The vertex contribution to the Kirste–Porod term

It is shown that, close to the origin, the correlation function [γ(r)] of any N-component sample with interfaces made up of planar facets is always a third-degree polynomial in r. Hence, the only monotonically decreasing terms present in the asymptotic expansion of the relevant small-angle scattered intensity are the Porod [−2γ'(0+)/h4] and the Kirste–Porod [4γ(3)(0+)/h6] contributions. The latter contribution is non-zero owing to the contributions arising from each vertex of the interphase surfaces. The general vertex contribution is evaluated in closed form and the γ(3)(0+) values relevant to the regular polyhedra are reported.