Origin of piezoelectricity for langasite A3Ga5SiO14 (A = La and Nd) under high pressure

The origin of piezoelectricity for langasite stated by a previous article has been clarified from the crystal structure under high pressure. The crystal structure of langasite with trigonal symmetry has the special empty-spaces located between A- and B-sites which are two large cation sites. The empty-space works for piezoelectricity. When a force is applied to the [1 0 0] direction, piezoelectricity was produced by the formation of polarity due to the shift of the A-cation in the [1 0 0] direction towards empty-space and deformation of the A-decahedron in the [−1 0 0] direction. In spite of the deformation of the A-site, the atomic distance between A- and B-ions is not changed due to the electrostatic repulsion. pty-space plays a role keeping of the A–B adjacent atomic distance and decreasing the B–A atomic distance throughout the empty-space. Under high pressure, it was clarified that the linear compressibility of the a-direction including the empty-space is larger than that of the c-direction. This shows the empty-space is contributing to the piezoelectricity. Also, it was clarified that the compressibility of the bond distance between A- and B-cations is smaller than that of the bond distance between A- and B-cations over the empty-space.