Estimation of the coherently scattering domain size in alloys from neutron diffraction data

An analysis of the diffraction spectra of the Fe74Al26 alloy was conducted using a high-resolution neutron diffractometer to determine the size distribution of structurally ordered clusters dispersed within the structurally disordered matrix of the alloy. The Scherrer method was generalized for this purpose, based on the analysis of diffraction peak profiles, determining peak widths at heights of 1/5 and 4/5 of the maximum, and assuming the validity of the gamma distribution for cluster sizes (Pielaszek method). A comparison of results obtained using the Scherrer, Williamson–Hall, and Pielaszek methods was carried out, demonstrating good agreement between them. An algorithm for calculating the log-normal distribution function of cluster/particle sizes is proposed. The experimental data were obtained using a time-of-flight neutron diffractometer, and the analysis was performed for two variants of variable scanning: in crystallographic (direct) (d-scale) and reciprocal (H-scale) spaces, with estimates of possible systematic errors. It was concluded that the determined average sizes possess the necessary degree of stability, meaning they weakly depend on the applied variable scanning and the total number of experimental data points.