Tuning mechanical and microstructural properties of Bi-2212 ceramics through optimal Nd3+ substitution: findings from experimental and theoretical approach

Abstract

This study systematically investigates the mechanical and structural behavior of Nd3+-substituted Bi2.0-xNdxSr2.0Ca1.0Cu2.0Oy ceramics synthesized by the conventional solid-state reaction method using combined experimental microhardness (Hv) testing and theoretical modeling approaches. Incorporating Nd ions into the Bi-2212 lattice enhances microstructural stability, grain boundary coupling, and crystallographic coherence, with optimal mechanical performance at x = 0.01. Complementary SEM, XRD, and EDX analyses confirm the correlation between improved surface morphology, crystallinity, and enhanced mechanical performance. EDX results further verified the successful replacement of Bi3+ for Nd3+ and compositional uniformity within the Bi-2212 lattice, supporting the structural integrity and hardness improvements. At this concentration, strong ionic and partial covalent bonding interactions between Nd3+ and the host lattice facilitate charge compensation, defect accommodation, and densification, resulting in superior Vickers hardness and resistance to deformation. As for the mechanical characterization examination, indentation behavior reveals classical Indentation Size Effect (ISE) behavior through all the synthesized compounds, with peak load resistance at x = 0.01 and marked degradation at higher dopant levels due to increased porosity, grain boundary decoupling, and strain localization. Bulk density (rho) measurements correlate strongly with microhardness trends, confirming the interdependence of atomic packing, structural integrity, porosity, intergranular coherence, and mechanical durability. Accordingly, the optimal mechanical and structural performance is observed at x = 0.01, corresponding to the highest measured rho value of 5.99 g/cm3 and Hv of 0.498 GPa at 0.295 N. These results indicate that Nd-3(+) substitution at this level promotes enhanced densification and grain boundary cohesion, leading to a defect-minimized microstructure with superior resistance to indentation and load-induced plastic deformation. Beyond this doping level, excessive Nd incorporation deteriorates crystallinity and promotes porosity formation, resulting in reduced mechanical durability and structural integrity. Consequently, the material exhibits increased susceptibility to load-induced plastic deformation and crack propagation along grain boundaries. At the highest substitution level, Hv decreases from 0.333 GPa to 0.280 GPa across the same range of applied loads, confirming the adverse impact of over-doping on mechanical performance. A near-linear relationship between rho and Hv is observed, validating bulk density as a predictive metric for key mechanical design features in Bi-2212 systems. Additionally, key mechanical performance metrics, including load-independent Hv results, are analyzed within the plateau limit (PL) regions of Nd-substituted Bi-2212 structures using established theoretical models to elucidate structure-property relationships and predict service life and material reliability under practical application conditions. Comparative analysis reveals that the Indentation-Induced Cracking (IIC) model provides the most accurate description of the mechanical response in the doped systems. The experimental findings and theoretical results highlight the critical role of rare-earth substitution at an optimal concentration level in tuning lattice cohesion, defect tolerance, and mechanical resilience, establishing x = 0. 01 for Nd/Bi-substituted Bi-2212 as a promising candidate for high-performance structural ceramic applications.