X-ray and neutron diffraction study of tetragonal barium titanate

An attempt is made to differentiate between the three previously proposed models of the structure of tetragonal BaTiO₃. In the new model, the serious parameter-interaction problem was avoided by the use of both neutron and X-ray diffraction data collected from c-domain single crystals. The result of the refinement gave the displacement of the Ti atom from its cubic position as 0.0135 ± 0.0004 Å; the R value was 0.027 and 0.024 for the neutron and X-ray data respectively. The analysis also showed that the temperature parameters, B₃₃, along the c axis are approximately independent of mass; B₃₃ = 0.32 ± 0.03 Ų from X-ray and 0.33 ± 0.04 Ų from neutron diffraction. The average value obtained for the B₁₁ temperature parameters, B₁₁ = 0.50 Ų, is considerably higher than the B₃₃ value, which thus clearly indicates the existence of low frequency optic modes at room temperature.