Abstract
We introduce a hardness formula for the multicomponent covalent and ionic solid solutions. This expression is tested on nitride spinel materials A3N4 (A=C,Si,Ge) and applied to titanium nitrogen carbide (TiN1−xCx with 0⩽x⩽1), off-stoichiometric transition-metal nitride (TiN1−x and VN1−x with x⩽0.25), and B-doped semiconductors (C1−xBx, Si1−xBx, and Ge1−xBx with x⩽0.1). In all cases, the theoretical hardness is in good agreement with experiments.
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