Atomistic modeling of brittleness in covalent materials

Despite a large number of model potentials having been developed in the last decades for silicon and group-IV elements, only a few of them correctly reproduce the brittle propagation of fracture and provide a proper estimate of the failure strength for such materials. We prove that the inability to model the brittle crack opening shown by most model potentials is related to their short-range character, a feature which overestimates the atomic force necessary to snap a bond. By using the universal energy relation we prove that any model potential aimed at studying fracture in covalent crystals should include interactions longer than the second-neighbor distance. We adopt the Tersoff force model to illustrate such a concept in the case of Si-Ge-C systems. Finally, we demonstrate that by means of a suitable modification of the Tersoff force model it is possible to recover the brittle fracture in Si, C, Ge, and SiC and to provide a quantitative prediction of many mechanical properties.