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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.
This is the method used in the original discovery of X-ray diffraction. Laue scattering provides much structural information with only a short exposure to the X-ray beam, and is therefore used in structural studies of very rapid events (time resolved crystallography). However, it is not as well-suited as monochromatic scattering for determining ...
D positions are calculated using Bragg’s law but because clay mineral analysis is one dimensional, l can substitute n, making the equation l λ = 2d sin Θ. When measuring the x-ray diffraction of clays, d is constant and λ is the known wavelength from the x-ray source, so the distance from one 00l peak to another is equal. [3]
The measurement of the angles can be used to determine crystal structure, see x-ray crystallography for more details. [ 5 ] [ 13 ] As a simple example, Bragg's law, as stated above, can be used to obtain the lattice spacing of a particular cubic system through the following relation:
Crystallographers also use the Free R-Factor [3] to assess possible overmodeling of the data. R F r e e {\displaystyle R_{Free}} is computed according to the same formula given above, but on a small, random sample of data that are set aside for the purpose and never included in the refinement.
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.
An X-ray diffraction pattern of a crystallized enzyme. The pattern of spots (reflections) and the relative strength of each spot (intensities) can be used to determine the structure of the enzyme. The relative intensities of the reflections provides information to determine the arrangement of molecules within the crystal in atomic detail.
If the crystal diffracts to high resolution (<1.2 Å), the initial phases can be estimated using direct methods. [1] Direct methods can be used in x-ray crystallography, [1] neutron crystallography, [7] and electron crystallography. [4] [5] A number of initial phases are tested and selected by this method.