Position-constrained and unconstrained powder-pattern-decomposition methods

Abstract The individual profile fitting, the Pawley, and the Rietveld methods are compared in Table 14.1. The first two methods, described in this chapter, are classified as pattern decomposition methods. With them, one executes the decomposition of the powder pattern into individual Bragg components without reference to a structural model (Young et al. 1982). The difference between these two models is that the peak positions are unconstrained, varied independently as adjustable parameters in the least-squares in the individual profile fitting method while they are constrained by adjustable unit-cell parameters in the Pawley method. Furthermore, in individual profile fittings, pattern decomposition is carried out in a small 20-range, changing the range of analysis successively, whereas the whole powder pattern is decomposed in one step by the Pawley method. These two methods do not require crystal structural data (atom site occupancy, positional, and thermal parameters) to start the least-squares fitting.