Thermal diffuse X-ray scattering study of anharmonicity in cubic barium titanate

Abstract

Two BaTiO 3 single crystals with one containing 0.3 at.% Fe 3+, substituted for Ti 4+, have been examined by in-situ X-ray thermal diffuse scattering (TDS) measurement above the Curie temperature (∼ 130°C). Results from the pure sample show two-dimensional TDS distribution on the {1 0 0}; they are attributed to the overdamped [0 1 0] TO mode and to the anisotropic on (1 0 0) TA modes. The TDS distribution and negative temperature dependence of the intensity near the zone center agree well with the previous neutron inelastic scattering results found in the literature. The TDS distribution from the doped sample showed a similar pattern to that of the pure sample. However, some differences were found at smaller wave vectors where a positive temperature dependence of the intensity is seen as well as a more isotropic distribution. The heterovalent doping is believed to have changed the lattice anharmonicity. The TDS intensity calculations have been carried out using the normal mode analysis under the harmonic approximation. The calculated results showed good agreement with the observed data at | q| > 0.25 for the two samples. The anharmonic correction was necessary, however, for the TDS intensity calculations near the zone center, i.e. | q| < 0.25 , for which the imaginary part of the response function for the [0 1 0] TO mode was used in the calculations. In curve fitting the damping constants of the pure sample were found slightly larger than those of the doped sample, implying a decrease of anharmonicity due to heterovalent doping. This effect may be understood using a hole/electron-relaxation coupling concept.