R. C. SCHOONMAKER, A. R. VENKITARAMAN, AND P. K. LEE
2676
The Vaporization of Zinc Phosphide'
by Richard C. Schoonmaker, A. R. Venkitaraman, and P. K. Lee Department of Chemistry, Oberlin College, Oberlin, Ohio
(Receieed February 10, 1967)
The sublimation of ZnaPz(c) has been investigated by torsion effusion, torsion surface vaporization, and mass spectrometric techniques. Vaporization occurs by a congruent decomposition to Zn(g), P4(g), and P,(g) in the temperature range 620-820°K. The total pressure in effusion cells exhibits a strong dependence upon orifice dimensions and the gross vaporization coefficient varies from 2.4 X at 620°K to 6.8 X at 820°K. Equations are given for the temperature dependences of the total pressure of vapor in equilibrium with ZnsPz(c) and for the equilibrium constant for the reaction Zn,P,(c) e 3Zn(g) '/ZP,(g). The standard heat of formation for ZnsPz(c) at 298°K from red phosphorus and crystalline zinc is -39.5 f 5 kcal/mole. The measured ratio of cross sections for ionization of Zn(g) and P4(g) by 70-ev electrons is cr(Zn)/cr(P,) = 0.49. Other thermodynamic and kinetic data are presented and discussed for the vaporization process.
+
Introduction Shchukarev and co-workers2 have measured the heat of combustion for ZnsP2(c)and have reported a heat of formation of -98 kcal/mole at 298°K. Karvelis3 has reported heats of formation for zinc phosphide at 298°K of -55 kcal/mole from measurement of the heat of reaction of the elements and -53.4 kcal/mole from a measurement of the heat of hydrolysis. These values may be compared to AHr" [CdaPz(c)] = -27 k ~ a l / m o l e . ~A difference of 70 kcal/mole between heats of formation of phosphides where the metals occupy adjacent places in a group in the periodic table seems anomalous and implies a marked change in bonding in the crystals. Brewer5 has suggested that zinc phosphide is one of several compounds which may be attractive as heat-transfer fluids in nuclear reactor fuel element cans. In order to evaluate the suitability of materials as heat-transfer agents it is desirable to have information about their thermal stabilities and rates of vaporization. In recent studies of the vaporization of G a V and Gap,' it was demonstrated that the nitride has a very low vaporization coefficient and that certain liquid metals may act as catalysts for the vaporization process. In the case of gallium phosphide, where the over-all vaporization process is analogous to that for the nitride, similar experimental techniques did not yield any detailed information about the mechanism of The Journal o f Physical Chemistry
vaporization and it was only possible to conclude that the coefficient for vaporization of GaP is much larger than the coefficient for GaN. In order to investigate the mechanism of vaporization of metal phosphides, it seemed desirable to study some, like those of zinc or cadmium, which might be expected to vaporize by a congruent decomposition process in which catalysis by a residual liquid phase could not preclude detection of coefficients less than unity for direct vaporization from the crystal. The present work on the zinc phosphide system constitutes part of a continuing program of studies of the vaporization of metal nitrides and phosphides for which there is a paucity of experimental data concerned with the equilibria and mechanism of the vaporization process.
(1) This work was supported by grants from the National Science Foundation and the U. S. Army Research Office (Durham). (2) S. A. Shchukarev, M. P. Morosova, and G. Grossman, Zh. Obshch. Khim., 2 5 , 633 (1955). ( 3 ) N. Karvelis, V i l n i a u s Unie. Mokslo Darbai, 2 8 , 110 (1959). (4) S. A. Shchukarev, M. P. Mororova, and M .M.Bortnikova, Zh.
Obshch. Khim., 2 8 , 3289 (1958). ( 5 ) L. Brewer, U. S. Atomic E n e r a Commission AECU-4537, 1959. (6) R. C. Schoonmaker, A. Buhl, and J. Lemley, J . Phys. Chem., 69, 3455 (1965).
(7) P. K. Lee and R. C. Schoonmaker, Proceedings of the International Symposium on Condensation and Evaporation of Solids, Gordon and Breach Publishing Co., New York, N. Y . , 1965, p 379.
