Many multiscale modeling problems may be gainfully addressed as reducing degrees of freedo in nonlinear systems of ordinary differential equations. For instance, a closed molecular dynamic assembly, a spatially discretized system of equations from continuum mechanics representing a strongly inhomogeneous, nonlinear and possibly dissipative material, or a granular assembly operating under Newton's laws and obeying elastic-viscous/plastic inter-particle contact laws serve as important examples of such systems. The primary multiscale analysis question may now be phrased as follows: We do not wish to solve the entire system but instead would like toconsider the evolution of only a selected number of degrees of freedom of the whole system. Given that the system is coupled, is it possible to devise a strategy, perhaps approximate, to achieve such a goal? In particular, we would like to deal with situations where there is no intrinsic separation of time-scales available nor any small parameters for asymptotic techniques — e.g. flows on the 'attractors' of a dissipative dynamical system like the Lorenz system. We use a method of reduction involving converting the underlying autonomous ODE 'fine' system to a system of first-order PDE, the latter essentially representing (local) invariant mmanifolds in fine phase space. The idea goes back to Jacobi, and resurfaced in dynamical msystems work since the middle 1960s (Sacker). Some methods of implementing Inertial Manifold Theory (IMT, Temam and co-workers) also employ the broad idea. It turns out that the type of solution one seeks to the PDE system is crucial in determining the practical success of the scheme with respect to model reduction. For example, it is known that the maximal reduction afforded by (IMT) is bounded below by the dimension of the 'attractor.' A practical consequence is that if the dimension of the attractor is large (e.g. Navier Stokes equations), then the reduced theory still contains a very large number of degrees of freedom. To us, this appears to be a direct consequence of requiring an autonomous (state-dependent) coarse theory that translates to seeking a solution of the system of PDE mentioned before as a graph over the entire coarse space. If this condition is relaxed, then it is possible to populate those regions of fine phase space where (segments of) trajectories to be coarse-grained exist by low dimensional, local invariant manifolds. A closed low dimensional coarse theory can now be set up whose solutions, essentially, ride this pre-computed set of local invariant manifolds of the fine theory, thus yielding self-consistency to coarse response. An important physical consequence is that the coarse theory in the case of such drastic reduction is, more often than not, history-dependent, i.e. produces self-intersecting trajectories in phase space; however, this history dependence is completely described by our method. Depending upon how energy in the coarse theory is defined, these ideas also demonstrate non-conservative coarse behavior arising from conservative fine systems. We have devised an algorithm based on the above idea that works reasonably on model problems. Its effectiveness in model reduction for the Lorenz system (chaotic behavior) as well as a nonlinear Hamiltonian system (periodic behavior) will be demonstrated. Time —permitting a few results from field dislocation mechanics will be demonstrated showing the emergence of microstructure at a very fine scale — coarse-graining such a theory to obtain a macroscopic theory of crystal plasticity is one of the goals of the model reduction method mentioned above. This is joint work with Aarti Sawant.
It is well known that in polycrystalline metals, a substantial increase in strength and hardness can be obtained by reducing the grain size to the nanometer scale. These attributes have generated considerable interest in the use of nanocrystalline metallic materials (grain sizes less than _ 100 nm), for a wide variety of structural applications. Typically, relative to their microcrystalline counterparts, nanocrystalline metals exhibit a very high tensile strength, but at the expense of a much reduced tensile ductility. The limited duc-tility is of major concern. For example, while the ultimate tensile strength levels approach _ 1500MPa in electro-deposited nanocrystalline nickel, the ductility that can be obtained in this material is generally low and usually does not exceed _ 3%. Physical experiments and atomistic simulations reported in the literature, show that grain-boundary-related slip and separation phenomena begin to play an important role in the overall inelastic response of a polycrystalline material when the grain-size decreases to diameters under _ 100 nm, and dislocation activity within the grain interiors becomes more difficult. In order to model the effects of grain boundaries in polycrystalline materials we have coupled a crystal-plasticity model for the grain interiors with a a new elastic-plastic grain- boundary interface model which accounts for both reversible elastic, as well irreversible inelastic sliding-separation deformations at the grain boundaries prior to failure. We have used this new computational capability to study the deformation and fracture response of nanocrystalline nickel. The results from the simulations capture the macroscopic experimentally-observed tensile stress-strain curves, and the dominant microstructural fracture mechanisms in this material. The macroscopically-observed nonlinearity in the stress-strain response is mainly due to the inelastic response of the grain boundaries. The stress concentrations at the tips of the distributed grain-boundary cracks, and at grain-boundary triple junctions, cause a limited amount of plastic deformation in the high-strength grain interiors. The competition of grain-boundary deformation with that in the grain interiors determines the observed macroscopic stress-strain response, and the overall ductility. In nanocrystalline nickel, the high yield strength of the grain interiors and relatively weaker grain-boundary interfaces account for the low ductility of this material in tension.
Multiscale calculation seeks to improve computational efficiency by describing a physical system on a hierarchy of different levels. Ideally, the results of such calculations should approach those of the most reliable member of the hierarchy in a well-defined limit. However, the necessarily approximate nature of the coarser levels of the hierarchy make this ideal elusive. This talk presents three examples of approaches which achieve ideal in the context of ab initio density-function theory calculations: (1) Use of multiresolution analysis (wavelet theory) to provide the first new electronic structure method to compete directly with full-potential linear augmented plane wave (FP-LAPW) calculations in terms of accuracy, but with far fewer and more transparent adjustable computational parameters; (2) Linkage of atomistic potential models with ab initio density functional theory calculations to compute exact density-functional thermal averages at greatly accelerated rates; (3) Introduction of a new, exact density-functional theorem allowing the rigorous separation of a system from its environment with application to the behavior of material and chemical systems in solution.
