Hardness of hexagonal AlB2-like diborides of s, p and d metals from semi-empirical estimations

The high-level ab initio calculations of elastic moduli of materials now become a routine procedure, and the renewed attention is paid to the semi-empirical macroscopic models, providing the correlations between the Vickers hardness HV and some elastic moduli. Such correlations, building up a bridge between Vickers hardness and elastic parameters, seem a helpful way to semi-quantitative estimations of hardness and to theoretical search of novel hard materials, based on the calculations of their elastic properties. Here, using the results of our calculations of elastic parameters of 14 hexagonal AlB2-like diborides of s, p and d metals MB2 (where M = Mg, Ca, Al, Sc, Y, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, and W), we have probed six recently proposed correlations between HV and bulk (B), shear (G), Young's moduli (E), as well as Poisson's ratio (ν), and the parameter k (the G/B ratio), and we compare the obtained results with the available experimental data. Our analysis reveals that for this family of related materials the correlations HV ~ G, and HV ~ E will be the most suitable approximations which enable us to roughly evaluate the Vickers hardness of diborides numerically.

Graphical abstractEstimations of Vickers hardness for 14 polycrystalline diborides MB2 obtained by semi-empirical relationships HV ~ G, and HV ~ Y in comparison with available experimental dataFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Six semi-empirical correlations between hardness and elastic parameters are examined. ► The elastic parameters of 14 hexagonal AlB2-like diborides were used. ► The most suitable approximations are found between hardness and shear, and Young's moduli.