VAPORIZATIOX OF Zrsc PHOSPHIDE
Experimental S2rtion Mass spectrometric, torsion effusion, and torsion surface vaporization studies were conducted on purified samples of zinc phosphide which were prepared from commercial Zn3PZ8by sublimation and vapor transport in a stream of prepurified, dry nitrogen. The product was analyzed for zinc by the usual volumetric p r o ~ e d u r e . ~B typical zinc analysis on a dense pellet of Zii3Pl which was condensed from vapor on a quartz collector at about 530" gave 75.64% zinc compared to a theoretical value of 75.99%. M a s s Spectroineter. Samples of purified Zn3Pzwere loaded in a high-density graphite Thudsen cell with an orifice diameter of 0.140 cm. The cell n-as mounted in a resistance heated furnace in the molecular beam source of a 12-in., 90" mass spectrometer.'O The analyzer, ion source, and molecular beam source sections of the spectrometer were differentially pumped arid typical residual gas pressures during operation were lops, lo-', and torr, respectively. The geometry of the ion source was arranged so that the molecular beam, ionizing; electron beam, and ion beam were niutually perpendicular. Effusion cell temperatures were measured with chromel-alumel thermocouples mounted at the top and bottom of the cell. During a run covering a 200" range in temperature, the differential bet\Yeeri the upper and lower thermocouple readings was in the range 1-4". Neutral molecules which effused from the graphite cell passed through a slit in a movable plate, which was used to distinguish between background and ions produced from effusing molecules, arid were crossed by an electron beam of variable energy. The ions produced by electron bombardment were accelerated, mass analyzed in a magnetic field, and collected on the first dynode of an electron multiplier. Torsion Efltision. The torsion effusion apparatus and torque cells have been previously described and a general discuss,ion of the torsion effusion technique has been ~resented.~,'The reliability of this apparatus and technique for measurement of vapor pressure and heats of vaporization has been established in experiments on the sublimation of zinc for which measuicmerits by several other investigators are available." Second- and third-law analyses of 59 data points covering a range of 103" with three cells and three torsion fibers gave = 30.3 and 31.4 kcal/mole, respectively, for Zn(c) e Zn(g) compared to Hultgren's recommended value of 31.25. In the work reported here, annealed tungsten torsion fibers of 0.0025- and 0.0051-cm diameter were employed together with three conventional double-orifice torque cells which were machined from high-density graphite and which dif-
2677
Table I : Geometrical Factors for Torsion Effusion Cellsn 7-2-.
-1---
Left
d, ern q, cm L, ern
f W Z / A'
Right
0.230 0.230 0.940 0.920 0 . 1 5 5 0.125 0.669 0.717 0,036
-3-
Left
Right
0.121 0.121 0.900 0.870 0.065 0.070 0.720 0.704 0.010
Left
Right
0.080 0.082 0.895 0.900 0.050 0.053 0.686 0.679 0,0045
a d, Orifice diameter; q , torque arm; 15,minimiim thickness of orifice; f , Searcy-Freemaii factor (I with the result that the set of eq 4-6 may be established to permit determination of the partial pressures of all major species in the vapor over ZnsPn(c). Mi is the mass of the ith vapor species. Equations 6 and 6'
pt = P z n
+ + PP2
(4)
PP,
= PP~"/PP,
(*5)
Kequil
(6)
are required by the constraint imposed by congruence of the vaporization process. Equation 6' is applicable under true equilibrium conditions when pt in eq 4 is replaced by p, while eq 4-6 apply to steady-state effusion.