Silicon nitride (Si3N4) films on silicon substrates have a wide variety of applications in electronics and photovoltaics [1]. Recent experiments by Kim and Yeom [2] indicate that the thermally grown Si3N4 film on Si(111) has an atomically abrupt and defect-free interface. Their finding supports the model used in the molecular-dynamics simulations presented. In both applications, the interface can be subject to extreme environments and conditions causing strains, e.g., occurring at various strain rates. Atomistic simulations complement experimental research to gain fundamental understanding of possible failure mechanisms, which, in turn, enables the production of reliable components in microelectronics and photovoltaics applications. Silicon is modeled by the well-known Stillinger-Weber potential [3] and was adapted to describe a silicon system that is expanded so that it perfectly matches silicon nitride.
Bulk Si3N4 is modeled using a combination of two- and three-body interactions, which include charge transfer, electronic polarizability, and covalent bonding effects [4]. The interface atoms are treated differently than those in the bulk to describe the bonding across the Si/Si3N4 interface. To account for all the structural correlations between silicon and silicon nitride, eight different components are used to model the silicon/silicon nitride system [5]. The mechanical strength of the Si/Si3N4 interface was investigated by applying tensile stress parallel to the interface. Calculations of the Young's modulus of this particular interface showed that the value of 185.498 (± 0.29) GPa for the silicon/silicon nitride interface lies, as expected, comfortably between the Young's moduli of silicon and silicon nitride, respectively. At low strain rates, we found that when systems were stretched continuously, those that were stretched more quickly failed at higher strains. The failure mechanism was a crack in silicon nitride and plastic deformation in silicon. At the highest strain rate the stress is released through plastic deformation in silicon nitride, a qualitatively different failure mechanism compared to the fracture in silicon nitride at lower strain rates. A detailed analysis of the failure of the silicon/silicon nitride interface will be presented.
* Priya Vashishta developed the model for the silicon/silicon nitride interface during my stay as post-doc with him, Rajiv Kalia, and Aiichiro Nakano at LSU. The work presented here was supported in part by NASA, NSF, and a WVU Faculty Senate Grant.
Two modeling studies related to the production of AlN crystals via vapor transport will be discussed. In the first study a new, parameter-free first principles strategy is used that not only yields mole fractions of gas-phase species as a function of reactor conditions, but also identifies growth precursors based on their degree of saturation with respect to the growing crystal. The strategy predicts that Al and N2 are present in high relative concentrations, in agreement with available experimental measurements, but that N2 molecules are undersaturated with respect to the AlN crystal and therefore are unlikely growth precursors. Instead, Al2N, Al3N, and Al4N species, while in much smaller concentrations than N2, are predicted to be supersaturated and therefore are the main source of nitrogen contributing to AlN crystal growth, in stark contrast to assumptions made in prior modeling studies. In recent experiments it has been noted that AlN crystals deposited in BN crucibles tend to grow faster in the c direction with smooth (0001) facets compared to crystals grown in W or TaC crucibles. We propose that trace boron impurities arising from the crucible preferentially incorporate into steps in the AlN surface and lower the Schwoebel diffusion barrier, leading to enhanced step growth and decreased secondary nucleation. This proposal is supported by molecular modeling studies using classical potentials, which show that the strain energy associated with B substitution drives B impurities to steps, and that the resulting strong B-N bond to surface adsorbates can reduce the
Schwoebel barrier.
*Funded by the Office of Naval Research through MURI contract N00014-01-1-0302.
The bridging between the mechanical behaviour of an individual phase or crystal and that of a polycrystal remains a topic of major interest and is at the heart of homogenization schemes developed to predict the behaviour of heterogeneous materials at different scales. Such schemes are based on the assumption that the mechanical behaviour of individual constituents can lead to the description of the mechanical response of a macroscopic aggregate through either suitable interaction laws or a numerical averaging process of a representative volume element (RVE) of the microstructure. In this presentation, a multiscale constitutive framework recently proposed to describe the mechanical behaviour of heterogeneous microstructures will be discussed. The framework enables explicit links between the dominant microstructural features at the microscopic and mesoscopic scales to be made with the macroscopic constitutive behaviour of the material. The approach has been implemented into the finite element method and is used to examine the effect of the volume fraction of eutectic microstructures and precipitates on the mechanical behaviour of a heterogeneous Ni-base single crystal and directionally solidified superalloys. The behaviour of suitable RVEs is computed from actual digitised images of typical microstructures, and a multiscale crystallographic constitutive model is then formulated to describe the mechanical behaviour of the homogenised material at the macroscale. The implications of using these types of multi-scale modeling capabilities within an industrial context and the potential for developing links with the atomistic scale will be discussed.
In this talk I will present a novel approach, called First Principles String Molecular Dynamics, to find chemical reaction pathways in the context of First Principles Molecular Dynamics simulations. Applications to selected chemical reactions in condensed and gas phases will be used to illustrate the scheme. As found by previous investigators, current GGA approximations of the exchange-correlation functional, tend to underestimate reaction barriers. I will show that, in the case of the reactions studied here, a recently developed meta-GGA functional results in barrier heights that are in closer agreement with experiment and with calculations based on more accurate quantum mechanical methods. Finally, I will show that meta-GGA improves significantly DFT based predictions of melting transitions.
