Scherrer equation

A perfect crystal would extend in all directions to infinity, so we can say that no crystal is perfect due to its limited sizes. Such a deviation from perfect crystallinity will lead to broadening of the diffraction peak. However, this type of peak broadening is negligible when the crystallite size is larger than 200 nm. Crystallite size is a measure of the size of a coherently diffracting domain. 

Due to the presence of polycrystalline diffracting domain aggregates, crystallite size may not be the same thing as particle size. 

Paul Scherrer (1918) first observed that small crystallite size could give rise to peak broadening. He derived a well-known equation for relating the crystallite size to the peak width, which is called the Scherrer formula

t = Kλ/(B cosθ) 

where 

t is the averaged dimension of crystallites; 

K is the Scherrer constant, somewhat arbitrary value that falls in the range 0.87-1.0 (it is usually assumed to be 1); 

λ is the wavelength of X-ray; and 

B is the integral breadth of a reflection (in radians 2θ) located at 2θ. 

 

Source: University of Washington Department of Chemistry, CHEM 364, Lecture #11

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Variants

  • Scherrer formula