A comparison of methods for modeling the effect of axial divergence in powder diffraction

The Edgeworth series model for the modification of diffraction peak shapes because of axial divergence is compared with the peak shapes computed by a numerical convolution method that is computationally slow. It is shown that if the width of an approximately Gaussian instrumental peak shape is comparable with the width of the modifying function, a condition that is generally satisfied in fixed-wavelength neutron diffraction and in many laboratory X-ray diffraction instruments, but not with synchrotron X-ray instruments, the Edgeworth model is nearly identical to the convolution model, while the computation is much simpler.