Hardness of cubic solid solutions

We demonstrate that a hardening rule exists in cubic solid solutions with various combinations of ionic, covalent and metallic bonding. It is revealed that the hardening stress ∆τFcg is determined by three factors: shear modulus G, the volume fraction of solute atoms f(v), and the size misfit degree δ(b). A simple hardening correlation in KCl-KBr solid-solution is proposed as ∆τFcg = 0.27 G[Image: see text]. It is applied to calculate the hardening behavior of the Ag-Au, KCl-KBr, InP-GaP, TiN-TiC, HfN-HfC, TiC-NbC and ZrC-NbC solid-solution systems. The composition dependence of hardness is elucidated quantitatively. The BN-BP solid-solution system is quantitatively predicted. We find a hardening plateau region around the x = 0.55–0.85 in BN(x)P(1−x), where BN(x)P(1−x) solid solutions are far harder than cubic BN. Because the prediction is quantitative, it sets the stage for a broad range of applications.