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The Scherrer equation, in X-ray diffraction and crystallography, is a formula that relates the size of sub-micrometre crystallites in a solid to the broadening of a peak in a diffraction pattern. It is often referred to, incorrectly, as a formula for particle size measurement or analysis.
The most common powder X-ray diffraction (XRD) refinement technique used today is based on the method proposed in the 1960s by Hugo Rietveld. [2] The Rietveld method fits a calculated profile (including all structural and instrumental parameters) to experimental data.
The units of the structure-factor amplitude depend on the incident radiation. For X-ray crystallography they are multiples of the unit of scattering by a single electron (2.82 m); for neutron scattering by atomic nuclei the unit of scattering length of m is commonly used.
This equation, Bragg's law, describes the condition on θ for constructive interference. [12] A map of the intensities of the scattered waves as a function of their angle is called a diffraction pattern. Strong intensities known as Bragg peaks are obtained in the diffraction pattern when the scattering angles satisfy Bragg condition.
In crystallography, the R-factor (sometimes called residual factor or reliability factor or the R-value or R Work) is a measure of the disagreement between the crystallographic model and the experimental X-ray diffraction data - lower the R value lower is the disagreement or better is the agreement.
Free-electron lasers have been developed for use in X-ray diffraction and crystallography. [27] These are the brightest X-ray sources currently available; with the X-rays coming in femtosecond bursts. The intensity of the source is such that atomic resolution diffraction patterns can be resolved for crystals otherwise too small for collection.
Miller indices are also used to designate reflections in X-ray crystallography. In this case the integers are not necessarily in lowest terms, and can be thought of as corresponding to planes spaced such that the reflections from adjacent planes would have a phase difference of exactly one wavelength (2 π ), regardless of whether there are ...
The use of computational methods for the powder X-ray diffraction data analysis is now generalized. It typically compares the experimental data to the simulated diffractogram of a model structure, taking into account the instrumental parameters, and refines the structural or microstructural parameters of the model using least squares based ...
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