Heterovalent andA-atom effects inA(B′B″)O3perovskite alloys

Using first-principles supercell calculations, we have investigated energetic, structural, and dielectric properties of three different ${A(B}^{\prime }{B}^{″}){\mathrm{O}}_3$ perovskite alloys: ${\mathrm{B}\mathrm{a}(\mathrm{Z}\mathrm{n}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_3$ (BZN), ${\mathrm{P}\mathrm{b}(\mathrm{Z}\mathrm{n}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_3$ (PZN), and ${\mathrm{P}\mathrm{b}(\mathrm{Z}\mathrm{r}}_{1/3}{\mathrm{Ti}}_{2/3}){\mathrm{O}}_3$ (PZT). In the homovalent alloy PZT, the energetics are found to be mainly driven by atomic relaxations. In the heterovalent alloys BZN and PZN, however, electrostatic interactions among $B^{\prime }$ and $B^{″}$ atoms are found to be very important. These electrostatic interactions are responsible for the stabilization of the observed compositional long-range order in BZN. On the other hand, cell relaxations and the formation of short Pb-O bonds could lead to a destabilization of the same ordered structure in PZN. Finally, comparing the dielectric properties of homovalent and heterovalent alloys, the most dramatic difference arises in connection with the effective charges of the $B^{\prime }$ atom. We find that the effective charge of Zr in PZT is anomalous, while in BZN and PZN the effective charge of Zn is close to its nominal ionic value.