From electrons to finite elements: A concurrent multiscale approach for metals

Abstract

We present a multiscale modeling approach that concurrently couples quantum-mechanical, classical atomistic, and continuum mechanical simulations in a unified fashion for metals. This approach is particularly useful for systems where chemical interactions in a small region can affect the macroscopic properties of a material. We discuss how the coupling across different scales can be accomplished efficiently, and we apply the method to multiscale simulations of an edge dislocation in aluminum in the absence and presence of H impurities. DOI: 10.1103/PhysRevB.73.024108 PACS number͑s͒: 71.15.Mb, 62.20.Mk, 71.15.Dx Some of the most fascinating problems in all fields of science involve multiple spatial and/or temporal scales: processes that occur at a certain scale govern the behavior of the system across several ͑usually larger͒ scales. In the context of materials science, the ultimate microscopic constituents of materials are ions and valence electrons; interactions among them at the atomic level determine the behavior of the material at the macroscopic scale, the latter being the scale of interest for technological applications. Conceptually, two categories of multiscale simulations can be envisioned, sequential, consisting of passing information across scales, and concurrent, consisting of seamless coupling of scales. 1 The majority of multiscale simulations that are currently in use are sequential ones, which are effective in systems where the different scales are weakly coupled. For systems whose behavior at each scale depends strongly on what happens at the other scales, concurrent approaches are usually required. In contrast to sequential approaches, concurrent simulations are still relatively new and only a few models have been developed to date. [1][2][3][4][5][6] A successful concurrent multiscale method is the quasicontinuum ͑QC͒ method originally proposed by Tadmor et al. 2 The idea underlying this method is that atomistic processes of interest often occur in very small spatial domains while the vast majority of atoms in the material behave according to well-established continuum theories. To exploit this fact, the QC method retains atomic resolution only where necessary and grades out to a continuum finite element description elsewhere. The original formulation of QC was limited to classical potentials for describing interactions between atoms. Since many materials properties depend explicitly on the behavior of electrons, such as bond breaking/ forming at crack tips or defect cores, chemical reactions with impurities, and surface reactions and reconstructions, it is desirable to incorporate appropriate quantum mechanical descriptions into the QC formalism. In this paper, we extend the original QC approach so that it can be directly coupled with quantum mechanical calculations based on density functional theory ͑DFT͒ for metallic systems. We refer to the new approach as QCDFT.The goal of the QC method is to model an atomistic system without explicitly treating every atom in the problem. 2,7 This is ...

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