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, preci pitates, grain boundaries, dislocation dipoles, and the like. However, in covalent substances, the bonding is localized in electron spin-pai rs, and the hardness is intrinsic. This results from low kink mobiliti es of dislocations. The standard model for dislocation mobility is tha t of Orowan, Peierls, and Nabarro. In this model, the atomic ''roughne ss'' of the glide plane is represented by a sinusoidal potential energ y. This model does not agree with observations, and is intrinsically f lawed because there are singularities at the cores of dislocations tha t cannot be represented by periodic potentials. The author has propose d that kink motion on dislocation lines is analogous with chemical exc hange 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 chemica l hardness and mechanical hardness have the same reaction barrier. It is the difference between the energy of the lowest unoccupied electron ic orbital (LUMO), and the highest occupied orbital (HOMO). This energ y gap determines the strengths of chemical bonds, so it is not surpris ing that it also determines mechanical strength, The theory accounts q uantitatively for the hardnesses of covalent semiconductors (C, Si, Ge , Sn, SiC, and III-V compounds); and with some modification for the ha rdnesses of ''hard metals'', such as TiC and WC.