1102
C. C . HERRICK AND ROYC . FEBER
Vaporization Studies on Arsenic1
by
C. C,Herrick and Roy C. Feber
Los Alamos Scientific Laboratory, University of California, Lo8 Alamos, New Mexico 87644
(Received June 14,1967)
Angular-displacement studies of the vaporization of solid arsenic have been made to 700°K using cylindrical effusion cells, free-vaporizing surfaces, and an effusion cell fabricated from sintered arsenic powder, An automated recording system was used. Arsenic samples were prepared and handled in such a manner as to minimize the effect of impurities. Effusion pressures did not vary as the orifice diameter ranged from 0.005 to 0.040 in. From the effusion measurements, the heat of sublimation of solid arsenic to Asr(g)at 298.15’K was found to be 38.54 k 0.10 kcal/mol of Asd(g), whereas the free-vaporization measurements gave 44.23 k 0.3 kcal/mol. For the calculation of these quantities, previously available thermodynamic functions for As(s) and As&) were replaced by recomputed values. A comparison of pressures resulting from these measurements suggests a temperature dependence of the condensation coefficient, which was confirmed by the angular displacement measurements on the arsenic effusion cell.
I. Introduction A study of the vapor pressure and vaporization rates of arsenic is desirable for at least two reasons. First, of course, a knowledge of the equilibrium vapor pressure and the thermodynamic quantities derived therefrom is of interest. These quantities are not well established. Also, such a study can add to an understanding of the extent to which complex vapor species can influence simple condensation and evaporation processes. Over the range of temperatures accessible to the usual experimental techniques as applied to this system, the vapor is essentially all As4(g),2and a very small condensation coefficient has been r e p ~ r t e d . ~Therefore, kinetic considerations of the evaporation and condensation processes become important. The discilssions of this sort by Stranski and ~ o w o r k e r of s ~situations ~~ are especially useful. Several methods have been used to measure the vapor pressure of arsenic. The data have been reviewed by Stull and Sinke6 and by Nesmeyanov.2 Stull and Sinke estimated the thermodynamic functions for As4(g) necessary for their computation of the thermodynamic properties of the system. Nesmeyanov gave an equation to represent his selected vapor pressures as a function of temperature. Vapor pressures tabulated as “best” in the two reviews are very similar. The vapor-density measurements of Preuner and Brockmoiler' showed that saturated arsenic vapor contains essentially all Ash molecules up to 500”, and that dissociation of As4 can be disregarded up to 800”. From an examination of the vapor flux from a Langmuirtype experiment in a mass spectrometer (530-620°K), Kane and Reynolds8 agreed that the vapor is predominantly As4. Other mass spectrometric studies leading to the same conclusion include those of Drowart and GoIdfinger,g Westmore, Mann, and Tickner,lo and Gutbier.” Ruff and Bergdahl12 determined the vapor pressure by a boiling point method, and later Ruff and The Journal of Physical Chemistry
A4ugdan13repeated the experiments. The remainder of the data were obtained by static methods, with the exception of the more recent measurements of Nesmeyanov,2 and Brewer and Kane.3 These authors used versions of the Knudsen method. Nesmeyanov rejected his data in his selection of the best values of the vapor pressure, and Brewer and Kane did not list their experimental results. Rosenblatt14 used the experiments of Brewer and Kane to formulate meaningful suggestions for the interpretation of Knudsen measurements on porous materials. Iilemm, et u Z . , ’ ~ ~ ’ ~ reported anomalies in the temperature dependencies of the crystallographic axes, the enthalpy, the diamagnetism, and the electrical resistivity of crystalline arsenic at about 500°K. These observations were not confirmed by Taylor, Bennett, (1) Work performed under the auspices of the United States Atomic Energy Commission, (2) A. N. Nesmeyanov, “Vapor Pressure of the Chemical Elements,” Elsevier Publishing Co., New York, N. Y.,1963. (3) L.Brewer and J. S. Kane, J . Phys. Chem., 59, 105 (1955). (4) I. N.Stranski and G. Wolff, Research, 4, 15 (1951). (5) W. Hirschwald and I. N. Stranski, “Condensation and Evaporation of Solids,” E. Rutner, P. Goldfinger, and J. P. Hirth, Ed., Gordon and Breach, New York, N. Y., 1964. (6) I).R. Stull and G. C. Sinke, “Thermodynamic Properties of the Elements,” Advances in Chemistry Series, No. 18,American Chemical Society, Washington, I).C., 1956. (7)G.Preuner and I. Brockmoller, 2.Phys. Chem. (Leipseig), 81,129 (1912). (8) J. S. Kane and J. H. Reynolds, J. Chem. Phya., 25, 342 (1956). (9) J. Drowart and P. Goldfinger, J . Chim. Phys., 55, 721 (1958). (10) J. B. Westmore, K. H. Mann, and A. W. Tickner, J . Phys. Chem.,68, 606 (1964). (11) H.B. Gutbier, 2.Naturforsch., 14a, 32 (1959). (12) 0.Ruff and B. Bergdahl, 2.Anorg. Chem., 106,76 (1919). (13) 0.Ruff and S. Mugdan, ibid., 117, 147 (1921). (14) G. Rosenblatt, J . Electrochem. SOC.,110, 563 (1963). (15) W.Klemm, H.Spitzer, and H. Niermann, Agnm. Chem., 72, 985 (1963). (16) W. Klemm and H. Niermann, Agnew. Chem. Intern. Ed., 2, 623 (1963).
