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

• Published in: Intermetallics Vol. 114; p. 106573
• Main Authors: Shi, Zhengtao, Yin, Haiqing, Xu, Zhifeng, Zhang, Tong, Yang, Guoqiang, Zheng, Qingjun, Rao, Ramesh S., Yang, Jun, Gao, Faming, Wu, Mao, Qu, Xuanhui
• Format: Journal Article
• Language: English
• Published: Barking Elsevier Ltd 01.11.2019; Elsevier BV
• Subjects: Bond strength; Bonding strength; Borides; Cermets; Chemical bonds; Cobalt; Diamond pyramid hardness; Elastic properties; Electronegativity; Energy gap; Enthalpy; First principles; First-principles calculations; Hardness; Industrial applications; Iron; Materials selection; Mechanical properties; Metallicity; Microhardness model; Molybdenum; Mulliken overlap populations; Nickel; Organic chemistry; Populations; Reaction boronizing sintering; Ternary borides; Transition metals; Microhardness model; First-principles calculations; Ternary borides; Hardness; Reaction boronizing sintering; Mulliken overlap populations
• ISSN: 0966-9795; 1879-0216
• DOI: 10.1016/j.intermet.2019.106573

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 M2X2B2 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 M2X2B2 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. •Hardness models for MX1B and M2X2B2 ternary borides were investigated.•The Vickers hardness of hard phases for cermets was determined.•The experimental results of ternary borides are in good agreement with the predicted results.•A modified hardness model based on chemical bonds and metallicity was obtained.