Abstract
Hybrid quantum/classical techniques can flexibly couple ab initio simulations to an empirical or elastic medium to model materials systems that cannot be contained in small periodic supercells. However, due to electronic non-locality a total energy cannot be defined, meaning energy barriers cannot be calculated. We provide a general solution using the principle of virtual work in a modified nudged elastic band algorithm. Our method enables the first ab initio calculations of the kink formation energy for <100> edge dislocations in molybdenum and lattice trapping barriers to brittle fracture in silicon.
Highlights
The two-way chemomechanical coupling of chemical and elastic fields creates inextricably multiscale problems with a simultaneous requirement for chemical accuracy and large system sizes
This problem is acute for crystal defects such as dislocation lines [3], grain boundaries [4], and cracks [5], which all possess a long-range elastic field that can rarely be contained in small periodic supercells without unrealistically strong image interactions or strain gradients
We find the modified embedded atom method (MEAM) migration barrier converges with increasing system size and dipole separation, as shown in Fig. 2; this size convergence was confirmed in calculations with a single dislocation in a cylindrical supercell, the outermost atoms fixed to the displacements predicted by anisotropic elasticity theory [39]
Summary
The two-way chemomechanical coupling of chemical and elastic fields creates inextricably multiscale problems with a simultaneous requirement for chemical accuracy and large system sizes. Density functional theory (DFT) has been shown to have excellent predictive power [1], but its typically high O(N 3) computational cost limits its application to problems with fewer than around 1000 atoms [2] This problem is acute for crystal defects such as dislocation lines [3], grain boundaries [4], and cracks [5], which all possess a long-range elastic field that can rarely be contained in small periodic supercells without unrealistically strong image interactions or strain gradients. We exploit the fact that ionic forces in both the classical and quantum region are well defined and localized, allowing us to apply the principle of virtual work to construct energy barriers for a given configurational pathway Combining this principle with the nudged elastic band routine for finding minimum energy pathways allows the calculation of energy barriers in systems much larger than can be treated in periodic DFT supercells. We demonstrate our method on two problems typically considered inaccessible to ab initio methods: kink formation on 100 edge dislocations in Mo and lattice trapping barriers to brittle fracture in Si
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