Interfacial crystallization at the intersection of thermodynamic and geometry

Interfacial crystallization appears as a crucial stage in the numeral natural phenomena and technological applications, such as industry of semi-conductors and manufacturing of nano-whiskers. Interfacial aspects of heterogeneous crystallization are surveyed. The review is focused on the interplay of thermodynamic and geometric aspects of the interfacial crystallization. Thermodynamic considerations leading to the Wulff construction are discussed. Equilibrium shape of the crystallized particle in the contact with a foreign substrate giving rise to the Winterbottom construction is treated. The concept of equivalent equilibrium contact angle θ_eq is introduced. The equivalent contact angle θ_eq applicable for isotropic crystals does not depend neither on the volume of the crystallized particles nor on the external fields. Bulk contributions to the free energy of the particle such as the bulk heat release in the case of reactive contact or latent heat of crystallization do not influence the equivalent contact angle θ_eq. Application of the Winterbottom constructions for prediction of the shape of nanoparticles grown on solid substrates is treated. Thermodynamics of interfacial crystallization is discussed. The thermodynamic condition predicting when surface crystallization is thermodynamically favored over homogeneous (bulk) crystallization is supplied. This thermodynamic relation coincides with the condition prescribing the partial wetting of a solid by its melt. Interfacial crystallization in its relation to the "coffee-stain" effect, salt creeping and development of anti-icing surfaces is addressed. Interfacial aspects of epitaxial growth of crystals are considered. The current state-of-art in the field is reviewed.