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),
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].
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Bilz, H., Kress, W. (1979). Phonon Dispersion Relations and Phonon Models. In: Phonon Dispersion Relations in Insulators. Springer Series in Solid-State Sciences, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81347-4_2
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DOI: https://doi.org/10.1007/978-3-642-81347-4_2
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