A Generalized Profile-Shape Exponent Framework for X-ray Diffraction Line Profile Analysis: The Pseudo-Voigt Mixing Parameter as a Continuous Descriptor of Broadening, Deconvolution, and Microstructure Extraction

The pseudo-Voigt function P(x) = ηL(x) + (1−η)G(x) is the standard empirical profile modelin X-ray diffraction (XRD) line profile analysis. We propose a generalized profile-shapeexponent framework in which the discrete exponent choice of the classical Ungár formulation(n = 1 or n = 2) is replaced by a continuous, data-driven, instrument-corrected profile-shapeexponent: n = f(S)where S denotes an intrinsic, instrument-corrected profile-shape descriptor. We investigate thepseudo-Voigt effective mixing parameter ηeff as one practical realization of S, yielding thefirst-order implementation:n = 2 − ηeff