Understanding the mechanism of crystal growth through oriented attachment of nanoparticles, such as in the self-assembly of metal oxide minerals in aqueous solution, poses many challenges, but also opens vast opportunities for materials design. We present a theoretical approach for modeling solvent controlled interactions between nanoparticles that reaches into the mesoscale, while retaining molecular details of the interacting particle surfaces and intervening solvent. The total Hamiltonian of the system includes contributions from long-range particle-particle dispersion interactions across solvent, that accounts for the influence of solvent structuring on the high frequency dielectric response and ion screening of the static response, and contributions from ion-mediated interactions. The latter include direct Coulomb interactions between ions and mineral surfaces with discrete facet-dependent distribution of charges, image interactions, interactions arising from density (excluded volume) and charge density (ion correlation) fluctuations, ion-mineral and ion-water dispersion interactions. The, ion-mineral dispersion contribution depends on dynamic excess polarizabilities of ions in water and on the dynamic dielectric function of the mineral surfaces providing the link between macroscopic and microscopic dispersion terms.
The model was validated against its ability to reproduce ion activity in 1:1, 2:1 and 3:1 electrolyte solutions in the 0-2M concentration range, and its ability to capture the qualitative ion-specific effect in 1:1 electrolytes at the air-water interface. We apply the approach to understand the influence of pH on facet-dependent interactions between anatase TiO₂ nanoparticles.

Progress in high-resolution electron and probe based, real space imaging techniques like (Scanning) Transmission Electron Microscopy (STEM) and Scanning Probe Microscopy (SPM) has consistently delivered imaging of atomic columns and surface atomic structures with ever growing precision. As the instruments evolve, the basic data processing principle - analysis of structure factor, or essentially a two point correlation function averaged over probing volume - remains invariant since the days of Bragg. We propose a multivariate statistics based approach to analyze the coordination spheres of individual atoms to reveal preferential structures and symmetries. The underlying mechanism is that for each atom, i, on the lattice site with indices (l, m), we construct a near coordination sphere vector , where is the radius-vector to j/2-th nearest neighbor. Once the set of N_i vectors is assembled, it is analyzed though cluster analysis and other multivariate methods to reveal and extract regions of symmetry, distortions, different phases, boundaries, defects, etc., that can be back projected on the atomically mapped surface. Results are presented on various model and real material systems including La_0.7Sr_0.3MnO₃, BiFeO₃, LaCoO₃ and discussed in light of physical parameter extraction.
Acknowledgement:
Research for (AB, QH, AB, SJ, SVK) was supported by the US Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division. Research was conducted at the Institute for Functional Imaging of Materials and Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy.

We describe the formulation, development, implementation and applications of Objective Density Functional Theory - a novel first principles simulation methodology for Objective Structures.
Objective Structures are atomic/molecular configurations which generalize the notion of crystals and are such that all the constituent atoms/molecules of the structure “see” the same environment up to orthogonal transformations and translations. Some of the most widely studied atomic/molecular structures in materials science and nanotechnology fall into the category of objective structures. The list of objective structures includes nanotubes, buckyballs, tail sheaths and capsids of viruses, graphene sheets and molecular bilayers. The presence of high degrees of symmetry in objective structures makes them likely to be associated with remarkable material properties - particularly, collective material properties such as ferromagnetism and ferroelectricity.
A systematic study of objective structures is likely to lead to the discovery of novel materials. At the same time, formulation and implementation of theoretical and computational methods specifically designed for studying objective structures, is likely to lead to the development of novel nanomechanics and materials simulation methodologies.
Following this line of thought, we have been developing Objective Density Functional Theory (Objective DFT) - a suite of rigorously formulated quantum mechanical theories and numerical algorithms for carrying out abinitio simulation studies of objective structures. The essential ingredients of Objective DFT include:
1) Usage of Group Representation Theory techniques for formulation of symmetry adapted cell problems for the equations of Kohn-Sham Density Functional Theory as applied to objective structures.
2) Spectral discretization schemes of these cell problems.
3) Efficient solution of the discretized problems using various state-of-the art numerical schemes.
These ingredients make Objective DFT a natural extension of the traditional plane-wave density functional theory method (for studying crystals), just as objective structures form a natural generalization of periodic structures.
We have incorporated these key ideas into a powerful, efficient and reliable computational package called ClusterES (Cluster Electronic Structure) that we have developed from scratch, in order to be able to study objective structures generated by finite groups (such as isolated clusters and molecules). We briefly describe some of the key features and capabilities of this novel computational tool. We end with a discussion of the large variety of applications of Objective DFT, including (but not limited to) the use of the ClusterES package to study the vibrational and optical properties of nanoclusters, the mechanics of nanobeams as well as the investigation of material properties such as flexo-electricity.

