Continuum Calculations Research Articles

Shape memory behavior in Fe3Al-modeling and experiments

The Fe3Al alloy with D03 structure exhibits large recoverable strains due to reversible slips. Tension and compression experiments were conducted on single crystals of Fe3Al, and the onset of slip in forward and reverse directions were obtained utilizing high-resolution digital image correlation technique. The back stress provides the driving force for reversal of deformation upon unloading, resulting in a superelastic phenomenon as in shape memory alloys. Using density functional theory simulations, we obtain the energy barriers (GSFE – generalized stacking fault energy) for {1 1 0}〈1 1 1〉 and {1 1 2}〈1 1 1〉 slips in D03 Fe3Al and the elastic moduli tensor, and undertake anisotropic continuum calculations to obtain the back stress and the frictional stress responsible for reversible slip. We compare the theoretically obtained slip stress magnitudes (friction and back stress) with the experimental measurements disclosing excellent agreement.

Strain shielding from mechanically activated covalent bond formation during nanoindentation of graphene delays the onset of failure.

Mechanical failure of an ideal crystal is dictated either by an elastic instability or a soft-mode instability. Previous interpretations of nanoindentation experiments on suspended graphene sheets,1,2 however, indicate an anomaly: the inferred strain in the graphene sheet directly beneath the diamond indenter at the measured failure load is anomalously large compared to the fracture strains predicted by both soft-mode and acoustic analyses. Through multiscale modeling combining the results of continuum, atomistic, and quantum calculations, and analysis of experiments, we identify a strain-shielding effect initiated by mechanochemical interactions at the graphene-indenter interface as the operative mechanism responsible for this anomaly. Transmission electron micrographs and a molecular model of the diamond indenter's tip suggest that the tip surface contains facets comprising crystallographic {111} and {100} planes. Ab initio and molecular dynamics (MD) simulations confirm that a covalent bond (weld) formation between graphene and the crystallographic {111} and {100} facets on the indenter's surface can be induced by compressive contact stresses of the order achieved in nanoindentation tests. Finite element analysis (FEA) and MD simulations of nanoindentation reveal that the shear stiction provided by the induced covalent bonding restricts relative slip of the graphene sheet at its contact with the indenter, thus initiating a local strain-shielding effect. As a result, subsequent to stress-induced bonding at the graphene-indenter interface, the spatial variation of continuing incremental strain is substantially redistributed, locally shielding the region directly beneath the indenter by limiting the buildup of strain while imparting deformation to the surrounding regions. The extent of strain shielding is governed by the strength of the shear stiction, which depends upon the level of hydrogen saturation at the indenter's surface. We show that at intermediate levels of hydrogen saturation the strain-shielding effect can enable the graphene to support experimentally determined fracture loads and displacements without prematurely reaching locally limiting states of stress and deformation.

Hybrid Gaussian–discrete-variable representation for one- and two-active-electron continuum calculations in molecules

A combined basis of analytic Gaussian functions and grid-based finite element-discrete variable representation spherical harmonic expansion is specialized for the description of continuum electron dynamics in the presence of electrons held fixed in core molecular orbitals. The applicability of this hybrid representation designed for general problems involving accurate determination of molecular continua wave functions is illustrated for photoionization of second-row diatomic molecules. Accurate descriptions of such electron continuum dynamics are a necessary step towards analyzing correlated double continua photoejections. Examination of this hybrid method in comparison to a more computationally expensive pure grid-based single-center expansion reveals several key advantages that by design make it attractive for describing processes involving one or more electrons moved to the continuum.

A predictive model of shell morphology in CdSe/CdS core/shell quantum dots.

Lattice mismatch in core/shell nanoparticles occurs when the core and shell materials have different lattice parameters. When there is a significant lattice mismatch, a coherent core-shell interface results in substantial lattice strain energy, which can affect the shell morphology. The shell can be of uniform thickness or can be rough, having thin and thick regions. A smooth shell minimizes the surface energy at the expense of increased lattice strain energy and a rough shell does the opposite. A quantitative treatment of the lattice strain energy in determining the shell morphology of CdSe/CdS core/shell nanoparticles is presented here. We use the inhomogeneity in hole tunneling rates through the shell to adsorbed hole acceptors to quantify the extent of shell thickness inhomogeneity. The results can be understood in terms of a model based on elastic continuum calculations, which indicate that the lattice strain energy depends on both core size and shell thickness. The model assumes thermodynamic equilibrium, i.e., that the shell morphology corresponds to a minimum total (lattice strain plus surface) energy. Comparison with the experimental results indicates that CdSe/CdS nanoparticles undergo an abrupt transition from smooth to rough shells when the total lattice strain energy exceeds about 27 eV or the strain energy density exceeds 0.59 eV/nm(2). We also find that the predictions of this model are not followed for CdSe/CdS nanoparticles when the shell is deposited at very low temperature and therefore equilibrium is not established.