Point defects in silicon and silicon surfaces. Silicon based devices recover an enormous importance in material science. In the bulk material, the formation, diffusion and interaction of defects largely affect the electronic properties. Concerning surfaces, the comprehension of the phenomena of surface relaxation, reconstruction, passivation, and more generally of the adsorption of external elements, could support the interpretation of the processes of passivation, crystal epitaxial growth and the engineering of self-assembled layers. In the last few years, we studied the processes of migration and clustering of native point defects in silicon.[1, 2] They act as intermediates for the growth of intrinsic extended defects, and determine many properties of the bulk material such as, for example, its behavior under irradiation. To investigate these systems we devised a two step strategy. First, we used a semiempirical approach (periodic Tight Binding Molecular Dynamics) to model the dynamical evolution of the defective crystal. Secondly, we selected representative instantaneous atomic configurations from the dynamical simulations to study the electronic properties of the defects. At this stage, first principles computations (Hartree-Fock) were performed on appropriate silicon cluster models with geometries derived from the simulations. We then analysed how the bonding network and the atomic properties of the investigated systems evolve by performing a topological analysis of their electron density, within the formalism of the Quantum Theory of Atoms in Molecules.[3] Thecombination of these techniques enabled us to describe processes involving hundreds of atoms at an atomistic level. The approach may be extended to study non intrinsic defects which involve doping elements relevant for technological applications and industrial processes (for example hydrogen, boron, oxygen and metal impurities). As concerns silicon surfaces, we studied the systems which are more experimentally diffuse: clean and H-covered Si(111)(1x1);[4] clean Si(111)(2x1);[5] Si(100)(1x1):H; clean and H-covered Si(100)(2x1). We performed first principles computations (periodic Hartree-Fock and Density Functional) to optimize their geometry, and then we focused on the relations between structural and electronic rearrangements respect to the ideal crystal. We evaluated how the bonding and atomic properties of the surface atoms are related to the processes of relaxation, reconstruction and H covering. Analogously to the case of point defects, the combination between dynamical simulations and first principles computations could be very useful to model and understand quite complex phenomena occurring at the surface-vacuum interface. Moreover, the theoretical study of the electron density of regular surfaces is relevant in itself to establish a link with the recent experiments of surface X-ray scattering crystallography using synchrotron radiation facilities.
Thermoelectrics. Our research on thermoelectric materials was financed by the European Union under the
Nanothermel Project. This involved research institutions and industrial partners from six different European countries. Thermoelectric devices may be used as power generators and as coolers. In this latter case, they reach an efficiency of about 10% of the Carnot limit, which is about three times smaller than for traditional coolers. This claims for significant improvements to be pursued on these devices. The kernel of a thermoelectric device are the two materials forming each element, and the very important point is to optimize and increase the material's figure of merit ZT (ZT=TS2s/k;T=absolute temperature; S Seebeck coefficient; s=electrical conductivity; k=thermal conductivity). Most of the factors determining ZT are critically dependent on the material electronic band structure (S, s, and the electronic contribution to k), and the focus of our research was to understand, at an atomistic level, how to modify the band structure to improve ZT. On the experimental side, S, s and k are tuned mainly by means of doping and nanostructuring, but the optimization strategy may vary from material to material. According to the work plan of the whole project, we had the task to perform first principle computations for supporting the characterization and the selection of the most promising thermoelectrics. More precisely, we studied the role of point defects in determining the thermoelectric properties, giving, if possible, indications on optimal doping elements and doping level. Secondly, we supported the interpretation of structural experiments, especially when these latter did non provide clear cut answers. Third, we characterized the nature of the chemical interactions present in these materials within the formalism of the Quantum Theory of Atoms in Molecules. These general guidelines have been applied to the study of Skutterudites,[6] inorganic Clathrates[7] and Zinc-Antimonides. [8] Additional information of these systems may be recovered by studying the role of point defects and nanostructuring in determining the lattice contribution to k.
The properties of matter at the nanoscale are quite different than their macroscopic counterparts. For example, optical excitations in porous silicon are strongly blue shifted from crystalline silicon owing to quantum confinement. I will illustrate some recent theoretical progress in developing numerical approaches to compute the optical and electronic properties of semiconductor materials whose physical dimensions are on the nanoscale. I will focus on real space methods for solving the electronic structure problem in this size regime.
Recent References:
S. Ogut, R. Burdick, Y. Saad, and J.R. Chelikowsky: "Ab Initio Calculations for the Large Dielectric Matrices of Confined Systems," Phys. Rev. Lett. 90, 127401 (2003). D.V. Melnikov and J.R. Chelikowsky: "Quantum confinement in phosphorus-doped silicon nanocrystals," Phys. Rev. Lett. 92, 046802 (2004).
An intriguing and unexpected feature has recently been discovered during epitaxial growth of metal thin films on semiconductors. Instead of forming three-dimensional (3D) islands of various size as commonly observed for nonreactive interfaces, the metal atoms can arrange themselves into plateaus or islands of selective heights with flat tops and steep edges under certain growth conditions. This unusual behavior has been observed in quite a few systems including Ag/GaAs, Ag/Si(111), and Pb/Si(111). The implication could be significant, since the formation of these uniform, self-organized atomic structures points to a potentially interesting pathway to prepare functional nanostructures. It is believed that this extra stability of metal films with specific thickness has an electronic origin, and can be explained by the so-called quantum size effects due to electron confinement. These quantum well (QW) states also give rise to an oscillatory work function as the thickness varies, and thus affect the details of the surface adsorption processes. In addition, the QW states are directly connected to the oscillation in the exchange coupling between two magnetic materials across a nonmagnetic spacer layer of various thickness. In this talk, I will present our recent density-functional calculations to study these effects in Ag/Fe(100), Pb/Si(111), and various freestanding films. The role played by the substrate and the crystal band structure will also be discussed.
