Comparison of the different distribution functions in Gd-doped ceria system by molecular dynamics simulations

Cerium dioxide-based materials are among the most studied for applications in the energy and environmental fields and are also of interest in biology and medicine. The fluorite structure of CeO₂is locally distorted by the concomitant presence of doping cations, such as Gd³⁺and oxygen vacancies. The cation-anion bond length distribution then becomes increasingly asymmetric with the doping ratio and temperature. In these cases, the MD simulation results indicate that the commonly used maximum of the pair correlation functiong(r) first peak can no longer be adopted to estimate the mean bond length. To determine the true cation-anion bond length, the analysis of the radial distribution functionR(r) first peak is necessary. Furthermore, the asymmetry of this peak must be accounted for when extracting the mean value of the distribution. The gap between theg(r) maximum and theR(r) mean position derived from the fit using a skewed Gaussian function clearly increases with the doping ratio and temperature, leading to different conclusions concerning bond length evolution. The present study also suggests that care must be taken when the bond length is deduced from the pair distribution functionsG^pdf(r) as is the case in total scattering experiments (x-ray and neutrons). Finally, relations between the cumulants of the effective distribution of distances as determined in extended x-ray absorption fine structure experiments and the cumulants describing the real distance distribution are proposed considering that both these distributions are modelled by a skewed Gaussian function.