Theoretical study of the optical dispersion and anisotropy of the oxygen polarisability of PbTiO 3 in the tetragonal phase K. Bammou, D. Khatib

this article, we present in section 2 the model description, in section 3 the results of the calculation of anisotropic oxygen polarizability. Finally, in section 4 we make a summary and some discussions about the global results. II. MODEL DESCRIPTION In the similar manner to the previous work on BaTiO 3 the dipole-dipole interaction acting on the constituent ions of PbTiO 3 is expressed as: () [] - = n m l r n m l n m l ij r j p n m l ij r j p ) , , ( 1 , , 5 ) , , ( 2 2 ) , , ( . 3 (1) where represents a Cartesian coordinate ( = 1, 2, 3), p is the dipole moment of the j-ion. In the equation (1), r is the distance between i and j-ions and the indices (l, m, n) represent the coordinates of a unit cell in the whole lattice. At wavelength , the electronic polarization ( P of the i-ion in the direction can be written : + = j j j ij i i i ) ( , (2) where ) ( represents the electronic polarizability of the i-ion, the N i is the number of the i-ions per unit volume and N is the number of the unit cells in the lattice. K. BAMMOU, D. KHATIB, F. BENSAMKA... The relation between dielectric constant ) ( polarization ) ( P and electric field ) ( E is: ) ( ) ( ) ( 4 1 E + = (3) where ) ( P is calculated by summation of the electronic polarization ) ( P of j-ion