  K$_{1-x}$Li$_{x}$TaO$_3$ (KLT) solid solutions exhibit a variety of
interesting physical phenomena related to large displacements of Li-ions from
ideal perovskite A-site positions. First-principles calculations for KLT
supercells were used to investigate these phenomena. Lattice dynamics
calculations for KLT exhibit a Li off-centering instability. The energetics of
Li-displacements for isolated Li-ions and for Li-Li pairs up to 4th neighbors
were calculated. Interactions between nearest neighbor Li-ions, in a Li-Li
pair, strongly favor ferroelectric alignment along the pair axis. Such Li-Li
pairs can be considered "seeds" for polar nanoclusters in KLT.
Electrostriction, local oxygen relaxation, coupling to the KT soft-mode, and
interactions with neighboring Li-ions all enhance the polarization from Li
off-centering. Calculated hopping barriers for isolated Li-ions and for nearest
neighbor Li-Li pairs are in good agreement with Arrhenius fits to experimental
dielectric data.
