Yttria-stabilized zirconia YSZ is modeled using a cluster expansion statistical thermodynamics method built upon a density-functional theory database. The reliability of cluster expansions in predicting atomic ordering is explored by comparing with the extensive experimental database. The cluster expansion of YSZ is utilized in lattice Monte Carlo simulations to compute the ordering of dopant a...

We derive a cluster expansion for the electric susceptibility kernel of a dielectric suspension of spherically symmetric inclusions in a uniform background. This also leads to a cluster expansion for the effective dielectric constant. It is shown that the cluster integrals of any order are absolutely convergent, so that the dielectric constant is well defined and independent of the shape of the...