Microscopic theory of hardness and optimized hardness model of MX1B and M2X2B2 (M = W, X1=Fe, Co, X2=Fe, Co, Ni) transition-metal ternary borides by the first-principles calculations and experimental verification

Hardness is very complex to describe although it was extensively investigated due to its application in industry. A reliable method is necessary to predict the hardness of compounds as the candidates of the hard phase for cermets. The current review presents the four most popular of microhardness models with average energy gap, bond strength, Mulliken overlap populations and electronegativity. The hardness of the MX1B and M(2)X2B(2) ternary borides was predicted using the above models, Specially, the pseudo-binary crystals (chemical bonds), the overlapping of chemical bonds and overlap populations, the total number of different bonds and the deviation caused by metallicity were discussed when using the Gao's model with overlap populations. Meanwhile, the cohesive energy, formation enthalpy and elastic constants of these borides were calculated via the first-principles calculations, and the results indicate that borides are thermodynamically and mechanically stable. Then the selected materials were prepared by reaction boronizing sintering and the hardness of hard phases was measured using a Micro Vickers hardness tester. The calculated hardness was compared with experimental results to evaluate the feasibility of predicting the mechanical properties of borides. A modified micro hardness model was obtained for predicting the hardness of the MX1B and M(2)X2B(2) ternary borides after verified with the experimental data. The modified model can be used as a quantitative guide to accelerate the selection for advanced high hardness ceramic materials.