VAPORIZATION STUDIESON ARSENIC and Heyding." Similar problems arise, although on a more complicated scale, in studies on graphite. The present work was undertaken because the relatively few measurements of the vapor pressure were not in good agreement. Applying the third-law check to the vapor pressures selected in the two reviews mentioned above gave very temperature dependent heats of sublimation at 298.15"K. The two most obvious potential sources of difficulty are the presence of arsenic oxide as an impurity and the impossibility of attaining near-equilibrium conditions in an effusion system due to the low Condensation coefficient. Therefore, in addition to special care to remove oxide impurities from the eff usion-cell samples, confirmation was sought for the magnitude of the condensation coefficient by free-vaporization studies. From measurements of pressures using effusion cells with orifice diameters ranging from 0.005 to 0.040 in., the possible effect of a low condensation coefficient on the determination of vapor pressures by an effusion technique could be studied. Measurements of the effusion fluxes were made in CaF2, YZO3, and Al2O3 cylindrical cells. The freevaporization studies used TaC-coated graphite holders. A continuously monitoring device was used in conjunction with an electronic computer to evaluate these angular-displacement studies. Condensation-coefficient data were obtained from the results of the effusion and free-vaporization experiments and from an effusion cell made of sintered arsenic powder.
11. Experimental Section Materials. Arsenic, stated to be 99.999% pure with respect to to tal metallic impurities, was obtained in lump, crystalline, and powder forms. The first two forms were received in 25-g lots, and the powder was received in a 100-g lot. All were sealed under vacuum. The powder, on analysis, was found to contain S% by weight of oxygen. Before using the powder for the effusion measurements, oxygen was removed by a twostep process. Samples of the powder were mixed with zirconium powder which had been previously heated to 1000" under vacuum, -10-e torr. The mixture was sealed in a quartz cylinder 3 in. long and 2 in. in diameter which was provided along its axis with a 10-mm tube extending from within 0.25 in. of the cylinder to 6 in. below its base. Arsenic was distilled from the mixture at about 600°, and the distilled fraction was removed by sealing off the condensate tube. Further purification was accomplished by repeated sublimations in a split-tube furnace. The number of such sublimations depended on the amount of waxlike, light-yellow flakes of As203which appeared on quenching. X-Ray analysis of the flakes showed them to be primarily Asz03 with lesser amounts of an unidentified cubic phase. Because one section of the furnace was held at about 650" and the other section was some 100" cooler, the cubic phase may have been one of the solid
1103 arsenic phases reported to form on quenching from the vapor phase. The crystalline arsenic was subjected only to sublimation in the gradient furnace. One sublimation was usually sufficient for this material. For the free-vaporization experiments, 0.120 in. thick slices were initially cut from the lump material with a small diamond wheel. The slices were subsequently ground to 0.060-in. thickness on silicon carbide paper. Immediately prior to an experiment, any surface oxide present was removed with an 8. S. White dental unit. The arsenic effusion cell was fabricated from asreceived arsenic by first pressing a 1.5 X 1.5411. slug at 340" under 15,000 lb of pressure in a graphite die. The desired internal cell dimensions were then obtained by a combination of electrical and mechanical machining. Crucibles and Holders. Crucibles for this work, illustrated in Figure l, were slip cast from A1203,YzO~, and CaFz powders of at least 99.9% purity. Small orifices were drilled in the "green" state. The larger orifices were made with a diamond drill after firing. The oxide crucibles were fired in air a t 1750" for 16 hr, and the fluoride crucibles were fired a t 960" for 4 hr. Lids were ground and lapped to fit. Holders for the free-vaporization studies, shown in Figure 2, were fabricated from high-density graphite. The center section, mask, and screws were coated to a depth of 0.002 in. with TaC and heat treated to 1900°.18 Furnace-Torsion System. The furnace-torsion system has been described in an earlier report.19 Data-Taking