Peak Shape Functions III. Pearson VII

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Pearson VII Function

The Pearson VII function was a popular function during the 1980s and 1990s for describing peak shapes from conventional X-ray powder diffraction patterns, though it has now been superceded in popularity by the pseudo-Voigt peak-shape function (described on the next page). The Pearson VII function is basically a Lorentz function raised to a power m:

where m can be chosen to suit a particular peak shape and w is related to the peak width. Special cases of this function are that it becomes a Lorentzian as m → 1 and approaches a Gaussian as m → ∞ (e.g. m > 10). The main features of the Lorentzian function are:

• that it can handle different tail-shapes of a peak, better than say a Gaussian or Lorentzian function, by varying the m parameter
• its calculation is simpler than some of its competitors, though this is not significant in computing terms

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