A comparative study in estimating structural parameters of X-ray diffraction line broadening and a statistically based thermodynamic approach via the geometrical and Miedema semi-empirical model in NiCoFe(SiMn)x high entropy alloys

Abstract

NiCoFe(SiMn)x HEAs were effectively synthesized by mechanical alloying and subsequently evaluated using X-ray diffraction analysis (XRD) and high-resolution transmission electron microscopy (HRTEM). The structural analysis revealed that the prepared sample exhibits a single-phase solid solution with an FCC crystal structure. The crystallite size (Dcrystal) was examined by using X-ray peak broadening, employing many methodologies: Scherrer, Williamson Hall (W–H), Size-Strain plot (SSP), and Halder-Wagner method (HWM). The W–H approaches employed three model types: uniform deformation model (UDM), uniform stress deformation model (USDM), and uniform deformation energy density model (UDEDM), yielding essential physical parameters such as stress (σ), lattice strain (εstrain), and energy density (u). These approaches were employed to analyze the distinct contributions of Dcrystal and εstrain to the peak broadening of the HEAs. It has been observed that Dcrystal decreases with Si-Mn content because of the εstrain and dislocations resulting from the reconfiguration of bonding connections among atoms of NiCoFe with SiMn content, as validated by HRTEM analysis. The SSP and HWM methods in the present investigation show strong correlation with the HRTEM analysis compared with other methods. Moreover, to confirm the formation of solid solution, a comparative analysis of different geometrical models has been performed based on the data of the five sub-binary systems. It has been found that the general solution model (GSM) provides linear dependency and the correctness of the enthalpy value with a similarity coefficient ″ξi(ij)(k)″ lies within the range of 0 ≤ ξi(ij)(k)≤ 1, giving good agreement with other geometrical models. © 2025 Elsevier B.V.