A comparative study in estimating of crystallite sizes of synthesized and natural hydroxyapatites using Scherrer Method, Williamson-Hall model, Size-Strain Plot and Halder-Wagner Method

In this study, an approach was made to create hydroxyapatite (HAp) crystals on nanoscale ranges from CaCO3 and H3PO4 utilizing a wet chemical process. Both fish and cow bones were used effectively for making bone powder as the natural sources of HAp. X-ray diffraction approach proved that powdered bone and HAp were in the crystalline phase. The determination of crystallite size in synthesized HAp crystals and bone powders was investigated using a range of techniques, including Linear Straight-Line Method (LSLM), Williamson-Hall Method (WHM), Size-Strain Plot (SSP), Halder-Wagner Method (HWM), and Sahadat-Scherrer Method (SSM). We also employed different Williamson-Hall models to quantify the stress and strain of the powdered materials for all diffraction peaks, including the Uniform Deformation Model (UDM), Uniform Stress Deformation Model (USDM), and Uniform Deformation Energy Density Model (UDEDM). Williamson-Hall is regarded as the best approach out of all of them since it was used to find the energy density, lattice stress, lattice strain, and crystallite size of the formed crystal. All the results from each model were compared to check the variation of analyzed data. The obtained results confirmed that there was an interrelation between the particle sizes of the Size Strain Plot and the Williamson-Hall method.