Errors in quantitative analysis of diffuse scattering from alloys

Abstract

Errors in separating diffuse scattering resulting from local order from that from static and dynamic displacements have been examined; the Borie-Sparks symmetry procedure was employed, which includes second-order terms in the displacements. The largest source of error when X-rays are employed is the variation in the ratio of scattering factors across the volume measured in reciprocal space. Large errors in the Warren local-order parameters result for clustering systems with displacement terms of the same order as the local-order parameters (or larger), but not if the size terms are smaller. For systems with local order the errors in these parameters are small. Uncertainties in the size terms are always appreciable. Other errors that were considered are: higher-order terms, extrapolation under Bragg peaks, errors in Compton scattering, background and surface roughness, and uncertainties in composition or polarization resulting from a monochromator.

Direct and Indirect Methods of the Analysis of Interatomic Interaction and Kinetics of a Relaxation of the Short-Range Order in Close-Packed Substitutional (Interstitial) Solid Solutions

“…Аналіз можливих похибок міститься в роботах [12,13]. По мірі вдосконалення методики значення (0) на-ближаються до 1 [2,128].…”

X‐Ray and Neutron Diffuse Scattering Measurements

“…However, the Warren-Cowley α's are found to have typical errors of ~10% or less for binary alloys with a preference for unlike first-neighbor pairs with either the BS or GC analysis. For clustering systems, the BS method was reported to give large errors of 20% to 50% of the recovered α's (Gragg et al, 1973). Smaller errors were reported on the α's for clustering systems with the GC method (Wu et al, 1983).…”

“…Results from GC's error analysis (which included statistical, roundoff, x-ray scattering factors, sample roughness, and extraneous backgrounds) showed that errors in the x-ray atomic scattering factors had the largest effect, particularly on the Q terms. They concluded, based on an error analysis of the BS method by Gragg et al (1973), that the errors in the GC method were no worse than for the BS method and provided correct directions for the first moment displacements.…”

X-ray diffraction study of basal-(ab)-plane structure and diffuse scattering from silver atoms in disordered stage-2 Ag0.18TiS2

“…As pointed out by Gragg, Hayakawa & Cohen (1973), there are several sources of error that occur in obtaining Fourier coefficients from the total diffuse scattering.…”