Optical phonon anisotropies in the layer crystals Sn<span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> and Sn<span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Se</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>

G. Lucovsky; J. C. Mikkelsen, Jr; W. Y. Liang; R. M. White; R. M. Martin

doi:10.1103/PhysRevB.14.1663

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Optical phonon anisotropies in the layer crystals Sn $S_{2}$ and Sn ${Se}_{2}$

G. Lucovsky and J. C. Mikkelsen, Jr.

W. Y. Liang

R. M. White and R. M. Martin

Xerox Palo Alto Research Center, Palo Alto, California 94304

Cavendish Laboratory, Cambridge, United Kingdom

Xerox Palo Alto Research Center, Palo Alto, California 94304

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Phys. Rev. B 14, 1663 – Published 15 August, 1976

DOI: https://doi.org/10.1103/PhysRevB.14.1663

Abstract

We have measured the far-ir reflectance spectra for the layer crystals Sn $S_{2}$ and Sn ${Se}_{2}$ for the two principal polarizations, $\vec{E} ⊥ \vec{c}$ and $\vec{E} ∥ \vec{c}$ . We find a large difference in the frequencies of the two ir-active phonons, $ν_{TO} (A_{2 u}) > ν_{TO} (E_{u})$ . Analysis of the lattice dynamics indicates that this anisotropy is due to Coulomb forces associated with charge localized on the atomic sites and as such it provides an empirical measure of the bond ionicity. On the other hand, anisotropies in the Raman modes are explained by noncentral intralayer forces, with smaller contributions from interlayer and Coulomb terms.

References (27)

J. L. Verble and T. J. Wieting, Phys. Rev. Lett. 25, 362 (1970) T. J. Wieting and J. L. Verble, Phys. Rev. B 3, 4286 (1971) J. L. Verble, T. J. Wieting and P. R. Reed, Solid State Commun. 11, 941 (1972)
P. C. Leung, G. Andersman, W. G. Spitzer, and C. A. Mead, J. Phys. Chem. Solids 27, 849 (1966) T. J. Wieting and J. L. Verble, Phys. Rev. B 5, 1473 (1972) J. C. Irwin, R. M. Hoff, B. P. Clayman, and R. A. Bromley, Solid State Commun. 13, 1531 (1973) M. Hayek, O. Brafman and R. M. A. Lieth, Phys. Rev. B 8, 2772 (1973) A. Mercier and J. P. Voitchovsky, Solid State Commun. 14, 757 (1974) E. Finkman and A. Rizzo ibid. 15, 1841 (1974)
R. Zallen, M. L. Slade and A. T. Ward, Phys. Rev. B 3, 4257 (1971)
D. Treacy and P. C. Taylor, Phys. Rev. B 11, 2941 (1975)
R. Zallen and M. L. Slade, Solid State Commun. 17, 1561 (1975) G. Lucovsky, R. M. White, W. Y. Liang, R. Zallen, and Ph. Schmid, ibid. 18, 811 (1976)
J. C. Mikkelsen, Jr., G. Lucovsky, R. M. Martin, R. Zallen, and M. L. Slade, Bull. Am. Phys. Soc. 21, 225 (1976)
J. E. Smith, Jr., M. I. Nathan, M. W. Shafer, and J. B. Torrance, in Proceedings of the Eleventh International Conference on the Physics of Semiconductors (Polish Scientific, Warsaw, 1972), p. 1306 G. Lucovsky, R. M. White, J. A. Benda, and J. F. Revelli, Phys. Rev. B 7, 3859 (1973) G. Lucovsky, W. Y. Liang, R. M. White, and K. R. Pisharody, Solid State Commun. (to be published)
R. Zallen and M. L. Slade, Phys. Rev. B 9, 1627 (1974) R. Zallen, Proceedings of the Twelfth International Conference on the Physics of Semiconductors (Teubner, Stuttgart, 1974), p. 621
A. J. Smith and W. Y. Liang (private communication)
A. S. Barker, Jr., Phys. Rev. 165, 917 (1968)
B. B. Varga, Phys. Rev. 137, A1896 (1965) E. Burstein, in Dynamical Processes in Solid State Optics (Benjamin, New York, 1967)
D. T. Hon and W. L. Faust, J. Appl. Phys. 1, 241 (1973)
E. Burstein, M. H. Brodsky and G. Lucovsky, J. Quantum Chem. 1S, 759 (1967)
M. J. P. Musgrave and J. A. Pople, Proc. R. Soc. 260, 474 (1962)
R. M. Martin, G. Lucovsky and K. Helliwell, Phys. Rev. B 13, 1383 (1976)
R. Zallen, G. Lucovsky and R. M. Martin (unpublished)
B. Szigeti, Trans. Faraday Soc. 45, 155 (1949)
J. Tessman, A. Kahn, and W. Shockley, Phys. Rev. 92, 890 (1953)
M. H. Brodsky and E. Burstein, J. Phys. Chem. Solids 28, 1655 (1967)
F. Stern, Elementary Theory of the Optical Properties of Solids, Solid State Physics, edited by F. Seitz and D. Turnbull (Academic, New York, 1964), Vol. 15
G. Lucovsky, R. M. Martin, and E. Burstein, Phys. Rev. B 4, 1367 (1971)
H. Mueller, Phys. Rev. 50, 547 (1936)
E. W. Kellermann, Philos. Trans. R. Soc. 238, 513 (1940) Proc. R. Soc. A 178, 17 (1941)
J. C. Phillips and J. A. VanVechten, Phys. Rev. Lett. 22, 705 (1969)
R. M. White and G. Lucovsky, Solid State Commun. 11, 1369 (1972)
L. Pauling, The Nature of the Chemical Bond (Cornell U.P., Ithaca, N.Y., 1960)
G. Lucovsky and R. M. White, in Proceedings of the Conference on Layered Semiconductors and Metals, 1976, Bari, Italy (unpublished)

