Neutron scattering investigation of layer-bending modes in alkali-metal—graphite intercalation compounds

H. Zabel; W. A. Kamitakahara; R. M. Nicklow

doi:10.1103/PhysRevB.26.5919

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Neutron scattering investigation of layer-bending modes in alkali-metal—graphite intercalation compounds

H. Zabel

W. A. Kamitakahara

R. M. Nicklow

Department of Physics and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

Ames Laboratory and Department of Physics, Iowa State University, Ames, Iowa 50011

Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830

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Phys. Rev. B 26, 5919 – Published 15 November, 1982

DOI: https://doi.org/10.1103/PhysRevB.26.5919

Abstract

Phonon dispersion curves for low-frequency transverse modes propagating in the basal plane have been measured in the alkali-metal—graphite intercalation compounds K $C_{8}$ , Cs $C_{8}$ , K $C_{24}$ , and Rb $C_{24}$ by means of neutron spectroscopy. The acoustic branches show an almost quadratic dispersion relation at small $q$ , characteristic of strongly layered materials. The optical branches of stage-1 compounds can be classified as either graphitelike branches showing dispersion, or as almost dispersionless alkali-metal-like modes. Macroscopic shear constants $C_{44}$ and layer-bending moduli have been obtained for the intercalation compounds by analyzing the data in terms of a simple semicontinuum model. In stage-2 compounds, a dramatic softening of the shear constant by about a factor of 8 compared with pure graphite has been observed. Low-temperature results on K $C_{24}$ indicate the opening of a frequency gap near the alkali-metal Brillouin-zone boundary, possibly due to the formation of the alkali-metal superstructure.

References (25)

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[c1] Lord Rayleigh, Theory of Sound (MacMillan, London, 1894), Vol. 1, p. 352 L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon, New York, 1970)

[c2] R. M. Nicklow, N. Wakabayashi, and H. G. Smith, Phys. Rev. B 5, 4951 (1972)

[c3] N. Wakabayashi, H. G. Smith, and R. M. Nicklow, Phys. Rev. B 12, 659 (1975)

[c4] H. Zabel and A. Magerl, Phys. Rev. B 25, 2461 (1982)

[c5] W. A. Kamitakahara, N. Wada, and S. A. Solin, J. Phys. (Paris) Colloq. 42, C6-311 (1981) Solid State Commun. (in press)

[c6] N. Wada, M. V. Klein, and H. Zable, J. Phys. (Paris) Colloq. 42, C6-350 (1981)

[c7] P. C. Eklund, J. Giergiel, and P. Boolchand, in Physics of Intercalation Compounds, Vol. 38 of Springer Series in Solid State Sciences, edited by L. Pietronero and E. Tosatti (Springer, Berlin, 1981)

[c8] J. Giergiel, P. C. Eklund, R. Al-Jishi, and G. Dresselhaus, Phys. Rev. B (in press)

[c9] W. A. Kamitakahara, H. Zabel, and R. M. Nicklow (unpublished)

[c10] P. C. Eklund, G. Dresselhaus, M. S. Dresselhaus, and J. E. Fischer, Phys. Rev. B 21, 4705 (1980)

[c11] R. J. Nemanich, S. A. Solin, and D. Guérard, Phys. Rev. B 16, 2965 (1977)

[c12] C. Horie, M. Maeda, and Y. Kuramoto, Physica (Utrecht) 99, 430 (1980)

[c13] S. Y. Leung, G. Dresselhaus, and M. S. Dresselhaus, Phys. Rev. B 24, 6083 (1981)

[c14] R. Al-Jishi and G. Dresselhaus, Phys. Rev. B 26, 4514 (1982)

[c15] P. Lagrange, D. Guérard, M. El Makrini, and A. Hérold, C. R. Acad. Sci., Ser. C 287, 179 (1978)

[c16] D. E. Nixon and G. S. Parry, Br. J. Appl. Phys. Ser. 2 1, 291 (1968)

[c17] W. D. Ellenson, D. Semmingson, D. Guérard, D. G. Onn, and J. E. Fischer, Mater. Sci. Eng. 31, 137 (1977)

[c18] G. S. Parry and D. W. Nixon, Nature (London) 216, 909 (1967)

[c19] H. Zabel, S. C. Moss, N. Caswell, and S. A. Solin, Phys. Rev. Lett. 43, 2022 (1979)

[c20] M. Suzuki, H. Ikeda, H. Suematsu, Y. Endoh, H. Shiba, and M. T. Hutchings, J. Phys. Soc. Jpn. 49, 671 (1980)

[c21] M. Mori, S. C. Moss, Y. M. Jan, and H. Zabel, Phys. Rev. B 25, 1287 (1982)

[c22] R. Clarke, J. N. Gray, H. Homma, and M. J. Winokur, Phys. Rev. Lett. 47, 1407 (1981)

[c23] A. Magerl and H. Zabel (unpublished)

[c24] D. M. Hwang, B. F. O'Donnell, and A. Y. Wu, in Physics of Intercalation Compounds, Vol. 38 of the Springer Series in Solid State Sciences, edited by L. Pietronero and E. Tosatti (Springer, Berlin, 1981)

[c25] K. Komatsu, J. Phys. Soc. Jpn. 10, 346 (1955)

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Neutron scattering investigation of layer-bending modes in alkali-metal—graphite intercalation compounds

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