Quantitative interpretation of X-ray diffraction patterns of mixtures. II. Adiabatic principle of X-ray diffraction analysis of mixtures

TLDR

X‑ray diffraction patterns encode the quantitative composition of a mixture, and analysts have long sought to decode this information directly from the pattern without calibration curves or internal standards. The study aims to achieve direct quantitative analysis by applying the matrix‑flushing theory and the newly proposed adiabatic principle. The authors employ the matrix‑flushing theory, which provides a matrix‑effect‑free intensity–concentration equation that reduces to auto‑flushing for binary mixtures, and the adiabatic principle, which guarantees that pairwise intensity–concentration relationships remain unchanged by other components, to derive a key decoding equation. Experimental validation confirms that both the matrix‑flushing theory and the adiabatic principle accurately predict component concentrations from diffraction patterns.

Abstract

All the information relating to the quantitative composition of a mixture is coded and stored in its X-ray diffraction pattern. It has been the goal of X-ray diffraction analysts since the discovery of X-rays to retrieve and decode this information directly from the X-ray diffraction pattern rather than resort to calibration curves or internal standards. This goal appears to be attained by the application of the `matrix-flushing theory' and the now-proposed `adiabatic principle' in applied X-ray diffraction analysis. The matrix-flushing theory offers a simple intensity-concentration equation free from matrix effects which degenerates to `auto-flushing' for binary systems. The adiabatic principle establishes that the intensity–concentration relationship between each and every pair of components in a multi component system is not perturbed by the presence or absence of other components. A key equation is derived which conducts the decoding process. Both the matrix-flushing theory and the adiabatic principle are experimentally verified.