Materials Science and Engineering A 400–401 (2005) 72–75 Vacancy formation energy near an edge dislocation: A hybrid quantum-classical study F. Tavazza, R. Wagner, A.M. Chaka, L.E. Levine ∗ NationalInstituteofStandardsandTechnology,Gaithersburg,MD20899,USA Received 13 September 2004; received in revised form 1 February 2005; accepted 28 March 2005 Abstract In this work, the formation energy of a single vacancy in aluminum at different distances from an edge dislocation core is studied using a new, hybrid ab initio-classical potential methodology. Such an approach allows us to conduct large-scale atomistic simulations with a simple classical potential (embedded atom method (EAM), for instance) while simultaneously using the more accurate ab initio approach (first principles quantum mechanics) for critical embedded regions. The coupling is made through shared shells of atoms where the two atomistic modeling approaches are relaxed in an iterative, self-consistent manner. The small, critical region is relaxed using all electron density functional theory (DFT) and the much larger cell in which this is embedded is relaxed using a minimization algorithm with EAM potentials. © 2005 Elsevier B.V. All rights reserved. Keywords: Vacancy formation; Al; Electron density functional theory; Embedded atom method 1. Introduction Understanding dislocation behavior is a key for designing materials with improved properties; however, despite a mas- sive body of literature [1], much is still unknown about the subject. In this work, the formation energy of a vacancy in the proximity of an edge dislocation is analyzed, together with the atomic relaxations that occur near the vacancy itself. To determine the behavior of the formation energy as a function of the distance from the dislocation, it is necessary to simulate reasonably large systems, so that several distances could be studied. The ab initio methods usually utilized to investigate dislocation cores [2–9] currently do not allow treatment of systems large enough for our purposes. Empirical techniques are fast enough to treat millions of atoms, but are intrinsi- cally limited by the approximations made in constructing the potentials, and hence, may be inadequate for the accurate determination of the properties under examination. To overcome such an impasse, we utilize a hybrid quantum-classical algorithm that is designed to conduct ∗ Corresponding author. Fax: +1 301 975 4553. E-mailaddress: lyle.levine@nist.gov (L.E. Levine). large-scale atomistic simulations with simple classical poten- tials while simultaneously using the more accurate ab initio approach for critical embedded regions. This methodology allows us to take advantage of the accuracy of the density functional theory (DFT) calculations in the region of interest, while the large, classical, embedding cell eliminates concerns related to the effect of cluster termination on a small system and the necessity of artificially including long range elastic ef- fects as required by the presence of a dislocation. In most hy- brid methods, the shaking-hand zone is given by an interface ([10,11] for instance); on one side of the interface the bonds are derived from the ab initio (or tight-binding) Hamiltonian, while on the other side they are derived from a classical in- teratomic potential. In our method, the shaking-hand zone is a shell several Angstrom thick whose atoms are moved, iteratively, both classically and quantum-mechanically. The most significant difference between this algorithm and other hybrid methods, though, is the fact that we consider a critical region large enough to include most of the effect of any de- sired perturbation. This requirement guarantees that outside the critical region the description of the material provided by the classical approximation is very similar to that due to the quantum approach. It also means that we are not extremely 0921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2005.03.079