1368
NOTES B*
C*
+M+B +M +
C* +decomposition M+ C M
+
(5) (6)
(7)
where B* and C* refer to excited molecules of 1-butene and methylcyclopropane, respectively. This mechanism will predict a maximum for the quantum yield of
C. On the assumption that a similar mechanism may be operative in the present study, equations 2 t’o 7 can be rewritten as (with B and C representing 1,5-hexadiene and allylcyclopropane, respectively)
B
+ Hg*
B*
B* +H* H*+ M+H
+M
( 14)
(15)
H* -+ decomposition (16) These equations will lead to an expression of the following nature for either Cor H .
which is exactly similar to equation 1 that was derived by Cvetanovic and Doyle2 in the case of 1-butene. It follows that the yields of both allylcyclopropaiie and bicyclo [ 2 . l .llhexane should show a maximum with pressure whereas in fact (Fig. 1) only the former shows such a maximum. The explanation for the disagreement may be one of two possibilities. (i) I n equation 17, the pressure a t which @ is a niaximum will be a function of a, b, and c which in turn are ratios of the rate constants k 8 . . . . k16. Since the rate constants for the formation and decomposition of allylcyclopropane and bicyclohexane may differ considerably, the maximum for the latter will be different from that for the former.6 Cvetanovic has pointed out6 that a combination of a relatively high value for Mmax and a relatively low value for emax may make it experzmentally difficult to locate the maximum in the case of bicyclo [2 . 1. 1]hexane. (ii) A second explanation is based on an alternative mechanism. The electronically excited triplet 1,shexadiene molecule that is formed in reaction 8 may contain up to 20 kcal./mole of vibrational energy which it may lose stepwise in several collisions. If the vibrational levels are designated by subscripts, the molecule of B that is formed in (8) will he Bn*. The deactivation reactions may be represented by the general equation
31
+ Bn* +M + B , *
Bn*
(18)
From three of these levels (or sets of levels), n, m, and the three products, free radicals, C, and H may be formed 0,
( 5 ) It can be predicted t h a t the maximum for bicyclo[Z.l.l]hexane mill occur at a higher pressure of l,5-hexadicne than the maximum for allylcyclopropane. (6) R. J. Cvetanovic, private communication.
+free radicals
(19)
B,* +C Bo* +H With the addition of one more step to provide formation of excited 1,S-hexadiene molecules zeroth vibrational level
+
M R,* it can be derived that @free radical = h 9 / k 1 9
@C
+ EIg
(8) and so on with equation 9 through 13 replacing equations 3 through 7. The following additional steps would account for the formation of bicyclo [2.1.1]hexane ( H ) . --+
Vol. 67
add
aH
+
--+
Bo*
+M
kl8lCf
+ k&T)(k:o + kz2M)
=
kl&zoM/(klg
=
k18k22M2/(klg klsW!)(k20 k&)
+
+
(20)
(21)
for the in the (22)
(23) (24) (25)
This mechanism is seen to predict the pressure dependence of all three of the products ~ o r r e c t l y . ~I n particular, the expression for @c,is identical with eq. 17 and is capable of the same simplifications to give a linear dependence of (M/@C)”~ us. M. The present study admittedly does not resolve this conflict. However, it is clear that the experimental pressure dependence curves can be generated on the basis of more than one mechanism. Acknowledgment.-The author wishes to thank Dr. R. J. Cvetanovic for his friendly criticism during the course of a lengthy correspondence. He is grateful to the members of the organic chemistry group a t the Research Center for their advice and encouragement. (7) T h e prediction of the trends in the formation of bicyclohexane is only qualitatively correct. A comparison of the curve in Fig. 1 with eq. 25 clearly shows t h a t other steps which involve H should be included in the mechanism.
A LANGMUIR DETERMINATIOS O F THE SUBLIMATION PRESSURE OF BOROK1 B Y ROBERT c. P.4ULE
AND
JOHN L.
MARGRAVE
Department of Chemistry, Unisersity of Wisconsin, Madison, Wiseonsin Received January 9, 1968
Alt,hough several different groups of workers have reported Knudsen vapor pressure measurements on boron, no two sets of measurements agree and there is a difference of about 5 x lo4 in vapor pressure values between the two extreme sets of measurements. Searcy and Myers2 have made B-vapor pressure measurements using an initial and final weighing technique with C, Ta, and ZrBz Knudsen crucibles. The lids and orifices of all three types of crucibles were made of Ta. Considerable reaction occurred between the B and the C or Ta crucibles and lids. ilfter the experiments, some free B was found in the Knudsen cells. Since the borides of T a and C are considerably less volatile tha,n B, i t was assumed that the vapor pressure of B was measured. Searcy and Myers gave a higher reliability to the vapor pressure measurements made in the ZrBz crucibles (with T a lids and orifices), since thesc cells minimized boride formation. Akishin, et aL,3 made B-vapor pressure nieasurements (1) Abstracted, in part from the thesis of Robert C. Paule presented in partial fulfillment of the requirements for the Ph.D. degree of the University of Wisconsin, January, 1962. ( 2 ) A. W. Searcy and C . E. Myers, J . Phgs. Chem., 61, 967 (1967). (3) P. A. Akishin, 0. T. Mikitin, and L. N. Gorokhov, Dokl. A k a d . Nauk S S S R , 129, 1077 (1959).
1369
NOTES
June, 1963
TABLE I LANGMUI~Z SUBLIMATION DATAFOR BORON Expt. no.
2a
AV,b volts
0.1014 .0356 ,0590 ,1010 ,1571
At,
T.
see.
