Validity of crystallite size determination methods based on XRD peak broadening in pure and metal-doped nickel ferrites

Abstract

The current work is focused on a crystallographic investigation and comparative analysis of crystallite size estimation of pure and metal-doped (Co, Cu, Zn) nickel ferrite samples (J1–J4). Pure NF and doped-NF (Co-NF, Cu-NF, Zn-NF) were achieved through the sol-gel method at 700 °C and subjected to characterization using X-ray Diffraction. To calculate the crystallite size of pure NF and doped-NF, various methods, including the Classical Scherrer (C-S), Munshi Scherrer (M − S), Williamson-Hall (W-H), Linear Straight-Line Model (LSLM), Size Strain Plot (SSP), Halder Wagner (H-W), and Sahadat Scherrer Model (SSM) were employed. Depending on the method employed, satisfactory results have been obtained from all the listed models, excluding the LSLM. LSLM produced invalid outcomes for all the synthesized samples, particularly for sample J3 (797.08 nm). The C-S method yields the smallest sizes, ranging from 34.74 to 57.38 nm, whereas W-H, H-W, and SSP produced significantly larger sizes, up to 132.05 nm for J4, proving the crucial influence of microstrain on peak broadening. The Shahadat Scherrer method consistently reported intermediate values, suggesting a balance between simplicity and improved accuracy. The most consistent and relatively uniform microstructure crystallite sizes across most models (except LSLM) were exhibited by sample J1, while sample J4 showed the highest discrepancy, highlighting strain-induced effects. Overall, the Halder–Wagner and SSP methods appear to offer more robust and accurate size predictions, making them preferable tools for characterizing crystallite dimensions in strain-sensitive systems. All the crystallographic information obtained here is a potential source for estimating crystallite sizes of pure and metal-doped nickel ferrites for various technological applications.