MICROSCOPIC CALCULATIONS OF FERROELECTRIC INSTABILITY IN PEROVSKITE CRYSTALS

First-principles calculations are performed relating to the stability of a series of perovskite crystals with respect to transition to the f erroelectric and the antiferroelectric state. The calculations employ the generalized Gordon-Kim method, in which the total charge density o f an ionic crystal is represented as a superposition of the densities of the individual ions. In the spirit of the nonequilibrium thermodyna mics of Leontovich the charge density of an individual ion is calculat ed in the presence of external auxiliary fields which deform this dens ity. Multipole deformations up to quadrupole are taken into account. T he actual magnitude of the deformation is found by minimizing the tota l energy of the crystal in the Thomas-Fermi-Dirac approximation. The c alculated values of the ion shifts in the ferroelectric phase for BaTi O3, and also the electron contribution to the dielectric constant epsi lon(infinity) and the dynamic Born effective charges Z(eff) are found to be in good agreement with the experimental data. The proposed metho d allows one to obtain an analytical expression for epsilon(infinity), Z(eff), and the dynamic vibration matrix. It is shown that these expr essions formally coincide with the expressions arising in the phenomen ological models of the polarized and deformed ion. Analysis of the exp ressions obtained confirms the validity of the classical theory of fer roelectrics of displacement type for perovskite crystals. (C) 1998 Ame rican Institute of Physics.