* Supported by the National Science Foundation and the Department of Energy
Advances in modeling material systems since the development of quantum mechanics in the 1920's came much slower than progress in unraveling the electronic structure of atoms. This is particularly evident when one compares the identification of spectral features. For atomic spectra, lines are sharp and identification in terms of electronic transitions is much easier than for the case of solids where spectral features are generally broad. At first, empirical approaches paved the way, and eventually, it became possible to explain electronic and structural properties of fairly complex solids from first principles using only information about their constituent atoms as input. Because of the central role of electronic structure in understanding bonding and other properties, much of the focus has been on obtaining band structures and electron density maps. Eventually, this led to accurate determinations of ground-state mechanical and vibrational properties. In fact, at this time, ground-state calculations are of high precision and have been extended to compute electron-lattice interactions. In turn, these are used to explain and predict superconductivity in materials and to provide detailed calculations of superconducting properties. The model used for much of this work is based on pseudopotentials and density functional theory. It is sometimes referred to as the "Standard Model of Solids". The approach is a result of the development of many new conceptual models and the great progress in computation. Currently, excited states can be treated with excellent precision so that optical and photoemission data can be interpreted using first-principles theory. The fact that theory is now at a point where specific experiments for real materials can often be reproduced motivates a deeper and broader collaborative effort between experiment and theory. In addition, theory has produced successful predictions related to new materials and material properties. This has also enhanced experimental-theoretical collaborations. Some promising new avenues for research in the near term are the studies of the effects of confinement such as those arising in nanostructures, studies of systems where strong electron-electron correlation effects are dominant, exploration of multiscale properties going from nano to macro, etc. Much of the success of this research will depend on extending our current conceptual base and computational techniques. An example of the latter is the current effort to develop "order N" techniques to deal with more complex materials without overloading computers. The goals for researchers doing multiscale studies, molecular dynamics, and "order N" studies overlap, and progress is being made. Summarizing, there are a variety of opportunities in the field of modeling material systems ranging from development of new computational techniques to the invention of new concepts on how to view materials to explaining and predicting phenomena and properties. This presentation will survey the background in this area and explore some of the current proposals for future research.
The development of finite element simulation of material forming processes started about 30 years ago in academic laboratories, while the introduction of the corresponding commercial computer codes in industry is less than twenty years old. Numerical simulation is now a well-established tool for accelerating and improving design and optimization of material forming processes. It is currently used in industry for metals, polymers, glasses and other materials forming. From the computational point of view material forming is between fluid and solid mechanics and it combines both related techniques. This presentation will review the main achievements in simulation of complex process : bulk metal forming processes like forging using a Lagrangian approach with remeshing and injection moulding using an Eulerian approach and VoF technique with extension to metal casting. Computationnal method and numerical techniques will be discussed: mixed finite element methods, Eulerian, convection diffusion solution, levelset or VoF method, Lagrangian approach, remeshing and adaptive remeshing, anisotropic meshing. In the same time, the need of a more accurate modeling of the behaviour of the material during flowing and also during its solidification require to go further in the physical model contained in the constitutive equation. Moreover the future of material forming process simulation to go further in the prediction of the final properties of the work-piece, via the description of the microstructure evolution and using more often a multiscale modelling approach. Examples of complex multiscale material modeling will be discussed:
The magnetic properties of diluted magnetic semiconductors are calculated within the framework of the KKR-CPA, using a mapping on a Heisenberg model. Effective exchange coupling constants are evaluated by embedding two impurities in the CPA medium. Curie temperatures (Tc) are estimated by the mean-field approximation (MFA), the random phase approximation (RPA) and by monte carlo methods. In MFA and RPA, Tc is proportional to the square root of Mn concentration c for (Ga, Mn)N, while in (Ga, Mn)Sb Tc is linear to c. Since the extended hole states mediate the ferromagnetism in (Ga,Mn)Sb (p-d) exchange), the interaction is long range leading to a flat spin wave dispersion. Thus, the MFA gives similar results as the RPA. In (Ga, Mn)N, due to the broadening of the impurity bands in the gap, the ferromagnetic state is stabilized by double exchange. Since the impurity states are well localized, the exchange interaction is short range leading to pronounced percolation effects for smaller concentrations, which cannot be described by the MFA or RPA. Monte Carlo calculations show that the Curie temperature is strongly reduced as compared to the MFA values.
In this talk, a brief overview of our recent work on modelling strength and plasticity of nanocrystalline metallic materials will be given, along with a cursory discussion of aspects relating to thermal stability of such materials. In a concluding part of the talk, modelling of severe plastic deformation, particularly by equal channel angular pressing, leading to extreme grain refinement will also be discussed. The models used are macroscopic in nature, but they import information obtained at dislocation dynamics scale and involve nanostructure-related parameters, thus providing a frame for linking various length scales.
The role of computation in understanding experimentally observed behavior of submicron semiconductor material structures will be illustrated through brief descriptions of several examples drawn from recent work. The examples include aspects of behavior that have been observed in either fabrication or functional performance of small structures and that arise through the influence of mechanical strain on essential characteristics of the material system. The examples include (i) the origin of the (105) crystallographic surface orientation that dominates morphology in the early stages of formation of SiGe/Si(100) quantum dots by strain driven selfassembly, (ii) the evolution of arrays of islands of these same materials during vapor deposition, including island interactions, and (iii) the modification of current-voltage transport characteristics of a resonant tunnel diode due to inhomogeneous strain distributions induced through fabrication. The computational approaches used in these studies include molecular dynamics or first principles analysis of the structure of strained crystal surfaces in example (i), the incorporation of anisotropic surface energy into a continuum model of morphology evolution in example (ii), and illustration of the use of deformation potential theory within the effective mass model of quantum transport in example (iii). In each case, the synergy among experiment, theory and computation has been crucial to resolution of issues of importance for the advancement of certain nanoelectronic technologies.
