Sampling volumes in powder diffraction experiments

We present a simple analytical formalism based on the Lorentz-Scherrer equation and Bernoulli statistics for estimating the fraction of crystallites (and the associated uncertainty parameters) contributing to all finite Bragg peaks of a typical powder pattern obtained from a static polycrystalline sample. We test and validate this formalism using numerical simulations, and show that they can be applied to experiments using monochromatic or polychromatic (pink-beam) radiation. Our results show that enhancing the sampling efficiency of a given powder diffraction experiment for such samples requires optimizing the sum of the multiplicities of reflections included in the pattern along with the wavelength used in acquiring the pattern. Utilizing these equations in planning powder diffraction experiments for sampling efficiency is also discussed.