ESTIMATES OF ANDERSON ELECTRON-PHONON-COUPLING CONSTANTS FOR NONADIABATIC SMALL POLARONS IN N-TYPE BATIO3 USING A POLARIZABLE POINT-ION SHELL-MODEL

Using a combination of the attractive potential of a polaron proposed by Anderson and the polarizable point-ion shell model developed by Dienes et al., Anderson's electron-phonon-coupling constants (lambda) and changes in interionic spacings (x) due to nonadiabatic small polarons in n-type BaTiO3 have been estimated by adjusting the calculated values to fit the experimental results, i.e., the polaron binding energy and the deformation energy. Although these values are important for an understanding of the dynamics of small polarons, they are quite difficult to estimate experimentally. In the shell model, the repulsive interactions between ions have been evaluated by the free-ion model constructed by Wedepohl. Though the shell parameters representing the effective numbers of polarizable electrons in ions are determined empirically, they are very close in values to the theoretical ones of Shankar et al. Since there is no information on the nature of the electrons localized on Ti ions, two possibilities have been considered, i.e., 3d electrons or s-like electrons. The calculations have been carried out in cubic and rhombohedral structures. In the cubic structure, lambda and x between Ti3+ and Ti4+ in <110> are approximately -3.60 eV/angstrom and approximately -0.01 angstrom and those between Ti3+ and O2- in <100> are approximately 0.82 eV/angstrom and approximately 0.03 angstrom for 3d electrons. In the case of s-like electrons, lambda and x for the ion pair Ti3+ and Ba2+ in <111> and those of Ti3+-O2- pairs are approximately -1.29 eV/angstrom, approximately -0.02 angstrom and approximately 0.60 eV/angstrom, approximately 0.03 angstrom, respectively. In the rhombohedral structure, the values for lambda and x are a little different from those in the cubic structure. These calculations suggest clearly that small polarons are stabilized in both the cubic and rhombohedral structures and the polaronic conduction is also confirmed theoretically to take place in n-type BaTiO3.