Understanding the precise manner in which materials microstructure and its evolution controls the performance and lifetime of engineering materials has represented one of the greatest forefronts in materials research throughout the last century. We discuss the role of large-scale Dislocation Dynamics simulations in designing advanced materials for demanding electronic and structural applications. Advances in the method of Dislocation Dynamics will be presented, with special emphasis on utilizing massively parallel computer simulations to access investigations of realistic conditions that can be readily verified by experiments. Examples of the utilization of massively parallel computing at UCLA with a newly constructed 200-node Beowulf cluster (ISIS) will be given. The first example will demonstrate microstructure evolution in single crystals, and shows the important role of elastic anisotropy. The second example will focus on the application of dislocation dynamics to understand the fundamental origins of plastic flow localization and embrittlement in structural materials developed for nuclear energy applications (fission and fusion). The last example will demonstrate how nanolayer superlattices can be designed for superior strength and ductility for aerospace applications.
Fabrication of next generation materials and devices comprised of molecular and nanoscopic building blocks tailor-made for specific applications will rely to a great extent on processes of self-assembly, in which instructions for organization emerge from the nature of the forces acting between constituents. Ideally, self-assembly will lead to synthetic structures whose form and function are explicitly encoded in the system at the molecular level, as in biological systems. However, the intermolecular forces required to produce organized assemblies of synthetic nanoparticles and nanostructured molecules with the precision and reliability typical of biological structures are not understood. Developing new approaches to self-assembly, especially bio-inspired approaches, is one of the most fundamental challenges of nanotechnology. Computational materials science has much to contribute to this exciting arena through the development of suitable theories, models and simulation methods capable of spanning from the scale of individual atoms to mesoscopic assemblies. Through simulation, it is possible to elucidate the fundamental principles of self-assembly and the properties of self-organized structures. In this talk, we present our recent molecular and mesoscale simulation studies of the selfassembly of collections of anisometric, amphiphilic nanocrystals and nanostructured molecules, and discuss opportunities for progress and the challenges inherent to these and other problems in computational nanoscience.
Modeling and simulation of micro-casting processes with commercial tools is limited to simple materials. When it comes to process feedstocks from ceramic nanopowders in cavities with dimensions of a few tens of micrometers or even below the important geometrical features in the mould perilously approach the size of the solid particles in the material. On the other hand the injection moulding machine is a macroscopic object and has macroscopic material reservoirs. To tackle the flow of multicomponent materials all the way down from macroscopic reservoirs to the last microscopic cavity needs to account for various material properties. The simulation process with a continuum model will not perform well on the micro-scale, as well as microscopic particle based methods will be prohibitive in their application to macroscopic geometries. Therefore we propose a combination of particle based methods and continuum models for the simulation of this scale spanning problem. In an outlook we will indicate the usefulness of our approach to similar challenges.
This presentation surveys recent progress and experience with spacetime discontinuous Galerkin (SDG) models, emphasizing their use as a practical tool and a conceptual framework for multiscale materials modeling. Discontinuous Galerkin finite element models are constructed with basis functions that are discontinuous across element boundaries; the Galerkin projection enforces weakly the jump conditions generated by the continuum balance laws and by kinematical compatibility. In the spacetime version, an unstructured mesh partitions the analysis domain in†Ed ¥ R, and the relevant balance laws and jump conditions are enforced directly on each cell and across each cell boundary. When applied to hyperbolic problems, SDG methods satisfy the balance laws to within machine precision on every element; they feature linear complexity in the number of elements, superior stability properties, and a rich parallel structure. Thus, they can provide high-resolution approximations in demanding materials-related applications. Spacetime discontinuous Galerkin methods are an attractive option for multiscale continuum simulations. They facilitate hp-adaptive finite element methods that bridge multiple length scales, because they admit nonconforming grids and nonconforming basis functions in adjacent elements. When applied to sharp interface models for material phase boundaries, SDG meshes can continuously track moving interfaces without suffering the numerical errors associated with element distortion and data projection that plague conventional moving grid methods. Their superior shock-capturing capabilities make SDG models an attractive choice for dynamic simulation problems, such as Austenite-Martensite transitions in shape memory alloys subjected to shock loading (whether by a sharp or diffuse interface model) and in certain forms of dynamic fracture. Cohesive fracture models are easy to implement, because displacement discontinuities across element interfaces are part of the basic SDG framework. We discuss prospects for the use of SDG methodologies in atomistic modeling and as a bridging mechanism in simulations that attempt to couple atomistic and continuummodels. For example, our parallel and spacetime-adaptive†O N ( ) solution technology can be used to solve the Schrödinger equation in time-dependent density functional theory. Beyond discontinuities in the continuum fields, the SDG framework can be used to address discontinuities in the physical model itself. In contrast to purely kinematical coupling, we are investigating weak SDG formulations that couple continuum and atomistic models by enforcing weakly the jump conditions from physical balance laws.
