Abstract
A collection of scholarly scripts dealing with the mathematics and physics of peak profile functions in X-ray powder diffraction has been written using the Wolfram language in Mathematica. Common distribution functions, the concept of convolution in real and Fourier space, instrumental aberrations, and microstructural effects are visualized in an interactive manner and explained in detail. This paper is the first part of a series dealing with the mathematical description of powder diffraction patterns for teaching and education purposes.
Highlights
X-ray powder diffraction (XRPD), an established technique for the study of crystal structures, finds increasing application in qualitative and quantitative phase analysis and the study of microstructure for micro- and nanocrystalline materials.For the study of crystalline materials, a powder pattern can be divided into Bragg reflections and background, where the latter among other contributions contains diffuse scattering from the sample
In this series of papers dealing with the visualization of mathematical functions used to describe a powder pattern, we present a collection of user-friendly, interactive and freely distributable Mathematica (Wolfram Research, https:// mathworld.wolfram.com/) teaching scripts
The various contributions to the peak profile in a powder diffraction pattern are described in terms of physical models and the effect they have on the peak shape
Summary
X-ray powder diffraction (XRPD), an established technique for the study of crystal structures, finds increasing application in qualitative and quantitative phase analysis and the study of microstructure for micro- and nanocrystalline materials. The following three parts of this series are envisaged: part I, the peak profile of a powder pattern (this paper); part II, common correction functions in powder diffraction; part III, total scattering In this first paper, the various contributions to the peak profile in a powder diffraction pattern are described in terms of physical models and the effect they have on the peak shape. (ii) Alternatively, because many contributions to powder diffraction peaks have a nearly Gaussian or Lorentzian shape, the Voigt function, which is a convolution of Gaussian and Lorentzian components, or more commonly the pseudo-Voigt function for faster computation, is widely used to describe peak profiles in powder diffraction The latter approach is empirical, and all interpretations of MS parameters based on the Voigt profile must be carefully evaluated.
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