Multiscale Simulations of Brittle Fracture and the Quantum-Mechanical Nature of Bonding in Silicon
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Multiscale Simulations of Brittle Fracture and the Quantum-Mechanical Nature of Bonding in Silicon
N. Bernstein and D. Hess Center for Computational Materials Science, Naval Research Laboratory, Washington, DC 20375, USA. ABSTRACT We simulate the microscopic details of brittle fracture in silicon by dynamically coupling empirical-potential molecular dynamics of a strained sample to a quantum-mechanical description of interatomic bonding at the crack tip. Our simulations show brittle fracture at loads comparable to experiment, in contrast with empirical potential simulations that show only ductile crack propagation at much higher loading. While the ductility of the empirical potentials can be attributed to their short range, it is unclear whether the increased range of the tight-binding description is sufficient to explain its brittle behavior. Using the multiscale method we show that at a temperature of 1100 K, but not at 900 K, a dislocation is sometimes nucleated when the crack tip impinges on a vacancy. While this result is too limited in length and time scales to directly correspond to experimental observations, it is suggestive of the experimentally observed brittle to ductile transition. INTRODUCTION Many materials, ranging from silicon to ferritic steels, exhibit a transition between brittle and ductile fracture as a function of temperature [1]. The qualitative differences between these two modes of failure lead to great differences in material toughness. While long-range elastic strain fields, well described by continuum elasticity theory, provide the energy that drives fracture and failure, the nature of fracture itself is ultimately determined on the scale of atoms and the electrons that bind them. Therefore, a microscopic description is required for reliable prediction of the nature of fracture in a given material. Silicon has become a model system for the brittle to ductile transition (BDT) since it shows a particularly sharp transition between the two types of behavior [1]. Below the BDT temperature (about 850 K) failure occurs at the Griffith criterion [2], when elastic energy relief due to crack elongation balances the energetic cost of the new surface. Atomistic simulations of fracture in silicon using empirical potentials (EP) show a disordered zone around an atomically blunt crack, shown in Fig. 1, which propagates only at much higher loadings than the Griffith criterion [3, 4, 5]. Ab-initio simulations of quasistatic fracture of small samples show brittle behavior with some lattice trapping but no disorder [6, 7]. To explore the nature of fracture in silicon at the atomic scale, we have developed an atomistic simulation technique based on molecular dynamics (MD). The method incorporates a simple quantum-mechanical description of atomic interactions near the crack tip, dynamically coupled to EP MD far from the crack tip. In contrast to simulations
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