International
Tables for
Crystallography
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 3.6, p. 301
https://doi.org/10.1107/97809553602060000951

Appendix A3.6.1. Functions for profile shapes

M. Leonia*

aDepartment of Civil, Environmental and Mechanical Engineering, University of Trento, via Mesiano 77, 38123 Trento, Italy
Correspondence e-mail: Matteo.Leoni@unitn.it

The unit-area Gaussian G(x, ω) and Lorentzian L(x, ω) functions are defined as[\eqalignno{G(x,\omega) &= {{2\sqrt{\ln 2/\pi}} \over \omega }\exp \left(- {{4x^2\ln 2} \over {\omega^2}}\right), & (3.6.61)\cr L(x,\omega) &= {2 \over {\pi \omega}} \left({1 \over {1 + 4x^2/\omega^2}} \right), & (3.6.62)}]where x is the running variable and ω is the full-width at half-maximum. Based on these definitions, the Voigt and pseudo-Voigt are[V(x,\omega_L,\omega_G) = L(x,\omega_L) \otimes G(x,\omega_G) \eqno (3.6.63)]and [{\rm pV}(x,\omega_L,\omega_G) = \eta L(x,\omega_L) + (1 - \eta)G(x,\omega_G), \eqno (3.6.64)]respectively, where η is the mixing parameter (ranging between 0 and 1) and wL and wG are the width of the Lorentzian and Gaussian components, respectively.








































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