Unveiling Superior Fracture Toughness in MnCoSb Half-Heusler Alloy: A First-Principles Guide for Designing Damage-Tolerant Functional Materials

In this study, the stability, electronic, structural, and fracture toughness, and mechanical properties of the Half-Heusler(HH) alloys MnCoSb, MnCoAs, MnCoP, and MnNiSb were comprehensively investigated using first-principles calculations based on density functional theory (DFT). The calculated results reveal that all four alloys exhibit half-metallic characteristics, characterized by the presence of a substantial band gap in the spin-down channel. The phonon spectra and negative formation energies confirm that these alloys possess both dynamic and thermodynamic stability. The Born criteria further validate the structural stability in terms of mechanical properties. Three-dimensional representations of the Young’s modulus, bulk modulus, and shear modulus for the four alloys indicate that MnCoP exhibits the most pronounced anisotropy. The overall fracture toughness of the alloys ranges from 1.58 MPa·m1/2 to 2.63 MPa·m1/2, which falls within the typical range for half-metallic materials, albeit at the lower end, attributable to the relatively ductile nature of the four alloys. Although the two methods yield different absolute values, the explicit crack model (Method I) is considered more reliable for anisotropic systems because it directly simulates crack propagation and accounts for local relaxations, while the empirical formula (Method II) provides a useful reference for high-throughput screening. Among the alloys, MnCoSb demonstrates a superior mechanical performance, with KIC values of 2.63 MPa·m1/2 and 1.58 MPa·m1/2 and brittleness indices M of 8.97 and 14.94, indicating excellent damage tolerance compared to the other three alloys. In contrast, MnCoP exhibits higher brittleness and lower mechanical reliability, with KIC values of 2.00 MPa·m1/2 and 1.63 MPa·m1/2 and higher M values of 13.83 and 16.99. This study provides quantitative predictions of fracture toughness and establishes a relationship between microscopic and mechanical properties. These findings offer a theoretical foundation for the application of damage-tolerant HH alloys in fields such as spintronics and magnetism.