Elastic Origins of Hardness in Quenchable High-Pressure Metal Nitrides: A Unified Structure-Elasticity Baseline

We review bulk transition-metal nitrides synthesized at high pressure–high temperature and recoverable at ambient conditions. We establish an elasticity-anchored framework that links crystal structure and bonding to elastic descriptors and hardness at the phase-resolved level, enabling fair cross-study comparison. Overall, hardness shows a robust association with the shear modulus G, while the Pugh ratio k = G/B modulates relative rankings across phases. When metallic bonding or non-stoichiometry/defects are pronounced, systematic deviations arise; accordingly, elasticity-based models are best used for cross-phase trends and qualitative guidance rather than absolute predictions, especially for metallic or defect-rich phases. Building on this baseline, we outline application pathways and future research directions, and we propose a minimal reporting checklist to improve reproducibility and cross-study comparability.