Xystevi. Because a complete description of the continuously monitoring data-acquisition system has also been given elsewhere,20only a brief outline follows. The system is based on the properties of the ellipse. The mirror, sensing the angular displacement due to the vaporizing flux, is suspended inside the vacuum system at one focal point. A unifaced mirror rotating at 1800 rpm is located outside the vacuum system at the second focal point. A light beam reflected from the suspended mirror defines an angle 0, which is a measure of the angular position of interest. The beam is then reflected from an elliptical surface and, because of the properties of an ellipse, onto the rotating mirror at the second focal point and finally onto a photodiode. A second angle, cy, the one actually measured, is defined as the angle between a normal to the rotating mirror when that mirror sees the beam reflected from the ellipse and a reference line established (17) J. B. Taylor, S. L. Bennett, and R. D. Heyding, J. Phys. Chem. Solids, 26, 69 (1965). (18) M. Bowman, personal communication, Los Alamos Scientific
Laboratory, 1966. (19) C. C. Herrick, Trans. Met. Soc. A I M E , 230, 1439 (1964). (20) D. Peters and C. C. Herrick, Rev. Sci. Instrum., in print. Voltime 72,Number 4 April 1968
C. C. HERIICK AND ROYC. FEBER
1104
point standwd. For each calibration, about 5 g of zinc was cut into small chips and cleaned with a magnet while in a glove box filled with nitrogen. After was added to the cell, the lid was positioned and the cell was transferred to the torsion system. During this period, the apparatus was flushed with nitrogen gas first passed through a liquid nitrogen trap. The torsion system was then evacuated, heated to about 200", and allowed to stand overnight to permit cell oscillations to cease. A sequence of data points was obtained with increasine or decreasing temoeratures over the interval 425700°K. About 4-8 hr'was required to cover this temperature range. An analogous procedure was used for the arsenic measurements. The proxy thermocouple, which was shaped in the form of a fish hook, was calibrated by replacing the effusion cell with a dummy cell containing a standard Pt-Pt-lOyo Rh thermocouple previously calibrated against the freezing points of Sn, Zn, Al, and Ag. Furnace temperatures were on occasion increased beyond the experimental range to clean out the cells and redistribute condensed material to a cold zone of the furnace tube.
7
I
Figure 1. Ceramic effusion cells.
I
111. Calculations Because no effect of orifice size was detected in the torsion-effusion measurements, the process studied is assumed to be 4As(s, T , P) 2 % A s k , T,P)
(2)
k- >
Figure 2. Fresvaporization holders.
The process taking place in the free-vaporization studies was taken to be
by the reflection of a fixed beam from the rotating mirror onto a second photodiode. The magnitude of a is proportional to the time between the two pulses, which is measured by an electric counter. An integrating circuit is used to produce a voltage to operate a recorder and a digital voltmeter. The digital voltmeter readings are also punched on paper tape. The thermocouple voltage is simultaneously monitored by a recorder and punched on the tape. Records are made on the paper tape every 2 min. A measured angle, ai,is related to the corresponding angular position, Si, by the relation Si = arctan [-sin 2ai/(kl
+ kz cos 2ai)]
(1)
where kl = 2ae/b, kz = caa2/bz,a = semimajor axis = 10.250 in., b = semiminor axis = 7.125 in., e = (a' b2)"'. Procedure. Cells for the effusion experiments were cleaned before adding the samples by heating to 900" under vacuum, lo-' torr. They were calibrated by
l h e Jouiml of Physiml Chemiahy
4As(s, T , lo-' torr)
-%
Asl(g, T ,
torr)
(3)
We thus assumed that the primary subliming species in eq 3 is the tetramer. Data obtained from the studies of these processes were treated in two steps. First, data from the paper tapes were transferred to magnetic tape. As a part of this step, the data were plotted on an oscilloscope and bad points due to scanner failure in reading the paper tapes or due to worn hammers on the paper punch were given a weight of zero with a pen light. A modified version of a computer uroeram for a nonlinear least-sauares methodzL(hereafter referred to as a nonlinear analysis) was used to evaluate the data in its natural plane. The equation of Volmer describes the dependence of the pressure on the angular position.