Growth is a classic example of a multiscale problem. At the continuum scale, there are problems of lattice matching and the generation of stress fields. At the atomic scale, there are issues of the detailed mechanisms involved in the growth process.The problem of reaching the timescales required is particularly serious when attempts are made to simulate growth. Molecular dynamics simulations of MBE often assume growth rates of 104-106 times those available to any experimentalist. Attempts to simulate nucleation events can run into even more drastic problems. We consider two examples, one from hard material interface, one from a hard/soft interface to illustrate the problems. A simple example of the growth of one material on another is the growth of thin layers of ceramic oxide on a ceramic substrate. The difficulty here is that the barriers for processes are often high. We require a method that can reach the timescales needed without assuming what the processes involved are. We have demonstrated that a combination of the temperature-assisted hyperdynamics scheme of Voter and coworkers2 with kinetic Monte Carlo achieve this. The simulations show the importance of a wide range of cooperative transport mechanisms that have usually been ignored in ionic diffusion. Our simulations show that exchange mechanisms can dominate diffusion of ionic molecules over the surfaces of oxides with the rock salt structure. We also discuss the important issue of whether it is possible to grow atomically sharp interfaces in ceramic hetero-interfaces, or whether the exchange mechanism makes mixing unavoidable. An example that combines the problems of interfacial lattice-matching and nucleation is that of biomineralization. Living organisms can control the size, shape and structure of minerals. Attempts to reproduce this biological control in the laboratory often use Langmuir monolayers of long-chain carboxylic acids3. It is usually assumed that this control is exercised by the organic layer acting as a template which controls the growth morphology of the mineral. We use a combination of large-scale molecular dynamics simulations and the Wulff-Kaishew theorem to predict the morphologies of calcite crystals grown on stearic (octadecanoic) acid monolayers and find good agreement with experiments. We show that, while templating ideas are important, it must be remembered that organic monolayers are not rigid structures in a vacuum. They are flexible, chemically active surfaces in contact with water. Any theory of mineral growth must include these effects. A case of particular interest is when a mineral grows in a polar direction. This introduces a new constraint . the necessity to quench the macroscopic dipole . that must also be included.
This presentation will focus on crack propagation in glasses, nanostructured ceramics, and nanocomposites. We have performed multimillion-atom molecular dynamics simulations to investigate the morphology and dynamics of crack fronts in these systems. The results on atomistic mechanism of fracture in glasses are in excellent agreement with recent AFM studies. Roughness exponents of fracture surfaces are also determined and the results are in accordance with experiments.
Computational Materials Science focuses on understanding the magnetic, optical, electrical and mechanical properties of materials and the relationship between their physical properties, chemical composition and atomic structures. It is based on ab-initio electronic structure calculations which use only our knowledge of quantum mechanics and the fundamental physical constants to interpret experiments using a minimum of experimental input, and to make material-specific predictions. Three main themes can be identified: ground state properties, electronic transport, and electronic excitations. In this presentation, I outline the current state of the art in regard to parameter-free electronic transport calculations.
Complex fluids such as amphiphilic mixtures, colloidal suspensions, and polymer solutions, mixtures, and melts are characterized by structure on mesoscopic length-scales. ranging from nano- to micrometers.and energy scales comparable to the thermal energy kBT. The meso-scale structures of these systems endows them with many interesting and unique features, and they are widely used in the processing, chemical, and energy industries. Complex fluids present a challenge for conventional methods of simulation due to the presence of disparate time scales in their dynamics. The unique problems associated with the modeling and analysis of the behavior of these systems has created the need for new simulation techniques that overcome some of the di_culties associated with the use of atomistic molecular dynamics simulations and macroscopic approaches based on the numerical solution of continuum equations. The modeling of these systems requires the use of "coarse-grained" or mesoscopic approaches that mimic the behavior of atomistic systems on the length scales of interest. The goal is to incorporate the essential features of the microscopic and mesoscopic physics in models which are computationally e_cient and are easily implemented in complex geometries and on parallel computers. Recent research involving the development and application of a range of mesoscale simulation techniques will be summarized. In particular, work involving the use of coarsegrained dynamically triangulated surface models of membranes to analyze flicker spectroscopy data of giant nonspherical vesicles, the budding of crystalline (clathrin-coated pits) in fluid membranes, and the phase behavior and structure of microemulsions. membranes of fluctuating topology.will be described. A range of applications of recently developed particle-based mesoscopic simulation techniques will also be discussed. Some future research involving extensions of these techniques to model the dynamics and rheology of complex mixtures is outlined.
Calculation of the various properties of materials often requires very differenttheoretical and computational approaches because of the complex interactions and diverse behaviors in condensed matter. In particular, the restricted geometry and symmetry of nanostructures often give rise to interesting quantum confinement, enhanced many-electron interaction, and other effects related to reduced dimensionality. These effects can lead to novel physical properties and phenomena, which also are potentially useful in applications. In this talk, I will discuss some of our recent studies on the electron transport, optical, and mechanical properties of nanotubes and molecular junctions. For examples, molecular electronic devices, i.e., electrical transport through a single molecule can produce highly nonlinear I-V characteristics. The optical spectra of small diameter carbon nanotubes exhibit dramatic excitonic effects. Also friction on the nanoscale may be very different from that on the human scale. The talk will be on the theory and computation of these phenomena. We will present results on the nonlinear transport behavior of molecular junctions calculated using a newly developed ab initio scattering-state method, the optical response of nanotubes employing a first-principles many-particle Green's function approach, and the behaviors of mechanical energy dissipation in double-walled carbon nanotube oscillators from molecular dynamics simulations. The physical origin of the calculated behaviors will be examined.
The fracture of macroscopic brittle materials is sensitive to details at the atomic scale. I will discuss two implications of this idea. First, I will discuss ideal brittle twodimensional materials as a testing ground for the understanding of fracture, and show that solvable models violate established rules for how cracks move. Second, I will discuss efforts to bring theory and experiment into accord for the fracture of single-crystal silicon, and show that theory and experiment remain disconcertingly far apart.
