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

S. Ciccariello; J.-M. Schneider; B. Schönfeld; G. Kostorz

doi:10.1209/epl/i2000-00312-y

All issues

Volume 50 / No 5 (June I 2000)

Europhys. Lett., 50 5 (2000) 601-607

Abstract

Issue		Europhys. Lett. Volume 50, Number 5, June I 2000


Page(s)		601 - 607
Section		Condensed matter: structure, mechanical and thermal properties
DOI		https://doi.org/10.1209/epl/i2000-00312-y
Published online		01 September 2002

Europhys. Lett., 50 (5), pp. 601-607 (2000)

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

S. Ciccariello¹, J.-M. Schneider², B. Schönfeld² and G. Kostorz²

¹ Dipartimento di Fisica “G. Galilei" and INFM, sezione di Padova via Marzolo 8, I-35131 Padova, Italy
² ETH Zürich, Institut für Angewandte Physik - CH-8093 Zürich, Switzerland

Received: 19 October 1999
Accepted: 29 March 2000

Abstract

Small-angle scattering from anisotropic samples, consisting of homogeneous particles inside a homogeneous medium with a scattering contrast $(\Delta n)^2$ , is considered. Along any direction ${\hat {\bm q}}\equiv{\bm q}/|{\bm q}|$ of reciprocal space, at large $q\,({}\equiv |{\bm q}|)$ the Porod plot of the scattering intensity (i.e. $q^4I({\bm q})$ vs. q) shows a plateau whose height depends on ${\hat {\bm q}}$ and reads $4\pi^2 (\Delta n)^2 \sum_{j,l} (1/|\kappa_{{\ab{G},j,l}} (\pm{\hat {\bm q}})|)$ . 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 ${\hat {\bm q}}$ , and $\kappa_{{\ab{G},j,l}}(\pm{\hat {\bm q}})$ is the corresponding Gaussian curvature value.

PACS: 61.10.Dp – Theories of diffraction and scattering / 61.10.Eq – X-ray scattering (including small-angle scattering) / 61.12.Bt – Theories of diffraction and scattering

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