Physical chemistry of intrinsic hardness

In simple metals and ionic substances, the bonding is delocalized, and hardness is determined by extrinsic factors such as impurities, precipitates, grain boundaries, dislocation dipoles, and the like. However, in covalent substances, the bonding is localized in electron spin-pairs, and the hardness is intrinsic. This results from low kink mobilities of dislocations. The standard model for dislocation mobility is that of Orowan, Peierls, and Nabarro. In this model, the atomic ''roughness'' of the glide plane is represented by a sinusoidal potential energy. This model does not agree with observations, and is intrinsically flawed because there are singularities at the cores of dislocations that cannot be represented by periodic potentials. The author has proposed that kink motion on dislocation lines is analogous with chemical exchange reactions. Adjacent atoms lying at the top and bottom of a glide plane exchange their partners for new partners when a kink moves. The reaction is of the disconcerted type, so it is sluggish for covalent bonds, making the kink mobility low, The theory indicates that chemical hardness and mechanical hardness have the same reaction barrier. It is the difference between the energy of the lowest unoccupied electronic orbital (LUMO), and the highest occupied orbital (HOMO). This energy gap determines the strengths of chemical bonds, so it is not surprising that it also determines mechanical strength, The theory accounts quantitatively for the hardnesses of covalent semiconductors (C, Si, Ge, Sn, SiC, and III-V compounds); and with some modification for the hardnesses of ''hard metals'', such as TiC and WC.