Tables for
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

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:

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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