Why is NiTi the best shape memory alloy? In recent years desirable features of phase transformations such as low hysteresis and reversibility have been linked to compatibility conditions between phases. We review these conditions and propose a route to highly reversible shape memory alloys. NiTi does not satisfy any of these conditions of compatibility, not even close. Ren and Otsuka (Scripta Mat. 38 (1998), 1669) theorized that the unique properties of NiTi are due to the simultaneous softening of two moduli of the B2 austenite phase, which they took as suggestive of a coupling of two modes of deformation, and this mechanism has been examined in more detail recently by first principles calculations. Based on results of an mathematical algorithm that systematically finds transformation mechanisms, we suggest that the widely accepted mechanism of transformation in NiTi is incorrect. A revised mechanism provides a new view of the origins of reversible shape memory in NiTi, and unexpectedly links the ideas of Ren and Otsuka with the conditions of compatibility.

I will present a family of continuum models for active liquid crystals and study their inherent instability due to activities and their ramifications to flows of the active liquid crystal system. Various patterns and spatial-temporal structures will be identified and classified in relation to the instability of the model system. Applications of the continuum model to model cell motility and bacterial colonies will be discussed in the end.

Spatial multiscale methods have been useful for extending the length scales accessible by conventional molecular dynamics at zero temperature. Recently, extensions of these spatial multiscale methods such as the finite-temperature quasicontinuum (hot-QC) methods have been used to allow for molecular dynamics simulations at finite temperature. In an effort to increase our understanding of such methods and their applications to dynamics, we examine how coarse-graining an atomistic system held at constant temperature affects transition rates. Specifically, we analyze the transition state theory (TST) rate approximation made by coarse-grained molecular dynamics (CGMD) and compare it to the TST rate of the fully atomistic system. The validity of such an approach to computing the TST rate is verified through a relative error analysis, and the resulting analysis is then used to determine the major contributions to the error. Finally, we perform numerical simulations using the method for the case of a 1-D chain before relating these results and the error analysis back to the hot-QC methods. Joint with A. Binder, W.-K. Kim, D. Perez. E. Tadmor. and A. Voter.

Nonlocal continuum models are used in many scientific and engineering applications where the material response and dynamics depend on the micro-structure. Such models differ from the classical, local, models in the fact that interactions can occur at distance, without contact; for this reason they are used for accurately resolve small scale features such as crack tips or dislocations that can affect the global material behavior. However, nonlocal models are often computationally too expensive, sometimes even intractable. Therefore, methods for the coupling of nonlocal and local models have been proposed for efficient and accurate solutions; these methods employ nonlocal models in small parts of the domain and use local, macroscopic, models elsewhere. We propose an optimization-based coupling method for nonlocal diffusion problems; we split the domain in a nonlocal and local domain such that they feature a non-zero intersection and we minimize the difference between the nonlocal and local solutions in the overlapping regions tuning their values on the common boundaries and volumes. We formulate the problem as a control problem where the states are the solutions of the nonlocal and local equations, the controls are the nonlocal volume constraint and the local boundary condition, and the objective of the optimization is a matching functional for the state variables in the intersection of the domains. The problem is treated in a variational sense and its analysis is conducted using the nonlocal vector calculus, a recently developed tool that allows one to solve a nonlocal problem similarly as the local counterpart. Specifically, we show that the coupling problem is well-posed, we study the modeling error and, for finite element discretizations, we analyze the approximation error. Furthermore, we present numerical results in a one-dimensional setting; though preliminary, our tests show the consistency of the method, illustrate the theoretical results and provide the basis for realistic simulations.

