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A method of reducing termination errors in radial distribution functions
Author(s) -
Narayan R.,
Ramaseshan S.
Publication year - 1979
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/s0021889879013297
Subject(s) - range (aeronautics) , function (biology) , radial distribution function , scattering , work (physics) , radial function , distribution (mathematics) , current (fluid) , distribution function , radial basis function , yield (engineering) , computational physics , physics , algorithm , mathematical analysis , materials science , mathematics , computer science , optics , molecular dynamics , quantum mechanics , thermodynamics , artificial neural network , evolutionary biology , composite material , biology , machine learning
The radial distribution function [ g ( r )] of a liquid can be obtained from an integral transform of its X‐ray scattering intensity I ( μ ). Experimentally, I ( μ ) can be measured over only a limited range, leading to termination errors in g ( r ). Using the strict positivity of g ( r ), an iterative method is proposed to reduce these errors. The negative portions of each successive distorted approximation of g ( r ) are replaced by the value zero and this function is used to generate I ( μ ) in the non‐measured range. Computer calculations on a model function yield encouraging results. The method appears to have an advantage over current approaches as it does not require a knowledge of the hard‐core diameter of the atoms. It is also expected to work in the case of molecular liquids where there are some difficulties in applying the current methods.