Functions chosen a priori

These functions of the Bragg angle are expressed as follows  

As we have already mentioned, the development of high resolution X-ray diffraction devices made it possible to show that Gaussians did not fit the experimental profiles well. Generally speaking, when instrumental aberrations lead to symmetrical increases in peak width, the peaks can usually be approximated as Gaussian or Loientzian functions. The latter are expressed as follows  

3 The terms Lorentzian function and Cauchy function refer to the same mathematical object. 

Therefore, the resulting profiles are bounded by these two Gaussian and Lorentzian limits. They can be described by a Pearson Vn function which is expressed as [ELD 69, HAL 77]  

The Voigt function is known to be a very good description of the diffraction peaks, however, it is a difficult function to program and pseudo-Voigt functions are often used [WER 74] these are linear combinations of Gaussian and Lorentzian functions  

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