By using theoretical and computational approaches, we study Brownian motion of a massive and large particle, which is subject to a harmonic potential and suspended in an ideal gas confined by two parallel walls. This system corresponds to an optical trap experiment of a macromolecule in a slit pore filled with a gas. Based on that diffusion-related physical quantities such as the mean squared displacement and velocity autocorrelation function of the Brownian particle can be calculated from its memory function, we analyze diffusion phenomena of the system by investigating the memory function. More specifically, compared with the unbounded case, an enhanced long-time tail appears in the memory function, from which we study the effects of confinement and the dependence on the shape of the Brownian particle and the stochastic character of the thermal walls.
As an analytic model, we consider a d-dimensional (dge;2) hypercube and elastic walls. Under the infinite-mass limit, we obtain analytic expressions for the force autocorrelation function and the memory function. The transverse-direction memory function possesses a nonnegative tail decaying like t^-(d-1) at large time t, from which anomalous diffusion is expected for d=2. For d=3, the position-dependent friction coefficient becomes larger than the unconfined case and the increment is inversely proportional to the square of the distance from the wall. We also perform molecular dynamics simulations with thermal walls and/or a finite-mass hypercube. We observe faster decay due to the thermal wall (t^-3 for d=2 and t^-5 for d=3 under the fully thermalizing wall) and convergence behaviors of the finite-mass memory function, which are different from the unconfined case.
For a disk (d=2) and a sphere (d=3), we observe from molecular dynamics simulations that the longitudinal direction memory function also contains a power-law decaying tail. Its dependence on the stochastic character of the walls and implications on the normal/anomalous diffusion along the longitudinal direction of the channel are discussed.

The classic Smoothed Particle Hydrodynamics (SPH) is a particle-based method commonly used to solve fluid dynamics equations. SPH is amenable to parallelization and it has been applied successfully to fluids with low viscosity. However, it can perform poorly when applied to low Reynolds number flows in complex geometry. In this talk we present an accurate implicit implementation of SPH that can be used with unsteady low Reynolds number flows and that features good parallel scalability. The fluid dynamics equations are discretized in a Lagrangian fashion using an incremental pressure projection scheme and second-order accurate differential operators. The implementation uses the molecular dynamics library LAMMPS exploiting the common computational structure of particle methods. In our formulation of implicit SPH the solutions to Poisson and Helmholtz linear systems, required at each timestep, are performed using linear solvers provided in the Trilinos library. Using the same framework we solve the nonlinear Poisson-Bolztman (PB) equations which, in fact, reduce to a Poisson system after the application of the Newton method. We demonstrate the efficiency, accuracy and scalability of the implementation on large-scale three-dimensional simulations. Finally we show results for realistic electrokinetic applications in the micro-/nano-scale.

We derive an asymptotic method for solving the steady Boltzmann equation describing phonon transport in the small Knudsen number limit. We show that accurate solutions can be obtained by expanding the unknown phonon distribution function by treating the Knudsen number (Kn) as a small parameter. This procedure can be used to show that, in the bulk, the temperature field obeys the Laplace (steady heat conduction) equation to all orders in Kn. As expected, deviations from the classical heat equation as Kn increases (from very small values) first appear at the boundaries. Specifically, the inhomogeneity introduced by the boundaries requires the presence of a kinetic boundary layer of thickness on the order of a few mean free paths. Matching this boundary layer to the bulk solution yields boundary conditions for the heat conduction equation.
For the case of a boundary at a prescribed temperature, this analysis shows that the traditional no-jump boundary conditions provide solutions consistent with the Boltzmann equation only to zeroth order in Kn. Considering first and second order terms in Kn can be used to show that the appropriate boundary conditions for the heat conduction equation are of the jump (slip) type, with jump coefficients that depend on the material model and the phonon-boundary interaction model. In this work we consider various types of boundaries, such as adiabatic diffusive and adiabatic specular walls, as well as interfaces characterized by frequency-dependent transmission coefficients.
In addition to providing a prescription for obtaining solutions consistent with the Boltzmann equation at significantly less complexity or numerical cost, these results also provide physical insight on the role of size effects and the mechanism by which classical heat conduction theory breaks down. They also provide rigorous justification and quantitative characterization of temperature jumps at material boundaries/interfaces observed in previous studies of size effects.

Electron-phonon coupling is one of the main incoherent inelastic scattering mechanisms in a wide variety of crystalline material systems at room temperature. Therefore, it is necessary to incorporate those effects in any realistic calculation of transport or thermoelectric properties. We do so by extending our density functional theory (DFT) based Korringa-Kohn-Rostocker (KKR) Green's function formalism code.
Instead of including the electron-phonon coupling in the Kohn-Sham Hamiltonian via an adjusted effective potential V_eff, we calculate the Green's function of the 'free' system (i.e., free of electron-phonon coupling, but containing the electron-electron interaction in local density approximation (LDA)) and employ Dyson's equation G = G_free + G_free × Σ_e-ph × G to obtain the dressed Green's function.
The self-energy Σ_e-ph is calculated using Keldysh NEGF formalism, which - in conjunction with Wick's theorem - lends itself to a perturbative diagrammatic approach. Within this method it can be shown, that any term represented by a disconnected Feynman diagram must vanish. This feature makes an exact re-summation of all diagrams in terms of the reference Green's function G_free possible and leads to the customary electron-phonon self-energy formulas. Especially, both the so-called First Born Approximation (FBA) and Self-Consistent First Born Approximation (SCFBA) can be recovered.

