Growth of nano-domains in Gd-CeO₂ mixtures: Hybrid Monte Carlo simulations

Hybrid Monte Carlo (HMC) simulations are used to study the growth of Gd-rich domains in Gd doped CeO₂, and we probe the conductivity of the resulting and other configurations by molecular dynamics. Previous work has been restricted to the dilute defect limit, assumptions of particular cluster formation, and neglect of all temperature effects. Our methods suffer none of these restrictions. Even at low concentrations Gd³⁺ segregates into domains. We have examined the local environment of the Gd³⁺ ions using radial distribution functions and Steinhardt order parameters. The observed structure is consistent with the formation of cubic C-type (Gd₂O₃) domains, rather than the monoclinic B-type or pyrochlore clusters which have been suggested previously. In addition, previous detailed pair distribution function analysis of the solid solution has indicated different local cation environments from those from a Rietveld analysis-overall our results support the former analysis rather than the latter. At the elevated temperatures (1000 K) of the simulations there is no particular preference for vacancy and dopant cations to be located at second neighbour sites, an issue long discussed for this and similar systems. Both calculated and experimental conductivities show a similar variation with composition, passing through a maximum with increasing Gd concentration. The conductivities of the configurations generated in the hybrid Monte Carlo simulations are lower than those of configurations generated independently in which the Gd ions are distributed at random. The HMC thermally generated Gd nano-domains capture oxygen vacancies, reduce oxygen vacancy mobility and block diffusion paths.