First principles investigations of structural, elastic, dielectric and piezoelectric properties of \{Ba,Sr,Pb\}TiO$_3$, \{Ba,Sr,Pb\}ZrO$_3$ and \{Ba,Sr,Pb\}\{Zr,Ti\}O$_3$ ceramics

We use first-principle density-functional study of structural, anisotropic mechanical, dielectric and piezoelectric properties of \{Ba,Sr,Pb\}TiO$_3$, \{Ba,Sr,Pb\}ZrO$_3$ and \{Ba,Sr,Pb\}\{Zr,Ti\}O$_3$ alloys in cubic perovskite structures at zero temperature. Because there is significant interest in finding new piezoelectrics that do not contain toxic elements such as lead. In this study, we compare piezoelectric response of those alloys to synthesize outstanding piezoelectric materials. In perovskite structures, the spontaneous polarization is due to enormous values of Born effective charges computed by linear response within density functional perturbation theory, which are much larger than predicted nominal charge. We deeply investigated the effects of composition, order and site defects structure on piezoelectric constants.