In type II superconductors, there are two critical magnetic field values and when the applied magnetic field strength is in between of these two values, vortices with quantum magnetic fluxes appear in these superconductors. The Bogoliubov-de Gennes formalism [1] provides a microscopic description of the vortex formation, vortex symmetry and interaction between vortices. On the other hand, the generalized Hubbard model, which includes first- and second-neighbor correlated hopping interactions besides the onsite and nearest-neighbor Coulomb interactions, has been used to investigate the d-wave superconductivity in high-Tc ceramic superconductors [2]. In this work, we report an extension of the Bogoliubov-de Gennes formalism for the mentioned generalized Hubbard model, which leads to 2N coupled self-consistent equations for a supercell of N atoms. These equations allow to determine the spatial variation of the superconducting gap as a function of the electron concentration and electron-electron interactions. The supercell averaged superconducting gap shows a qualitatively different dependence on the external magnetic field, being larger the second critical magnetic field of d-wave superconductors than those corresponding to isotropic and anisotropic s-wave ones. Finally, the electronic specific heat as a function of the temperature for a given applied magnetic field is calculated and compared with experimental data.
This work has been partially supported by CONACyT 131596, UNAM IN106714 and IN113714. Computations were performed at Miztli of DGTIC-UNAM.
[1] P.G. de Gennes, Superconductivity of metals and alloys (Addison-Wesley Pub. Co., New York, 1989).
[2] C.G. Galvan, L.A. Perez, and C. Wang, Phys. Lett. A 376, 1380 (2012).

Various promising applications such as acoustic cloaking, sub-wavelength imaging, acoustic wave manipulation, transmission or reflection control etc. are feasible because of the ability of manipulating sounds and vibrations using artificially engineered “Acoustics meta-materials”. Recent works on space-coiling acoustic metamaterials show their extreme constitutive parameters like large refractive index, double negativity and zero mass density. Three dimensional structures have a wide application in sub-wavelength broadband acoustic wave suppression due to huge attenuation. Here we report the study of propagated and transmitted wave through self-designed 2D and 3D acoustic metamaterials structure using finite element method. Our simulations on 2D structure show large refractive index, double negativity and zero mass density for a broad frequency range and 3-D structure show a huge absorption/damping over few hundreds kilohertz frequency range. Simulation studies of refractive index, impedance, bulk modulus and mass density using S-parameter for both 2D and 3D structures along with experimental results will be presented.

Quantum dots have discrete energy levels that can be engineered by tuning their composition, density, organization, size and morphology. These features make quantum dots attractive for the design and fabrication of novel electronic, magnetic and photonic devices. Stranski-Krastanow (SK) growth technique leads to the formation of dislocation-free nano-islands, which are interconnected with a thin flat wetting layer, and hence has attracted great attention. In the formation of such nano-systems, the diffusion anisotropy, crystallographic orientation and the surface roughness may have a significant influence. Here, we based our study on continuum level dynamical simulations for the spontaneous evolution of quantum dots on stochastically rough thin films having random (white noise) surface undulations with well-defined strengths. During the development of SK islands through the mass accumulation at randomly selected regions of the film via surface drift-diffusion (induced by the capillary and mismatch stresses), we observed the formation of an extremely thin wetting layer. Above a certain threshold level of the mismatch strain and/or the size of the patch, the formation of multiple islands separated by shallow wetting layers is also observed as metastable states such as doublets even multiplets. These islands are converted into a distinct SK islands after long annealing times by coalescence through the long range surface diffusion. Based on the simulation results, we generated stability (including the equilibrium shape) phase diagrams as a function of the misfit stress and the equilibrium dihedral angle between the film and the substrate or the amplitude of the surface undulations. Supported by TUBITAK grants no 111T343 and 213M481, and TUBA GEBIP award to Oren EE.

