¹Uzhhorod National University, Faculty of Physics,
3, Narodna Sq., 88000 Uzhhorod, Ukraine
²Mukachevo State University,
26, Uzhhorodska str., 89600 Mukachevo, Ukraine
³Institute of Experimental Physics, Slovak Academy of Sciences
47, Watsonova str., 04001 Košice, Slovakia
E-mail: ivan.nebola@uzhnu.edu.ua

Abstract. In the concept of superspatial symmetry the crystal structure of Cu₇SiS₅I and Ag₇SiS₅I superionic conductors has been analyzed. To calculate the phonon spectra, the model of FCC superlattice (8а, 8а, 0; 8а, 0, 8а; 0, 8а, 8а) in the metric of protocrystal (а, а, 0; а, 0, а; 0, а, а) has been developed. For the developed model, the general (3+3)-dimensional basis, the array of modulation vectors and mass modulation functions have been presented. The model calculations of phonon spectra dispersion for Cu₇SiS₅I and Ag₇SiS₅I crystals in schemes with various partial occupation of crystallographic orbits by Cu(Ag) atoms have been performed. The dispersion dependences of phonon spectra for Cu₇SiS₅I and Ag₇SiS₅I crystals in the high-symmetric directions of Brillouin zone have been presented. The genesis of phonon branches of vibrational spectra has been analyzed.

Keywords:superionic conductor, phonon spectra, crystal structure, superlattice, protocrystal.

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