NOTES
744
The reactions were carried out in a 25-mm 0.d. Pyrex tube at room temperature (25') and pressures near 3 torr. A 1P21 photomultiplier in combination with a filter transmitting at 5350 A was used to monitor the NO titrations. ICN, carried in a stream of argon, was introduced into an excess of atomic oxygen through one inlet jet, and excess I 2 was similarly introduced through a second jet, ca. 30 msec downstream from the first. The products of reaction at the second jet were trapped at 77°K and later analyzed for the presence of cyanide. No cyanide was ever detected in the trapped products. Instead, a brown film of CN polymer formed on the walls of the reaction tube, near to and on the ICN inlet and extending a short distance along the tube. The white iodine oxide film which formed at the same time extended for a much greater distance. It was therefore concluded that the reaction of 0 atoms with ICN is not a very convenient source of CN radicals because the wall reaction which removes CN is faster than that which removes iodine. Poisoning the walls with phosphoric acid did not affect this conclusion. The primary reaction in this system is given by
0
+ ICN
+ CN
(1)
+ ICN--.,I + CNO
(2)
--3
IO
The alternative reaction
0
can be ruled out on the basis of the evidence which follows. The reaction with discharged oxygen was accompanied by a bright, yellow-white luminescence which extended the whole length of the reaction tube (35 cm). When this luminescence was photographed, using a Hilger medium quartz, spectrograph and Ilford HP3 plates, it was found to be indistinguishable from the well-known NO-0 continuum. We therefore conclude that CN radicals reacted with 02,close to the ICN inlet, to produce NO according to the scheme4 CN
+0 2 4 C N O+0
CNO+OACO+NO
(3)
(4)
(The alternative four-center reaction4 CN
+
CO
0 2 4
+ NO
(5)
is expected to be too slow to produce appreciable amounts of NO in the short time available before the CN radicals polymerize on the wall.) No luminescence was observed when the oxygen atoms were prepared, in the absence of 0 2 , by the NO titration, but if reaction 2 did occur, some nitric oxide would be formed by the subsequent reaction 4, and the NO-0 continuum would be produced. Hence this reaction can be eliminated in favor of (1). A very small increase in photomultiplier current was noted when ICN was introduced at the null point of the NO titration; this was tentatively attributed to the presThe Journal
of
Physical Chemistry
ence of a trace of cyanogen resulting from the equilibrium 21CN
I2
+ C2Nz
The termolecular reaction
+ +
+
CN 0 M ----+ CNO M (7) which would also lead to NO formation by reaction 4, is expected to be much too slow to compete with CN polymer formation. The possibility of producing NO in absence of 0 2 was also investigated mass spectrometrically, using apparatus similar to that described by Phillips and Schiff.s When ICN was introduced into a stream of discharged O2 the peak a t mass 30 showed a large increase, corresponding to the formation of NO. But when ICN was introduced into a stream of discharged N2 to which had been added a very small excess of NO, the peak at mass 30 showed only a small decrease, due to the increased pressure in the flow system. No attempt was made to measure the rate of the primary reaction mass spectrometrically because of the need to avoid coating the mass spectrometer sampling leak with CN polymer. From the length of the polymer deposits on the walls of our reaction tubes we estimate that the rate constant of reaction 1 is 10'0 cma mole-' sec-l or greater.
Acknowledgments. This work was supported by the New Zealand Universities Research Committee and by Grant AF-AFOSR-1265-67 from the U. S. Air Force Office of Scientific Research. (4) N. Basco, Proc. Roy. SOC.(London), A283, 302 (1965). (5) L. F. Phillips and H. I. Schiff, J. Chem. Phys., 36, 1609 (1962).
Crystal-Field Splitting of Fundamentals in the Raman Spectrum of Rhombic Sulfur
by A. T. Ward Research Laboratories, Xerox Corporation Rochester, New York 14680 (Received Auguet 22, 1067)
The fundamental vibrational spectrum of the SS molecule in crystalline rhombic sulfur has been investigated previously by far-infrared methods1p2 and by Raman spectroscopy.a-Q Only in the far-infrared (1) R. B. Barnes, Phya. Rev., 39, 570 (1932). (2) G. W.Chantry, A. Anderson, and H. A. Gebbie, Speotrochim. Acta, 20, 1223 (1964). (3) D. W.Scott, A. B. Guthrie, J. F. Messerly, 8. 9. Todd, W. T. Berg, I. A. Hosaenlopp, and J. P. McCullough, J. Phys. Chem., 66, 911 (1962). (4) A. Caron and J. Donohue, Acta Cryst., 14, 648 (1961). (6) P. Krishnamurti, Indian J. Phys., 5 , 106 (1930).