In contrast to multiscale methods, which often encompass multiple simulation techniques, multiresolution models use the same general modeling technique with representations of a system at varying length and time scales. We present work on a complete framework for modeling of semidilute polymer solutions, containing both coarse-graining and reconstruction steps. The coarse-graining approach is based on the wavelet-accelerated Monte Carlo (WAMC) method [1], which forms a hierarchy of resolutions to model polymers at length scales that cannot be reached via atomistic or even "standard" coarse-grained simulations. Using multiple stages of resolution, it is possible to simulate polymers of up to millions of repeat units in length. Although previously applied only to individual chain statistics [2], we show here how it can be extended to the study of polymer solutions. Bonded and non-bonded potentials between coarse-grained superatoms are computed. The non-bonded potential is computed using the same approach used previously in the study of single chains while the bonded potentials are computed using reverse Monte Carlo. A universal scaling function is obtained so that potentials do not need to be recomputed as the scale of the system is changed. To model polymer solutions, the intermolecular potential between the CG beads is assumed to be equal to the non-bonded potential, which is a reasonable approximation in case of semidilute systems. Using these potentials, various radial distribution functions are calculated from the coarse-grained representation at different resolutions, which compare favorably with the results from the atomistic simulations. We show that coarse-grained polymer solutions can reproduce results obtained from the simulations of the more detailed atomistic system to a reasonable degree of accuracy.
The reconstruction proceeds in much the same way: using probability distributions obtained from the coarse-graining procedure with respect to bond lengths, angles, and torsions, as well as the non-bonded potentials, we can reconstruct a more detailed version of the polymer that is consistent both with geometric constraints as well as energetic considerations. Using a quality estimator model for the reconstruction process, we can successfully “reverse map” entire atomistic configurations from coarse-grained descriptions. Applications for the reconstruction of atomistic models from united-atom models and detailed models from coarse-grained models will be shown, using semi-dilute polymer solutions and self-assembled monolayers as test cases.
References
[1] A. E. Ismail, G. C. Rutledge, and G. Stephanopoulos, The Journal of Chemical Physics 118, 4414 (2003)
[2] A. E. Ismail, G. C. Rutledge, and G. Stephanopoulos, The Journal of Chemical Physics 118, 4424 (2003)

Bismuth is known for the measurements of quantum oscillations in magnetic field due to its semi-metallic band structure with electron and hole pockets of small effect masses, low charge carrier density and small energy overlap. Progress in fabricating single crystal Bismuth nanowires and the experiments on magneto-resistance provide access to the characters of surface states and bulk states with the confinement effect of nanowires. In this work, we study the theory of confinement in semi-metallic Bismuth nanowire and its effect on the change in the band structure and magnetoresistance. The band structure is investigated by density functional calculation, empirical tight-binding models and effective low-energy band models around the Fermi level. The understanding provides the method to engineer the bulk and surface states in nanowires.

Phenomena such as solute strengthening in lightweight alloys and alloyed high strength steels, and embrittlement of bimaterial interfaces and grain boundaries are controlled by quantum mechanical interactions of solutes or impurities with defects (dislocations, grain boundaries, interfaces, or cracks). The local stresses driving these atomic-scale process are determined by behavior occurring at much larger spatial and temporal scales. To maintain high resolution at large special scales, we will use a “Coupled Atomistic/Discrete-Dislocation” (CADD) to represent grain boundaries, crack tips and other defects while handling dislocation plasticity at both atomistic (MD) and continuum scales (FEM) simultaneously. The temporal scale of simulations at the atomic level, are typically about 8-10 orders of magnitude smaller than the temporal scale at other spatial levels. As a result, until now MD simulations can generally only probe behavior at high stresses and sliding rates that are not practically relevant.
We present a new model that provides a general purpose approach to couple the disparate temporal scales in existing concurrent multi-scale simulations. Kinetic Monte Carlo is used as the temporal scale buffer between the continuum and atomistic regions of the model. Since KMC is capable capturing atomistic rare events at the appropriate time scale, our innovative approach provides a means to synchronize MD and FEM based on events occurring in KMC. A domain with an initial Guassian distribution of vacancies is considered. Model details are presented for the temporal evolution of vacancy concentration in domain represented by (a) FEM/KMC, (b) KMC/MD and (c) FEM/KMC/MD. The FEM/KMC coupling involves iteratively solving for the correct vacancy concentration at the interface between the regions. The KMC/MD coupling requires careful synchronization of temporal scales during an event at this interface. Finally results of the coupled approach are presented for vacancy assisted climb of an atomistically represented dislocation for a range of temperatures from 300K to 900K.

The unique geometry, structure, and physical properties of the p