Results
Equation 1 relates pressure in a torque apparatus to angular deflection 0, torsion constant 7,and geometrical factors
for both eff usiori and surface vaporization studies. In surface vaporization measurements p is an apparent pressure12 which is derived from the rate of vaporization from a surface of area a and f is unity. In both effusion and surface vaporization studies the measured pressure is the sum of the partial pressures for all species present in the vapor. If the vaporization coefficient is small compared to unity, a marked dependence of pressure upon orifice dimensions may be expected in effusion studies. Hildenbrand13 has demonstrated the utility of an equation of type 2 for determination of the equilibrium pressure p, by linear extrapolation of
l/pk = M ( W a )
+ (Vpd
Table 11: Log p t (atm)
=
(-A/T)
+ B5
Cell
A
B
1
9658.4 9326.3 9063.0
7.5578 7.2201 6.9902
2 3
Pt = pzn
+ + p~p. PP,
(2)
measured pressures pk in a series of effusion cells with different effective orifice areas Wa. Motzfeld14 and Rosenblatt l5 have discussed the theoretical significance of equations of type 2 and the assumptions which make it possible to relate M , the slope of a plot of (l/pk) us. Wa, to the condensation or vaporization coefficients. In the section which follows, evidence will be presented to show that zinc phosphide vaporizes by congruent decomposition The Journal of Physical Chemistry
Figure 1 depicts the results of effusion measurements for several runs with torsion fibers of 0.0025- or 0.0051cm diameter combined with the torque cells described in Table I loaded with Zn3Pz(c). Equation 1 has been used to convert angular deflection of the torque cell to total pressure. The data for each of the three cells were smoothed by a least-squares procedure and total pressures were calculated from the appropriate equations, Table 11, for each cell a t 10" intervals over the
temperature range 620-820'K. Equation 2 was used for linear extrapolation of the measured total pressure to zero effective orifice area to provide values for the (12) I. Langmuir, Phys. Rev., 2, 329 (1913). (13) D.L. Hildenbrand and W. F. Hall, Proceedings of the International Symposium on Condensation and Evaporation of Solids, Gordon and Breach Publishing Co., New York, N. Y., 1965. (14) K.Motsfeld, J. Phys. Chem., 59, 139 (1955). (15) G. Rosenblatt, J. Electrocha. Sac., 110, 563 (1963).
VAPORIZATION OF ZINCPHOSPHIDE
2679
-8
-84 -
- 8 412
1.3
14
1.5
(VTOK)
18
x lo3
Figure 2. Temperature dependence of total pressure of all vapor species in equilibrium with Zn3P2(c).
tot'al pressure of vapor in equilibrium with solid zinc phosphide, Figure 2 and eq 7. In order to utilize the
log p , , (atm)
=
-9008.2 T
+ 6.9164
(7)
total equilibrium pressures for a thermodynamic analysis of the vaporization process, the mode of vaporization must be determined. Vaporizakion by decomposition is suggested by repeated observations of formation of a thin layer of metallic zinc on cooler portions of the apparatus during runs. Congruent vaporization is implied by the identity of X-ray diffraction spectra for fresh samples of Zn3P2(c)and residues from several vaporization runs. Confirmation of the proposed congruent decomposition was obtained in mass spectrometric analyses of vapors which effused from a graphite cell containing zinc phosphide where ion peaks corresponding to Zn+, P4+, Pz+,P3+, and P+ were observed in order of decreasing intensity, but no ions were detected which contained both zinc and phosphorus. If heteronuclear species containing zinc and phosphorus were present in the effusing molecu-
lar beam they would have been a t least three orders of magnitude less abundant than the molecular precursors of Zn+ or P4+. P3+and P+ arise largely from fragmentation of larger neutral species on electron impact while Pz+ is formed from a combination of dissociative ionization of P4(g) and simple ionization of Pz(g). The near invariance in the ratio Izn+/Ip, which was observed over a temperature range of about 200" is a result which would be expected if the vaporization were congruent with pp, >> pp, or if Zn+ and P4+ had the same molecular precursor. The latter possibility may be eliminated from consideration since the appearance potentials of Zn+ and P4+ were quite different. Thus, the mass spectrometric results are consistent with vaporization by the congruent decomposition represented by eq 3. Equations 4, 5 , and 6' may be used with equilibrium pressures determined from the effusion data and the thermodynamic data for phosphorus of Potter and DistefanoL6to calculate the partial pressures and equilibrium constants in Table 111. For the process represented by eq 8 ZnPdc)
3Zn(g)
+ 1/J?4(g)
(8)
(16) R. C. Potter and V. N. Distefano, J . Phys. Chem., 65, 849 (1961).
