A comparison of various commonly used correlation functions for describing total scattering

Abstract

Total scattering, an increasingly important crystallographic research area, is defined theoretically in terms of correlation functions. Different researchers use different definitions for these functions, frequently leading to confusion in the literature. Here, a consistent set of equations for total‐scattering correlation functions are developed and explicitly compared with other, often encountered, definitions. It is hoped that this will lead to increased transparency for newcomers to the field of total scattering.

Environment of titanium and aluminum in a magnesium alumino-silicate glass

“…Data were corrected for background and container scattering, absorption, multiple scattering and inelastic effects using the GUDRUN software to obtain the structure factor F N (Q). The notation for the structure factors and correlation functions are explained in previous papers [23,24].…”

Selecting reliable interatomic potentials for classical molecular dynamics simulations of glasses: The case of amorphous SiO2

“…In 8 this case, different classical interatomic potentials are usually collected from the literature and a decision on the 9 most accurate potential has to be made. The most common approach to make this decision is to use the available 10 interatomic potentials to predict structures and physical properties of crystals related to the amorphous system under 11 study, and compare the resulting predictions to available experimental results. In this paper we will demonstrate 12 that such approach may lead to incorrect choice of which interatomic potential is the best.…”

Structure analysis of multiphase systems by anomalous small-angle X-ray scattering

“…The same relations apply also for ASAXS, so that we can draw the conclusion that ASAXS is most fruitful if the resonant element, at whose absorption edge the measurement is performed, is contained in only one phase. Then, using (49) and (51), one obtains that the corresponding partial structure factor is proportional to the scattering function of the phase containing the resonant atoms…”

“…Equations (49) and (50) are mathematically equivalent to (8) and can be also presented in the form of (10). Since 49) and (50) show that there are p(p-1)/2 independent () Ŝ functions which is exactly the number of the linearly independent "stick probability functions" [39,41]. We should also 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 …”