. -
(4)
VAPORIZATION STUDIES ON ARSENIC
1105
where e, = ei when the vaporizing force is negligible, D = torsion constant of the wire = 2.899 dyn cm, a, = geometrical area of the j orifice, r j = lever arm of the j orifice,f, = transmittance of the j orifice. If it is assumed that the cell geometry is not affected by temperature over the experimental range, eq 4 can be written
pi =
w(ei - e,)
(5)
From thermodynamics the pressure is given by
P,
(6)
= exp( -AH,,zw’RT) exp(A(fef)/R)
where AHs,2g8is the heat of sublimation at 298.1.5”K, and A(fef) is the differencebetween a polynomial representing the free energy function of the products and one representing that of the reactants over the temperature range of the experiments. By combining eq 5 and 6 and substituting for Oi from eq 1, the following working relation is obtained.
ei
= arctan [--sin 2ai/(kl
+ lcz cos 2 4 1 =
K[exp(-AH,,zdRT f A(fef)lR)l
+
00
(7)
This relation contains the three parameters : K , AL\Hs02~s, and eo, and the two independent variables, temperature and A(fef). In principle, it should be posfiible to evaluate all three parameters from the effusion data for arsenic alone with a nonlinear analysis. However, to allow an unambiguous interpretation of data in a potentially nonequilibriuml situation, the parameter K was determined for esch cell by calibration with zinc. This, of course, is possible because K is a function only of the cell and its suspension. Calibration with zinc is appropriate because its vapor pressure is well established and measurements can be made over the same temperature range as that used with arsenic. The parameter K for the apparatus used in the freevaporization studies was determined by evaluating D with a known moment of inertia and measuring the orifice geometrical areas and lever arms. The area of the sample was taken to be the geometrical area, and f was assumed to be unity. The derivation of thermodynamic data from the experimental observations could proceed by several alternate techniques. 1. Either the angular-position differences, Bi - 00, or their vapor pressure equivalents as determined by calibration of the apparatus may be transformed to the logarithmic plane and plotted against reciprocal temperature. From the slope at each point a second-law heat of sublimation at temperature may be determined, although over moderate temperature ranges which do not include any phase changes in the condensed phase the plot is cominonly a straight line within the precision of the measurements. If pressures are used and heat capacity equations for the reactants and products are available, a 2 calculation may be used to produce a
straight-line plot for those systems for which a plot of log p us. 1/T is curved. 2. If absolute entropies are known and the experimental data expressed as pressures are transformed to the logarithmic plane, two additional procedures can be used. (a) With appropriate free-energy functions, values of AHsozg8may be calculated for each experimental point and an average taken of all of these values. This procedure is usually referred to as the third-law method. If only a few experimental points with relatively large scatter are available, it may be the only practicable procedure. The third-law method may be expressed as -R In p
+ A(fef) = AHs,298/T
(8)
Thus the method may be regarded as a plot of the lefthand side of eq 8 us. 1/T, and the individual values of AHs,29~ as slopes of lines between individual experimental points and the origin. This constraint limits the sensitivity of the method as an internal check on the reliability of the experimental data. Such a check is frequently sought from the agreement between third-law values from various investigations or from the agreement between second- and third-law values of a particular investigation. (b) Another procedure, which has been called the “slope-third-law” method,1gmay be used to provide an internal check of data reliability. This procedure, which removes the constraint noted above in the usual third-law method, is formulated by assuming that the uncertainty of an observed pressure may be expressed as Pequil
=
(9)
ZPosIcd
In the logarithmic plane, eq 6 then becomes
- R In Pcalcd
+ A(fef)
= AH,,zes/T
4- R In z (10)
A single value of AHs,zs~ will be obtained from the slope of a plot of the left-hand side of eq 10 us. 1/T. If the free-energy functions are reliable, a constant deviation of x from unity will indicate a constant systematic error in Pcalcd. In such a situation AHs,298 will correspond to a second-law heat and R In x will be the difference between calculated and observed entropies of vaporization. If R In x is 0, second- and third-law values are identical. The value Zn(s) = 31.204 kcal/mol was derived from a slope-third-law analysis of vapor pressure data in the literature. The free-energy functions used were essentially the same as those tabulated by Hultgren, et aLZ1 3. A nonlinear regression analysis2l-Z9may be used (22) T. G . Strand, D.A. Kohl, and R. A. Bonham, J. Chem. Phys., 39, 1307 (1963). (23) N. R. Draper and H. Smith, “Applied Regression Analysis,” John Wiley and Sons Inc., New York, N. Y., 1966,Chapter 10.
