Piezoelectricity in PbZr x Ti 1-x O 3 Studied by Density-Functional Perturbation Theory Supercell Calculations

First-principles calculations of the piezoresponses ( e 33 ) of PbZr x Ti 1- x O 3 (PZT) with various crystalline phases and Zr/Ti ratios (composition: B-site cations) are performed at room temperature using density-functional perturbation theory (DFPT) to understand the experimental observation that large piezoresponses occur at the morphotropic phase boundary (MPB). The results of ab initio calculations indicate that PZT (Zr/Ti = 52/48) with a tetragonal (P4MM) phase shows the lowest formation energy (stable) and the highest piezoelectric coefficient, e 33 , in the MPB region. The Z * /Δε ratio (where Z * is the Born effective charge and Δε is the variation in the internal strain) is computed, and we find that laterally bonded oxygen atoms are the main contributors to e 33 in the above structure owing to the low Δε 3 caused by perturbation.