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

• Published in: Acta crystallographica. Section A, Foundations of crystallography Foundations of crystallography, 2002-05, Vol.58 (3), p.221-231
• Main Authors: Schneider, J.-M., Ciccariello, S., Schönfeld, B, Kostorz, G.
• Format: Article
• Language: English
• Subjects: anisotropic Porod law; Condensed matter: structure, mechanical and thermal properties; Exact sciences and technology; Neutron diffraction and scattering; Neutron scattering techniques (including small-angle scattering); non-convex particles; Physics; small-angle scattering; Structure of solids and liquids; crystallography; X-ray diffraction and scattering; X-ray scattering (including small-angle scattering)
• ISSN: 0108-7673; 1600-5724
• DOI: 10.1107/S0108767302000934

For anisotropic particulate samples with scattering contrast , the leading asymptotic term of the scattering intensity, along a direction () of reciprocal space, is . Here, denotes the Gaussian curvature value at the points (labelled by ) of the interphase surface where the normal is either parallel or antiparallel to . If the Gaussian curvature vanishes at, say, the th of these points, the corresponding contribution takes the form with , and being determined by the local behaviour of the surface. However, the intensity detected by a counter pixel, with opening solid angle along (mean) direction , asymptotically still behaves as , where is the area of that part of the interface that has its normals inside .