Improved algorithms and software for the decomposition of powder diffraction pattern into individual Bragg reflections and the availability of good quality data from high resolution diffractometers have resulted in a renewed interest in the use of the integral breadth $\beta$ (= area/peak intensity) and other line-profiles parameters to characterize sample microstructure. The procedure has the advantage of speed and convenience over the elaborate Fourier analysis of line shapes and is applicable to a wider class of materials. The errors arising from the assumptions made in the two-stages analysis, i.e. instrumental correction and size/strain separation, have been reduced by using an analysis based on the Voigt function [1], particularly for the instrumental correction of observed integral breadths, if Voigt functions adequately describe both the instrumental $g$ and $h$ profiles. Compared with the Fourier method, generally restricted to a limited number of well resolved reflections for which two or more orders are available, the pattern-decomposition approach allows one to extract data from all reflections in the powder pattern, regardless of the symmetry.
The basic principles of pattern decomposition and the subsequent analysis in terms of crystallite or domain size, microstrain or other imperfection (e.g. stacking faults) will be discussed. Errors arising in pattern decompositions will be discussed through examples of simulated patterns for different mean apparent sizes [2] and the case of super-Lorentzian line shapes, for which an instrumental correction by the Voigt method is not possible, will be discussed.
Various applications will be presented, including microstructural changes due to thermal effects. These include the determination of size and 3-dimensional form of coherently-diffracting domains (crystallites) and stacking faults in zinc oxide powders produced from precursors stable at low temperatures. Other examples considered will be cerium oxide, yttrium oxide and cold-worked tungsten.
1. J.I.Langford:Accuracy in Powder Diffraction II, ed, by E.Prince
and J.K.Stalick (NIST Spec. Public. 846,
Gaithersburg),pp.110-126
2. D.Lou\"er: Adv. X-ray Anal. 37(1994) 27-35