Generalization of Porod's law of small-angle scattering to anisotropic samples

Small-angle scattering from anisotropic samples, consisting of homogeneous particles inside a homogencous medium with a scattering contrast (Delta n)(2), is considered. Along any direction (q) over cap q/ \q\ of reciprocal space, at large q( drop \q\) the Pored plot of the scattering intensity (i.c. q(4) I(q) vs. q) shows a plateau whose height depends on (q) over cap and reads 4 pi(2)(Delta n)(2) Sigma(j,l) (1/ \kappa(G,j,l)(+/-(q) over cap)\) . Here, the sum runs over all the points (labeled by (j, l)) of the surface of the j-th particle of the sample where the normal is either parallel or antiparallel to (q) over cap and kappa(G,j,l)(+/-(q) over cap) is the corresponding Gaussian curvature value.