Volume 7 1 , Number 8 July 1967
R. C. SCHOONMAKER, A. R. VENKITARAMAN, AND P. K. LEE
2680
Table I11 : Thermodynamic Data for the Decomposition of Zinc Phosphide K, =
T, Pw
OK
2.49 x 6.99 x 1.86 x 4.67 x 1.11 x 2.53 x 5.50 x 1.15 x 2.31 x 4.52 x 8.50 x
620 640 660 680
700 720 740 760 780 800 820 a
P Pz
1.62 x 5.37 x 1.66 X 4.82 x 1.31 X 3.36 x 8.21 x 1.92 x 4.10 x 9.17 x 1.90 x
10-8 10-8 10-7 10-7 10-6 10-6 10-6 10-5 10-5 10-5 10-5
3.46 x 9.67 x 2.54 x 6.39 x 1.51 x 3.40 x 7.37 x 1.52 x 2.81 x 5.92 X 1.11 x
10-10 10-10 10-o 10-9 10" 10-8 10-7 10-7 10-7 10-6
PZn'pP4'/2
PZn
PP4
10-9 10-8 10-7 10-7 10-7 10-6 10-6 10-6
2.13 x 5.97 x 1.59 x 3.98 x 9.50 x 2.16 X 4.68 X 9.80 X 1.99 x 3.84 x 7.20 x
10-8 10-8 10-7 10-7 10-7
lod6 10-5 10-5 10-5
5.67 X 2.09 x 6.40 x 1.59 x 3.34 x 5.91 x 8.80 x 1.16 X 1.32 x 1.38 X 1.24 x
10-25 10-23 10-22 10-21
10-20 10-17
10-15
All pressures are in atmospheres.
gives A s 0 7 0 0 = 107 eu for eq 8 and this value together with tabulated entropy datal7-I9 gives a value of s"700 [Zn3Pz(c)] = 62 i 6 eu. When pressures are in atmospheres, K , for eq 8 may be represented over the temperature interval 620-820°K by eq 10. The enthalpy change for eq 8 may also be determined from log K ,
=
31489 T
--
+ 23.5084
(10)
mass spectrometric measurements of the temperature dependences of the intensity of ions which are formed by electron impact on Zn(g) and P,(g) which effuse from a Knudsen cell. Since the partial pressure of the ith effusing species is related to ion intensity and temperature by pi = kiIi+T, the equilibrium constant for eq 8 may be formulated as K , = ~ T ' / ' I Z , + ~ I P ,= + ~k/X~ . Figure 3 includes a plot of log X vs. reciprocal temperature from which AH0700 = 141 f 4 kcal/mole is obtained for eq 8. In order to determine the standard heat of formation for zinc phosphide -261.2.
'
'
1.3 '
14
15
1.6
2P(red,c)
I
(1/ToU)x103 Figure 3. Temperature dependences of log K, and log of a quantity proportional to K , for Zn8P2(c) 3Zn(g) 1/2Pd(g): 0, torsion effusion results; 0 , mass spectrometric results.
+
K p = p~,,~pp,'/~ and Figure 3 shows a plot of log K , us. reciprocal temperature from which = 144 f 4 kcal/mole may be determined. The value for the enthalpy change for eq 8 may be combined with AH", for Pz(g) S 1/zP4(g)17 to give AHO,~= 171 f 4 kcal/mole for eq 9. Combination of AHoTand AGO,
Zn3P2(c)
G 3Zn(g) + Pdg)
The JOUTWZo.f Physical Chemistry
(9)
+ 3Zn(c)
Zn,P2(c)
(11)
it is necessary to know AHf0298 and [H0700 - H " 2 9 8 1 for Zn(g) and P,(g> and [ H 0 7 0 0 - H"zg8]for Zn3Pz(c). All the requisite thermodynamic data are availablel1J7J9except [ H 0 7 0 0 - H0zg8] for Zn3Pz(c) which must be approximated. Three methods of approximation have been investigated: (1)[H"700 - H"2981 (17) "JANAF Thermodynamic Tables," The Daw Chemical Co., Midland, Mich., 1961. (18) K. K. Kelley, U. S. Bureau of Mines Bulletin 592, U. S. Government Printing Office, Washington, D. C., 1960. (19) K. K. Kelley, U. S. Bureau of Mines Bulletin 584, U. S. Government Printing Office, Washington, D. C., 1960.
