Shapes of powder diffraction peaks

The observed peak shapes are best described by the so-called peak shape function (PSF), which is a convolution of three different functions instrumental broadening, Q, wavelength dispersion. A, and specimen function, E. Thus, PSF can be represented as follows  

The instrumental function, Q, depends on multiple geometrical parameters the locations and geometry of the source, monochromator(s). 

It is worth noting that unlike the instrumental and wavelength dispersion functions, the broadening effects introduced by the physical state of the specimen may be of interest in materials characterization. Thus, effects of the average crystallite size (x) and microstrain (s) on Bragg peak broadening (P, in radians) can be described in the first approximation as follows  

In general, three different approaches to the description of peak shapes can be used. The first employs empirical peak shape functions, which fit the profile without attempting to associate their parameters with physical quantities. The second is a semi-empirical approach that describes instrumental and wavelength dispersion functions using empirical functions, while specimen properties are modeled using realistic physical parameters. In the third, the so-called fundamental parameters approach, all three components of the peak shape function (Eq. 2.45) are modeled using rational physical quantities. 

Bergmann, Contributions to evaluation and experimental design in the fields of x-ray powder diffractometry, Ph.D. thesis (in German), Dresden University for Technology (1984). See http //www.bgmn.de/methods.html for more information and other references. 

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