NOTES
311
12
+ + O(X8Mw8)] (16)
h 2 (h 4-1)2
In these equations h is a parameter which characterizes the relative spread of the Schulz distribution; thus, for a monodisperse solute, h -+ m ; for an extremely broad distribution, h -+ 0; and for the most probable distribution where M,/M, = 2 ( M , is the number-average molecular weight), h = 1. By way of an example we consider the case in which AM, = 1and h = 1. Equ* tions 14-16 then yield A1 = 0.055, A2 = 0.437, and AS = 0.213. These values give not only the relative order of the three measures of deviation but also something about their absolute values. Finally, we wish to point out that thermodynamic nonideality of the solution generally acts to lessen the magnitudes of AI, A2, and AS. Thus, for In c us. 3, the plot may happen to be substantially linear over the entire range of IG despite the fact that the solute is quite heterogeneous. It is advisable, therefore, that sufficient caution be taken when information about solute homogeneity is derived from this plot. Acknowledgment. This investigation was supported by Grant GB 3321 from the Molecular Biology Section, National Science Foundation, and by Grant DAORD-11 from the U. S. Army Research Office.
The Vapor Pressure of Rhenium1 by Paul E. Blackburn Arthur D . Little, Inc., Cambridge, Massachusetts O$?l/tO (Received Auoust 8.. 1966) -
The nlelting point of rhenium (mp 3180”)z is exceeded, among the metals, only by that of tungsten. It has one of the lowest vapor pressures, with only tantalum and tungsten vaporizing at a lower rate. possesses especially good Neither Of these latter resistance to attack by oxides. Tantalum is the more reducing of the two, dissolving oxygen and f o k g TaO(g) at high temperatures when used as a container for Oxides* tungsten is better than tantalum, volatile oxides, WOZ and WOa, and mixed tungsten oxides are formed. Rhenium is more noble, the presence of stable oxides. being relatively inert and for estimated JANAF4 values for WOZ, we find that at 2000’K a
given oxide in contact with rhenium will produce a pressure of ReOz(g) 20 to 20,000 times lower than the WOz pressure produced with the same oxide in contact with tungsten. (The spread in relative pressures is due to uncertainties in estimates for ReOz(g).) For these reasons, rhenium is particularly well suited as a container for refractory oxides. It should be better than tungsten for crystal growing. We have used it for vapor pressure studies of BeO(c), A.hOa(l and e), and Si02(l).6 It has been found to give satisfactory results, with no detectable loss of rhenium oxides. Only one study of rhenium vapor pressure has been found in the literature. Sherwood, Rosenbaum, Blocher, and Campbell6 measured the evaporation rate of a 50-mil filament prepared in their laboratory, using emissivity measurements of Sims, Craighead, and Jaffee’ to correct the brightness temperatures. No analysis was given for the sample material, although the results obtained indicated the absence of volatile to torr impurities. Pressures of the order of were maintained in their apparatus during the measurements. Since high purity rhenium is now available and better vacuums are readily attained, it was thought desirable to remeasure the pressure of rhenium.
Experimental Section Apparatus. The apparatus consisted of a stainless steel vacuum system with internal work coil and vacuun balance. All openings were sealed with gold or copper gaskets and the work coil leads were brought into the furnace with Varian radiofrequency feedthroughs. Temperature was measured with a Leeds and Northrup optical pyrometer by sighting through a window in the side of the furnace between turns in the work coil into a blackbody hole. The pyrometer was calibrated with a standard lamp and corrections were made for window adsorption. Power from the 20kw Westinghouse generator was controlled with a pickup coil, C.A.T. controller, magnetic amplifier, and saturable reactor. Temperature was constant to *2’. (1) This work was supported by the U. 9. Air Force Office of Scientific Research under Contract No, AF 49(638)-1171, ARPA Order No. 315-62. (2) D. R.,?tull and G. C. Sinke, “Thermodynamic Properties of the Elements, American Chemical Society, Washington, D. C., 1956. (3) L. Brewer and G. M. Rosenblatt, Chem. Rev., 61, 257 (1961). (4) “ JANAF Thermochemical Tables,” Thermal Laboratory, The DOW Chemical CO., Midland, Mich. (5) To be published. (6) E. M. Sherwood, D. M. Rosenbaum, J. M. Blocher, Jr., and I. E. Campbell, J . Electrochem. SOC.,102, 660 (1955). (7) C. T.Sims, C. M. Craighead, and R. I. Jaffee, Trans. A.I.M.E., 203, 168 (1955).
