QUANTITATIVE PHASE ANALYSIS IN POWDER DIFFRACTION
Julius Schneider
Institut für Kristallographie und Angewandte Mineralogie Universität München, Theresienstrasse 41 D-80333 München, Germany,
Identification and determination of relative abundances of constituent components in polycristalline samples is of paramount importance in such diverse fields as crystallography, mineralogy, petrology, solid state chemistry, materials science, archeology, criminology, pharmacy, etc. Powder diffraction is one of the few techniques quich is truly phase sensitive rather than purely element sensitive like X-ray flourescence. It has proved to be an ideal tool for quantitative phase analysis (QPA) because of it's non-destructive nature and easy adaptability to a great number of problems.
Phase identification, which of course has to precede QPA, is nowadays almost exclusively performed with the aid of computerized databases, like the Powder Diffraction File (PDF, about 43000 entries) and the Inorganic Crystal Structure Database (ICSD, about 43000 entries). QPA is based on the fact that diffraction intensities of the individual phases are proportional to their relative amount within the mixture. However, the intensities are modified by absorption effects and are therefore not independent of the other phases present.
Essentially four ways of QPA have emerged to solve this problem:
The accuracy of QPA, be it discrete peak or whole pattern, may severly be hampered by sample induced aberations like particle size or particle statistics, sample preparation variability, preferred orientation, mikroabsorption, extinction, angle dependent absorption (thin samples), etc. Some of these systematic errors may be greatly reduced by experimental precautions like careful sample preparation, sample spinning, sample geometry etc. On the other hand, great effort has been put into the creation of mathematical models to simulate these errors and to integrate them into Rietveld systems. Being aware of pitfalls, verification of XRD-QPA is thus a very important step. First of all, checks for internal consistency like comparison of high and low angle data should be performed. Comparison with complementary diffraction information, like X-ray data at different wavelengths or neutron data can serve to detect and overcome absorption related errors. Possible common mode errors of Rietveld-based QPA, namely wrong structure models, may be cross-checked by non-diffraction methods like optical spectroscopy, calculations via normative analysis etc. Most recent applications include a chemometrics approach in which the whole diffraction pattern is used to derive information (QPA, plant operating conditions etc.) through the use of 'learning sets'. Many of the procedures decribed above have been integrated into software packages, the more prominent one's will be shortly discussed also. The review will be complemented by representative examples from diverse fields of application.