Scherrer constant

Equation (11) uses strongly varying values for the Scherrer constant D, depending on the Miller index of the peak under consideration and on the particle shape. Table 2 is a list of the correction factors from a literature compilation (Alexander and Klug, 1974). The deviations in values are significant in view of the custom in many literature studies of setting the constant equal to unity. 

TABLE 1 Values of the Scherrer constant for use with Equation (11) and various particle morphologies... 

Miller indices (hid) Particle shape Scherrer constant... 

K is known as the shape factor or Scherrer constant which varies in the range 0.89 < XT < 1, and usually K = 0.9 [H.P. Klug and L.E. Alexander, X-ray diffraction procedures for polycrystalline and amorphous materials, Second edition, John Wiley, NY (1974) p. 656]. L.W. Finger, D.E. Cox, A.P. Jephcoat. A correction for powder diffraction peak asymmetry due to axial divergence, J. Appl. Cryst. 27, 892 (1994). 

This Et has the same signification as the defined below from the Fourier analysis. In both cases, the true mean size is the product of the apparent dimension by the Scherrer constant relative to the variance, K . Tournarie and Wilson have tabulated K for different crystallite shapes as a function of the Miller indices hkl. 

FWHMcorr is corrected for the instrumental resolution and K varies with Ad/d and the FWHM. Setting the Scherrer constant K to unity one then plots FWHMcorr cost against sin0 as abscissa. One can then extract the scattering domain radius A from the intercept with the ordinate and Ad/d from the slope (see Figure 4). 

Here, B p and B, s, are the FWHM of experiment and the FWHM of instrument, respectively. The Scherrer constant K equals 0.94, is the X-ray wavelength, 6 is the diffraction angle, D is the average crystallite size and e is the lattice strain. The BET specific surface area measurement was performed using a standard nitrogen adsorption-desorption technique (Micromeritics ASAP2020). The TEM images of ACZ and CZ samples were observed by Hitachi HF-2000(FE TEM). 

The Scherrer constant (K) in the formula accounts for the shape of the particle and is generally taken to have the value 0.9 [70]. The size obtained from the Scherrer formula yields the average particle-size for a material. Powders of materials are generally aggregates of smaller particles, and thus consist of a distribution of particle sizes. 

Where Lhki is the crystallite size k is the Scherrer constant, taken as k=0.89 is the wavelength of X-ray 20 is dififraction angle p is the half width of various dififraction peaks. 

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