The asymptotic leading term of anisotropic small-angle scattering intensities. II. Non-convex particles

For anisotropic particulate samples with scattering contrast (delta n)(2), the leading asymptotic term of the scattering intensity, along a direction q (q/q) of reciprocal space, is [4 pi(2)(delta n)(2)/q(4)]sigmaj [1/kappaG.j(+/-q)]. Here, kappaG.j(+/-q)denotes the Gaussian curvature value at the points (labelled by j) of the interphase surface where the normal is either parallel or antiparallel to q. If the Gaussian curvature vanishes at, say, the jth of these points, the corresponding contribution takes the form Cj/qalpha with 2< or = alphaj<4, Cj and alphaj being determined by the local behaviour of the surface. However, the intensity detected by a counter pixel, with opening solid angle deltaomega(q0) along (mean) direction q0, asymptotically still behaves as 4pi(2) (delta n)(2)(deltaomega(q0))/q(4), where S(deltaomega(q0)) is the area of that part of the interface that has its normals inside deltaomega(q0).