I shall briefly some application of coarse-grained models to explore the properties of interfaces and surfaces of soft matter, e.g., the stability of thin polymer coatings[1,2], wetting properties[3] and self-assembly in multi-component polymer films, and the properties of bilayer membranes[4]. We investigate these systems by Monte Carlo / Molecular Dynamics simulations and by self-consistent field theory / density functional theory for polymeric systems. Both, the structure and thermodynamics as well as dynamical properties in thin films have been studied by our coarse-grained models. Literature:
Abstract: One of the most compelling frontiers for materials scientists is to be found in the living world. Recent advances in molecular biology, x-ray crystallography and electron tomography and single molecule biophysics have opened up possibilities ranging from synthetic proteins to devices and sensors inspired by their cellular hosts. The aim of this talk will be to describe some of the critical modeling challenges that must be faced in considering macromolecules and their complexes. I will feature two case studies, one involving the elasticity of DNA and its relevance to the packing of DNA in viruses and eucaryotic cells and the second which considers the physical mechanisms of mechanosensation. These case studies will highlight both the power and shortcomings of both atomistic and continuum descriptions of biological problems and will illustrate the important unanswered challenges in this area.
Kinetic Monte Carlo simulation is a useful tool to study the dynamics of physical and chemical systems on mesoscopic and macroscopic time scales much longer than the picosecond scales accessible with molecular dynamics. However, the Monte Carlo transition rates are not, in general, known from first principles. Often it is therefore assumed that 'minor' differences between dynamics are not very important, as long as they obey detailed balance and thus eventually bring the system to thermodynamic equilibrium. In this talk I will show that this view is too simplistic, and that very significant differences are found in the structure and mobility of driven interfaces [1], as well as in nucleation rates at low temperatures [2], between kinetic Ising systems evolving under different stochastic dynamics. In particular, I will discuss the differences between "hard" dynamics (such as the standard Glauber and Metropolis rates), in which the effects of the interactions and the applied field do not factorize in the transition rate, and "soft" dynamics that possess such a factorization property. In additin to the hard and soft Glauber cases, I will also consider rates that contain local energy barriers between the individual system states [3], including the one-step-dynamic [4] and the transitiondynamics- approximation [5]. The moral of my story is that great care must be shown in devising stochastic Monte Carlo dynamics for specific systems if the time-dependent results are going to be physically meaningful.
Friction, adhesion and nanoscale flows are all dominated by interfacial processes. However, the conditions at the interfaces are determined by deformation and flow at much larger scales. The challenge is to integrate an atomic-scale treatment of bondbreaking, sliding, and flow at interfaces, with large scale information that is most efficiently described with continuum algorithms. This talk will briefly highlight several different approaches being used in our group. The first example is a study of craze formation and the fracture energy of glassy polymers. Here, atomistic simulations are used to study different phases of deformation and fracture. They provide information about the fundamental processes of craze formation, as well as constitutive relations that can be used in continuum calculations of the fracture energy. The second example is a mesoscale model for immiscible fluids. Most previous models were chosen for simplicity or convenience. We have fit detailed molecular dynamics (MD) simulations to a mesoscale model and shown that it reproduces a wide range of behavior that is not included in the fit. The fit reveals several fundamental shortcomings of previous models. The final example is simultaneous multiscale modeling where different regions of space are described with different levels of detail. An algorithm for fluids has been applied to slip at rough walls and singular corner flows in cavities. A parallel algorithm for solids has been applied to stick-slip motion and contact of rough surfaces.
The talk will cover numerical methods and their application to bridge the time and length scale for the simulation of ultra-high density future magnetic storage systems. Examples will be given (1) For the estimation of the failure rate of magnetic random access memories calculating the relevant energy barriers. (2) For the simulution of magnetization processes in magneto-electronic field sensors describing the physics on a mesoscopic length scale. (3) For the simulation of the read and write process in magnetic recording using fast boundary methods to bridge the length scale.
To examine fundamental mechanisms associated with size effects in plasticity, we perform simulation studies of dislocation dynamics in two dimensions. While highly idealized, these model systems provide insight into forces driving dislocation patterning and the emergence of characteristic length scales in plastic deformation. To study the dynamics and patterning of screw dislocations in two dimensions, we consider an idealized crystal deformed with a two-dimensional anti-plane strain field z(x,y). A close analog of the 2-d XY model from statistical physics, this system can contain point screw dislocations with Burgers vector in/out of the plane, but no edge dislocations. We simulate the dynamics of the strain field, and our simulation methodology allows us to study dislocation nucleation, motion, and annihilation without explicitly calculating the interactions and trajectories of individual defects. In a bulk system under a constant applied shear strain rate, we observe the coalescence of dislocation-rich slip bands whose spacing distribution obeys a simple scaling law. We then study plastic deformation under a strain gradient in the fiber pull-out and channel flow geometries, and in the presence of a purely ductile crack loaded in mode III; in each case we vary the system size and find clear evidence of size effects. A careful analysis of the system's constitutive behavior in the channel flow geometry shows that while most of the system obeys the Bingham plastic law, a surface layer emerges whose dislocation density is lower than expected and whose yield stress is higher than that of the bulk. We argue that dislocation image interactions near the boundary force the Bingham plastic law inevitably to break down, so that the sample's mechanical response is always harder near the surface than in the bulk. Next we study the dynamics and patterning of edge dislocations under a strain gradient in two dimensions, by examining the response of a two-dimensional crystal under bending using both single crystalline and polycrystalline initial states. The system evolves via a Monte Carlo algorithm to approximate quasi-static loading at finite temperature. Deformation arises from nucleation and motion of edge dislocations. We observe the onset of spontaneous dislocation patterning and the nucleation and growth of welldefined tilt boundaries, and examine both size effects and strain rate effects in this system. Lastly, we discuss ways in which statistical mechanics may provide useful insights into the mechanisms driving dislocation patterning and the emergence of characteristic length scales in plastic deformation. This work was supported by the National Science Foundation under grant DMR- 0116090 and by the NIST Center for Theoretical/Computational Materials Science.
