The aim of this paper is to present a streamlined and fully three-dimensional version of the quasicontinuum (QC) theory of Tadmor et al. [18,19] and to analyze its accuracy and convergence characteristics. Specifically, we assess the effect of the summation rules on accuracy; we determine the rate of convergence of the method in the presence of strong singularities, such as point loads; and we assess the effect of the refinement tolerance, which controls the rate at which new nodes are inserted in the model, on the development of dislocation microstructures.

Electroactive interfaces distinguish electrochemistry from chemistry and enable electrochemical energy devices like batteries, fuel cells, and electric double layer capacitors. In batteries, electrolytes should be either thermodynamically stable at the electrode interfaces or kinetically stable by forming an electronically insulating but ionically conducting interphase. In addition to a traditional optimization of electrolytes by adding cosolvents and sacrificial additives to preferentially reduce or oxidize at the electrode surfaces, knowledge of the local electrolyte composition and structure within the double layer as a function of voltage constitutes the basis of manipulating an interphase and expanding the operating windows of electrochemical devices. In this work, we focus on how the molecular-scale insight into the solvent and ion partitioning in the electrolyte double layer as a function of applied potential could predict changes in electrolyte stability and its initial oxidation and reduction reactions. In molecular dynamics (MD) simulations, highly concentrated lithium aqueous and nonaqueous electrolytes were found to exclude the solvent molecules from directly interacting with the positive electrode surface, which provides an additional mechanism for extending the electrolyte oxidation stability in addition to the well-established simple elimination of "free" solvent at high salt concentrations. We demonstrate that depending on their chemical structures, the anions could be designed to preferentially adsorb or desorb from the positive electrode with increasing electrode potential. This provides additional leverage to dictate the order of anion oxidation and to effectively select a sacrificial anion for decomposition. The opposite electrosorption behaviors of bis(trifluoromethane)sulfonimide (TFSI) and trifluoromethanesulfonate (OTF) as predicted by MD simulation in highly concentrated aqueous electrolytes were confirmed by surface enhanced infrared spectroscopy. The proton transfer (H-transfer) reactions between solvent molecules on the cathode surface coupled with solvent oxidation were found to be ubiquitous for common Li-ion electrolyte components and dependent on the local molecular environment. Quantum chemistry (QC) calculations on the representative clusters showed that the majority of solvents such as carbonates, phosphates, sulfones, and ethers have significantly lower oxidation potential when oxidation is coupled with H-transfer, while without H-transfer their oxidation potentials reside well beyond battery operating potentials. Thus, screening of the solvent oxidation limits without considering H-transfer reactions is unlikely to be relevant, except for solvents containing unsaturated functionalities (such as C═C) that oxidize without H-transfer. On the anode, the F-transfer reaction and LiF formation during anion and fluorinated solvent reduction could be enhanced or diminished depending on salt and solvent partitioning in the double layer, again giving an additional tool to manipulate the ...

High throughput screening of solvents and additives with potential applications in lithium batteries is reported. The initial test set is limited to carbonate and phosphate-based compounds and focused on their electrochemical properties. Solvent stability towards first and second reduction and oxidation is reported from density functional theory (DFT) calculations performed on isolated solvents surrounded by implicit solvent. The reorganization energy is estimated from the difference between vertical and adiabatic redox energies and found to be especially important for the accurate prediction of reduction stability. A majority of tested compounds had the second reduction potential higher than the first reduction potential indicating that the second reduction reaction might play an important role in the passivation layer formation. Similarly, the second oxidation potential was smaller for a significant subset of tested molecules than the first oxidation potential. A number of potential sources of errors introduced during screening of the electrolyte electrochemical properties were examined. The formation of lithium fluoride during reduction of semifluorinated solvents such as fluoroethylene carbonate and the H-transfer during oxidation of solvents were found to shift the electrochemical potential by 1.5-2 V and could shrink the electrochemical stability window by as much as 3.5 V when such reactions are included in the screening procedure. The initial oxidation reaction of ethylene carbonate and dimethyl carbonate at the surface of the completely de-lithiated LiNi0.5Mn1.5O4 high voltage spinel cathode was examined using DFT. Depending on the molecular orientation at the cathode surface, a carbonate molecule either exhibited deprotonation or was found bound to the transition metal via its carbonyl oxygen.

