Influence of an Anharmonicity and Electron–Phonon Interaction on a Frequency Spectrum of Crystals with the Hexagonal Close-Packed Lattice

Abstract

In a given review, the description of the energy spectrum of electrons and the frequency spectrum of atomic vibrations of the crystal lattice are considered. The basic methods for investigation of influence of the anharmonicity effects on the physical properties of materials and a frequency spectrum of vibrations of the crystal lattice are reviewed. The self-consistent harmonic approximation, which is based on the method of double-time Green’s functions, are described. Within the scope of this approximation, the equation of motion for the ‘displacements–displacements’ Green’s functions, which is similar to the equation of motion in the harmonic approximation, is derived, but the force constants are renormalized and are determined by the thermodynamical averaging of second derivatives of potential rather than their equilibrium values. Appearances of the anharmonicity effects in the vibrational spectrum of the Ti0.93Al0.07 hexagonal close-packed crystal lattice as well as the electron-subsystem effects are investigated.

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