NOTES
745
investigation of Chantry, Anderson, and Gebbie,% however, was the instrumental resolution adequate for demonstration of the splitting of fundamentals expected from the operation of intermolecular forces in the crystal. In the present work, analogous effects have also been observed by Raman spectroscopy using a continuous He-Ne gas laser as the excitation source. The isolated s8 molecule is a puckered octagon of D4d symmetry, having eleven fundamental vibrations: 2E1 (infrared 2A1 3E2 2Ea (Raman active), B2 active), and B1 (inactive). In crystalline rhombic sulfur, sixteen 88 molecules occupy a unit cell of space group 10 D2hz4-(Fddd). The nodal planes of the molecules lie parallel to the c axis of the orthorhombic crystal and are oriented alternately parallel and perpendicular to the 110 plane.lO In principle, coupling between the vibrational motions of the sixteen molecules in the unit cell should yield sixteen new frequencies for every fundarriental vibration of the isolated molecule. In practice, such distinctions are not apparent in spectra obtained from samples at room temperature. The sulfur molecules have Cz site symmetry, i.e., they each have a twofold rotation axis in common with the lattice. However, as may be seen in Figure 1, the sulfur molecules are not all equivalent. The sulfur molecule X, oriented parallel to the 110 plane, has its molecular nodal plane and center of gravity in the same crystallographic plane. The sulfur molecule Y, oriented perpendicular to the 110 plane, has its molecular nodal plane at an angle (11' 48') to the crystallograpliic plane containing its center of gravity. Thus there are two types of 88 molecules in the crystal: those lying parallel to the 110 plane and those lying perpendicular to it. Applying site-symmetry arguments to an oppositely oriented pair of nearest neighbors leads to the expectation of 3n = 48 normal modes, of which 23 will belong to class A and 25 will belong to class B. Three of the normal modes are translational, 2B) and three more (A 2B) may be con(A sidered as restricted rotations. The remaining 42 modes (21A 21B) are vibrational. All of the normal modes will be both infrared and Raman active. Selection rules appropriate to the Cz site symmetry would be expected to hold completely only in the limit of strong intermolecular force fields. In the weak field case, when the intermolecular forces are small compared with the intramolecular forces, there will be only a slight interaction between corresponding energy levels of nearest-neighbor molecules. This perturbation will result in the formation of two new levels for each original level. Since the intermolecular forces in rhombic sulfur are of the weak van der Waals type, while the interatomic forces give rise to strong covalent sulfur-sulfur bonds, rhombic sulfur would be expected to conform to the weak field case: the nearest-neighbor interaction energy will be small compared with the vibrational energies associated with the Ssmolecule. The
+
+
+
+
+
+
-
0
a
5
IIO
Figure 1. Projection of a portion of the rhombic sulfur unit cell on the 001 plane showing molecular orientations relative to the 110 and 110 planes.
fundamental frequencies associated with the "free" Ss molecule (e.g., as observed by Ramanall' and infrared'~'~spectroscopy of sulfur solutions in carbon disulfide) should therefore be resolved into two relatively closely spaced components in the spectrum of the crystal. Raman spectra were excited by 6238-A radiation from a Spectra Physics Model 125 helium-neon laser, having an output power in excess of 50 mw. The laser light was mechanically chopped at 640 cps and then focused into the sample, a rhombic sulfur crystal grown from carbon disulfide solution to dimensions of approximately 5 X 1 X 1 cm. Light scattered at 90" to the incident-beam direction was focused onto the entrance slit of a double monochromator (Spex 1400) consisting of tandem 0.75-m grating monochromators. The resulting spectrum was detected by a photomultiplier (EM1 9558B) and lock-in amplifier (Princeton Applied Research Model HR-8). Output was displayed on a conventional strip chart recorder. Spectra were obtained with the electric vector of the exciting radiation polarized parallel to and perpendicular to the c axis of the crystal. However, any orientation dependence of the spectra was obscured by gross internal scattering of the laser light by flaws within the sample. The spectroscopic slit width used was 0.4 cm-' for the Stokes region and 0.6 cm-' for the anti-Stokes region of the spectra. The spectrum was not subject to interference from grating ghosts. These were identified in a (6) C. S. Venkateswaran, Proc. Indian Acad. Sci., 4A, 345, 414 (1936). (7) 8 . C. Sirkar and J. Gupta, Indian J . Phye., 10,473 (1936). (8) K. Venkateswaren, Proc. Indian Acad. Sei., IZA, 453 (1940). (9) R. Norris, ibid., 13A, 291 (1941); 16A, 287 (1942). (10) B. E. Warren and J. T. Burwell, J . Chem. Phys., 3, 6 (1935). (11) H. Gerding and R. Westrik, Rec. Trav. Chim., 6 2 , 68 (1943). (12) D. W. Scott, J. P. MoCullough, and E'. H. Kruse, J . Mol. Spectry., 13 313 (1964).