Volume 72,Number 4
April 1068
1106
C. C. HERRICK AND ROYC. BEBER
to fit observed angular positions in their natura1 plane to the relation defined by eq 7. As noted above, one has the option of deriving the three parameters: K , AHs,293, and eo, or previously evaluating K by calibration with a material of known vapor pressure. It should be noted that in the other procedures the selection of Bo is likely to be somewhat subjective, but it is maintained as a parameter in the nonlinear analysis. We chose to apply a nonlinear analysis to the vapor pressure data for arsenic. The choice was dictated by the fact that the uncertainty in the experimental observables, 6i is additive, whereas if the observables had been transformed to the logarithmic plane, the uncertainties would have been assumed to be niultiplicative. The two approaches may or may not give the same values for the thermodynamic parameters, depending on how well the data fit the assumed functional representation. McWilliams, Furchner, and Richmond24 have illustrated some situations in which the distinction is not trivial. Because in the present situation the measurement extends to relatively small values of Bi - eo, the data are most appropriately treated by insisting on the additivity of uncertainties. Thus for both the effusion and free-vaporization data, two parameters were optimized by the nonlinear analysis. Error analysis was as described by Moore and Zeigler.21 The thermodynamic functions for solid arsenic given in Table I are slightly different from those given by Stull and Sinke6 and Hultgren, et Most of the
Table I : Thermodynamic Functions for Solid Arsenic' -(Cor Temp, OK
298.15 300.00 310.00 320.00 330.00 340.00 350.00 400.00 450.00 500.00 550.00 600.00 650.00 700.00 750.00 800.00 850.00 900.00 950 00 1000.00 1050.00 1090.00 I
a
H O T
-
H ' ~ ~ . ~ ~ / HT% .,l s , kcal cal/gfw/ deg
gfw
8.534 8.534 8.539 8.549 8.564 8.583 8.607 8.768 8.979 9.215 9.465 9.721 9.978 10.234 10.486 10.734 10.977 11.215 11.448 11.675 11.897 12.071
0.000 0.011 0.070 0.129 0.189 0.249 0,309 0.611 0.916 1.224 1 536 1.851 2.169 2.491 2.816 3.144 3.478 3.811 4.149 4.491 4.835 5.114 I
Hazss.16 - H o o = 1.223 cal/gfw.
The Journal of Physical Chemistry
SOT,
(;"P!
