Equilibrium Shapes of Crystals

Abstract

The condition for equilibrium in a heterogeneous system including an anisotropic solid and a vapor, may be written, by analogy with (8.1.1), in the most general form as

$$ dG = {\mu ^{\left( g \right)}}dN + {\mu ^{\left( c \right)}}\frac{{dV}}{{{\upsilon _c}}} + \sum\limits_j {{\gamma _i}d{A_j}} = 0, $$

where V and v _c are the volumes of the entire solid and of one molecule in the crystal lattice, respectively, while γ _j and A _j are the surface tension and the area of the j-th face. Capillarity approximation is implicitly admitted through the assumptions μ ^(c) = μ ^(c) _∞ and γ _j = const. The expression is, therefore, valid for crystal sizes i ₀ < i < ∞ (cf. Sect. 8.1).