Method of calculating the coherent scattering power of crystals with unknown atomic arrangements and its application in the quantitative phase analysis

Quantitative phase analysis is one of the major applications of X-ray powder diffraction. The essential principle of quantitative phase analysis is that the diffraction intensity of a component phase in a mixture is proportional to its abundance. Nevertheless, the diffraction intensities of the component phases cannot be compared with each other directly since the coherent scattering power per unit cell (or chemical formula) of each component phase is usually different. The coherent scattering power per unit cell of a crystal is well represented by the sum of the squared structure factors, which cannot be calculated directly when the crystal structure data is unavailable. Presented here is a way to approximate the coherent scattering power per unit cell based solely on the unit cell parameters and the chemical contents. This approximation is useful when the atomic coordinates for one or more of the phases in a sample are unavailable. An assessment of the accuracy of the approximation is presented. This assessment indicates that the approximation will likely be within 10% when X-ray powder diffraction data is collected over a sufficient portion of the measurable pattern.