cal/gfw deg
cal/gfw deg
8.534 8.571 8.764 8.953 9.137 9.315 9.489 10.295 11.013 11.664 12.258 12.806 13.316 13.792 14.240 14.664 15.067 15.449 15.815 16.166 16.502 16.762
5.892 5.896 5.930 5 956 5.975 5.989 6.002 6.068 6.135 6.201 6.268 6.334 6.400 6.466 6.533 6.599 6.666 6.732 6.798 6.865 6.931 6.984
difference is due to the value SozssAs(s) = 8.534 eu calculated from the low-temperature heat-capacity data of Anderson (57 - 291°K)26and the recent data of Nogteva, Paukov, and Strelkov (13.9-289°K) .27 I n addition to the older data, thermodynamic functions for the solid above 298.15"K take into account the hightemperature heat-content data of Klemm, Spitzer, and Niermann.'s The regular tetrahedral structure of As4(g) has been recently confirmed by the gas electron-diffraction studies of Morino, Ukaji, and I ~ O who , ~have ~ given a more accurate value of the interatomic distance than previously available. From their values of the mean amplitude and the anharmonicity parameter, they estimated vibrational frequencies. The estimated frequencies have been used to calculate the thermodynamic functions for As4(g)given in Table 11. The uncertainty in free-energy functions corresponding to the uncertainties in the estimated frequencies is h1.3 eu. The calculated value of XozgsAs4(g) is some 3.8 eu greater than that tabulated by Stull and Sinke6 and Table I1 : Thermodynamic Functions for Asl(g)" --(GOT
-
H ' Z D 8 . 16)
/ T,
H O T
S O T ,
COP,
gfw
oal/gfw deg
cal/gfw deg
0.000 0.034 0.971 1.921 2.881 3.847 4.818 5.792 6.770 7.749 8.731 9.714 10.698 11.683 12.670 13.656 14.644 15.632 16.620 17.609 18.599 19.588
78.834 78.948 81.836 84.373 86.633 88.668 90.519 92.215 93.780 95.232 96,586 97 855 99.048 100,175 101.241 102,253 103.217 104.136 105.015 105.857 106.665 107.441
18.546 18.561 18.887 19.107 19.261 19.374 19.458 19.522 19.573 19.614 19.646 19.673 19.696 19.715 19.730 19.744 19.756 19.766 19.775 19.783 19.790 19.796
kcal/
OK
cal/gfw deg
298.15 300.00 350.00 400.00 450.00 500.00 550.00 600.00 650.00 700.00 750.00 800.00 850.00 900.00 950.00 1000.00 1050.00 1100.00 1150.00 1200.00 1250.00 1300.00
78.834 78.834 79.061 79.570 80,231 80 975 81.760 82.561 83.365 84.161 84.945 85.713 86.462 87.193 87.905 88.597 89.270 89.926 90.563 91,182 91.786 92.373
Temp,
I
-
HOzos.is,
I
(24) P. McWilliams, et al., Health Phys., 10, 817 (1964). (25) R. Hultgren, et al., "Selected Values of Thermodynamic Properties of Metals and Alloys, John Wiley and Sons, Inc., New York, N. Y., 1963, and subsequent loose leaf revisions and additions. (26) C . T. Anderson. J . Amer. Chem. SOC.,5 2 , 2296 (1930). (27) V. V. Nogteva, I. E. Paukov, and P. G. Strelkov, Soviet Phys.Solid State, 7 , 1884 (1965). (28) Y. Morino, T. Ukaji, and T. Ito, Bull. Chem. SOC.Jap., 39, 71 (1966).
VAPORIZATION STUDIES ON ARSENIC
1107 accounts for about one-half of the difference between the standard heat of sublimation reported here and that given by Stull and Sinke6 or Hultgren, et ~ 1 . ~
IV. Results and Discussion The results of our experiments using effusion cells
d
Y
are contained in Table 111. I n the second column the crucible material and diameter, in inches, of an individual orifice are presented. The fifth column indicates Bo, the arbitrary initial, angular position, and since it like ALHs,298 is a parameter, the standard devirtr tions are also listed. A negative value occurs when the initial position of the light beam lies to the right of the major axis of the ellipse and the cell direction is clockwise. The next to the last column contains the weighted variance, which was computed from the individual variances. These values were required to assure us that the points with the largest variances will have the least influence on the final f i t . 2 l The weighted variance can be looked upon as an average deviation of a data point. The final column lists the total sum of the squares of the deviations. With the large number of data points taken, the reliability of the data can be judged from the indices. Figure 3 illustrates the result given in Table IV as run no. 3. The solid line is the best fit. Figures 4 and 5 illustrate a slope-third law (AHs,298= 38,597) and a Clausius-Clayperon ( A H = 36.467 k 0.241) plot utilizing the data of run no. 7. In order to obtain meaningful results with these types of plots, it is essential that the smallest angular position difference be sufficiently large that experimental uncertainties do not produce a tailing off of the data. Such a tailing off results when the data shown in Figure 3 are plotted as djff erences. Table IV : Comparison of Effusion and Free-Vaporization Pressures P i r e e vaporization/ Peifusion
4
n
m
523.5 531.6 540.0 550.4 560.9 570.6 580.2 590.3
9.22 x 1.04 x 1.14 x 1.28 x 1.45 x 1.63 x 1.83 X 2.01 x
10-4 10-3 10-3 10-3 10-3 10-3 10-3 10-3
e We were unable t o distinguish any meaningful variation due to orifice area, nor were we able to find evidence for the development of sample porosity. An attempt was made to find a dependence on evaporating surface area. For this purpose two resublimed samples were used. The first sample was condensed at 550" and formed a single piece with many crystalline facets Volume 72, Number 4
April 1968
~
1108
C. C. HERRICK AND ROYC. FEBER
Figure 3. Angular displacement of arsenic.
