The Patterson Function and the Development of a New Method for Quantitative Phase Analysis of Individual Crystalline Phases Using X-ray Powder Diffraction Technique

Abstract

A new method, called the direct derivation DD method, for quantitative phase analysis QPA can derive weight fractions of individual crystalline phases from sets of observed intensities and chemical composition data. The Patterson function plays an important role in replacing the sum of squared structure factors, calculated in the Rietveld method, with the sum of squared numbers of electrons belonging to the atoms in the chemical formula unit. Therefore, the DD method can conduct QPA of Rietveld equivalent without referencing to structure parameters. It can be applied to QPA of mixtures containing known structure, unknown structure, and high and low crystalline materials.