Estimation of the Coherently Scattering Domain Size in Alloys from Neutron Diffraction Data

Abstract

To determine the size distribution of structurally ordered clusters dispersed within a structurally disordered alloy matrix, we analyze the diffraction patterns of the Fe₇₄Al₂₆ alloy obtained using a high-resolution neutron diffractometer. This analysis employs the generalized Scherrer method, which involves analyzing diffraction-peak profiles, determining peak widths at heights of 1/5 and 4/5 of the maximum, and assuming a gamma distribution for cluster sizes (Pielaszek method). We compare the results obtained using the Scherrer, Williamson–Hall, and Pielaszek methods, finding them to agree. We propose an algorithm to calculate the log-normal distribution function of cluster/particle sizes. Experimental data are obtained using a time-of-flight neutron diffractometer. The analysis is conducted for two scanning variable options: in the crystallographic (direct) (d scale) and reciprocal (H scale) spaces, and possible systematic errors are evaluated. We conclude that the average sizes determined in this manner possess the necessary degree of stability, showing a weak dependence on the applied scanning variable and the total number of experimental points.