VAPORIZATION OF ZINC PHOSPHIDE
2681
14.0 cal/mole, the tabulated value for Zr3N2;19 (2) [H07(X, - Ho298]'v 12.2 cal/mole, the tabulated value for Zn31\T2;16(:3) [ H 0 7 0 0 - H0298] cv 12.1 cal/mole, a value based upon the assumption that 1 mole of Zn3P2 may be represented by an assembly of 5N classical, independent three-dimensional harmonic oscillators. These three approximations give values for AHF"298[Zn3P,(c>] of -39.5, -37.7, and -37.5 kcal/mole, respectively, where the first value is considered to be preferable since the heat capacity data for Zr3Nz are probably more reliable than those for Zn3N2 and the uncertainty is estimated to be rt 5 kcal/mole. The results of torsion surface vaporization studies are , apparent total pressure shown in Figure 1 where p ~the due to vaporization of all species from the surface, has been calculated from measured angular deflections by use of eq 1 withf = 1 and a set equal to the geometrical area of the exposed plane surface of the pellet. Leastsquares treatment of the data gives eq 12. If a gross log p~ (atm)
=
- 11218 ____ T
+ 8.4400
(700-820" IO
vaporization coefficient is defined by aV= p ~ / p the , results in column 2 of Table IV are obtained when p~ from
Table IV : Gross Vaporization Coefficients for Zinc Phosphide T,OK
700 720 740 760 780 800
820 a
Evaluated from p ~ / p , .
Llv
x
1oza
av
x
1026
2.4 2.9 3.5 4.2 4.9
63.8 64.4
5.8 6.8
67.5 68.2
* Evaluated from M
65.0 65.7 66.5
(eq 2).
the surface vaporization measurements is combined with p, from extrapolated effusion data. These values for the vaporization coefficient may be compared to those determined as upper limits from M , the slope of a plot of (l/pk) us. effective orifice area in effusion studies, eq 2. The derivation of equations of type 2 involves the assumption that the vaporization and condensation coefficients, aV and CY,,are equal and it can be demonstrated15 that a particularly simple set of additional assumptions leads to M = l/apJ where A is the area from which vaporization occurs in an effusion cell. Since the cross-sectional area A' of the sample well represents a lower limit for the unknown vaporizing
surface area A of a finely powdered sample which covers the bottom of the effusion cell chamber, (Y 5 1,'MpJ'. Upper limits for the vaporization coefficient which have been calculated from M in eq 2 are listed in column 3 of Table IV. Finally, for systems which vaporize congruently it is possible to determine relative current production efficiencies for vapor species in a mass spectrometer. A t any temperature of interest, the total pressure in a mass spectrometer Knudsen cell of known effective orifice area may be determined by interpolation of a plot of l/pk us. Wa from torsion effusion measurements. With pt determined in this way, eq 4, 5, and 6 were used to evaluate partial pressures of Zn(g), P4(g), and P2(g) in the Knudsen cell and the ratio pzn/pp, mas combined with the ratio of measured ion intensities to give [ ~ ~ z ~ S Z ~ + / U=P ,0.35. S P , + ] If the usual square root of the mass correctionz0is applied for the relative electron multiplier ion detection efficiencies S e n+/ S p 4 + ,we obtain uzn/t7pp = 0.49 a t 640°K for the relative cross sections for ioiiization of Zn(g) and P,(g) by bombardment with 70-ev electrons.
Discussion The uncertainty in our value for the standard heat of formation of Zn,Pz(c> is probably at least rt5 kcall mole, but even at the upper limit of uncertainty our value lies well below the lower of the two previously reported result^.^,^ However, it should be noted that the two calorimetric values are widely discordant. Some measure of confidence in our results is provided by the good agreement between the values derived from mass spectrometric and torsion effusion data. Since the mass spectrometric measurements were made on a steady-state system which mas below vapor saturation, the AH"700 for reaction 8 based on ion intensity data should have been somewhat higher than the value based on equilibrium total pressures. The fact that our mass spectrometric result is 3 kcal/mole smaller than the effusion result does not represent a serious discrepancy since the uncertainty in the measurement of each value of AH from the slope of log K us. reciprocal temperature is estimated to be at least A 4 kcal/mole. The principal cause for the scatter in pressure measurements in Figure 1 is uncertainty in temperature. The treatment of the data for the vaporization of zinc phosphide involves a relatively short extrapolation to determine equilibrium pressures. I n a similar study of the vaporization of C ~ , P , ( C ) ~ ~ (20) h l . G. Inghram and R. J. Hayden, "A Handbook of Mass Spectroscopy," Nuclear Science Series Report No. 14, National Research Council Publication No. 311, 1954. (21) E. C. Schoonmaker and K. Rubinson, submitted for publication.
Volume 71, Number 8 July 1967
2652
R. C. SCHOONMAKER, A. R. VENKITARAMAN, AND P. I
