  We have examined the local structure of PMN-PT and PZN-PT solid solutions
using density functional theory. We find that the directions and magnitudes of
cation displacement can be explained by an interplay of cation-oxygen bonding,
electrostatic dipole-dipole interactions and short-range direct and through
oxygen Pb-B-cation repulsive interactions. We find that the Zn ions off-center
in the PZN-PT system, which also enables larger Pb and Nb/Ti displacements. The
off-centering behavior of Zn lessens Pb-B-cation repulsion, leading to a
relaxor to ferroelectric and a rhombohedral to tetragonal phase transition at
low PbTiO$_3$ content in the PZN-PT system. We also show that a simple
quadratic relationship exists between Pb and B-cation displacements and the
temperature maximum of dielectric constant, thus linking the enhanced
displacements in PZN-PT systems with the higher transition temperatures.
