Thompson-cox-hastings Pseudo-voigt Function May 2026

[ \Gamma_V = \left( \Gamma_G^5 + 2.69269 , \Gamma_G^4 \Gamma_L + 2.42843 , \Gamma_G^3 \Gamma_L^2 + 4.47163 , \Gamma_G^2 \Gamma_L^3 + 0.07842 , \Gamma_G \Gamma_L^4 + \Gamma_L^5 \right)^1/5 ]

return (1-eta)*G + eta*L P. Thompson, D. E. Cox, and J. B. Hastings, “Rietveld refinement of Debye–Scherrer synchrotron X‑ray data from Al₂O₃” , J. Appl. Cryst. (1987), 20, 79–83. The empirical FWHM and mixing coefficient formulas are given there. thompson-cox-hastings pseudo-voigt function

[ \eta = 1.36603 \left( \frac\Gamma_L\Gamma_V \right) - 0.47719 \left( \frac\Gamma_L\Gamma_V \right)^2 + 0.11116 \left( \frac\Gamma_L\Gamma_V \right)^3 ] [ \Gamma_V = \left( \Gamma_G^5 + 2

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