[c1] J. L. Verble and T. J. Wieting, Phys. Rev. Lett. 25, 362 (1970) T. J. Wieting and J. L. Verble, Phys. Rev. B 3, 4286 (1971) J. L. Verble, T. J. Wieting and P. R. Reed, Solid State Commun. 11, 941 (1972)

[c2] P. C. Leung, G. Andersman, W. G. Spitzer, and C. A. Mead, J. Phys. Chem. Solids 27, 849 (1966) T. J. Wieting and J. L. Verble, Phys. Rev. B 5, 1473 (1972) J. C. Irwin, R. M. Hoff, B. P. Clayman, and R. A. Bromley, Solid State Commun. 13, 1531 (1973) M. Hayek, O. Brafman and R. M. A. Lieth, Phys. Rev. B 8, 2772 (1973) A. Mercier and J. P. Voitchovsky, Solid State Commun. 14, 757 (1974) E. Finkman and A. Rizzo ibid. 15, 1841 (1974)

[c3] R. Zallen, M. L. Slade and A. T. Ward, Phys. Rev. B 3, 4257 (1971)

[c4] D. Treacy and P. C. Taylor, Phys. Rev. B 11, 2941 (1975)

[c5] R. Zallen and M. L. Slade, Solid State Commun. 17, 1561 (1975) G. Lucovsky, R. M. White, W. Y. Liang, R. Zallen, and Ph. Schmid, ibid. 18, 811 (1976)

[c6] J. C. Mikkelsen, Jr., G. Lucovsky, R. M. Martin, R. Zallen, and M. L. Slade, Bull. Am. Phys. Soc. 21, 225 (1976)

[c7] J. E. Smith, Jr., M. I. Nathan, M. W. Shafer, and J. B. Torrance, in Proceedings of the Eleventh International Conference on the Physics of Semiconductors (Polish Scientific, Warsaw, 1972), p. 1306 G. Lucovsky, R. M. White, J. A. Benda, and J. F. Revelli, Phys. Rev. B 7, 3859 (1973) G. Lucovsky, W. Y. Liang, R. M. White, and K. R. Pisharody, Solid State Commun. (to be published)

[c8] R. Zallen and M. L. Slade, Phys. Rev. B 9, 1627 (1974) R. Zallen, Proceedings of the Twelfth International Conference on the Physics of Semiconductors (Teubner, Stuttgart, 1974), p. 621

[c9] A. J. Smith and W. Y. Liang (private communication)

[c10] A. S. Barker, Jr., Phys. Rev. 165, 917 (1968)

[c11] B. B. Varga, Phys. Rev. 137, A1896 (1965) E. Burstein, in Dynamical Processes in Solid State Optics (Benjamin, New York, 1967)

[c12] D. T. Hon and W. L. Faust, J. Appl. Phys. 1, 241 (1973)

[c13] E. Burstein, M. H. Brodsky and G. Lucovsky, J. Quantum Chem. 1S, 759 (1967)

[c14] M. J. P. Musgrave and J. A. Pople, Proc. R. Soc. 260, 474 (1962)

[c15] R. M. Martin, G. Lucovsky and K. Helliwell, Phys. Rev. B 13, 1383 (1976)

[c16] R. Zallen, G. Lucovsky and R. M. Martin (unpublished)

[c17] B. Szigeti, Trans. Faraday Soc. 45, 155 (1949)

[c18] J. Tessman, A. Kahn, and W. Shockley, Phys. Rev. 92, 890 (1953)

[c19] M. H. Brodsky and E. Burstein, J. Phys. Chem. Solids 28, 1655 (1967)

[c20] F. Stern, Elementary Theory of the Optical Properties of Solids, Solid State Physics, edited by F. Seitz and D. Turnbull (Academic, New York, 1964), Vol. 15

[c21] G. Lucovsky, R. M. Martin, and E. Burstein, Phys. Rev. B 4, 1367 (1971)

[c22] H. Mueller, Phys. Rev. 50, 547 (1936)

[c23] E. W. Kellermann, Philos. Trans. R. Soc. 238, 513 (1940) Proc. R. Soc. A 178, 17 (1941)

[c24] J. C. Phillips and J. A. VanVechten, Phys. Rev. Lett. 22, 705 (1969)

[c25] R. M. White and G. Lucovsky, Solid State Commun. 11, 1369 (1972)

[c26] L. Pauling, The Nature of the Chemical Bond (Cornell U.P., Ithaca, N.Y., 1960)

[c27] G. Lucovsky and R. M. White, in Proceedings of the Conference on Layered Semiconductors and Metals, 1976, Bari, Italy (unpublished)

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Optical phonon anisotropies in the layer crystals Sn $S_{2}$ and Sn ${Se}_{2}$

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Optical phonon anisotropies in the layer crystals SnS2 and SnSe2

Abstract

References (27)

Optical phonon anisotropies in the layer crystals Sn $S_{2}$ and Sn ${Se}_{2}$