Theoretical and experimental study of the vibrational excitations in ethane monolayers adsorbed on graphite (0001) surfaces
1.See, for example, H. Taub, in Vibrational Spectroscopies for Adsorbed Species, edited by A. T. Bell and M. L. Hair, ACS Symp. Ser. No. 137 (American Chemical Society, Washington, D.C., 1980), p. 247.
2.J. M. Szeftel, S. Lehwald, H. Ibach, T. S. Rahman, J. E. Black, and D. L. Mills, Phys. Rev. Lett. 51, 268 (1983).
3.K. D. Gibson and S. J. Sibener, Phys. Rev. Lett. 55, 1514 (1985).
4.H. Taub, K. Carneiro, J. K. Kjems, L. Passell, and J. P. McTague, Phys. Rev. B 16, 4551 (1977).
5.H. Taub, H. R. Danner, Y. P. Sharma, H. L. McMurry, and R. M. Brugger, Phys. Rev. Lett. 39, 215 (1977);
5.H. Taub, H. R. Danner, Y. P. Sharma, H. L. McMurry, and R. M. Brugger, Surf. Sci. 76, 50 (1978).
6.B. H. Grier, L. Passell, J. Eckert, H. Patterson, D. Richter, and R. J. Rollefson, Phys. Rev. Lett. 53, 814 (1984).
7.B. F. Mason and B. R. Williams, Surf. Sci. 130, L329 (1983).
8.G. J. Trott, Ph.D. thesis, University of Missouri‐Columbia, 1981 (unpublished).
9.J. Suzanne, J. L. Seguin, H. Taub, and J. P. Biberian, Surf. Sci. 125, 153 (1983).
10.J. P. Coulomb, J. Suzanne, M. Bienfait, M. Matecki, A. Thomy, B. Croset, and C. Marti, J. Phys. (Paris) 41, 1155 (1980).
11.R. D. Diehl, M. F. Toney, and S. C. Fain, Jr., Phys. Rev. Lett. 43, 1329 (1982).
12.R. Wang, H. Taub, H. Shechter, R. Brener, J. Suzanne, and F. Y. Hansen, Phys. Rev. B 27, 5864 (1983).
13.J. Krim, J. Suzanne, H. Shechter, R. Wang, and H. Taub, Surf. Sci. 162, 446 (1985);
13.J. C. Newton, H. Taub, S.‐K. Wang, and R. Wang, Bull. Am. Phys. Soc. 31, 375 (1986).
14.G. Bomchil, A. Hüller, R. Rayment, S. J. Roser, M. V. Smalley, R. K. Thomas, and J. W. White, Philos. Trans. R. Soc. London Ser. B 290, 537 (1980).
15.F. Y. Hansen, R. Wang, H. Taub, H. Shechter, D. G. Reichel, H. R. Danner, and G. P. Alldredge, Phys. Rev. Lett. 53, 572 (1984).
16.See, for example, K. Mirsky, in Computing in Crystallography, edited by H. Schenck (Delft University, Delft, 1978), p. 169.
17.D. E. Williams, J. Chem. Phys. 45, 3770 (1966).
18.D. E. Williams, J. Chem. Phys. 47, 4680 (1967).
19.A. E. Kitaigorodskii, Molecular Crystals (Academic, New York, 1973).
20.G. J. Trott, H. Taub, F. Y. Hansen, and H. R. Danner, Chem. Phys. Lett. 78, 504 (1981).
21.The H‐H length scale for the Kitaigorodskii parameters is smaller than the used successfully for bulk methane [E. S. Severin and D. J. Tildesley, Mol. Phys. 41, 1401 (1980)]
21.and methane adsorbed on graphite [J. M. Phillips and M. D. Hammerbacher, Phys. Rev. B 29, 5859 (1984)]. We are unaware of calculations on bulk or adsorbed methane with the Kitaigorodskii potentials.
22.D. E. Williams and T. L. Starr, Comput. Chem. 1, 173 (1977).
23.F. Y. Hansen, G. P. Alldredge, L. W. Bruch, and H. Taub, J. Chem. Phys. 83, 348 (1985).
24.As discussed in Refs. 8 and 9, a third solid phase of ethane has been found at low temperature in a narrow range of coverage near monolayer completion. This so‐called S2 phase is believed to form a large‐mesh superlattice on the graphite basal plane (Ref. 9). Interpolation between the densities of the S1 and S3 phases suggests 12 molecules per unit cell. The molecular orientations have not been determined.
25.We have assumed a cutoff length of 10 Å beyond which all three atomatom potentials (C‐C, C‐H, and H‐H) are taken to be zero. We believe this approximation is justified, since we are primarily concerned in these calculations with relative and not absolute interaction strengths.
26.All molecules within the cluster are constrained to have the same height above the surface.
27.M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford University, Oxford, 1968).
28.K. A. Strong, AEC Report IN‐1237, Idaho Nuclear Corp.
29.H. Taub, H. J. Lauter, J. P. Biberian, and J. Suzanne (unpublished).
30.F. Y. Hansen and H. Taub, Phys. Rev. B 19, 6542 (1979).
31.E. de Rouffignac, G. P. Alldredge, and F. W. de Wette, Phys. Rev. B 24, 6050 (1981).
32.F. W. DeWette, B. Firey, E. de Rouffignac, and G. P. Alldredge, Phys. Rev. B 28, 4744 (1983).
33.H. L. McMurry and F. Y. Hansen, J. Chem. Phys. 72, 5540 (1980). This paper treats the lattice dynamics of Se and Te. The same method of expressing the intermolecular part of the potential energy function has also been applied to hexamethylenetetramine by these authors (unpublished).
34.F. Y. Hansen, Comput. Phys. Commun. 14, 193, 219 (1978).
35.O. V. Kovalev, Irreducible Representations of the Space Groups (Gordon and Breach, New York, 1965).
36.L. Radom and J. A. Pople, J. Am. Chem. Soc. 92, 16, 4786 (1970).
37.In the case of the S3 phase, several, but not all, of the off‐diagonal elements can be shown to vanish at some wave vectors. However, the symmetry of the S1 phase is too low for such considerations to be useful.
38.G. E. Bacon, Thermal Neutron Diffraction, 3rd ed. (Oxford University, Oxford, 1976).
39.W. Marshall and S. W. Lovesey, Theory of Thermal Neutron Scattering (Oxford University, Oxford, 1971), pp. 86–87.
40.Grafoil is the trademark of an expanded graphite product marketed by the Union Carbide Corp., Carbon Products Division, 270 Park Avenue, New York, NY 10017.
41.According to Eq. (13) the intensity of the inelastic spectra should increase as and their shape should be Q independent. We have obtained INS spectra from both the S1 and S3 phases at (not shown). Although these spectra are weaker than those at their intensity does not scale as Also, the spectra differ somewhat in shape; for example, a greater width is observed for the main peak in the S3 spectrum (perpendicular configuration). These Q‐dependent features of the spectra may be caused by multiple scattering effects.
42.A comparison of the observed S1 and S3 ethane monolayer structures on graphite with calculations which include electrostatic and substrate mediated interactions is in progress [F. Y. Hansen and H. Taub (unpublished)].
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