Electric Field Gradient Comparisons in Perovskites*

Piezoelectric and dielectric properties of Pb-based complex ferroelectric alloys with the A(B'B''B''')O$_3$ perovskite structure depend on composition and the local ordering of the B-site cations. A prototypical example is Pb(Sc$_{1/2}$Ta$_{1/2}$)O$_3$ (PST), which is a normal ferroelectric when the B atoms are ordered and becomes a relaxor when they are disordered. Electric field gradients (EFG) are sensitive to variations in local structure, and they can be probed using high-field nuclear magnetic resonance experiments. Calculations of EFGs are presented using the LAPW method within the local density approximation. We examine trends in B-site EFGs as a function of composition and order in PST, Pb(Zr$_{1-x}$Ti$_{x}$)O$_3$ (PZT), Pb(Sc$_{2/3}$W$_{1/3}$)O$_3$ (PSW), and Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$ (PMN). We discuss these results in terms of B- and Pb-atom off-centerings, and B-atom ordering.