Mechanical hardness: A semiempirical theory based on screened electrostatics and elastic smear

The equation H = AGh(s) is the first to describe the mechanical hardness H of materials having arbitrary crystal structure or bonding type, where A is a constant, G is the isotropic elastic shear modulus, and h(s) is a scaling relation for the chemical hardness of an indented solid. Here, h(s) is deemed to be the second derivative of the total electronic energy with respect to the electron population of atoms in the indented region of the solid. From this definition and semiempirical arguments, h(s) is a simple function of those atoms' effective nuclear charge Z(eff) and the number of nearest neighbors to the most electronegative atom in the perfect crystal, The model equation is used to calculate the hardness of 71 materials, having assorted crystal structures and bonding types, that are (A) I-atom or 2-atom nonmetals or (B) simple metals. The class-A calculated hardnesses lie within 20% (30%) of experiment for 77% (92%) of the materials. The class-B calculated hardnesses lie within 20% (30%) of experiment for 42% (61%) of the simple metals. The results enable mechanical hardness to be calculated solely in terms of the crystal structure geometry and intrinsic atomic-level properties Z(eff) and G, where G is obtained from monocrystal elastic constants using quasiisotropic polycrystalline bounding equations. Consequently, hardness may be estimated for proposed superhard ceramic materials by coupling the model equation with ab initio solid-state electronic structure calculations of the elastic constants. (C) 1998 Elsevier Science Ltd. All rights reserved.