Good afternoon,
I am working with X-ray diffraction data, for which I am particularly interested in understanding the contribution of the peaks intensity.
I found few papers of Istvan Groma, who studies the diffraction peak momentums to estimate dislocation density in metals.
I am looking at one of his paper from 1998 and I don't understand the first change from expression (1) to expression (2) -> see the picture linked to this message.
Could anyone explain to me this transition?
Thanks in advance!
Vincent J.
The scattered intensity of X-rays can be used to estimate the structural properties of a material, such as its crystal symmetry, unit cell parameters, and atomic positions.
The scattered intensity of X-rays can be estimated using the following equation: I(hkl) = K * I0 * |F(hkl)|^2 * * [P(hkl)]
where:
- I(hkl) is the scattered intensity at a particular set of Miller indices (hkl)
- K is a constant that accounts for the absorption of X-rays in the sample
- I0 is the incident X-ray intensity
- F(hkl) is the structure factor, which describes the diffraction of X-rays by the crystal lattice
- is the Debye-Scherrer shape factor, which accounts for the shape of the diffraction peaks
- [P(hkl)] is the preferred orientation factor, which accounts for any preferred orientation of the crystals in the sample
The structure factor F(hkl) can be calculated using the following equation: F(hkl) = ∑n [fj * exp(-2πi (hxj + kyj + lzj))]
where:
- n is the number of atoms in the unit cell
- fj is the atomic scattering factor for the jth atom
- xj, yj, zj are the coordinates of the jth atom in the unit cell
- h, k, l are the Miller indices of the diffraction peak
The scattered intensity can be measured by using X-ray diffractometer and it is usually plotted as a function of the diffraction angle 2θ, which is related to the wavelength of the X-rays and the Miller indices (hkl) of the diffraction peak. The intensities are usually normalized to the incident X-ray intensity and to the number of unit cells in the sample.
It's worth noting that this is a simplified explanation, and in reality, the scattered intensity can be influenced by many factors such as sample size, crystal quality, impurities, defects, and preferred orientation, which need to be taken into account while analyzing the XRD data.
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