Evaluation Methods of Line Profiles

Evaluation Methods of Line Profiles

Copyright: © 2014 |Pages: 41
DOI: 10.4018/978-1-4666-5852-3.ch006
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Abstract

The evaluation procedures of X-ray line profiles are overviewed in this chapter. These methods can be classified into four groups, namely (1) the most simple methods that evaluate only the breadths of diffraction peaks, (2) procedures using the Fourier-transforms of line profiles for the determination of the parameters of microstructures, (3) variance methods evaluating the restricted moments of peaks, and (4) procedures fitting the whole diffraction pattern. The crystallite size distribution and the densities of lattice defects cannot be determined from the peak width alone as the rule of summation of breadths of size, strain, and instrumental profiles depends on their shape. However, the breadth methods can be used for a qualitative assessment of the main origins of line broadening (size, dislocations, planar faults) (e.g. for checking the model of microstructure used in whole powder pattern fitting procedures). The application of Fourier and variance methods is limited if the diffraction peaks are overlapping. In the case of pattern fitting procedures, usually a microstructure model is needed for the calculation of the theoretical fitting functions. The reliability of these methods increases with increasing the number of fitted peaks.
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Classical And Modified Warren-Averbach Methods

In chapter 3 of this book, the simultaneous effects of crystallite size and lattice strains on line profiles are investigated in details. Equation (3.8) reveals that the scattered intensity can be expressed as the convolution of the line profile functions caused by the finite crystallite size and the lattice distortions. These functions are referred to as “size” and “strain” (or “distortion”) line profiles. Therefore, after the instrumental correction (see chapter 9) the Fourier transform (or the Fourier coefficients) of the total intensity profile can be obtained as the product of the Fourier transforms (or Fourier coefficients) of “size” and “distortion” line profiles denoted by AS and AD, respectively (Guinier, 1963):

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