Full width at half maximum of low-angle basal phyllosilicate X-ray diffraction reflections; fitted peaks vs. diffraction traces

Bernard Kubler measured illite 'crystallinity', the half-height width or full width at half maximum (FWHM) of the X-ray diffraction line of illite/mica at 10 Aa, directly on the diffraction traces; this procedure has since been followed by the vast majority of workers. However, some workers have recently measured the FWHM of the fitted Pearson VII function rather than on the diffraction traces. The FWHM of this function for low-angle phyllosilicate diffraction peaks (FWHM* (sub PVII) ) is almost consistently 'broader' than those measured directly on the diffraction trace profiles (FWHM (sub trace) ) by up to 0.08 degrees Delta 2theta for the broader peaks. The Pearson VII function shows gentle curvature ('smoothing') at its tops and fast fading of the tails relative to virtually all 10 Aa diffraction traces. The broad FWHM* (sub PVII) results from the consequent lowering/'under-fitting' of the peak tops and the upper tails and compensatory broadening/'over-fitting' of the intermediate peak flanks. FWHM* (sub PVII) 'contraction' with respect to FWHM (sub trace) and enhancement of the peak maximum is found on traces of muscovite strips. The fitting reliabilities of the Cauchy function are almost invariably better than those of the Pearson VII function. Their FWHM* (sub Cauchy) values are narrower for both the illite/mica 10 Aa and the chlorite 7 Aa reflections; although they still differ somewhat from the FWHM (sub trace) , they are much closer, usually within 0.02 degrees Delta 2theta . This markedly lesser broadening of FWHM* of the Cauchy of the Pearson VII function is the result of its stronger top curvature and notably faster tail fading (less 'smoothening'). For higher-angle mica peaks, the FWHM* values of the Pearson VII and Cauchy functions converge, usually differing only by 0.01-0.03 degrees Delta 2theta for the 5 Aa peak, and even less for the 3.3 Aa peak. It is therefore strongly recommended that FWHM values of the illite/mica 10 Aa reflections be measured on the diffraction traces rather than on fitted functions. Where peak fitting is unavoidable (e.g. in order to separate the contributions of adjoining, partly resolved or unresolved reflections on broadened 10 Aa reflections), Cauchy rather than Pearson VII functions should be used.