Volume 7.2, Number 2 February 196%
NOTES
746
474cm-1
\
434cm-1
SLIT WIDTH
251.5~m-~
Figure 2.
Raman spectrum of rhombic sulfur (Stokes region).
separate experiment involving direct passage of the attenuated laser beam into the monochromator. Under such conditions grating ghosts were observed a t 14 and 19 crn-l. Raman peaks centered at 86 cm-1 (E2), 218 cm-l (A1), and 437 cm-' (E3)were each cleanly resolved, in both Stokes and anti-Stokes spectra, as shown in Figure 2, into doublets with components separated by 4.5, 4, and 6.5 cm-', respectively. The peaks centered at 152 cm-' (E2),248 cm-' (E3), and 475 cm-I (A1 and Ez)showed incipient splittings of the same order (4.5 1+ 0.5 cm-1). The assignments used here are those of Scott, McCullough, and Kruse.12 According to these assignments, there is an accidental degeneracy of an AI and an Ez mode at 475 cm-l. This should split into four components under suitably high resolution. In addition, the Raman-forbidden fundamental centered at 191 cm-l (El) appeared weakly in the high-resolution spectra. Using a slit width of 1.8 cm-', the forbidden line appeared with appreciable intensity as an asymmetric peak with components at 189 and 194 cm-l. Group theory also predicts three Raman-active rotational modes (A2 2Ea), and three infrared-active translational modes (Bz 2E1), for the isolated SS molecule. Intermolecular forces will cause the rot& tions to be somewhat hindered in the crystalline state and may be strong enough to cause transgression of the selection rules forbidding Raman activity of the translational modes. However, since the interaction is weak, the principal effect expected should be the splitting of each rotational fundamental into two components, in the same way as explained for the vibrational fundamentals. Translational modes should not appear in the Raman spectrum. Experimentally, four of the six expected rotational fundamentals were observed. These occurred at 26, 42.5, 49.5, and 61, respectively, with the peak at 61 em-' appearing as a shoulder to the intense line at 49.5 cm-l. Inspection of the disposition of the molecules in the unit cell indicates that only rotations, R,, about the x molecular axis (perpendicular to the nodal plane) will experience little hindrance from neighboring molecules. It is reasonable
+
+
The Journal of Physical Chemistry
to assume, therefore, that R, rotations should have lower energy than either R, or R, (rotations about the orthogonal axes in the nodal plane), which will be highly hindered. On this basis, the Raman peak of moderate intensity centered at 26-om-' is assigned to the unresolved components of the At (R,) fundamental, and the triplet comprising the peaks at 42.5, 49.5, and 61 cm-l is assigned to the incompletely resolved quartet expected for the two Ea rotational modes R,, R,. The results are to be compared with those of Chantry, et aL2 These workers were able to resolve the splittings of the two infrared-active vibrational fundamentals Bz and El lying below 400 cm-' using an interferometer with an effective slit width of 4 cm-l. The Ba mode, which they observed at 186 cm-1 in spectra of saturated solutions of sulfur in carbon disulfide, was resolved into components at 186 and 197 cm-', in the spectrum of the solid. The El mode, observed by them at 239 cm-I in the spectra of the carbon disulfide solutions, was also split into a doublet, but with much smaller spacing. In addition, two infrared-forbidden fundamentals, 152 cm-' (Ez)and 216 cm-' (A1),appeared with moderate intensity in the rhombic sulfur spectrum. It is apparent that the results of the infrared and Raman investigations are complementary. The splitting of fundamentals by from 4 to 11 cm-', observed by both methods, is considered to arise as a consequence of a small perturbation of the molecular force field produced by van der Waals forces between oppositely oriented nearest neighbors. The number and activity of fundamentals predicted according to the site-symmetry approach is not in accord with the spectral data obtained here from a sample at room temperature. Better agreement with the site-symmetry predictions might be obtained at lower temperatures, where additional lines might become resolvable due to a decrease in thermal line broadening. Acknowledgment. Helpful discussions with G. Lucovsky and R. Zallen of this laboratory are gratefully acknowledged.
The Determination of Activation Energies in Solid-State Kinetic Processes
by H. N. Murty, D. L. Biederman, and E. A. Heintz Research Laboratory, 8peer Carbon Division, Air Reduction Company, Inc., Niagara Falls, New Yorlc l@O9 (Received August 30,1967)
The isothermal kinetic changes of a given property in many solid-state processes can be expressed by an empirical equation of the form
