Analytical functions

The functions for fitting are selected in Function choice submenu of the Fit menu. The following functions can be used for the fitting (A ... free parameters, y .. intensities, x .. angles).

Functions

Functions are not given in common normalized shape.
Ai refinable parameters:
A1 ... peak height, A2 ... peak position, A3 ...related to FWHM (halfwidth), A4 ...shape parameter
Gauss

wpe2.jpg (2689 bytes)
Cauchy

wpe1.jpg (2643 bytes)
Pearson VII

wpe3.jpg (2999 bytes)
Voigt
(not used)

wpe4.jpg (1642 bytes)
Pseudo-Voigt

wpe5.jpg (3070 bytes)
Rational

wpe6.jpg (3995 bytes)

 

Asymmetric version of Pearson function I

Shape and width parameters are multiplied for right side of the profile, i.e A3 is replaced by A3A5 and A4 by A4A6.

These functions are used for the description of the singlet Ka1 line. The total fit function for one diffraction peak includes the Ka2 profile which is shifted by the known value (for the given wavelength, see instrumental parameters) and the profile parameters of which can be related to the shape of Ka1by the multiplication of corresponding parameters Ai, as defined in configuration file. The default value of A (Ka2)/ A (Ka1) is 0.5 and for other parameters equal to 1.

Total fit function for selected segment of diffraction pattern is the sum of all doublets within the current theta limits and optionally includes also background.