Joint first-principles/continuum calculations of electromechanical properties of MoS2 monolayer

Joint first-principles and continuum calculations were conducted on a system of a MoS2 monolayer inside water electrolyte, showing that the monolayer thickness and inplane dimension decreases and increases, respectively, and almost linearly with negative or positive excess charges. The calculated charge volume expansion coefficient of 0.081 |e| −1 under negative charging is about 27 times as high as that of 0.003 |e| −1 under positive charging. The changes in Fermi level and band structure induced by excess charges are also investigated by the joint calculations.

Modeling thermophoretic effects in solid-state nanopores.

Local modulation of temperature has emerged as a new mechanism for regulation of molecular transport through nanopores. Predicting the effect of such modulations on nanopore transport requires simulation protocols capable of reproducing non-uniform temperature gradients observed in experiment. Conventional molecular dynamics (MD) method typically employs a single thermostat for maintaining a uniform distribution of temperature in the entire simulation domain, and, therefore, can not model local temperature variations. In this article, we describe a set of simulation protocols that enable modeling of nanopore systems featuring non-uniform distributions of temperature. First, we describe a method to impose a temperature gradient in all-atom MD simulations based on a boundary-driven non-equilibrium MD protocol. Then, we use this method to study the effect of temperature gradient on the distribution of ions in bulk solution (the thermophoretic effect). We show that DNA nucleotides exhibit differential response to the same temperature gradient. Next, we describe a method to directly compute the effective force of a thermal gradient on a prototypical biomolecule-a fragment of double-stranded DNA. Following that, we demonstrate an all-atom MD protocol for modeling thermophoretic effects in solid-state nanopores. We show that local heating of a nanopore volume can be used to regulate the nanopore ionic current. Finally, we show how continuum calculations can be coupled to a coarse-grained model of DNA to study the effect of local temperature modulation on electrophoretic motion of DNA through plasmonic nanopores. The computational methods described in this article are expected to find applications in rational design of temperature-responsive nanopore systems.

Rates of exponential decay in systems of discrete energy levels by Stieltjes imaging.

An isolated bound state coupled to a continuum shows an exponential decay of its survival probability. Rates of the exponential decay occurring due to the bound-continuum coupling can be recovered from discretized continuum (L(2)) calculations using a computational technique known as Stieltjes-Chebyshev moment theory or Stieltjes imaging. At the same time, some genuinely discrete level systems, e.g., Bixon-Jortner model, also show an exponential (or approximately exponential) decay of the initially populated level before the onset of quantum revivals. Here, we demonstrate numerically that Stieltjes imaging can be used for calculation of the rates of the exponential decay in such discrete level systems. We apply the Stieltjes imaging technique to the approximately exponential decay of inner-valence vacancies in trans-butadiene in order to show that the breakdown of the molecular orbital picture of ionization in the inner valence region can be physically interpreted as an energy-forbidden Coster-Kronig transition.

Coupling between Neurotransmitter Translocation and Protonation State of a Titratable Residue during Na+-Coupled Transport

Coupling between Neurotransmitter Translocation and Protonation State of a Titratable Residue during Na+-Coupled Transport

ECS Student Achievement Award of the IEEE Division Integration of a 2+1D Kinetic Monte Carlo Algorithm with Continuum Models for SEI Layer Analysis of Lithium-Ion Batteries