The sub 10nm length scale of CMOS devices creates new materials challenges for which modelling of materials, interfaces, dopants, and defects becomes crucial to process design and understanding device performance. The critical integrated circuit components will comprise tens of thousands of atoms or less, so approaching molecular scales. The widely-recognised intrinsic parameter fluctuations from discreteness of charge and matter will be a major factor limiting scaling and integration. Despite some progress in understanding these phenomena, there are no adequate models or simulation tools able to predict accurately the origins, characteristics, scale and consequences of the intrinsic fluctuations in such molecular-size devices. I will discuss two interrelated issues: i) how to bridge the gap between materials modelling and device simulation, and ii) how modeling of Atomic Force Microscopy (AFM) may help to study defects in oxides and manipulate molecules to produce molecular devices. Both represent applications of multiscale computational approach to modelling complex processes at surfaces and interfaces of wide-gap insulators. I will outline challenges related to disorder and statistical nature of defect states in these nano- scale devices and demonstrate how one can use an embedded cluster method to tackle some of these issues. Recent experiments using noncontact AFM demonstrate that the short-range interaction forces can be measured selectively above chemically identified sites on surfaces of insulators. These experiments and atomically resolved AFM imaging of insulators rely on multi-scale theoretical models for their interpretation. I will discuss the applications of AFM modelling to study the structure and spectroscopic properties of surface point defects and adsorbed molecules and for molecular manipulation.
Snapshot from the molecular dynamics simulations of a CF2 fragment bonding to polystyrene chains. C in the CF2 is shown in green, C in the polystyrene is shown in blue, F is shown in red, and H is shown in white.
Fluorocarbon plasmas are widely used to chemically modify surfaces and deposit thin films. It is well-accepted that polyatomic ions and neutrals within low-energy plasmas have asignificant effect on the surface chemistry induced by the plasma. For this reason, the deposition of mass selected fluorocarbon ions are useful for isolating the effects specific to polyatomic ions. In this study, the detailed chemical modifications that result from of the deposition of beams of polyatomic fluorocarbon ions (C3F5+ and CF3 +) on polystyrene surfaces at experimental fluxes are identified using classical molecular dynamics simulations with many-body empirical potentials. To facilitate these simulations, a new CH- F potential is developed based on the second generation reactive empirical bond-order potential for hydrocarbons developed by Brenner. Lennard- Jones potentials are used to model long-range van der Waals interactions. Both beams are deposited normal to the surface at incident energies of 50 eV/ion. For CF3 + deposition, F atoms play the most important role in fluorinating the polystyrene surface, as the majority of them are covalently attached to the polymer chains through replacement of native H atoms or capping the end of broken chains. CF2 fragments are also an important longlived species. In contrast, F atoms are a minor bi-product and CF2 fragments are the most dominant species for C3F5 + deposition on polystyrene. Thus the simulations explain the experimental finding that C3F5 + is more efficient at producing fluorocarbon thin films. In particular, many larger fragments produced by C3F5 + ion deposition, such as CF2, C2Fn and C3F5, contain more than one C atom and may have more than one active site. These larger fragments readily react and connect with other fluorocarbon ions or fragments to grow polymer-like structures, as illustrated in the figure. In contrast, F atoms, the most dominant fragment in CF3 + deposition, effectively deactivate potential film nucleation sites when they fluorinate the polymer surface. These findings can be generalized to state that larger polyatomic ions produce a wider variety of precursors for film growth than smaller polyatomic ions and thus should be more effective at growing thin films from plasma. Additionally, they suggest that CF2 is an important precursor for film growth from fluorocarbon polyatomic ions. This work is supported by the National Science Foundation (CHE-0200838).
Spin-polarized electronics is a rapidly expanding research area, both because of the fascinating fundamental physics observed in new spintronic materials, and because of their potentially far-reaching technological applications. Here we illustrate the utility of modern computational methods in the design and optimization of new spintronic systems by describing the successful prediction and subsequent synthesis of a new "multiferroic'' material (which is simultaneously ferromagnetic and ferroelectric). Finally we mention some recent advances in computational methods that have allowed us both to understand the novel phenomena observed in spintronic materials, and to design improved materials for specific technological applications.
A significant problem in the atomistic simulation of materials is that molecular dynamics simulations are limited to nanoseconds, while important reactions and diffusive event often occur on time scales of microseconds and longer. Although rate constants for slow events can be computed directly using transition state theory (with dynamical corrections, if desired, to give exact rates), this requires first knowing the transition state. Often, however, we cannot even guess what events will occur. For example, in vapor-deposited metallic surface growth, surprisingly complicated exchange events are pervasive. I will discuss recently developed methods (hyperdynamics, parallel replica dynamics, and temperature accelerated dynamics) for treating this problem of complex, infrequent-event processes. The idea is to directly accelerate the dynamics to achieve longer times without prior knowledge of the available reaction paths. Time permitting, I will present our latest method developments and some recent applications, including metallic surface growth, deformation and dynamics of carbon nanotubes, and annealing after radiation damage events in MgO.