Phonon Dispersion Relations and Phonon Models

  • Heinz Bilz
  • Winfried Kress
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 10)

Abstract

The lattice potential ϕ of a crystal in thermal equilibrium can be derived from the free energy F(T,V). ϕ reads in the classical harmonic approximation (ϕ ≃ ϕ2),
$${\phi _2} = \frac{1}{2}\,\,\sum\limits_{L,L} , \,\underline u \left( L \right)\underline \phi(LL')\underline u (L')$$
(2.1)
where L = (ℓ, κ) denotes the κth particle in the ℓth cell. The u(ℓ, κ) denote the displacement vectors of the ions with equilibrium positions, X(ℓ, κ) = X(ℓ) + X(κ), where X(ℓ) is pointing to the £ cell of the crystal and X(ℓ) describes the relative position of the κth ion in the cell. The 3 × 3 two-ion force constant matrices ϕ(L, L’) are subject to the conservation laws of energy, momentum, and angular momentum and to the symmetry restrictions of the space group [2.2].

Keywords

Paraffin Germanium Librium Halide ZnSe 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Heinz Bilz
    • 1
  • Winfried Kress
    • 1
  1. 1.Max-Planck-Institut für FestkörperforschungStuttgart 80Fed. Rep. of Germany

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