International
Tables for Crystallography Volume H Powder diffraction Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk © International Union of Crystallography 2018 |
International Tables for Crystallography (2018). Vol. H, ch. 3.2, p. 258
Section 3.2.3.2. Absorption with multiphase samples^{a}Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794–3800, USA |
One important application of powder diffraction is the quantitative analysis of mixtures. Quantitative phase analysis is covered in detail in Chapter 3.9 of this volume; here we set the stage. If a sample is a mixture of several phases, the powder-diffraction pattern will be the sum of the patterns of each phase, weighted by the fraction of the illuminated volume occupied by that phase. The most common configuration for quantitative analysis by X-ray diffraction is reflection from an optically deep flat-plate sample. In this case, the integrated intensity of a particular reflection from the jth phase iswhere V(j), w_{m}(j) and ρ(j) are the unit-cell volumes, mass fraction and density of phase j, respectively. Here I_{0} is an overall intensity scale factor, LP(θ) is the Lorentz and polarization factor common to all phases, and is the absorption coefficient of all solid phases in the sample. The summation includes all solid phases, even amorphous materials.
Note that the intensity of peaks from a particular phase is not simply proportional to the fraction of that phase present. For example, if there are two phases A and B, the intensity of A peaks will be proportional to