Estimate Av. Crystallite Size & Willisom Hall & Modified Scherrer Plot via Pseudo Viogt Function

The Williamson–Hall plot (β cosθ vs. sinθ) is obtained from XRD results. As the laser impact increases, the slope of the Williamson–Hall plot increases. Due to strain hardening, the width of the diffraction peak increases as a result of the increase in lattice micro-strain and the decrease in crystallite size.

Modified Scherrer equation plots lnβ against ln(1/cosθ) and obtain the intercept of a least squares line regression, ln=Kλ/L, from which a single value of L is obtained through all of the available peaks.