An atomistic study of cracks in diamond-structure crystals

Abstract
The structure of atomically sharp equilibrium cracks in diamond, silicon and germanium is calculated. The treatment considers a long plane crack formed by bond rupture across the (111) cleavage plane, critically loaded in tension. Within a small ‘core’ region immediately surrounding the crack tip the interatomic interactions are represented by a potential function specially constructed to match macroscopic fracture parameters. Anisotropic linear elastic theory is invoked to provide boundary conditions for the core region, and a first approximation for lattice-point displacements within. The core atoms are then relaxed to a configuration of minimum potential energy by computer. The results indicate that continuum theory is capable of giving remarkably accurate predictions of the crack-tip displacement field, except within about three atom spacings from the tip, despite marked nonlinearity in the interatomic force function. These results are discussed in terms of existing continuum models of crack-tip structure: in particular, Barenblatt’s model of a cusp-shaped tip region is found to be inapplicable to diamond-structure crystals. The crack-tip geometry is better pictured as a narrow slit terminated by a single line of bonds close to the rupture point. Brief reference is made to the possible extension of the treatment to other classes of highly brittle solid, especially glassy materials, and to the relevance of the results to some fracture problems of practical importance.

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