Powder diffraction peak shapes. Parameterization of the pseudo-Voigt as a Voigt function

The Voigt function is now recognized to be one of the best mathematical descriptions of the symmetrical component of the peak shape in constant-wavelength X-ray and neutron powder diffraction. The simpler pseudo-Voigt function has been used previously to provide an empirical fit to observed peak shapes. In this paper, a parameterization of this function is obtained to make it, to a very good approximation, equivalent to a Voigt function, and, additionally, it is described by the half-width parameters of the Gaussian and Lorentzian components of that Voigt function. This new construction allows for greater flexibility in peak-shape description and, in particular, allows for a more straightforward convolution of additional functional contributions into the `Voigt' component of a peak shape description.