Comparing Methods for Calculating Nano Crystal Size of Natural Hydroxyapatite Using X-Ray Diffraction

Estimating crystal size from X-ray diffraction remains a challenge in nanomaterials research. While multiple methods exist, no single approach has emerged as universally reliable. Prior work has shown that crystal size calculations often vary significantly based on the method used. Researchers have already demonstrated that different models can yield vastly different results from the same dataset. That uncertainty drove this study to evaluate which methods produce values closest to experimental measurements. No prior work had resolved whether one method consistently outperforms others across diverse samples. This gap motivated a direct comparison of multiple XRD-based methods using natural hydroxyapatite. The need for accurate and reproducible crystal size estimation remains unmet in many nanomaterials studies. This paper's contribution lies in systematically comparing these methods against experimental data.

The aim was to evaluate and compare various XRD-based methods for calculating crystal size in natural hydroxyapatite. Researchers focused on resolving discrepancies between theoretical and experimental measurements. They selected hydroxyapatite from cow, pig, and chicken bones as test samples. The specific problem addressed was the lack of consensus on which method provides the most accurate results. Motivation came from the need for reliable crystal size estimation in nanomaterials research. The study aimed to identify which method best aligns with experimental data from BET and TEM. Researchers also sought to determine which methods offer the best balance of accuracy and ease of use. This work fills a gap in the literature by directly comparing multiple models under identical conditions.

The study compared seven different XRD-based methods for crystal size calculation. These included three Scherrer models, Monshi-Scherrer, three Williamson-Hall models, Halder-Wanger, and Size Strain Plot. Each method was applied to XRD patterns from hydroxyapatite derived from three animal bones. X-Pert software was used to extract and process the XRD data. The researchers calculated crystal sizes using each method's specific algorithm. They also performed experimental validation using BET and TEM measurements. The comparison focused on accuracy, ease of calculation, and consistency with experimental data. Researchers evaluated each method's output against the same dataset to ensure fair comparison.

The Scherrer method with the straight line model gave 1371, 457, and 196 nm for cow, pig, and chicken samples. A revised Scherrer model gave 60, 60, and 53 nm for the same samples. The average model produced 56, 58, and 52 nm. The Monshi-Scherrer method gave 60, 60, and 57 nm. UDM results were 56, 62, and 65 nm. USDM values were 60, 62, and 62 nm. UDEDM results were 62, 62, and 65 nm. H-W method gave 4 nm for all samples. SSP method produced 43, 62, and 57 nm. The Scherrer method's original model showed unreasonable values. Other methods produced results within acceptable ranges. BET measurements gave 56, 52, and 49 nm. These aligned closely with Monshi-Scherrer results.

The study found that the Scherrer method's straight line model produced inaccurate values. Other methods gave results consistent with experimental data from BET and TEM. Monshi-Scherrer showed advantages in ease of calculation and error reduction. The slope of the linear plot serves as a useful check for accuracy. The intercept in Monshi-Scherrer provided the most accurate crystal size estimates. Researchers noted that this method's results aligned closely with experimental measurements. The study supports using Monshi-Scherrer for future nanomaterials research. The findings suggest this method balances accuracy with practical usability.