Rechargeable lithium-ion batteries have been extensively used in mobile communication and portable instruments due to their high volumetric and gravimetric energy density and low self-discharge rate, leading many scientists and engineers to work towards developing lithium-ion batteries with improved performance and longer life.In normal operation, an active solid-electrolyte-interface (SEI) layer forms in the first cycle of charging, due to reactions of lithium and solvent at the active surface (1,2). The SEI layer provides a barrier between the electrolyte and electrode to prevent further reaction while allowing lithium ions to permeate through the SEI layer in order to intercalate into and out of the bulk solid to store and release energy. However, the SEI layer continues to grow under repeated cycling. This growth increases the diffusion resistance of the lithium ions to the bulk active material, and removes cyclable lithium from the system, reducing the efficiency of the battery (1,2). This increased resistance can produce high temperature and can result in thermal runaway (3-5) within the battery. The properties and chemical composition of the SEI layer (active and passive) has been a subject of intense research due to its importance in the safety, capacity fade, and cycle life of Li-ion secondary batteries (6-12). Examination of the growth of the SEI layer as a mechanism for capacity fade has been performed using Kinetic Monte Carlo (KMC) simulations (13). This has provided valuable insight into the growth of the SEI layer and has shown the effects of high rates of charging on SEI layer passivation. These KMC simulations can be used to study the surface heterogeneity of the electrode surface as the passive layer is formed.The KMC model used will be expanded to a 2+1D model which tracks the thickness of the SEI layer over a representative surface of the solid particle. This will give a sense of the heterogeneity that arises in the SEI layer and will be coupled with the pseudo 2D model to simulate full battery operation. The P2D model will be converted from a system of partial differential equations to a system of ordinary differential equations by using reformulation techniques developed for the continuum model (14). The KMC model studies the events that occur in the SEI layer and the particle surface. For example, diffusion of the solvent in the SEI layer is modeled using the KMC approach. The reactions at the active material surface are modeled by considering the relative rate constants and using a random number generator to determine the event which occurs. In contrast, the continuum P2D model explains what happens in the bulk phases, and is deterministic. This coupled model will perform continuum calculations simultaneously with the KMC calculations. As passivation is considered in the KMC model, the capacity of the battery will fade with time, allowing for life time studies to be performed. This will lead to better understanding of the conditions which lead to capacity fade and better operation of lithium-ion batteries. Acknowledgements The authors acknowledge financial support by the National Science Foundation under grant numbers CBET-0828002, CBET-0828123, and CBET-1008692, and the Advanced Research Projects Agency – Energy (ARPA-E), U.S. Department of Energy, under Award Number DE-AR0000275.

Anomalous transport with overlap fermions

Anomalous correlators of vector and axial currents which enter the Kubo formulae for the chiral magnetic and the chiral separation conductivities are explicitly calculated for free overlap fermions on the lattice. The results are confronted with continuum calculations in the finite-temperature regularization, and a subtle point of such regularization for chiral magnetic conductivity related to the correct counting of the chiral states is highlighted. In agreement with some previous claims in the literature, we find that in a lattice regularization which respects gauge invariance, the chiral magnetic conductivity vanishes. We point out that the relation of anomalous transport coefficients to axial anomaly is nontrivial due to the non-commutativity of their infrared limit and the Taylor expansion in baryon or chiral chemical potential. In particular, we argue that the vector and axial Ward identities fix the asymptotic behavior of anomalous current-current correlators in the limit of large momenta. Basing on the work of Knecht et al. on the perturbative non-renormalization of the transverse part of the correlator of two vector and one axial currents, we demonstrate that the relation of the anomalous vector-vector correlator to axial anomaly holds perturbatively in massless QCD but might be subject to non-perturbative corrections. Finally, we identify kinematical regimes in which the anomalous transport coefficients can be extracted from lattice measurements.

Mechanisms of hydrogen-enhanced localized plasticity: An atomistic study using α-Fe as a model system

Atomistic simulations of the effects of H on edge dislocation mobility and pile-ups are performed to investigate possible nanoscale mechanisms for hydrogen-enhanced localized plasticity (HELP). α-Fe is used as a model system because H diffusion is fast enough to capture kinetics within the time scales of molecular dynamics and because edge dislocation glide in α-Fe is similar to glide in face-centered cubic metals. Results over a wide range of H concentrations sufficient to generate a range of sizes in the Cottrell atmospheres show that the Cottrell atmospheres follow the moving dislocations, leading to a resistance to dislocation motion that is consistent with solute drag theory; thus, H reduces the dislocation mobility. Furthermore, once motion stops and a pile-up is established, the H Cottrell atmospheres do not affect the equilibrium spacing of dislocations in the pile-up; thus, the H atmosphere provides no “shielding” of dislocation–dislocation interactions. This result is consistent with conclusions from previous continuum calculations. Two oft-proposed mechanisms for HELP (H-induced increase in true dislocation mobility and decrease in dislocation–dislocation pile-up interactions) are therefore not supported by the present simulations. A mechanistic understanding of HELP phenomena observed in various experiments thus requires evaluation of more complex H–dislocation interactions.