state energy, subject to a fixed number of elements in the finite-element mesh. To this end, we first develop an estimate for the finite-element discretization error in the Kohn-Sham ground-state energy as a function of the characteristic mesh-size distribution, h(r), and the exact ground-state electronic fields comprising of wavefunctions and electrostatic potential. We subsequently determine the optimal mesh distribution for the chosen representative solution by determining the h(r) that minimizes the discretization error. The resulting expressions for the optimal mesh distribution are in terms of the degree of the interpolating polynomial and the exact solution fields of the Kohn-Sham DFT problem. Since the exact solution fields are a priori unknown, we use the asymptotic behavior of the atomic wavefunctions [38] away from the nuclei to determine the coarse-graining rates for the finite-element meshes used in our numerical study. Though the resulting finite-element meshes are not necessarily optimal near the vicinity of the nuclei, the mesh coarsening rate away from the nuclei provides an efficient way of resolving the vacuum in non-periodic calculations.We next implement an efficient solution strategy for solving the finite-element discretized eigenvalue problem, which is crucial before assessing the computational efficiency of the basis. We note that the non-orthogonality of the finite-element basis results in a discrete generalized eigenvalue problem, which is computationally more expensive than the standard eigenvalue problem that results from using an orthogonal basis like planewaves. We address this issue by employing a spectral finite-element discretization and Gauss-Lobatto quadrature rules to evaluate the integrals which results in a diagonal overlap matrix, and allows for a trivial transformation to a standard eigenvalue problem. Further, we use the Chebyshev acceleration technique for standard eigenvalue problems to efficiently compute the occupied eigenspace (cf. e.g. [39] in the context of electronic structure calculations). Our investigations suggest that the use of spectral finite-elements and Gauss-Lobatto rules in conjunction with Chebyshev acceleration techniques to compute the eigenspace gives a 10 − 20 fold computational advantage, even for modest materials system sizes, in comparison to traditional methods of solving the standard eigenvalue problem where the eigenvectors are computed explicitly. Further, the proposed approach has been observed to provide a staggering 100 − 200 fold computational advantage over the solution of a generalized eigenvalue problem that does not take advantage of the spectral finite-element discretization and Gauss-Lobatto quadrature rules. In our implementation, we use a self-consistent field (SCF) iteration with Anderson mixing [40], and employ the finite-temperature Fermi-Dirac smearing [3] to suppress the charge sloshing associated with degenerate or close to degenerate eigenstates around the Fermi energy.We next study various numerical aspects of the finite-...

a b s t r a c tA continuum phase field theory and corresponding numerical solution methods are developed to describe deformation twinning in crystalline solids. An order parameter is associated with the magnitude of twinning shear, i.e., the lattice transformation associated with twinning. The general theory addresses the following physics: large deformations, nonlinear anisotropic elastic behavior, and anisotropic phase boundary energy. The theory is applied towards prediction of equilibrium phenomena in the athermal and non-dissipative limit, whereby equilibrium configurations of an externally stressed crystal are obtained via incremental minimization of a free energy functional. Outcomes of such calculations are elastic fields (e.g., displacement, strain, stress, and strain energy density) and the order parameter field that describes the size and shape of energetically stable twin(s). Numerical simulations of homogeneous twin nucleation in magnesium single crystals demonstrate fair agreement between phase field solutions and available analytical elasticity solutions. Results suggest that critical far-field displacement gradients associated with nucleation of a twin embryo of minimum realistic size are 4.5%-5.0%, with particular values of applied shear strain and equilibrium shapes of the twin somewhat sensitive to far-field boundary conditions and anisotropy of twin boundary surface energy.Published by Elsevier B.V.

