  We investigate the effect of ferroelectric polarization direction on the
geometric properties of Pd deposited on the positive and negative surfaces of
LiNbO$_3$ (0001). We predict preferred geometries and diffusion properties of
small Pd clusters using density functional theory, and use these calculations
as the basis for kinetic Monte Carlo simulations of Pd deposition on a larger
scale. Our results show that on the positive surface, Pd atoms favor a
clustered configuration, while on the negative surface, Pd atoms are adsorbed
in a more dispersed pattern due to suppression of diffusion and agglomeration.
This suggests that the effect of LiNbO$_3$ polarization direction on the
catalytic activity of Pd [J. Phys. Chem. \textbf{88}, 1148 (1984)] is due, at
least in part, to differences in adsorption geometry. Further investigations
using these methods can aid the search for catalysts whose activities switch
reversibly with the polarization of their ferroelectric substrates.