Volume 70,Number 1 January 1966
NOTEB
312
The automatic null recording vacuum microbalance designed by Cochran8was used to measure the weight gain of a glass cover slide target suspended over the sample. The fraction of vapor sticking to the target was determined by weighing sample and target before and after a series of measurements. Sample. The sample consisted of a hollow cylinder and lid 1.11 ern in diameter and 1.85 cm high. A hole was drilled in the side for temperature measurements. The sample was fabricated by spark gap machining a cylindrical bar of high purity (99.97%) rhenium, obtained from the Rembar Co. The principal impurities as determined by the supplier were in (ppm): Fe, 70; Mo, 25; C, 20; N, 10; and 0,40.
Results and Discussion The 24-g sample was degassed, and lost 55 mg before the experiments began. Pressures in the system were usually in the lo-' to torr range, never greater than 3 X torr. The data are summarized in Table I. Heats of vaporization in Table I1 were calculated using Stull and Sinke's free energy functions for the solid and gas. The average heat at 298'K is 184.5 1.5 kcal/g-atom, which agrees very well with the study on rhenium by Sherwood, et aL6 These authors found AHozss = 185.7 f 1.0 kcal/g-atom (recalculated with Stull and Sinke's free energy functions). Sherwood measured the evaporation rate of a rhenium filament using an optical pyrometer and Sims' emissivity data' for rhenium to determine temperature. An earlier measurement of emissivity at 2800' by Levi and Espersenefalls on Sims'curve, which covers a wide temperature range. A more recent study by MarplelO gives higher emissivities than those of Sims in the temperature range where Sherwood's vapor pressure measurements were made. Using Marple's emissivities decreases Sherwood's temperatures by an average of 20' and yields a heat of vaporization 1.3 kcal lower, AHozes = 184.4 f 1.0 kcal/gatom, practically identical with our value of 184.5 f 1.5 kcal/g-atom. The present data are scattered and exhibit a trend with temperature. The trend would appear to be due to thermal gradients in the sample, perhaps as high as
*
A
Table I: Vapor Pressure of Rhenium
Time,
Evap rate,b g-cm-e
Target gain, Irg
Sample loss," mg
sea-1 X 107
Atm X
O K
8ec X 10-8
2694 2731 2768 2787 2821 2847 2877 2905
9.00 4.20 4.20 4.80 6.00 3.60 3.00 3.00
50 30 38 60 80 50 60 110
40.0 24.0 30.4 48.0 64.0 40.0 48.0 88.0
5.28 6.78 8.59 11.9 12.6 13.2 19.0 34.0
4.53 5.86 7.47 10.3 11.1 11.7 16.8 31.1
T,
108
" Fraction of total evaporated metal condensed on target is 1.25 x 10-8. Sample area = 8.42 cm2.
Table IT: Heat of Vaporization of Rhenium AHOzas,
T,OK
- R In P , OaVdeg
csl/deg
kcal/gstom
2694 2731 2768 2787 2821 2847 2877 2905
33.62 33.09 32.61 31.97 31.82 31.72 31.00 29.78
33.97 33.94 33.91 33.89 33.86 33.84 33.82 33.80
182.1 183.1 184.1 183.6 185.3 186.6 186.5 184.7
-AM,
-
Av 184.5 f 1 . 5
50' between the lid and the base. Since Sherwood's data fail to show a temperature trend, and since both his and our data are in good agreement, the pressures and free energy functions are apparently reasonably accurate.
Acknowledgment. We wish to express our appreciation to John T. Larson for assisting in the measurements. (8) C. N. Coohran, Rev. SC~. 1'7&8tT., 29, 1135 (1958). (9) R. Levi asd G. Espersen, Phys. Rev., 78, 231 (1950). (10) D.F. T.Marple, J. Opt. SOC.Am., 46,490 (1956).
