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 fv , and the size misfit degree δb . A simple hardening correlation in KCl-KBr solid-solution is proposed as ∆τFcg = 0.27 G. 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 BNx P1-x , where BNx P1-x solid solutions are far harder than cubic BN. Because the prediction is quantitative, it sets the stage for a broad range of applications.