Vapor Pressure of MolybdenumP. A. Vozzella, A. D. Miller, and M. A. DeCrescente Citation: The Journal of Chemical Physics 41, 589 (1964); doi: 10.1063/1.1725929 View online: http://dx.doi.org/10.1063/1.1725929 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/41/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Bifacial solar cell with SnS absorber by vapor transport deposition Appl. Phys. Lett. 105, 173904 (2014); 10.1063/1.4898092 On vapor shielding of dust grains of iron, molybdenum, and tungsten in fusion plasmas Phys. Plasmas 21, 024501 (2014); 10.1063/1.4866599 Atom insertion into grain boundaries and stress generation in physically vapor deposited films Appl. Phys. Lett. 103, 051910 (2013); 10.1063/1.4817669 Yield strength of molybdenum at high pressures Rev. Sci. Instrum. 78, 073906 (2007); 10.1063/1.2758549 Processing tungsten single crystal by chemical vapor deposition AIP Conf. Proc. 504, 1454 (2000); 10.1063/1.1290965

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LETTERS TO THE EDITOR 589

molecular orbitals in the density p=2I>Pk2 which fur­nish nonvanishing contributions to the integral in Eq. (2) are the bond orbitals CPI, CP2, CPa which point to the hydrogen atoms HI, H 2, Ha. These bond orbitals are, however, independent of e. In this particular case, Eq. (2) can therefore be integrated to give

This quasielectrostatic energy expression differs from the one usually intuitively considered by the absence of electron repulsion terms.

The first term in the parenthesis yields the nuclear term .1 V nn used in Eq. (1). It is obvious tha t, because of the large distance between the bond orbital CPI and the nuclei 4, 5, 6, the second term in the parenthesis has the same character (but opposite sigp.) as the first, and hence will have the result of attenuating the magnitude of the total effect. This can be seen by the following estimate.

We replace the spatial charge distribution cpl2 by a linear charge distribution of constant density along the bond axis from C to HI. With this simplification one obtains for the integral in the case of ethane

(4)

where x is the linear coordinate along the CHI bond axis, rk(x) is the distance of the corresponding point on the bond axis from the hydrogen atom H k , and Lis the CH bond length. The reduction by the factor 0.36 arises of course because the charges closer to the C-C axis give rise to smaller energy differences upon rotation than the charges close to the H atom. Although the total result obtained by our crude integral approximation is too small, viz.,

.1E=0.28.1 V nn, (5)

it is to be expected that, for the same qualitative reasons, the actual integral in Eq. (3) will also be smaller than the corresponding nuclear term, and per­haps more so [a reduction factor of 0.2 in Eq. (4) gives the correct result of Eq. (1)]. It seems unlikely that the slight expansion of the orbitals occurring in ac­cordance with the virial theorem would seriously change the value of the integral. A more accurate evaluation of the integral will be given elsewhere.

The author acknowledges the stimulation by a pre­print of R. G. Parr, dealing with the internal rotation problem by means of a new "Theorem Governing Changes in Molecular Conformation,"4 and by an ear­lier discussion with Professor J. Richardson at Purdue University who had independently derived a slightly more general theorem,5 though not applied to the hin-

dered rotation problem. The author has also profited from discussions with Professor R. G. Parr.

* Work supported by the National Science Foundation Grant Number GP 129.

1 M. Karplus and R. G. Parr, J. Chern. Phys. 38,1547 (1963). 2 H. Hellmann, Quantenchemie (Fra.nz Deuticke, Leipzig,

Germany, 1937); R. P. Feynmann, Phys. Rev. 56, 340 (1939). 3 C. Edmiston and K. Ruedenberg, Rev. Mod. Phys. 35, 457

(1963) . 4 R. G. Parr, J. Chern. Phys (to be published). 5 J. W. Richardson, J. Chern. Phys. (to be published).

Vapor Pressure of Molybdenum * P. A. VOZZELLA, A. D. MILLER, AND M. A. DECRESCENTE

Pratt is' Whitney Aircraft, Division of United Aircraft Corporation CANEL, Middletown, Connecticut

(Received 4 March 1964)

THE vapor pressure of molybdenum was determined over the temperature interval 2140° to 2535°K

using a modified Langmuir apparatus constructed for the purpose of investigating the thermal decomposition of high-temperature materials. Molybdenum was studied because its vapor pressure is measurable in the temperature range of interest (2000° to 25000 K) and a comparison could be made with data available from two independent laboratories. Since publication of a formal report concerning molybdenum is not anticipated, these data are presented here to add further support to the reliability of molybdenum vapor pressure data.

