Calculation of crystallite sizes of pure and metals doped hydroxyapatite engaging Scherrer method, Halder-Wagner method, Williamson-Hall model, and size-strain plot

Abstract

This research paper dealt with the synthesis and characterization of pure and metal-doped hydroxyapatite covering an in-depth crystallographic analysis. The Scherrer equation, Linear Straight-Line Model, Munshi Scherrer Model, Uniform Deformation Model, Uniform Stress Deformation Model, Uniform Deformation Energy Density Model, Size Strain Model, Halder Wagner Model, and Sahadat Scherrer Model were engaged to estimate crystallite size as well as strain, stress, and energy density from few models. All the models were evaluated with their merits and demerits along with usefulness. All the mentioned models showed acceptable results as the crystallite size ranges were from 22 to 77 nm except Linear Straight-Line Model (revealed invalid results for all the synthesized samples). The modified Williamson-Hall model (Uniform Deformation Model, Uniform Stress Deformation Model, Uniform Deformation Energy Density Model) exerted strain, stress and energy density positive and negative. But Size Strain Model, and Halder Wagner Model resulted in only positive values.

Keywords

• X-ray diffraction
• Crystallite size
• Strain
• Stress
• Energy density