8.86 6.50 4.77 3.08
6.13 X 3.09 X 1.56 x 10-14 7.40 x 10-14 3 . 3 0 x 10-13
All pressures are in atmospheres.
Figure 3 is a plot of log K , us. reciprocal temperature from the slope of which AH"sm = 124 f 4 kcal/mole may be determined for the decomposition represented by eq 3. Temperature dependences of ion intensities corresponding to Cd+ and P4+ from mass spectrometric measurements on vapors effusing from a Knudsen cell The Journal 01' Physical Chemistry
\
\
t
1.54
the torque cell with the largest orifice, P2(g)is a neglible species in the analysis since the ratio ppl/pp, = over the temperature interval of this work.
PCd'PP,
1 1.58
1.62 1.66 1.70 1.74 (1/T) x 108,OK-'.
1.78 1.82
1.86
Figure 3. Logarithm of K , us. reciprocal temperature for CdaPz(c) 3Cd(g) '/Zp4(g).
+
gave values of 128 and 133 kcal/mole from the slopes " ~ ]reciprocal temperaof plots of log [ ~ " ~ ~ ~ + 3 1 p , +us. ture. The torsion effusion value of 124 kcal/mole for (3) may be combined with thermochemical data from standard references*+Dfor phosphorus and cadmium and [H"w,o= 9.1 kcal/mole for Cd3P2(c),estimated from the classical harmonic oscillator approximation, to give a value of -29.5 f 5 kcal/mole for the enthalpy of formation of CdsP2(c)from crystalline red phosphorus and cadmium. From the relation 01 5 ( l / M p J ' ) , where M is the slope in eq 1 and A' is the cross-sectional area of the torque cell sample chamber, upper limits to the gross coefficient for condensation or vaporization of cadmium phosphide may be calculated which vary with temperaat 650°K. at 530°K to 5.6 X ture from 6.1 X
Discussion Zinc and cadmium phosphides both vaporize by congruent decomposition in the temperature range around 600°K and both compounds have low gross coefficients for condensation on or vaporization from the M3Pz crystal surface. The heat of formation of ~
(8) K. K. Kelley, Bureau of Mines Bulletin 584, U. S. Government
Printing Office, Washington, D. C., 1960. (9) "JANAF Thermodynamic Data," Dow Chemical Co., Midland, Mich., 1961.
NOTES
Cd3P2(c) determined by the torsion effusion method employed in this work is in good agreement with Shchukarev's value2 which was obtained by calorimetry in a KBr-Br2 solution. The results for Cd3P2,like those of SVL5 for Zn3P2, suggest that a is temperature dependent and that the deviation from unity may be caused, in part at least, by an enthalpy barrier to activation for vaporization which exceeds the equilibrium enthalpy change. The foregoing implies that the torsion effusion value for aHoTfor the vaporization process should be smaller than the mass spectrometrically determined values since the latter were determined by measurement of ion intensities in a steady-state system in which the vapor pressure was below saturation. The dependence of pressure on sample surface area which was observed in this work is consistent with a predictionlo which was based on a theoretical model for vaporization from porous solids of substances with low vaporization coefficients. llotzfeld" and Rosenblatt'O have discussed the derivation and limitations of equations of type (1); and, in particular, they have directed attention to the assumptions which are necessary to obtain a simple relationship between a and M . If eq 1 is more than an empirical relation which is useful for extrapolation purposes and if the limiting values for a are meaningful, comparison of values of a from the present work with those of SVL5 suggests that the gross coefficient for vaporization for cadmium phosphide may be considerably smaller than for zinc phosphide. There is some evidence to suggest that in both cases as well as for the vaporization of red phosphorus12 and arsenicI3 the low vaporization coefficient may be the result of an excess enthalpy of activation associated with rearrangement of bond distances and angles in the formation of Xd units which do not exist in the crystal. Cd3P2 has a tetragonal D5$ structure4 in which each phosphorus atom has 12 near neighbors, 4 a t 4.26 A, 4 a t 4.34 A, and 4 at 4.45 A. The P-P distance in P4(g) is 2.21 A.'* Although Zn3P2 and Cd3P2have similar crystal structures, the nearest neighbor phosphorus distances are considerably larger in the latter, and it is possible that the additional separation of phosphorus atoms is responsible for the lower coefficient for vaporization of the cadmium compound. Unfortunately, a test of this hypothesis cannot be extended to mercuric phosphide since apparently there is no well-defined Hg3P2 phase'5 in the mercury-phosphorus system in t h e temperature range of interest. The abnormally high initial rate of vaporization from fresh Of Cd3P2 found in this work is reminiscent of a result previously observed in the Vaporization Of P,(g) from red phosphorus.12 We can
3357
offer no explanation which is preferable to Brewer and Kane's suggestion that the phenomenon may have been the result of distorted or defective crystals in which the atoms were not so rigidly fixed as in a perfect crystal.
Acknowledgment. R. C . Schoonmaker wishes to thank the National Science Foundation for a fellowship and Professor C. A. Coulson, Mathematical Institute, Oxford University, for providing facilities and generous hospitality during a sabbatical leave when this note was prepared. (10) G.M. Rosenblatt, J. Electrochem. Soc., 110, 563 (1963). (11) K. Motzfeld, J. Phys. Chem., 59, 139 (1955). (12) L. Brewer and J. S. Kane, ibid., 59, 105 (1955). (13) G.M. Rosenblatt, P. K. Lee, and M. B. Dowell, J. Chem. Phya., 45, 3454 (1966). (14) C.R.Maxwell, S. B. Hendricks, and V. M.Mosley, ibid., 3, 699 (1935). (15) B. Aronson, T.Lunstrom, and S. Rundquist, "Borides, Silicides,
and Phosphides, a Critical Review of their Preparation, Properties, and Crystal Structure," Methuen & Co. Ltd., London, 1965.
A Posteriori Separation of Faradaic and Double-Layer Charging Processes : Analysis of the Transient Equivalent Network for Electrode Reactions
by W. D . Weir Department of Chemistry, Harvard Univereity, Cambridge, Massachusett8 08138 (Received February 84, 1967)
In a recent critique of the assumptions upon which several treatments of nonstationary-state elect,rochemical processes have been based, Delahay has shown that a priori separation of faradaic and double-layer charging processes is without operational justification.' The coordinate conclusion that a posteriori separation can have only formal and not operational significance2 seems unwarranted, however. This communication suggests an operational justification for a posteriori separation under appropriate conditions through an analysis of the transient equivalent network proposed by Weir and Enke.a (1) p. Delahay, J. Phy8. Chem., 70, 2373 (1966). (2) p. Delahay and G. Susbielles, ibid., 70, 3150 (1966). (3) w. D. Weir and C. G. Enke, ibid., 71, 280 (1967).
Volume 71,Number 10
September 1967
