Calculating the reference intensity ratio of crystalline phases with unknown atomic arrangements using the lattice parameters and chemical information

The reference intensity ratio (RIR) is the intensity ratio of a specified peak of the target crystalline phase to a certain peak of the reference phase in the powder X-ray diffraction pattern of a mixture of the target and reference phases in a weight ratio of 1:1. The RIR represents the diffraction power of the target phase compared with that of the reference phase. A quantitative phase analysis (QPA) can be readily made on the basis of only a powder pattern when the RIR values of all component phases in the mixture are available. The RIR of a target phase can be measured experimentally or calculated in accordance with its crystal structure. RIR values are given in most powder diffraction files (PDFs) published by the International Centre for Diffraction Data, but there are still more than 110 000 PDFs for which the RIR is absent. Newly discovered phases may be present in a mixture as components of unknown weight fractions, for which the RIR values can be neither measured nor calculated with the currently available method. Herein is presented a new method of calculating the RIR of a crystalline phase from its lattice parameters, the chemical content of the unit cell and a list of normalized intensities of reflections over a sufficiently large diffraction angle range. The new method can be used to calculate not only the absent RIRs in the PDFs but also the RIR of a component phase of a mixture of unknown weight fraction when the lattice parameters and chemical content of the unit cell of the corresponding phase are known.