Molecular Dynamics Simulation of the Motion of Colloidal Nanoparticles in a Solute Concentration Gradient and a Comparison to the Continuum Limit

Chemical-mechanical transduction mechanisms which can actuate the movement of colloids through liquids are highly sought after as engines to propel miniaturized micro- and nanobots. One mechanism involves harnessing the long-range van der Waals attractive forces between the colloid and solute molecules dissolved in the liquid around the particle. If a concentration gradient of this solute is applied across the particle, then the imbalance in the van der Waals attraction drives the particle towards the higher concentration of solute. We present a molecular dynamics simulation using Lennard-Jones interactions between molecules of the solvent, solute, and colloid cluster which include short-range repulsive and long-range attractive potentials. The simulations demonstrate that a solute gradient can propel nanosized colloids, and that the velocity decreases with the colloid size. The solute-colloid short-range repulsive interactions are observed to be restricted to a region of specifically adsorbed solutes on the particle surface which are symmetrically adsorbed and do not contribute to the motion. The size of this region provides a cutoff for a continuum level description of the motion, and with this cutoff, continuum calculations are in excellent agreement with the molecular dynamics simulation results, completing a description of the propulsion from the nano- to the microscale.

Analytical transformed harmonic oscillator basis for three-body nuclei of astrophysical interest: Application to6He

Recently, a square-integrable discrete basis, obtained performing a simple analytical local scale transformation to the harmonic oscillator basis, has been proposed and successfully applied to study the properties of two-body systems. Here, the method is generalized to study three-body systems. To test the goodness of the formalism and establish its applicability and limitations, the capture reaction rate for the nucleosynthesis of the Borromean nucleus ${}^{6}$He (${}^{4}\text{He}+n+n$) is addressed. Results are compared with previous publications and with calculations based on actual three-body continuum wave functions, which can be generated for this simple case. The obtained results encourage the application to other Borromean nuclei of astrophysical interest such as ${}^{9}$Be and ${}^{12}$C, for which actual three-body continuum calculations are very involved.

The missing term in the decomposition of finite deformation

In finite inelasticity, the gradient of total deformation is typically split into a product of two terms: a reversible (elastic) term whose strain vanishes upon load removal at some scale, and an irreversible (plastic) component that remains. In this work it is argued that this decomposition represents a limiting case for which defects are absent from the volume of interest, with compatible elastic distortion associated with externally applied stress and plastic deformation associated with history of dislocation glide through the element. An additional (third) term should be incorporated in the multiplicative decomposition when applied to an element of material of any realistic volume, accounting for local lattice distortion due to defects within. In the limiting case that this volume approaches a few lattice spacings, the probability of interior defects tends towards zero, but a very small volume element containing a few defects, or a larger element containing a large density of defects, requires a third term in the multiplicative decomposition to represent contributions of defects to residual lattice distortion. Physical experiments and reported atomic and continuum calculations support these theoretical arguments. The magnitude of distortion from the “missing” third term is estimated analytically using elasticity solutions for straight dislocations. Advances to crystal plasticity theory involving a three-term decomposition are suggested.

Removal of Mercury from the Environment: A Quantum-Chemical Study with the Normalized Elimination of the Small Component Method

1,3-Benzenediamidoethanethiolatemercury [BDT-Hg or BD(S)-Hg] and its derivatives are investigated utilizing the Dirac exact relativistic normalized elimination of the small component method in connection with B3LYP, CCSD(T), and polarizable continuum calculations. It is shown that the chelating energy of BDT-Hg can be significantly increased by replacing sulfur with selenium or tellurium, thus leading to BD(Se)-Hg or BD(Te)-Hg. In this particular case, the chalcogenophilicity of mercury increases from S to Te because increasing the E-Hg bond lengths leads to a reduction of ring strain. Various possibilities of increasing the metal (M) chelating strength in BDT-M complexes are investigated, and suggestions for new chelating agents based on the BDT-M template are made.

