The Theory of Phonons in Metals

Abstract

The review considers evolution of theoretical grounds for calculations of the phonon spectra in crystals. The principal difficulties in the application of the standard perturbation theory for transition metals are shown. The phenomenological theories based on both the theory of groups for finding non-equivalent elements of the dynamic matrix and experimental values of the phonon frequencies in high-symmetry directions are analysed in details. By the example of the hexagonal close-packed transition metals Y, Sc, Tc, and Ru, phonon spectra and phonon density of states are calculated within the framework of the linear response theory. As a basis for the calculation of the electron spectrum, the Linear Muffin-Tin Orbitals are used in the calculation model taking into account the real Full Potential in the Linear-Muffin-Tin-Orbital method (FPLMTO). The abovementioned metals are interesting, at least, from two theoretical points of view. Firstly, they are well studied experimentally. It allows us to compare the calculations with the data of neutron spectroscopy as well as to evaluate the accuracy of phenomenological models used previously to calculate the phonon spectra. Secondly, for all of the above-mentioned h.c.p. metals, value of the ratio of lattice parameters, c/a, deviates from the ideal value (8/3)(1/2). Thus, spherical approximation of the crystal potential in muffin-tin sphere, as opposed to the f.c.c. lattice, for example, will have a topological error, which correlates with the deviation of the value of c/a from ideal one. Application of FP LMTO removes the last problem.

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