Figure 5. Second-law plot for arsenic.
(run no. 2). The second sample (run no. 4) was condensed at room temperature and produced a thin tube which was easily crumbled into tiny fragments of large surface area. Standard heats of sublimation for these two samples, calculated from data taken in a YZOscell of 0.020-in. orifice diameter, were 38,555 and 38,536 cal/mol, respectively. Figure 6 illustrates the results of a free-vaporization experiment with 3/8-in. masks and a counterclockwise rotation. A prior experiment was made with 0.25-in. masks and a clockwise rotation. The combination of experiments should minimize any effect due to imperfections in the mirrors. I n the experiment with the 0.25-in. masks we found a “knee” in the angular position a t about 600°K with increasing temperature and a “spike” at the same temperature with decreasing temperature. I n the experiment with the masks
only the spike with decreasing temperature was observed. Although the cause for the gross effect is not known, the different character with increasing and decreasing temperature is probably due to a change in the product of the condensation coefficient times the area of the vaporizing surface. During the course of the second experiment, a small portion of the sample was placed at one end of an evacuated quartz tube, and the temperature was increased at the same rate as in the angular-displacement experiment. The other end of the quartz tube was at room temperature. Thermal etching was not noticeable to the naked eye until the highest temperature was reached, at which point a dendrite-like surface became evident. A quantitative analysis of the free-vaporization experiments is complicated by the appearance of the knees or spikes. However, an analysis which treated
The Journal of Physical Chemistry
1109
VAPORIZATION STUDIESON ARSENIC portions of the results separately gave the values 44,048 and 44,228 cal/mol for the heat of sublimation to Asd(g). This is in agreement with a previously reported result of 43 f 3 kcal/mol obtained from Langmuir ~ t u d i e s . ~ The free-vaporization samples were removed from the TaC holder and run in an Ale03 effusion cell. The ratios of the free-vaporization pressures to the effusion cell pressures are given in Table IV. A simple demonstration of the existence of a condensation coefficient for arsenic can be made by constructing an effusion cell of the vaporizing material. This type of experiment has been previously made by WesseLZ9 Unfortunately, the arsenic cell, constructed as described above, was fabricated before the large amount of oxide impurity in the powder was known. Although the temperature and reducing conditions would reduce the oxygen content, exposure during the machining operations would tend to increase it. For an uncontaminated cell of this type, the freevaporization relation for the external exposed surfaces is
p1 = K1’(el - e,)
L
(1 1)
I
For the contribution from the interior surfaces p Z = &’(ez
- e,)
0
(12) -I
If Pz can be equated to Pep, the condensation coefficient becomes
-2
CY
=
P1/Pe,
N
PlIP2
(13)
The symmetry of the cell permits the angular displacement to be written as
-E
-
-3
-4
P
(14)
9
-5
-6
If the condensation coefficient, CY, is unity, the angular displacement is zero. The results of this experiment are shown in Figuire 7, in which only points for increasing temperature are plotted. Large oscillations terminated th2 run a t about 600°K, the same temperature a t which knees or spikes were observed in the free-vaporization experiments. Although the almost certain presence of oxide limits the conclusions that can be drawn, the observation of an angular displacement is taken to confirm the existence of a small condensation
-7
-8
-9
-10
-11
-I2 0
Table V : Vaporization Studies on Arsenic (Selected Data) 7 -
Temp, OK
300 400 500 600 700 800
Stiill and Binke
8.28 X 1.43 x 6.98 X 1.77 X 8.67 x 1.47 x
10-17 10-lo 10-7 10-8 10-1
Vapor pressure, atmNesmeyanov
This work
1.72 x 1O-lo 8.20 X 10-7 2.01 x 9.57 x 1.59 x 10-l
4.92 x 10-19 4.65 x 10-18 6 . 2 4 X 10-8 3.22 x 10-6 2.60 x 10-8 6.61 x lo-*
IO
12
14
16
18
20
22
24
26
io4n Figure 8. Vapor pressure of arsenic: A, Ruff and Bergdall; V, Ruff and Mugdan; H, Preuner and Grockmoller; 0, Weichmann and Heimburg; 0 , Gibson; 0, Horbia; 0, Nesmeyanov; -, these authors.