OK.
3 , 660 5 ,220 53,640 1,200 690
1998' 191SC 1822' 2071 2152
Patm
7.159 7.777 8.580 6.669 6.228
deg. -1 mole-'
35.68 35.70 35.73 35.65 35.62
deg. -1 mole -1
32.76 35.59 39.26 30.56 28.50
AH%% kcal./mole
-1
136.7 136.7 136.6 137.0 138.0
137.0 136.9 136.8 136.4 137.2 136.9 Av. 136.9 f 0 . 3 kcal./mole In Calibration showed A V / A M = 23.8 mv./mg. a Area of sample = 5.14 cm.2for expt. no. 2 and 1.596 cm.2 for expt. no. 3. addition to the normal pyrometer sighting window and mirror correction, a factor of 25' was added to correct for an initially undetected film on the mirror. 35
0.0069 ,0237 ,0462 ,0503 .0319 .0247
51,660 15,000 7,320 87,060 8,160 28,080
1781 1905 1980 1845 1959 1873
8.992 7.905 7.294 8.348 7.505 8.163
by observing with a mass spectrometer the vapors effusing from Ta and Mo Knudsen cells. Their data show a considerable scatter. Priselkov, et aZ.,4amade B vapor pressure measurements by observing the rate of vapor condensation on cold plates placed in front of 210 and Ta Knudseii cells. Their data show a very strong dependence on the size of the orifice, with smaller orifices yielding higher measured vapor pressures. This dependence could indicate a very small evaporation coefficient for B. On the other hand, it could indicate that incorrect vapor pressure calculations were made since this same effect could arise from failure t o correct for channeling in the orifice or from borides forming on the lid of the cell. Verhaegen and D r o ~ v a r thave ~ ~ recently reported a heat of sublimation of 128.0 =t2.5 kcal./mole from mass spectrometer studies of the effusate from B or B& contained in a graphite Knudsen cell, and cite agreement with other mass spectrometer studies15 while noting that weight-loss experiments seem to yield a higher There have been heat, i.e., a lower vapor no previous Langmuir studies on boron. Experimental Experimental Techniques and Apparatus.-In this work, the vapor pressure of B has been measured by the Langmuir technique, since this method allows one to minimize the problem of sample contamination or reaction a t high temperatures. The experimental apparatus and general procedures have been described previously.8 I n addition to the previously described apparatus, a closed bottom Ta cylindrical sleeve was fitted into the graphite furnace and was used in two of the three boron experiments in order to reduce the possibility of a reaction between the boron sample and furnace vapors. Polycrystalline B was deposited a t Texaco Experiment, Incorporated, on a thin W filament by chemical vapor plating using Hz and BBra. The B rod had a purity in excess of 99%. Emission spectrographic analysis revealed approximately 40 p.p.m. Fe, 20 p.p.m. Si, 3 p.p.m. Cu, and 1 p.p.m. Mg for similarly prepared rods. The sample was suspended from a W wire and no significant TV-B interaction was observed. (4) (a) Yu. 4.Priselkov, Yu. A. Sapozhnikov, a n d A. V. Tseplyaeva, Akad. hiauk S S S R , Iav. Otd. Tekhn. N a u k Metal I Toplzvo, 1, 134 (1960); (b) G. Verhaegen a n d J. Drowart, J . Chern. Phys., S T , 1367 (1962). ( 5 ) W. A. Chupka, Brnonne Kational Laboratory Report ANL-5CG7, 1957, p. 75. (6) P. Schissel and Vi-.'&7illiams, Bull. Am. Phys. Soc., 4, 139 (1959). (7) 1%. Robson, P h . D . Thesis, University of Kansas, 1959. (8) L. Dreger and J. L. Margrave, J. P h y s . Chem., 66, 1556 (1962), and earlier papers
35.75 35.71 35.69 35.73 35.70 35.72
41 15 36 17 33.38 38.20 34 I34 37.35
Results Visual inspection and X-ray diffraction spectra of the sample surfaces, made after the vapor pressure experiments, indicated varying degrees of B surface contamination, in the form of B4C. At the temperature of the experiments, the vapor pressure of (3, per se, is too low to contribute significantly to the formation of B4C. It is more likely that vapors of the diffusion pump oil were absorbed onto the carbon of the cold furnace prior to the experiment and then desorbed and pyrolyzed a t the higher temperatures of the experiment. Experiment no. 1 was performed in the bare graphite furnace, which resulted in the formation of a considerable amount of B&, and the observed vapor pressure results were lorn, clearly indicating the formation of a surface film. Experinieiit no. 2 was run with the Ta sleeve inside the furnace and showed only a small amount of B4C. Experiment no. 3 was also run with a Ta sleeve and special care was taken while heating the furnace in order to keep the ambient pressure as low as possible. As a result, sample no. 3 was only slightly contaminated with B4C. Because of the observed high degree of reactivity of B a t high temperatures, and because the heat of formait is assumed that tion of TaBz is < - 45 k~al./mole,~ complete reaction occurred between the B vapor atoms and the Ta sleeve (or the graphite furnace). The possible products, TaBz or B4C, are considerably less volatile than B. The appropriate equation relating the measured pressure, P, to the equilibrium pressure, P,,, is
where aeois the evaporation coefficient i n vacuo. For the improbable case that the B vapor atoms did not react with the Ta sleeve or with the furnace walls, a multiplicative correction factor which could be as high as 2.56 might be necessary to correct for the channeling effect of the heating sleeve. The vapor pressure of B was measured over the temperature range 1781-2152°1
