Threshold crack speed in dynamic fracture of silicon
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Threshold crack speed in dynamic fracture of silicon Markus J. Buehler1, Harvey Tang2, Adri C.T. van Duin3, and William A. Goddard3 1 Civil and Environmental Engrg, MIT, 77 Mass Ave, Cambridge, MA, 02139 2 Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 77 Mass Ave, Cambridge, MA, 02139 3 Chemistry, California Institute of Technology, 1200 E. Calif. Blvd., Pasadena, CA, 91125 Corresponding author, electronic address: [email protected] ABSTRACT We report a study of dynamic cracking of a silicon single crystal in which the ReaxFF reactive force field is used for about 3,000 atoms near the crack tip while the other 100,000 atoms of the model system are described with a simple nonreactive force field. The ReaxFF is completely derived from quantum mechanical calculations of simple silicon systems without any empirical parameters. This model has been successfully used to study crack dynamics in silicon, capable of reproducing key experimental results such as orientation dependence of crack dynamics (Buehler et al., Phys. Rev. Lett., 2006). Here we focus on crack speeds as a function of loading and crack propagation mechanisms. We find that the steady state crack speed does not increase continuously with applied load, but instead jumps to a finite value immediately after the critical load, followed by a regime of slow increase. Our results quantitatively reproduce experimental observations of crack speeds during fracture in silicon along the (111) planes, confirming the existence of lattice trapping effects. We find that the underlying reason for this behavior is formation of a 5-7-double ring defect at the tip of the crack, effectively hindering nucleation of the crack at the Griffith load. We develop a simple continuum model that explains the qualitative behavior of the fracture dynamics. INTRODUCTION Brittle fracture is characterized by breaking of atomic bonds leading to formation of two new materials surfaces. Most existing atomistic models of fracture assume an empirical relationship between bond stretch and force. However, breaking of bonds in real materials is an extremely complicated process that could previously only be captured with sufficient accuracy only by using quantum mechanical (QM) methods, which are limited to ~100 atoms. Here we present a new theoretical concept based on building a multi-scale simulation model completely derived from QM principles, while being computationally efficient and capable of treating thousands of atoms with QM accuracy, implemented in a Python based simulation environment. Fracture of silicon has received tremendous attention due to its complexity of bond breaking and due to interesting failure dynamics observed experimentally [1-5].
Figure 1: Subplot (a): The interpolation method for defining a mixed Hamiltonian in the transition region between two different paradigms, as implemented in the CMDF framework. As an alternative to the linear interpolation, we have also implemented smooth interpolation function based on a sinusoida
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