Dynamic Fracture of Silicon: Concurrent Simulation of Quantum Electrons, Classical Atoms, and the Continuum Solid
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Silicon: Concurrent Simulation of Quantum Electrons, Classical Atoms, and the Continuum Solid
Farid F. Abraham, Noam Bernstein, Jeremy Q. Broughton, and Daryl Hess Introduction Our understanding of materials phenomena is based on a hierarchy of physical descriptions spanning the space-time regimes of electrons, atoms, and matter and given by the theories of quantum mechanics, statistical mechanics, and continuum mechanics. The pioneering work of Clementi and co-workers1 provides a lucid example of the traditional approach to incorporating multiscale phenomena associated with these three mechanics. Using quantum mechanics, they evaluated the interactions of several water molecules. From this data base, they created an empirical potential for use in atomistic mechanics and evaluated the viscosity of water. From this computed viscosity, they performed a fluid-dynamics simulation to predict the tidal circulation in Buzzard’s Bay. This is a powerful example of the sequential coupling of length and time scales: a series of calculations is used as input to the next rung up the length/time-scale ladder. However, there are situations where the physics on different length scales interacts dynamically, and an adequate description is not possible using the sequentialcoupling scheme employed by Clementi. MRS BULLETIN/MAY 2000
Dynamic fracture is a very good example. Energy from large-scale elastic fields is concentrated on the angstrom scale of the electrons that participate in atomic bonding. A simulation of this phenomenon requires an accurate description of atoms bonding at the crack tip, while at the same time including a proper description for very large volumes of strained material, the resolution varying with distance from the crack tip. Far away, it is adequate to use the equations of motion for a macroscopic-averaged continuum field. With decreasing distance from the crack tip, singularities in the elastic field are cut off by atomic-scale phenomena and the eventual breaking of electronic bonds. These phenomena on the one hand require more information to describe, but on the other hand, they dominate in successively smaller regions of materials. This suggests a natural physical-domain decomposition: Å3 volumes where electronic excitations must be considered explicitly, nm3 regions where atomic processes must be described, and m3 regions where displacement fields are sufficient. This spatial decomposition makes it possible to combine different
simulation methods describing the different physical regions into a single, powerful simulation tool. We present a method that dynamically couples continuum mechanics far from the crack, empirical potential MD near the crack, and quantum tight-binding (TB) dynamics at the crack tip, to simulate fracture in silicon. Continuum mechanics has long been fruitfully applied to the study of fracture2 by explicitly putting in preexisting cracks or a phenomenological description of material decohesion. We use it to efficiently describe large parts of the system that are elastically def
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