Effects of Gravity on Equilibrium Crystal Shapes.

The effects of gravity on the two-dimensional equilibrium shapes (ES) of crystals and menisci are investigated for different geometries (positions) of the substrate. In the gravity-free case, the equilibrium crystal shape (ECS) is characterized by a scale invariance. The presence of gravity breaks the scale invariance and the resulting ECS changes as the volume of the crystal V is changed. Moreover, the presence of gravity breaks the translational invariance along the direction it acts. Physically realized by the necessity of a support, this is manifested by the existence of an inhomogeneous effective pressure P_{rm eff}, which divides the space into two regions, with P_ {rm eff} either negative or positive. The ECS changes as the crystal passes from one region to another, being concave where P_{rm eff } < 0, and convex where P _{rm eff} > 0. In all cases it was possible to express the corresponding ECS in terms of the gravity-free one. For the hung crystal, i.e., a crystal pinned to a vertical wall at the top, it is shown that some orientations are missing from the ECS that otherwise will be present in the gravity-free ECS, adsorbed on the same substrate. Thus, facets could disappear from the crystal shape as the volume V or the gravitational acceleration g is increased. A critical volume V_{rm c} is found, so that if the crystal volume V exceeds V_{rm c}, the crystal cannot be pinned. The ECS can exhibit both concave and convex portions. For a crystal, pinned to a vertical wall at its lower end, we find that it will never develop a concave part. On the other hand, new orientations, absent from the gravity-free crystal, will be present on its ECS. The ES of a free and pinned crystal meniscus is also solved and an expression for the excess (depleted) volume DeltaV is derived. The solution for the crystal meniscus between two walls is also presented. For the pendant crystal, i.e., a crystal hanging from a horizontal support, we find that it can exhibit both concave and convex portions on its ECS. An expression for the facet length in the presence of gravity is obtained that is valid for all types of support. (Abstract shortened with permission of author.).