The aim of this paper is the development of equilibrium and non-equilibrium extensions of the quasicontinuum (QC) method. We first use variational mean-field theory and the maximum-entropy formalism for deriving approximate probability distribution and partition functions for the system. The resulting probability distribution depends locally on atomic temperatures defined for every atom and the corresponding thermodynamic potentials are explicit and local in nature. The method requires an interatomic potential as the sole empirical input. Numerical validation is performed by simulating thermal equilibrium properties of selected materials using the LennardJones pair potential and the EAM potential and comparing with molecular dynamics results as well as experimental data. The max-ent variational approach is then taken as a basis for developing a three-dimensional non-equilibrium finite temperature extension of the quasicontinuum method. This extension is accomplished by coupling the local temperature-dependent free energy furnished by the max-ent approximation scheme to the heat equation in a joint thermo-mechanical variational setting. Results for finite-temperature nanoindentation tests demonstrate the ability of the method to capture non-equilibrium transport properties and differentiate between slow and fast indentation.

We propose an approach to perform orbital-free density functional theory calculations in a non-periodic setting using the finite-element method. We consider this a step towards constructing a seamless multi-scale approach for studying defects like vacancies, dislocations and cracks that require quantum mechanical resolution at the core and are sensitive to long range continuum stresses. In this paper, we describe a local real space variational formulation for orbital-free density functional theory, including the electrostatic terms and prove existence results. We prove the convergence of the finite-element approximation including numerical quadratures for our variational formulation. Finally, we demonstrate our method using examples.

We address the question of whether results obtained for small indenters scale to indenter sizes in the experimental range. The quasicontinuum method is used in order to extend the computational cell size to 2 2 1 m 3 , nominally containing of order 2:5 10 11 atoms, and in order to permit consideration of indenter radii in the range 70 ÿ 700 A. The dislocation structures for the large indenter are found to be less sharp and to extend over a larger region than for the small indenter. In addition, the large-indenter force-displacement curve differs from that corresponding to the small indenter in one important respect, namely, the absence of force drops during indentation, despite profuse dislocation activity. Based on these observations, we conclude that the indenter force is not a reliable indicator of the onset of dislocation activity and plastic deformation for indenter sizes in the experimental range. DOI: 10.1103/PhysRevLett.90.226102 PACS numbers: 02.70.-c, 31.15.-p, 46.15.-x The objective of this work is to ascertain the effect of indenter radius on the mechanics of nanoindentation of ductile fcc crystals at zero temperature (see, e.g., [1][2][3][4][5][6][7][8][9] for experimental background). For definiteness, we specifically focus on the indentation of Au (001) by spherical indenters of tip radii 70 and 700 A. One reason why the tip radius size is of concern is that straight molecular dynamics calculations have often relied on artificially small indenters in order to reduce the size of the computational cell [10 -20], and the scaling of the results to larger indenters is not straightforward. In particular, it is not immediately clear how dislocation activity depends onand how effective properties such as the force vs depthof-indentation relation scales with -indenter size.The technique we use in order to sidestep the size restrictions of straight molecular dynamics is the quasicontinuum method of Tadmor and co-workers [21][22][23]. Thus, by coarsening the level of spatial resolution of the computational mesh away from the indenter we are able to span realistic material samples of the order of 2 2 1 m 3 , which nominally contain 2:5 10 11 atoms. This helps to capture the elastic field of the indenter without introducing spurious or parasitic effects associated with periodicity or small sample sizes. By adapting the mesh size to the deformation field, the calculations provide full atomistic resolution over an appropriate region under the indenter. In this manner, the calculation is reduced to a coarse-grained system of size several orders of magnitude smaller than the original one, without appreciable loss of accuracy. In addition, this model reduction enables us to consider a wide range of indenters (70 to 700 A in the work presented here).The particular implementation of the quasicontinuum method used in the calculations has been described in [23]. In particular, following [21-23] we adopt as adaption indicatorwhere K denotes a simplex in the triangulation, II E K denotes the second invariant of the L...