Ca-induced phonon softening in BaTiO revealed by inelastic X-ray and neutron scattering

Kimura, Koji*; Tsutsui, Satoshi*; Yamamoto, Yuta*; Nakano, Akitoshi*; Kawamura, Keisuke*; Kajimoto, Ryoichi  ; Kamazawa, Kazuya*; Martin, A.*; Webber, K. G.*; Kakimoto, Kenichi*; Hayashi, Koichi*

We performed inelastic X-ray and neutron scattering (IXS and INS) experiments for (Ba,Ca)TiO single crystals to elucidate the effect of Ca doing on the atomic dynamics. Dispersion relations of transverse phonons in BaTiO, (BaCa)TiO, and (BaCa)TiO were determined. The -site-O vibrational mode as well as the acoustic mode were observed both by IXS and INS, whereas the Ti-O soft mode was detected only by INS. It was found that the -site-O vibration exhibits significant softening with increasing Ca concentration, while the Ti-O soft mode is almost unaffected by the Ca doping. This finding is discussed in comparison with the polarization hysteresis loops and piezoelectric coefficients of (Ba,Ca)TiO. It is indicated that the softening of the -site-O vibration contributes to the enhancement of the piezoelectricity of Ca-doped BaTiO-based materials.