NOTES
4044
x = k/PC, t Time Y Defined in eq. 7 w Angular velocity 6 Boundary layer thickness for thermal diffusion Boundary layer thickness for ordinary diffusion Acknowledgment. It is a pleasure to acknowledge assistance to this work from the Office of Naval Research (Contract Nonr-285-37 with New York University).
The Vapor Pressure and Heat of Sublimation of Chromium by D. S. Dickson,' J. R. Myers, and R. K. Saxer Department of Mechanics, Air Force Institute of Technology, Wright-Patterson AFB, Ohio (Received June 11, 1966)
A number of references describing the vapor pressure of solid chromium appear in the literature. These data were determined by a variety of techniques and are in fairly good agreement with the results of this investigation; however, the temperature ranges covered by previous investigators did not exceed 1675°K. The vapor pressures determined during this study by means of the Knudsen effusion technique included the temperature range 1560-1800°K. Because hightemperature vapor pressure data are lacking, it was considered that the results obtained during this study were significant.
Experimental Section Equipment and Procedure. The Knudsen method developed by means of statistical thermodynamics and kinetic theory postulates that the rate of effusion of a gas through an orifice into a high vacuum is related to the vapor pressure above the metal. The rate of effusion is related to the vapor pressure of the metal by the expression -,
At
I-
- m2.258 X 1 0 - z dTn
(1)
In these expressions, P is the vapor pressure in atmospheres, W is weight loss in grams during the effusion time interval, A is orifice area in square centimeters, t is effusion time in seconds, R is the universal gas constant, T is absolute temperature in OK., M is the molecular weight of the metal, and m is the effusion rate in grams per second per square centimeter. The Journal of Physical Chemistry
It is assumed in the above expressions that the orifice is ideal ( i e . , infinite thinness). In actual practice, the orifice does have measurable thickness and approximates a short tube or channel. Speiser2 has given equations to correct for this condition. The need for correction factors was avoided in this work by reaming the orifice to a knife-edge of 30" included angle. Calculations based on Ba1son1s3 derivation showed the orifice to be nearly ideal. The vacuum chamber used was fabricated from a 7in. diameter brass cylinder which measured 13 in. high. Copper tubing was used to circulate coolant water around the chamber and through hollow electrode leads to the resistance furnace. A mechanical forepump and an oil diffusion pump were used to create an operating vacuum of at least loF6 mm. A liquid nitrogen trap prevented water and oil vapor in the diffusion pump from reaching the vacuum chamber. Operating temperatures were obtained with a wound, resistance-type, tungsten-wire furnace surrounded by three cylindrical tantalum heat shields. Power was supplied to the furnace by means of a constant-voltage transformer. The Knudsen cells which contained the samples were fabricated from seamless tantalum tubing of 1-in. outside diameter and 0.020-in. wall thickness; cell bases and covers were formed from 0.010-in. thick tantalum sheet and welded in an argon atmosphere to the cells. A Leeds and Northrup disappearing-filament type optical pyrometer, calibrated against a Xational Bureau of Standards pyrometer by means of a standard tungsten ribbon filament lamp, was used to determine temperatures. The calibration was performed with the glass viewport in place to avoid corrections for window transmissibility. All temperature measurements were made at the orifice of the cell, which closely approximated blackbody conditions and eliminated the need for emissivity corrections. Effective times at temperature were calculated to compensate for heating and cooling periods. The effective time was calculated from the equation t e f f = ZAt,[e- A H v / R T A + A H ~ / R T R
1
(2) where At1 is the time interval between any two temperatures, TA is the average temperature during that interval, TR is the temperature of the test, and AHv is the heat of vaporization of chromium in calories per (1) Submitted in partial fulfillment of the requirements for the degree of Master of Science. (2) R. Speiser, "Vapor Pressure of Metals," Engineering Experiment Station, The Ohio State University, Columbus, Ohio, Vol. 19, No. 5. 1947, p. 12. (3) E. W. Balson, J . Phys. Chem., 6 5 , 1151 (1961).
KOTES
4045
gram-atom. An initial value for AH., of 91.0 kcal./ g.-atom was obtained from H ~ l t g r e n . ~Measurements of experimental data were made to the following accuracy: weight loss to within *0.05 mg., time to within =k60 see., temperature to within f4', and orifice area to within =kO.OOl Orifice dimensions were corrected to account for the thermal expansion5 of the tantalum cell cover. Specimen analysis is given in Table I.
Table 11: Vapor Pressure of Pure Solid Chromium
1 2 3 4 5 6 7
8 Table I : Chromium Specimen Analysis Element
Wt. %
Fe
0.008 0.007 0.005 0.003 0.015 0.0003 0.010 Balance
S C Si 0 H ?u'
Cr
Time, sec.
Wt. loss,
OK.
g.
Orifice area, cm.2
1559 1582 1602 1607 1624 1624 1648 1682 1704 1710 1718 1736 1750 1790 1805
20420 14100 16010 7390 13900 16500 8810 10740 6950 8690 7910 4530 8480 5190 6190
0.0059 0.0054 0.0104 0.0058 0.0136 0.0152 0.0150 0.0384 0.0251 0.0380 0.0504 0.0299 0.0859 0.0796 0.1186
0.0256 0.0256 0.0219 0.0257 0.0219 0.0257 0.0257 0.0257 0.0210 0.0263 0.0257 0.0210 0.0257 0.0262 0.0257
Temp., Test
9 10 11 12 13 14 15
Pressure, atm.
1.4 x 1.9 X 3.71 X 3.9 X 5.63 X 4.90 x 8.71 X 1.84 X 2.12 X 2.19 X 1.51 X 3.91 X 5.15 X 7.75 X 1.02 X
10-6 lo4 loh6 loW5 loh5
lo-&
Table 111: Heat of Vaporization of Chromium at Absolute Zero
The vapor pressure of solid chromium in the temperature range 1560 to 1800"1
