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Collimation correction for non‐isotropic small‐angle X‐ray scattering curves from lamellar systems
Author(s) -
Pape E. H.
Publication year - 1978
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889878013527
Subject(s) - scattering , lamellar structure , collimated light , small angle x ray scattering , intensity (physics) , isotropy , optics , physics , materials science , gaussian , distribution (mathematics) , anisotropy , distribution function , orientation (vector space) , computational physics , geometry , mathematics , mathematical analysis , laser , quantum mechanics , composite material
A collimation‐correction method is presented which is suitable for scattering curves of large lamellae with a partial disorientation of their axes. If it is assumed that the orientation of the lamellar multilayers can be characterized by a mosaic spread, the intensity at a given scattering angle is limited to a defined arc on the corresponding Debye‐Scherrer ring and the distribution of the intensity along this arc depends on the distribution function of the multilayer orientations. It is further assumed that this orientation distribution function can be approximated by a Gaussian (normal distribution). Its width can be estimated from a short‐time pin‐hole collimated X‐ray film exposure. Thus, an additional condition has to be inserted into the smearing integral equation, which is solved using the iterative method of Lake [ Acta Cryst. (1967), 23 , 191–1943]. The procedure has been successfully tested on lamellar intensity functions from models and thereafter has been applied to the small‐angle X‐ray scattering curves of partially oriented erythrocyte ghost membranes.