relate scherrer expression with Bragg's law and this law with size. structure
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Answer:
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. It is named after Paul Scherrer.[1][2] It is used in the determination of size of crystals in the form of powder.
The Scherrer equation can be written as:
{\displaystyle \tau ={\frac {K\lambda }{\beta \cos \theta }}}\tau ={\frac {K\lambda }{\beta \cos \theta }}
where:
{\displaystyle \tau }\tau is the mean size of the ordered (crystalline) domains, which may be smaller or equal to the grain size, which may be smaller or equal to the particle size;
{\displaystyle K}K is a dimensionless shape factor, with a value close to unity. The shape factor has a typical value of about 0.9, but varies with the actual shape of the crystallite;
{\displaystyle \lambda }\lambda is the X-ray wavelength;
{\displaystyle \beta }\beta is the line broadening at half the maximum intensity (FWHM), after subtracting the instrumental line broadening, in radians. This quantity is also sometimes denoted as {\displaystyle \Delta \left(2\theta \right)}{\displaystyle \Delta \left(2\theta \right)};
{\displaystyle \theta }\theta is the Bragg angle.
Answer:
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Scherrer equation - /topics/materials-science/scherrer-equation
Scherrer Equation - an overview | ScienceDirect Topics
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Scherrer Equation - an overview | ScienceDirect Topics