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Title

Observations on Two Commonly Used Profile Shape Functions
Authors

B. Courant
Organization: Laboratoire d'Application des Materiaux a la Mechanique
B. Bourniquel
Organization: Laboratoire d'Application des Materiaux a la Mechanique
M. Francois
Organization: Laboratoire d'Application des Materiaux a la Mechanique
M. Bessiere
Organization: LURE
Department: Universite Paris XI
Journal / Anthology

Materials Science Forum
Year: 2000
Volume: 347-9
Page range: 23-28
Description

The most widely used profile shape functions are the pseudo-Voigt and the Pearson VII. Using the standard Mathematica package "Statistics NonlinearFit" and high resolution synchrotron data, we have compared their convenience to numerical computation. With respect to this point, the pseudo-Voigt is better than the Pearson VII function. However the physical meaning of the pseudo-Voigt may be questioned since its variance is not defined. A good fit is obtained with a composite model, sum of a Pearson VII function with a finite variance and of a gaussian function. This gaussian function is assumed to described the thermal diffuse scattering.
Subjects

*Mathematica Technology > Application Packages > Applications from Independent Developers > Experimental Data Analyst
*Mathematics > Probability and Statistics
Keywords

Goodness of Fit Criterion, Pearson VII Function, Profile Fitting, Pseudo-Voigt Function, Thermal Diffuse Scattering, Variance of a Diffraction Line, Variance Stabilization