Recent advancements in Whole Powder Pattern Modelling

Abstract

Abstract. Advantages of Whole Powder Pattern Modelling against conventional Line Profile Analysis methods are briefly reviewed, and a specific example is discussed on the possible ambiguity in the interpretation of the Williamson-Hall plot for polydisperse systems. Ad-vancements in WPPM concerning dislocation line broadening are illustrated with examples taken from the recent literature. Reliability and limits in the application of WPPM to nanocrystalline systems are also discussed. 1. Introduction In recent years, the growing interest in nanomaterials gave considerable momentum to dif-fraction Line Profile Analysis (LPA), recognised as one of the most used techniques to study crystalline domain shape and size distribution, as well as nature and amount of lattice defects [1]. As a consequence, LPA methods developed considerably: traditional methods based on diffraction peak integral breadths (e.g., Scherrer formula and Williamson-Hall (WH) plot [2,3]) or on the Fourier analysis of isolated peak profiles (e.g., the Warren-Averbach method [2,4]) have been paralleled by several new approaches with increasing tendency to deal with the full diffraction pattern [5,6]. It is useful to introduce a distinction between methods based on the use of some flexible but arbitrary profile function (e.g., Voigt, pseudo-Voigt, Pearson VII functions [7]), and methods that exclusively rely on physical models of the microstruc-ture (e.g., describing coherent scattering effects from dispersed systems of crystalline do-mains, strain fields of lattice defects, etc.): we will refer to Whole Powder Pattern Fitting (WPPF) for the former and Whole Powder Pattern Modelling (WPPM) for the latter [8-10]. Profile fitting is almost invariably a need when dealing with X-ray Diffraction (XRD) pat-terns from finely dispersed and/or highly deformed systems – most cases of interest to LPA – to separate overlapping peak profiles and background. However, despite the simplicity in developing WPPF software [11] and the flexibility of this approach, WPPF is biased by the choice of the profile function which replaces, at some stage of the analysis, the experimental dataset, so that LPA is actually performed on the fitting parameters more than on the data. This can give results that do not match the original data [12].