Existence of a surface-induced pressure in anisotropic crystals

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Abstract
The liquid-drop model which is usually used to interpret the lattice-parameter contractions occurring in small crystalline solids assumes that the shape of the microcrystal is a sphere and that the surface forces reduce to a hydrostatic pressure. In this paper, the virial of the surface forces which gives the volume change of the crystal is calculated for a real crystal with a general faceted shape. The authors show, in particular, that the concept of pressure can still be defined inside a small crystal if a property called gamma -symmetry is satisfied. This property involves a relation between the geometry of the crystal and the surface tensions. When the surface forces are all applied normal to the edges of the faces, the gamma -symmetry can be explained in terms of the geometrical symmetry of the crystal. Particular cases, such as the regular Wulff polyhedron typical of a cubic structure or the multi-twinned particles observed for some metals, are discussed.