Abstract
The ballistic heat flux radiating from a point source of heat in a cold crystal displays a complex pattern of caustics due to phonon focusing. The caustics correspond to folds in the elastic-wave surface of the crystal. The pattern of caustics is independent of phonon frequency unless the phonon wavelength is comparable to the lattice spacing; i.e., for values of wavevectork approaching π/a. We have measured both the shift in the caustic pattern (angular dispersion) and the increasing time-of-flight (velocity dispersion) for ballistic phonons in InSb with wavevectors up to 40% of the Brillouin-zone boundary. Comparison with existing lattice-dynamics models favors the Bond Charge Model (BCM). The phonon-imaging method gives information about theshapes of the wave surfaces which is complementary to the dispersion curves measured only along symmetry directions by neutron scattering.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
See for example Musgrave, M.J.P.: Crystal acoustics. San Fracisco: Holden-Day 1970
Northrop, G.A., Wolfe, J.P.: Phys. Rev. B22, 6196 (1980)
Every, A.G.: Phys. Rev. B24, 3456 (1981)
Tamura, S.: Phys. Rev. B28, 897 (1983)
Northrop, G.A., Wolfe, J.P.: Phys. Rev. Lett.43, 1424 (1979)
Northrop, G.A., Wolfe, J.P.: Proceedings on a NATO Advanced Study Institute of Nonequilibrium Phonon Dynamics, Les Arcs, France 1984. Bron, W.E. (ed.). New York: Plenum Press 1985
Born, M., Huang: Dynamical theory of crystal lattices. New York: Oxford University Press 1954
Brockhouse, B.N.: Inelastic scattering of neutrons in solids and liquids. Vienna: International Atomic Energy Agency 1961; Thermal neutron scattering. Egelstaff, P.A. (ed.) London: Academic Press 1965
Dietsche, W., Northrop, G.A., Wolfe, J.P.: Phys. Rev. Lett.47, 660 (1981)
Northrop, G.A.: Phys. Rev. B26, 903 (1982)
Northrop, G.A., Hebboul, S.E., Wolfe, J.P.: Phys. Rev. Lett.55, 95 (1985)
Hebboul, S.E., Wolfe, J.P.: Phys. Rev. B34, 3948 (1986)
Schreiber, M., Fieseler, M., Mazur, A., Pollman, J., Stock, B., Ulbrich, R.G.: Proceedings of the 18th International Conference on the Physics of Semiconductors. Engström, Olof (ed.), p. 1373. Singapore: World Scientific 1987; Hebboul, S.E., Wolfe, J.P.: p. 1377
Eisenmenger, W., Dayem, A.H.: Phys. Rev. Lett.18, 125 (1967);
Dayem, A.H., Miller, B.I., Wiegand, J.J.: Phys. Rev. B3, 2949 (1971)
Kinder, H.: Proceedings of a NATO Advanced Study Institute on Nonequilibrium Phonon Dynamics. Bron, W.E. (ed.). New York: Plenum Press 1985
Rustagi, K.C., Weber, W.: Solid State Commun.18, 673 (1976)
The undoped InSb crystals were grown by E. Swiggard of the Naval Research Laboratory
Eisenmenger, W.: Physical acoustics, principles and methods. Mason, W.P., Thurston, R.N. (eds.), Vol. 12, p. 79. New York: Academic Press 1976
Huang, H.C.W., Serrano, C.M.: J. Vac. Sci. Technol. A1, 1409 (1983)
Gundlach, K.H., Takada, S., Zahn, M., Hartfusse, H.J.: Appl. Phys. Lett.41, 294 (1982)
Deutscher, G., Gennes, P.G. de: In: Superconductivity. Parks, R.D. (ed.), Vol. 2, p. 1005. New York: Marcel Dekker 1969
Townsend, P., Sutton, J.: Phys. Rev.128, 591 (1962)
Claeson, T., Grimvall, G.: J. Phys. Chem. Solids29, 387 (1968);
Claeson, T.: Phys. Rev.147, 340 (1966)
Adler, J.G., Ng, S.C.: Can. J. Phys.43, 594 (1965)
Giaever, I., Megerle, K.: Phys. Rev.122, 1101 (1961)
Maki, K.: Superconductivity. Parks, R.D. (ed.), Vol. 2, p. 1035. New York: Marcel Dekker 1969
Handbook of Chemistry and Physics. Weast, R.C. (ed.). Boca Raton: CRC Press 1980
McMillan, W.L., Rowell, J.M.: Superconductivity. Parks, R.D. (ed.) Vol. 1, p. 561. New York: Marcel Dekker 1969
Ulbrich, R.G., Narayanamurti, V., Chin, M.A.: Phys. Rev. Lett.45, 1432 (1980); Orbach, R.: Phys. Rev. Lett.16, 15 (1966)
Klemens, P.G.: Proc. Phys. Soc. London68, 113 (1955)
At zero temperature, the onset of tunneling in normal metal-insulator-superconductor junctions occurs atV=Δ
Hurley, D.C., Wolfe, J.P.: Phys. Rev. B32, 2568 (1985)
See for example Bevington, P.R.: Data reduction and error analysis for the physical sciences. New York: McGraw-Hill 1969
See the original work by von Gutfeld, R.J., Nethercot, A.H. Jr.: Phys. Rev. Lett.12, 641 (1964)
Huet, D., Maneval, J.P., Zylbersztejn, A.: Phys. Rev. Lett.29, 1092 (1972)
Tamura, S.: Phys. Rev. B32, 5245 (1985)
Bilz, H., Strauch, D., Wehner, R.K.: Encyclopedia of physics. Genzel, L. (ed.), Vol. 25. Berlin, Heidelberg, New York: Springer 1984
For a recent review, see Hanke, W.: Adv. Phys.27, 287 (1978)
Ashcroft, N.W., Mermin, N.D.: Solid state physics. Chap. 22. Saunders College 1976
Kunc, K., Balkanski, M., Nusimovici, M.A.: Phys. Status Solidi B71, 341 (1975);72, 229 (1975)
Kunc, K., Nielson, O.H.: Comput. Phys. Commun.16, 181 (1979)
Borchards, P.H., Kunc, K.: J. Phys. C11, 4145 (1978)
Kunc, K., Nielson, O.H.: Comput. Phys. Commun.17, 413 (1979)
Yip, S.K., Chang, Y.C.: Phys. Rev. B30, 7037 (1984)
Kunc, K., Balkanski, M., Nusimovici, M.A.: Phys. Rev. B12, 4346 (1975)
Tamura, S.: Phys. Rev. B30, 849 (1984)
Hildebrand, F.B.: Introduction to numerical analysis. 2nd Edn., p. 111. New York: McGraw-Hill 1974
Huet, D., Pannetier, B., Ladan, F.R., Maneval, J.P.: J. Phys. (Paris)37, 521 (1976)
Similar plots were also shown in Ref. 4
Price, D.L., Rowe, J.M., Nicklow, R.M.: Phys. Rev. B3, 1268 (1971)
McSkimin, H.J.: IRE Trans. Ultrason. Eng.PGUE-5, 25 (1957)
Weber, W.: Phys. Rev. B15, 4789 (1977)
Weber, W.: Phys. Rev. Lett.33, 371 (1974)
Hebboul, S.E.: Ph.D. Thesis, University of Illinois 1988
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hebboul, S.E., Wolfe, J.P. Lattice dynamics of InSb from phonon imaging. Z. Physik B - Condensed Matter 73, 437–466 (1989). https://doi.org/10.1007/BF01319374
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01319374