Equilibrium shape of an anisotropic crystal confined between two planar parallel walls

Experimentally, the surface-free-energy anisotropy of a crystal-liquid interface is usually inferred from the surface-shape anisotropy of a solid germ at equilibrium with the melt. However, the crystal is usually not free. For example, in thin samples, the crystal touches the two limiting glass plates:mHere, we analyze theoretically how the shape anisotropy of the crystal depends on the wetting conditions in this particular geometry. We calculate the equilibrium shape of an anisotropic crystal (of uniaxial, cubic, or hexagonal symmetry) confined between two planar parallel walls as a function of its size and of the wetting conditions on the walls. We find an analytic solution for the shape of the meniscus in the sample thickness and its anisotropy in the midplane parallel to the walls in the limit of very large radius and vanishing surface tension anisotropy. In other cases, a numerical solution is given. Neglecting the meniscus effect leads to errors as large as 25% for the inferred anisotropy.