Abstract

The crystalline structure of the Cu₇GeS₅I type is considered and its supra-spatial description is described, considering the latter as a natural superlattice. The complete (3 + 3)-mean basis, a set of modulation vectors and mass modulation functions are given. The dispersion of the phonon spectrum is calculated, and the dispersion dependences of the phonon spectrum in highly symmetric directions (Г - X - M - R - Г - M) of the Brillouin zone of the given crystal.
Introduction. The compound Cu₇GeS₅I relates to a large family of complex chalcogenides, which crystallize in the structures of argillaceites. At ambient temperature, the crystals under investigation are characterized by high symmetry: cubic sinongion, spatial group F - 43m. The main feature of copper-bearing argillites is the high solid-state ion conductivity of Cu + ions, which makes it possible to use these argilloid crystals as functional electronic materials.
Purpose. The main goal of this work was to develop a program suitable for theoretical calculation of the phonon spectra of Cu₇GeS₅I argillites and to carry out appropriate calculations (within the concept of superspace symmetry).
Methods. In the present work, the crystalline structure of Cu₇GeS₅I argillites was analyzed and described using the superspace symmetry concept.
Results. A program working in the Maple environment is developed and is suitable for theoretical calculation of the phonon spectra of Cu₇GeS₅I argillate crystals. Phonon spectra were calculated and presented for the model phases of Cu₇GeS₅I. The eigenvalues of the generalized dynamical matrix are found and the dispersion dependences for the directions of the Brightouin zone Г - X - M - R - Г - M are constructed

Keywords: argyrodites, crystal structure, protocrystal, phonon spectrum, Maple

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