Sol–gel obtained YSZ nanocrystals on a substrate: A Monte Carlo approach of the crystallographic orientation

Sol–gel obtained yttria stabilized zirconia (YZS) nanocrystals have different morphologies when they grow on an image-alumina substrate after thermal treatment. When the substrate has planar defects, the nanocrystals grow in height and are narrow with a crystallographic orientation image in the vertical direction, while when the substrate is a perfect plane at the nanometric scale, the nanocrystals are rather extended over the substrate and do not grow in height, with a crystallographic orientation image in the vertical direction. We present here a Monte Carlo approach which computes the actions of the substrate on the nanocrystals during thermal treatment: one action is the change in crystallographic orientation depending on the presence of defects and the other is the action on the morphology of the nanocrystals. The equivalent of thermal treatment is obtained after applying the Metropolis algorithm with adequate expressions of the energy depending on the inter-plane spacings and surface diffusion. Our numerical approach is in good agreement with the experimental results on the orientations and morphologies of the YSZ nanocrystals growing on a image-alumina substrate with planar defects [R. Bachelet, A. Boulle, B. Soulestin, F. Rossignol, A. Dauger, R. Guinebretiere, Thin Solid Films 515 (2007) 7080].