Dopant control over the crystal morphology of ceramic materials

Doping is a common way to activate the behavior of ceramics. Its effect is not limited to the bulk: segregation of dopants to the surfaces also yields a way to modify, and ultimately control the crystal morphology. We propose a model that allows us to calculate the surface energy beyond the Langmuir isotherm for doped and defective surfaces from atomic-level simulations. The model also allows us to account for different compositions between the bulk and surface. Computational materials design can thus be applied to optimize simultaneously the crystal behavior at the atomic (surface structure and composition) and mesoscopic (crystal size and shape) length scales. We exemplify the model with orthorhombic CaTiO₃ perovskite doped with Mg²⁺, Fe²⁺, Ni²⁺, Sr²⁺, Ba²⁺ and Cd²⁺ ions, by predicting the effect that different dopants and dopant concentrations have on the crystal morphology. We find that a higher proportion of reactive {0 2 1} and {1 1 1} surfaces are exposed with the presence of divalent Mg²⁺, Fe²⁺ and Ni²⁺ ions than in the undoped material and in perovskite doped with Ba²⁺ and Sr²⁺. Cd²⁺ has only minor effects on crystal morphologies. These findings have important implications for predicting the reactivity of crystals doped with different ions and we show how this can be related to a simple parameter such as the ionic radius. We have tested our newly derived model by comparison with laboratory flux grown single crystals of CaTiO₃, (Ni, Ca)TiO₃ and (Ba, Ca)TiO₃ and find excellent agreement between theory and experiment.