The apparatus, shown schematically in Fig. 1, was evacuated by means of a 75-liter/sec ion pump to 10-8-10-7 Torr at all temperatures. The sample was suspended from a molybdenum wire which in turn was attached to one pan of an automatic recording, semi­micro vacuum balance by a 1-mm-diam quartz rod. Temperature measurements were made with a cali­brated optical pyrometer sighted on a 0.063-in.-diamX 0.625-in.-deep blackbody hole drilled in the center of the

VAClJUI..1 BALANCE QUARTZ ROD

SPECIMEN SHIELDS-.::::=H/,-,...j

=c:J=jl OPTCAL

PYROMETER

RECORDER

FIG. 1. Schematic of Langmuir vaporization apparatus.

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590 LETTERS TO THE EDITOR

TABLE I. Molybdenum weight-loss data.

Rate of

Run Temp. Weight Joss Time evaporation

Average gcm-1 Pressure No. oK gXIQ3 secXlO-a area cm2 sec1X107 atmX107

7 2141 0.94 6.60 8 2259 5.38 6.90 2 2261 1.24 1.80 6 2286 4.18 3.60 3 2366 6.11 1.80 9 2380 7.48 1.80 5 2386 12.12 2.70

10 2422 9.39 1.20 1 2452 8.19 0.90 4 2458 21.43 1.86

11 2497 18.03 0.90 12 2533 21.09 0.66

specimen. The specimen was a solid cylinder 0.187 in. in diameter and 0.854-in. high containing 30 ppm oxygen, 70 ppm carbon, and less than 1000 ppm of iron, nickel, chromium, and silicon.

The weight loss data and the calculated vapor pres­sures are shown in Table I and are plotted in Fig. 2. Vapor-pressure calculations were made using the Langmuir equation as given in Bockris et al. l The condensation coefficient was assumed to be equal to unity. These data are represented by the linear least­squares derived equation

logloPMo(atm) = 7.064-3.317 X 1041'-1,

where T is in Kelvin degrees. I' Also shown in Fig. 2 are the data of Edwards, Johnston, and Blackburn2 and vapor-pressure values of Jones, Langmuir, and MacKay3 as calculated from the

o

40 4.1 4.2 43 44 45 46

10 I T'K

FIG. 2. Vapor pressure of molybdenum: <>, Jones, Langmuir, and MacKay; G, Edwards, Johnston, and Blackburn; 0, this research.

3.563 0.400 0.043 3.561 2.190 0.240 3.588 1.920 0.210 3.564 3.258 0.359 3.586 9.466 1.060 3.557 11.68 1.312 3.568 12.58 1.415 3.553 22.03 2.496 3.593 25.33 2.888 3.578 32.20 3.677 3.544 56.52 6.504 3.533 90.45 10.48

latter's published evaporation-rate data. The agree­ment between the three sets of data is quite good over most of the temperature range investigated. At the higher temperatures the vapor-pressure data of Jones et at. tends to deviate from linearity while the data of this work and that of Edwards et at. remain essentially linear and in agreement, within experimental error.

TABLE II. Molybdenum third-law data.

Run Temp. -RTlnP -.6.FEF .6.H0298

No. OK kcaI/gfw cal/deg/gfw kcal/gfw

7 2141 81.991 35.06 157.05 8 2259 78.755 34.96 157.73 2 2261 79.416 34.96 158.46 6 2286 77.866 34.94 157.74 3 2366 75.498 34.87 158.00 9 2380 74.935 34.86 157.90 5 2386 74.766 34.85 157.92

10 2422 73.163 34.82 157.50 1 2452 73.358 34.80 158.69 4 2458 72.359 34.79 157.87

11 2497 70.677 34.75 157.45 12 2533 69.295 34.72 157.24

Average = 157 .80 Mean deviation= 0.34

Using the free-energy function data of Stull and Sinke4 for the solid and gaseous states of molybdenum, the standard heat of sublimation at 298°K was calcu­lated by the third-law method and these data are shown in Table II. The average value, 157.80±O.34 kcal/ gfw is in excellent agreement with the value of 157.500 kcaljgfw calculated by Stull and Sinke4 by averaging the data of Jones with that of Edwards.

* This work was sponsored by the U. S. Atomic Energy Com­mission, Division of Reactor Development, under contract number AT (30--1) 2789.

1 J. O'M. Bockris, J. L. White, and J. D. MacKenzie, Physico­chemical Measurements at High Temperatures (Academic Press Inc., New York, 1959).

2 J. W. Edwards, H. L. Johnston, and P. E. Blackburn, J. Am. Chem. Soc. 74, 1539 (1952).

3 H. A. Jones, 1. Langmuir, and G. M. J. MacKay, Phys. Rev. 30,201 (1927).

• D. R. Stull and G. C. Sinke, Thermodynamic Properties of the Elements, Advances in Chemistry Series No. 18 (American Chemical Society, Washington, D. C., 1946).

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