Possibilities of the X-ray Diffraction Data Processing Method for Detecting Reflections with Intensity Below the Background Noise Component

TL;DR

This work tackles the problem of detecting X-ray diffraction reflections whose intensity is below background noise in multiphase materials. It introduces a correlation-analysis framework using a permutation test and a Gaussian reflection model to extract weak signals, yielding an initial correlation value $S_0$ and calculated intensities $I_i^{c}$ for background features. Applied to $I_q^{d}$ and background $ΔI_b$, the method enables phase analysis with contents down to $0.1\ \,\mathrm{wt.\%}$ and can reveal reflections at relatively low $\text{SNR}$, provided $I_q^{d}/ΔI_b$ exceeds about $0.4$ (with reduced reliability near $0.2$). The approach complements conventional diffraction analyses and software like Match!, improving the detection of weak reflections and enabling more reliable identification of low-content crystalline phases in practical materials.

Abstract

The values of the signal-to-noise ratio are determined, at which the method of processing X-ray diffraction data reveals reflections with intensity less than the noise component of the background. The possibilities of the method are demonstrated on weak reflections of $α$-quartz. The method of processing X-ray diffraction data makes it possible to increase the possibilities of X-ray phase analysis in determining the qualitative phase composition of multiphase materials with a small (down to $0.1$ wt. \%) content of several (up to eight) phases.