coefficient. Visual inspection of the cell showed the surface to be porous. (29)
G . Wessel, 2.Phu8., 130, 639 (1961). Volume 78,Number 4
A p Q 1068
1110 The vapor pressures selected by Nesmeyanov2 and Stull and Sinkee and those selected from this study are listed in Table V. The results obtained in this study and the experimental results of previous investigators are plotted in Figure 8. If conventional third-law calculations are made using the data of individual investigations directly, temperature dependencies of the standard heats of sublimation are found from the data of Weichmann and Heimburga0 and Preuner and Brockmoller.’ The data of Ruff and Mugdanla do not show such a dependence. Both the data of Horbita31 and the experiments of Kesmeyanov2have a temperature dependence, mostly at low pressures. It is clear that the data of Ruff and Mugdan, the authors, and most of the data of Horbita along with the experimental data of Nesmeyanov, form a consistent set. Because four different experimental techniques are represented : boiling point, static, Knudsen effusion, and torsion-effusion, the consistency is quite satisfying. The use of effusion for the determination of the vapor pressure of arsenic has been justifiably questioned by Nesmeyanov.2 The problem of molecular flow from a torsion-eff usion cell, in which the vaporizing surface cannot “see” outside the cell, has not yet been solved.a2 Such a solution would enable one to predict cell dimensions necessary to obtain near-equilibrium conditions within the effusion cell. As a first approximation, the relation of Rossman and Yarwoodaafor the coaxial-effusion case may be applied to the present situation. We write
where S is the area of the vaporizing surface and the other quantities have their previously assigned mean-
The Journal of Physical Chemistrv
C.C. HERRICK AND ROYC. FEBER ings. S is calculated from the internal diameter of the cells, or 1.5 in., a! is taken from Table 111, and f, is from the results of a Monte Carlo calculation,a4 e.g., 0.1094 for a cell with a 0.020-in. orifice. The expected ratios of pressures then become 1.00, 1.07, and 1.54 for cells with orifice diameters of 0.005,0.020, and 0.040 in., respectively. Because no dependence on orifice diameter was observed experimentally, the use of eq 15 may be questionable. Its application here involves the assumptions that the cells may be considered spherical, that the condensation coefficient is independent of pressure, and that the geometrical area is equal to the area of the vaporizing surface. The first assumption is probably reasonable, the second is suspect, the third is likely to be valid only for liquids or a solid for which faceting is unimportant. Also, samples prepared under varying conditions could have different vaporization-condensation rates.
V. Conclusions The experimental results of this study confirm the existence of a small condensation coefficient for the sublimation of polycrystalline arsenic. A standard heat of sublimation at 298.15OK of 38.540 f 0.100 kcal/mol of As4(g) was selected for arsenic samples prepared by resublimation. This value is consistent with some, but not all, of the previous investigations using boiling point, static, and Knudsen effusion techniques. (30) F. Weichmann and M. Heimburg, 2. Anorg. Chem., 240, 129 (1938). (31) 8. Horbita, 2.Phys. C h m . (Leipseig), 106, 295 (1923). (32) V. I. Losgachev, Soviet Phys.-Tech. Phys., 7, 827 (1963). (33) M. G. Rossman and J. Yerwood, J . Chem. Phys., 21, 1406 (1953) (34) M. Fraser, R. C. Feber, and C. C. Herrick, Regional Meeting, American Chemical Society, Albuquerque, N, M., Dec 1966. I
