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Numerical conversion between the Pearson VII and pseudo‐Voigt functions
Author(s) -
Wang Hejing,
Zhou Jian
Publication year - 2005
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/s0021889805024490
Subject(s) - voigt profile , pearson product moment correlation coefficient , intensity (physics) , mathematics , kelvin–voigt material , measure (data warehouse) , mathematical analysis , physics , statistics , optics , thermodynamics , computer science , spectral line , quantum mechanics , viscoelasticity , database
The shape coefficient of a curve, which is defined as the ratio of its full width at half‐maximum intensity to integral width, is a measure of variation in shape. From the definitions of the pseudo‐Voigt, Pearson VII and Voigt functions used in X‐ray diffractometry, three shape‐converting formulae are deduced. Numerical solution helps to establish a numerical model for interconverting the shapes of the pseudo‐Voigt, Pearson VII and Voigt functions. Assessment of the error level and some comments on the shape of the pseudo‐Voigt and Pearson VII functions are thereby made.