Estimating the sizes of small single crystals satisfying the Wolf theorem

Abstract

Geometric estimates of the characteristic sizes of simple single crystals with tetragonal, cubic, and octahedral shapes of the surface are obtained. The Wolf theorem with independent contributions from each face to the surface tension can be applied to these if the edge size is at least ~53 lattice constants. Energy estimates of the individuality of free energy contributions from each face are consistent with this estimate. The resulting minimum edge sizes also agree with an independent estimate obtained earlier using the contributions from fluctuations in the near-surface region of the phase.