The first-principles (ab initio) computations of the structural, electronic, and phonon properties have been performed for cubic and low-temperature tetragonal phases of BaTiO₃ and SrTiO₃ perovskite crystals, both stoichiometric and non-stoichiometric (with neutral oxygen vacancies). Calculations were performed with the CRYSTAL17 computer code within the linear combination of atomic orbitals approximation, using the B1WC advanced hybrid exchange-correlation functional of the density-functional-theory (DFT) and the periodic supercell approach. Various possible spin states of the defective systems were considered by means of unrestricted (open shell) DFT calculations. It was demonstrated that oxygen reduction leads to the appearance of new local vibrational modes associated with oxygen vacancies and new first-order peaks in the Raman spectra, which could be used for defect identification. The calculated Raman spectra for different vacancy positions and spins of the system, as well as other properties of defective crystals, are compared with the relevant experimental data.

The standard Lotka-type model, which was introduced for the first time by Mai et al. [J. Phys. A 30, 4171 (1997)] for a simplified description of autocatalytic surface reactions, is generalized here for a case of mobile and energetically interacting reactants. The mathematical formalism is proposed for determining the dependence of transition rates on the interaction energy (and temperature) for the general mathematical model, and the Lotka-type model, in particular. By means of Monte Carlo computer simulations, we have studied the impact of diffusion (with and without energetic interactions between reactants) on oscillatory properties of the $A+\overrightarrow{B}2B$ reaction. The diffusion leads to a desynchronization of oscillations and a subsequent decrease of oscillation amplitude. The energetic interaction between reactants has a dual effect depending on the type of mobile reactants. In the limiting case of mobile reactants B the repulsion results in a decrease of amplitudes. However, these amplitudes increase if reactants A are mobile and repulse each other. A simplified interpretation of the obtained results is given.

Long-range positional and orientational correlations of nanocubes in self-assembled mesocrystals are highly sensitive to the presence of dipoles.

A six-fold increase of the e₃₃ piezoelectric constant is theoretically predicted for a lead-free perovskite superlattice.

An enhancement of the piezoelectric properties of lead-free materials, which allow conversion of mechanical energy into electricity, is a task of great importance and interest. Results of first-principles calculations of piezoelectric/electromechanical properties of the Ba_(1–x)Sr_xTiO₃ (BSTO) ferroelectric solid solution with a perovskite structure are presented and discussed. Calculations are performed within the linear combination of atomic orbitals (LCAO) approximation and periodic-boundary conditions, using the advanced hybrid functionals of density functional theory (DFT). A supercell model allows the investigation of multiple chemical compositions x. In particular, three BSTO solid solutions with x = 0, 0.125, 0.25 are considered within the experimental stability domain of the ferroelectric tetragonal phase of the solid solution (x < 0.3). The configurational disorder with x = 0.25 composition is also investigated explicitly considering the seven possible atomic configurations corresponding to this composition. It is predicted that Sr-doping of BaTiO₃ makes it mechanically harder and enhances its electromechanical/piezoelectric properties, which are important for relevant applications.