Modified Scherrer Equation to Estimate More Accurately Nano-Crystallite Size Using XRD

Scherrer Equation, L=Kλ/β.cosθ, was developed in 1918, to calculate the nano crystallite size (L) by XRD radiation of wavelength λ (nm) from measuring full width at half maximum of peaks (β) in radian located at any 2θ in the pattern. Shape factor of K can be 0.62 - 2.08 and is usually taken as about 0.89. But, if all of the peaks of a pattern are going to give a similar value of L, then β.cosθ must be identical. This means that for a typical 5nm crystallite size and λ Cukα1 = 0.15405 nm the peak at 2θ = 170° must be more than ten times wide with respect to the peak at 2θ = 10°, which is never observed. The purpose of modified Scherrer equation given in this paper is to provide a new approach to the kind of…