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

Abstract

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.

Microstructural Analysis of Boehmite Nanoparticles Prepared by Rapid Hydrolysis of Aluminum Sec-butoxide

“…However, regardless of the difference in processing parameters, boehmite crystallites in all products are of nanometric size with a pronounced size anisotropy. 22,23 In all diffraction patterns the size contribution to the line broadening appeared to be anisotropic with a significantly smaller D V value in the direction parallel to the broadening axis 010 than in the directions perpendicular to the broadening axis 010 (Table 2).…”

X-ray scattering characterisation of nanoparticles

“…[87] More complex models describing the crystallite shape can also be derived. [88] Stacking faults. Crystal faults occur when the regular stacking of atomic planes in a crystallite is interrupted (deformation faults) or reversed (twin faults).…”

Application of statistical methodology for the evaluation of mechanically activated phase transformation in nanocrystalline TiO2

“…Popa fitting model [34] was utilized to analyze the XRD patterns. The crystallographic information as well as starting parameters of site occupancies and lattice parameters were taken from database of the analyzing Rietveld program (MAUD).…”