Thompson-cox-hastings Pseudo-voigt Function Work

The TCH pseudo-Voigt is the industry standard for several reasons:

In modern Rietveld software (e.g., GSAS-II, FullProf, Topas), the user does not refine $\eta$ directly. Instead, they refine for the Gaussian FWHM and Scherrer/Lorentzian parameters for the Lorentzian FWHM. The TCH function then dynamically calculates $\eta$ for each Bragg reflection.

The Gaussian function is given by:

The success of TCH inspired several improvements:

For any scientist performing quantitative powder diffraction on nanoscale, microstrained, or disordered materials, mastering the TCH pseudo-Voigt is not optional—it is essential.