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New analytical models for precise calculation of crystallite size: application to synthetic hydroxyapatite and natural eggshell crystalline materials

Md. Sahadat Hossain, Monika Mahmud, Mashrafi Bin Mobarak, Sazia Sultana, Md. Aftab Ali Shaikh, and Samina Ahmed

Institute of Glass and Ceramic Research and Testing, Bangladesh Council of Scientific and Industrial Research (BCSIR), Dhaka, Bangladesh



Received: 8 November 2021  Accepted: 6 June 2022


Crystallite size is the most significant property of solid crystalline materials. Concerning the point of practical features or applicability any accurate estimation of crystallite size is extremely beneficial. Hence, this research presents two new simulations (Model 1 and Model 2) for precise calculations of crystallite size. Using hydroxyapatite (Hap) and eggshell (ES) as synthetic and natural crystalline materials, respectively, the applicability of these proposed models was studied. The calculated values of crystallite size of Hap and ES were found to be 35–101 nm and 72 nm, respectively, (in case of developed Model 1) while for Model 2 the values were in the range of 46–81 nm and 72 nm accordingly, which were assumed to be within the acceptable limit. The crystallite size calculated from the two new models increased with the increment of temperature. Furthermore, the defects of straight line model in Scherrer method (SLMSM) and Monshi–Scherrer equation were discussed.

Keywords: Scherrer method; Williamson–Hall model; Monshi–Scherrer equation; X-ray diffraction

Full paper is available at

DOI: 10.1007/s11696-022-02377-9


Chemical Papers 76 (11) 7245–7251 (2022)

Sunday, May 19, 2024

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