Spontaneously nucleated crystals can grow with various orientations. In such processes, surviving crystals are selected simply by their geometrical relation with the substrate surface. As a result, various textures of polycrystalline aggregates appear that are controlled by the form of the substrate surface. Spherulite, sheaf-like, and confeito-like polycrystalline aggregates or the curved banding patterns seen in agate are all formed by a simple geometrical selection process. This principle has been practically utilized in single crystal synthesis and in epitaxial growth. It also acts in the formation of calculus in the internal organs of human bodies.

Geometrical selection

When nucleation occurs freely on a flat substrate surface under uncontrolled conditions, numerous crystals are formed at random orientations if there is no epitaxial relation between the substrate and the crystal. Crystals inclined to the substrate surface will make contact with crystals growing perpendicularly and stop their growth. If we assume the existence of equi-concentration lines parallel to the substrate surface, the growth of crystals perpendicular to the substrate will be promoted further, since their tips are in an ambient phase of higher driving force. In this way, only the crystals growing perpendicularly to the substrate surface will survive and continue to grow among many crystals formed on the substrate surface, and this is accompanied by a decrease in the number of individuals and appearance of textures consisting of many crystals aligned in a specific orientation.