Atomic positions and displacements in piezoelectric materials Ca₃TaGa₃Si₂O₁₄ and Ca₃TaGa_1.5Al_1.5Si₂O₁₄ investigated by Ta-Lα X-ray fluorescence holography

The atomic positions and displacements of atoms around the Ta atom in piezoelectric materials Ca₃TaGa₃Si₂O₇ (CTGS) and Ca₃TaGa_1.5Al_1.5Si₂O₇ (CTGAS) were investigated at 100 K by Ta-Lα X-ray fluorescence holography (XFH). The experimental atomic images were compared with the simulated ones using the crystal structures of CTGS and CTGAS, which were determined by single crystal X-ray diffractometry (SC-XRD). The atomic positions agreed between XFH and SC-XRD experiments. With the help of XFH simulation, the displacements of Ta, Ca, Si, and Ga atoms relative to the Ta atom were qualitatively analyzed using experimental atomic image intensities. The relative displacement of the Ca atom was increased by Al substitution, while those of the Ta and Ga atoms were decreased. The first principles calculation based on density-functional theory (DFT) was performed to understand bonding character between constituents. The evaluation of the crystal orbital Hamilton population (COHP) clarified that the Ca-O bond has strong ionic character different with the other bonds, suggesting that the positional shift of the Ca atom is responsible for the piezoelectricity in CTGS. The effect of Al substitution on piezoelectricity was also considered based on the change in the Ca-O bond.