Non-Equivalence of Interatomic Interaction in Model Calculations of the Phonon Dispersion

Consecutive inclusion of additional physical parameters (color, phase, sign of charge, spin, etc.) in the symmetric description led to creation of the theory of color symmetry and the concept of superspatial symmetry. Being based on the latter approach, a method for calculating the phonon dependences of complex crystals was developed in continuation. Among the varieties of generalized symmetry, the concept of superspatial symmetry is quite convenient and visual when constructing ($3+d$) dimensional models for describing the crystal structure of complex crystals and systems united by a single metric and scale of the protocrystal carrier function. Software was developed and model calculations of phonon spectra of crystals of BaTiO<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> type crystals in equidistant and non-equidistant approximations for the field of force interaction were carried out. It is shown that the non-physical 5-fold degeneracy at the point R of the Brillouin zone in the calculations in the equidistant approximation of the force field splits when considering the non-equivalent force interaction.