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A new method for the determination of particle size distributions from small‐angle neutron scattering measurements
Author(s) -
Potton J. A.,
Daniell G. J.,
Rainford B. D.
Publication year - 1988
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/s0021889888004595
Subject(s) - astron , small angle scattering , principle of maximum entropy , statistical physics , scattering , computational physics , inverse , physics , void (composites) , particle size , data set , neutron scattering , materials science , mathematics , optics , statistics , nuclear physics , geometry , chemistry , composite material
The determination of a particle size distribution p ( R ) from small‐angle scattering data is an example of a practical linear inverse problem for which there is no unique solution. It is shown (i) how the maximum entropy algorithm may be used to extract a unique solution which is the most uniform function compatible with the data set and is necessarily positive, and (ii) how the Backus–Gilbert [ Geophys. J. R. Astron. Soc. (1968), 16 , 169–205] method may be used to judge the significance of features in distributions derived from a data set of given statistical accuracy. As an illustration, void size distributions are presented for a sample of irradiated stainless steel which was successively annealed at increasing temperatures.