Abstract
One major subfield of lattice dynamics is concerned with the evaluation of the physical properties of a defectless or ideal crystal for which the adiabatic approximation should be valid. In this approximation one assumes that the solid is well modeled by a collection of atoms which interact through an interatomic potential and that electronic effects, except as they contribute to the potential, are negligible. This approximation is appropriate for insulating crystals and should be especially good for the solid isotopes of helium, commonly called the quantum crystals, and the rare gas solids. In practice, it is also found to work even for the lattice dynamics of metals.
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References
HA treats effects caused by changes of the lattice constant as perturbations whereas QHA uses a different set of bare quantities at each lattice constant. Since the latter approach only requires the change of one data element in a computer program, we see little need to consider the former approach at all. Thus, in Section III what could be called SCQHA is called SCHA.
M. Born and K. Huang, Dynamical Theory of Crystal Lattices. (Oxford University Press, London, 1954 ).
A. A. Maradudin, E. W. Montroll and G. H. Weiss, Solid State Physics (ed. by F. Seitz and D. Turnbull) (Academic Press, New York, 1963 ), Suppl. 3.
A. A. Maradudin, P. A. Flinn and R. A. Coldwell-Horsfull, Ann. Phys. (N.Y.) 15, 337 (1961).
R. A. Cowley, Advan. Phys. 12, 421 (1963).
N. R. Werthamer, Phys. Rev. A2, 2050 (1970).
R. A. Cowley, Rept. Progr. Phys. 31, 123 (1968).
M. L. Klein, G. K. Horton and J. L. Feldman, Phys. Rev. 184, 968 (1969).
W.J.L. Buyers and R. A. Cowley, Phys. Rev. 180, 755 (1969).
T. Högberg and R. Sandström, Phys. Stat. Solidi 33, 169 (1969); T. R. Koehler, N. S. Gillis and D. C. Wallace, Phys. Rev. B1, 4521 (1970); and T. R. Koehler and N. S. Gillis, Phys. Rev. B3, 3568 (1971).
M. Born, Fest. d. Akad. Wiss. Gottingen (1951). A translation of this article has been issued as Bell Laboratories TR.70-14.
D. J. Hooton, Phil. Mag. 46, 422 and 433 (1955).
The appropriate references can be found in Ref. 14 and 15. Of these two, Ref. 14 has the simplest exposition of the theory.
N. R. Werthamer, Am. J. Phys. 37, 763 (1969).
N. R. Werthamer, Phys. Rev. B1, 572 (1970).
N. S. Gillis, N. R. Werthamer and T. R. Koehler, Phys. Rev. 165, 951 (1968).
T. R. Koehler, Phys. Rev. 165, 942 (1968).
T. R. Koehler, Phys. Rev. 144, 789 (1966).
T. R. Koehler, Phys. Rev. Letters 17, 589 (1966).
M. L. Klein, V. V. Goldman and G. K. Horton, J. Phys. Chem. Solids 31, 2441 (1970). References to other calculations by these authors may be found in this reference.
T. R. Koehler, unpublished.
F. W. de Wette and B.R.A. Nijboer, Phys. Letters 18, 19 (1965).
T. R. Koehler and N. R. Werthamer, Phys. Rev. A2074 (1971); and P. Gillissen and W. Biem, Z. Phys. 242, 250 (1971).
T. R. Koehler and N. R. Werthamer, to be published.
H. R. Glyde and F. C. Khanna, to be published.
B. H. Brandow, Phys. Rev. A4, 422 (1971).
R. A. Guyer in Solid State Physics, Vol. 23 (ed. by F. Seitz D. Turnball and H. Ehrenreich) (Academic Press, New York, 1969 ).
N. S. Gillis and T. R. Koehler, Phys. Rev. to be published.
T. R. Koehler and R. L. Gray, Bull. Am. Phys. Soc. 16, 439 (1971).
R. C. Shukla and E. R. Cowley, Phys. Rev. B3, 4055 (1971).
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Koehler, T.R. (1972). Computational Aspects of Anharmonic Lattice Dynamics. In: Herman, F., Dalton, N.W., Koehler, T.R. (eds) Computational Solid State Physics. The IBM Research Symposia Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1977-1_30
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DOI: https://doi.org/10.1007/978-1-4684-1977-1_30
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