Structural dependence of electric field gradients inPb(Zr1−xTix)O3from first principles

First-principles all-electron density functional theory calculations of electric field gradients (EFGs) are presented for $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ and structural models of $\mathrm{Pb}\left({\mathrm{Zr}}_{1∕2}{\mathrm{Ti}}_{1∕2}\right){\mathrm{O}}_3$. Calculations were carried out as a function of $B$-site chemical ordering, applied strain, and imposed symmetry. Large changes in the EFGs are seen as the electric polarization rotates between the tetragonal and monoclinic structures. The onset of polarization rotation in $Cm$ symmetry strongly correlates with the shearing of the $\mathrm{Ti}{\mathrm{O}}_6$ octahedra, and there is a sharp change in slope in plots of Ti EFGs vs octahedral distortion index. Trends in the calculated oxygen EFGs are consistent with recent nuclear magnetic resonance (NMR) measurements, which indicate significant sensitivity of oxygen NMR peaks to changes in the local structure as a function of Ti concentration. Calculated Ti EFGs are considerably larger than those inferred from the NMR measurements. Based on comparisons with experiment, the calculated results are interpreted in terms of static and dynamic structural models of $\mathrm{Pb}\left({\mathrm{Zr}}_{1-x}{\mathrm{Ti}}_x\right){\mathrm{O}}_3$.