Equilibrium Shapes of Crystals

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).