Mathematical Modeling of Debye Temperature, Vickers Hardness, and In-teratomic Bonding Behavior in CoNbSn and FeNbSn Half-Heusler Alloys un-der High Hydrostatic Compression up to 80 GPa

Abstract

The present study focuses on the mathematical modeling and quantitative analysis of the impact of high hydrostatic compression, up to 80 GPa, on key thermomechanical properties of hypothetical half-Heusler compounds with a Niobium base atom, specifically CoNbSn and FeNbSn. Using elastic constants and structural parameters as reported in Revista Mexicana de Física, 70(4), 041002 (2024), we derive pressure-dependent behaviors of sound velocities, Debye temperature, minimum thermal conductivity, Vickers hardness, and Cauchy pressure. At zero pressure, our computed values for Vickers hardness and Debye temperature are 11.12 GPa and 395.5 K for CoNbSn, and 9.35 GPa and 409.2 K for FeNbSn, re-spectively. The analytical results indicate a monotonic increase in thermal conductivity, Debye temper-ature, and hardness as pressure increases, reaching maximal values at 80 GPa. Conversely, the Cauchy pressure Cp exhibits a nonlinear and strictly decreasing trend with increasing pressure for both com-pounds. These trends are described using pressure-dependent mathematical models derived from the elastic tensor components, highlighting the interplay between mechanical stability and pressure-in-duced structural behavior in XNbSn (X = Co, Fe) systems.