Thompson-Cox-Hastings (TCH) pseudo-Voigt function a specialized version of the pseudo-Voigt profile used primarily in Rietveld refinement of X-ray and neutron powder diffraction data ResearchGate
pV(x)=η⋅L(x)+(1−η)⋅G(x)p cap V open paren x close paren equals eta center dot cap L open paren x close paren plus open paren 1 minus eta close paren center dot cap G open paren x close paren (eta) is the mixing parameter. The TCH Breakthrough
Thus, Rietveld refinement using TCH correctly identifies that the broadening is size-dominated, not instrumental. Refining $\eta$ freely (simple pseudo-Voigt) would also give 0.98, but with higher correlation to scale factor. thompson-cox-hastings pseudo-voigt function
: It uses a specific formula to calculate the "mixing ratio" between the Gaussian ( ) and Lorentzian (
G(x) = (1/√(2π)) * (w/√(2ln(2))) * exp(-((x-x0)^2) / (2 * (w/√(2ln(2)))^2)) : It uses a specific formula to calculate
While newer methods like the fully numerical Voigt or the Schlenker double-Voigt exist, the TCH function remains dominant because:
Always refine a standard material (e.g., LaB₆, NIST SRM 660c) with a purely Gaussian model first. Fix the Lorentzian broadening to zero. This extracts the true instrument U, V, W . Then for samples, keep U, V, W fixed while refining Lorentzian terms. This prevents unphysical microstrain/size correlations. Then for samples, keep U, V, W fixed
where: