Size-broadening anisotropy in whole powder pattern fitting. Application to zinc oxide and interpretation of the apparent crystallites in terms of physical models

A new anisotropic size-broadening model based on a spherical-harmonics representation allowing determination of both volume- and area-averaged apparent crystallites and convenient for implementation into Rietveld programs is described. The model effectiveness is demonstrated on a ZnO powder pattern exhibiting strongly anisotropic size broadening and pronounced super-Lorentzian peak shapes. Moreover, it is shown how the apparent crystallites can be interpreted in terms of physical models by using ellipsoidal and cylindrical crystallites with lognormal size distributions. This interpretation is critically assessed and it is argued that both simplified physical models and a priori complementary information (obtained by transmission electron microscopy, for instance) are often needed to avoid unstable and non-unique solutions.