On the Weak Coupling Limit for Massive Yang–Mills

For small values of the gauge coupling constant, we compare the densities of the energy of the vacuum and of the order parameter, evaluated in the lattice Monte Carlo simulation and in the perturbative field theory at two loop (Minkowski). The continuum calculation allows a very good fit of the simulation results, away from the phase transition line. This confirms the conjecture that the lattice provides a regularization of the (nonrenormalizable) massive Yang-Mills and moreover it shows the physical meaning of the parameters used in the simulation.

Competing alignments of nematic liquid crystals on square-patterned substrates

A theoretical analysis is presented of a nematic liquid crystal confined between substrates patterned with squares that promote vertical and planar alignment. Two approaches are used to elucidate the behavior across a wide range of length scales: Monte Carlo simulation of hard particles and Frank-Oseen continuum theory. Both approaches predict bistable degenerate azimuthal alignment in the bulk along the edges of the squares; the continuum calculation additionally reveals the possibility of an anchoring transition to diagonal alignment if the polar anchoring energy associated with the pattern is sufficiently weak. Unlike the striped systems previously analyzed, the Monte Carlo simulations suggest that there is no "bridging" transition for sufficiently thin cells. The extent to which these geometrically patterned systems resemble topographically patterned substrates, such as square wells, is also discussed.

Modelling of electronic excitation and radiation in the Direct Simulation Monte Carlo Macroscopic Chemistry Method

One of the most useful tools for modelling rarefied hypersonic flows is the Direct Simulation Monte Carlo (DSMC) method. Simulator particle movement and collision calculations are combined with statistical procedures to model thermal non-equilibrium flow-fields described by the Boltzmann equation. The Macroscopic Chemistry Method for DSMC simulations was developed to simplify the inclusion of complex thermal non-equilibrium chemistry. The macroscopic approach uses statistical information which is calculated during the DSMC solution process in the modelling procedures. Here it is shown how inclusion of macroscopic information in models of chemical kinetics, electronic excitation, ionization, and radiation can enhance the capabilities of DSMC to model flow-fields where a range of physical processes occur. The approach is applied to the modelling of a 6.4 km/s nitrogen shock wave and results are compared with those from existing shock-tube experiments and continuum calculations. Reasonable agreement between the methods is obtained. The quality of the comparison is highly dependent on the set of vibrational relaxation and chemical kinetic parameters employed.

Management Criterion for Large Deformation Tunnels

The limit displacement was calculated with regard to a large deflection tunnel. The continuum calculation model was established with actual parameters of the surrounding rock of the tunnel as input. In the simulation calculation, the action occasion of the support structure was determined based on the ratio of the measured rock pressure to the geo-stress, and the bearing capacity of the R.C. compressive bending component of the support was expressed with the axial force and bending moment on losing capacity of the support structure in loading; The limit displacement of the tunnel wais determined finally combined with the measured displacement of control points on collapsed or gauge-intrusive sections and cracked primary support or secondary lining sections. Since the deforming rate is more concerned than the displacement in drill and blast tunnel construction, three-level-management of deflection and deforming rate was proposed based on the statistical analysis of measured deforming rate, and the safety requirement for deflection control in construction. The management criterion has reference value to other similar tunnels where difficulty is encountered due to large deflection occurring in construction.

Benchmark calculations for elastic fermion-dimer scattering

We present continuum and lattice calculations for elastic scattering between a fermion and a bound dimer in the shallow binding limit. For the lattice calculation we use the finite-volume method of L\"uscher. We take into account topological finite-volume corrections to the dimer binding energy which depend on the momentum of the dimer. After subtracting these effects, we find from the lattice calculation $\ensuremath{\kappa}{a}_{fd}=1.174(9)$ and $\ensuremath{\kappa}{r}_{fd}=\ensuremath{-}0.029(13)$. These results agree well with the continuum values $\ensuremath{\kappa}{a}_{fd}=1.17907(1)$ and $\ensuremath{\kappa}{r}_{fd}=\ensuremath{-}0.0383(3)$ obtained from the STM equation. We discuss applications to cold atomic Fermi gases, deuteron-neutron scattering in the spin-quartet channel, and lattice calculations of scattering for nuclei and hadronic molecules at finite volume.