Abstract

Objective. Considering the composite regulation and modulation of power in the construction of permanent generalized dynamic matrix concept superspace symmetry allows to do the analysis of its structure and calculate the phonon spectrum, with the possibility of modifying the concentration of vacancies and constant change of power in one software. It’s very important while studying phase transitions shift type and nature of instability crystal lattice singleexcitation
spectra calculations.
Methods. The dynamics of crystal lattice of types ABC₃ represented within the formalism Bourne Van Karman for a perfect crystal in the harmonic approaching using the model axially symmetric permanent atomic interaction. To account for the modulation constant force in the construction of complex dynamic matrix crystal approximation equidistantly applied force field. Studying of vacancies on the features of the phonon spectrum was carried out in three ways: by taking into account modulation "mass" performance, by taking into account modulation and constant power by taking into account simultaneous modulation "mass" and power characteristics
Results. The tendency of changing frequencies of the phonon spectrum in the points of high symmetry Brilyuen depending on variations in mass and strength characteristics was bound. The most likely "soft" modes of crystal ABC₃ there are fashion is Г₁₅, M₃, M3I and R₂₅. In the high symmetry areas of zone Brilyuen Г- R and Г- M for defect perovskites with cationic vacancies there is a strong damping of phonons "soft" fashion, particularly when such αB-C(1) →0, αA-B(3) →0 crystals A□C₃ and αA-C(2) →0, αA-B(3)→0 crystals with type □BC₃ (□-vacancy). Thus, the frequency of the acoustic phonon spectrum branches both types of crystals rapidly approaching zero. 
Discussion. In the limit of vacancies due to lack of heavy cations A in structures such BC₃ , as a stabilizing factor, the deformation motive of octahedral BC₃ leads to instability of the crystal lattice (vanishing points and a frequency R and M). Its elimination is possible by increasing the period of primitive cell multiplication.
Conclusions. The effect of vacancies in the crystal transformation phonon spectrum, including modulation "mass" and modulation characteristics of constant power, which is important to control doping atoms in the synthesis of new materials with predictable physical properties was shown

Keywords: phonon spectrum, force constants, ferroelectric, perovskite, cation vacancy

Suggested citation