A CLASSICAL ELECTROSTATIC MODEL FOR TETRAGONAL SINGLE-CRYSTALS OF BARIUM-TITANATE

Experimental observations of the ionic coordinates in single crystals of tetragonal barium titanate, together with theoretical estimates of the ionic charges, are taken as the starting point of a classical anal ysis of an electrostatic model of the crystal in which each ion is rep resented by a point charge carrying a point dipole; this dipole repres ents that arising from the electronic polarizability of the ion of the crystal. The positions occupied by the ions are such that their charg es cause ionic polarization of the unit cells of the crystal. The char ges also cause an electric field to exist at each ion; its calculation is based upon the Lorentz formula for internal field, but with a cruc ial difference in the manner of its application from the manner in whi ch it previously has been applied. The ion exhibits electronic polariz ation caused not only by the field acting on it due to ionic charges, but also by that due to the electronic dipoles created at all other io ns; the electronic polarization process is consequently highly interac tive, These considerations lead to the derivation of an equation which must be satisfied if the spontaneous polarization is to be predicted; a similar procedure leads to another independent equation for the pre diction of the refractive index. The electronic polarizabilities of th e ions are constituents of each of these equations, and the insertion into them of literature values for the electronic polarizabilities of the barium and titanium ions permits the evaluation of the electronic polarizabilities of the oxygen ions in their two different crystallogr aphic positions. The fields acting at, and the electrostatic forces ac ting on, each ion are then calculated.