Comparisons of Piezoelectricities of Lead Zirconate Titanate for Various Phases by a First-Principles Method

We calculated and compared the piezoelectric coefficients and Born effective charges of various PZT crystals, which have different B-site orderings and crystal symmetries by a first-principles method. The piezoelectric coefficient of rhombohedral structures is smaller than that of tetragonal structures because of the weakness of the hybridization change between the oxygen and B-site orbitals. We discuss this reason using a simple analytic model. We also performed the first-principles calculation of the piezoelectric coefficient with emphasis on its dependencies on the k-point number and calculation scheme (GGA or LDA), and found that calculated piezoelectric coefficients are very sensitive to these factors. This is due to the fact that the piezoelectric coefficient strongly depends on the small changes of the internal displacement gradient.