International Tables for Crystallography

Access to online content requires a licence


Quantitative phase analysis
I. C. Madsen, N. V. Y. Scarlett, R. Kleeberg and K. Knorr. International Tables for Crystallography (2019). Vol. H, ch. 3.9, pp. 344-373  [ doi:10.1107/97809553602060000954 ]

Abstract

The most common use of powder diffraction in analytical science is the identification of crystalline components, or phases, present in samples of interest. For multiphase samples, once the nature of the phases present has been established, the next most common application is the quantitative determination of the abundance of each phase. There are a number of non-diffraction methods, such as gravimetric analysis following density or magnetic separation, for the estimation of phase abundance. In general, these rely upon specific phase properties and hence do not have broad applicability. Quantitative phase analysis (QPA) by diffraction methods is the only analytical technique that is truly phase sensitive: the near universal applicability of diffraction for QPA derives from the fact that the contribution of each component to the observed diffraction pattern is (i) derived directly from its crystal structure and (ii) has intensity which is proportional to the amount present. While the basis of diffraction-based QPA, initially developed using a single-peak approach, is well established, the field remains dynamic with more recent developments incorporating whole-pattern data-analysis methodologies. In addition, the need to extract QPA from in situ studies, where the sample is undergoing change imposed by an external variable, requires careful application of methods to extract absolute, rather than relative, phase abundances. This chapter describes the basis of QPA for both single-peak and whole-pattern approaches and provides worked examples for selected methods. Discussion of how to select and apply some of the methods, particularly in the context of the derivation of absolute phase abundances and the determination of poorly crystalline or amorphous phases, is included. The presence of amorphous content requires extension of the basic methods but, once these are established, they can be shown to produce QPA with similar accuracy and lower limits of detection as for crystalline phases.


Access, prices and ordering

International Tables for Crystallography is available online as a full set of volumes through Wiley.

set

If you have already registered and are using a computer listed in your registration details, please email support@iucr.org for assistance.

About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The multi-volume series comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.