Publications

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This paper derives a methodology to enable spatial and temporal control of thermally inhomogeneous molecular dynamics (MD) simulations. The primary goal is to perform non-equilibrium MD of thermal transport analogous to continuum solutions of heat flow which have complex initial and boundary conditions, moving MD beyond quasi-equilibrium simulations using periodic boundary conditions. In our paradigm, the entire spatial domain is filled with atoms and overlaid with a finite element (FE) mesh. The representation of continuous variables on this mesh allows fixed temperature and fixed heat flux boundary conditions to be applied, non-equilibrium initial conditions to be imposed and source terms to be added to the atomistic system. In effect, the FE mesh defines a large length scale over which atomic quantities can be locally averaged to derive continuous fields. Unlike coupling methods which require a surrogate model of thermal transport like Fourier's law, in this work the FE grid is only employed for its projection, averaging and interpolation properties. Inherent in this approach is the assumption that MD observables of interest, e.g. temperature, can be mapped to a continuous representation in a non-equilibrium setting. This assumption is taken advantage of to derive a single, unified set of control forces based on Gaussian isokinetic thermostats to regulate the temperature and heat flux locally in the MD. Example problems are used to illustrate potential applications. In addition to the physical results, data relevant to understanding the numerical effects of the method on these systems are also presented. © 2010 IOP Publishing Ltd.

Understanding charge transport processes at a molecular level using computational techniques is currently hindered by a lack of appropriate models for incorporating anisotropic electric fields, as occur at charged fluid/solid interfaces, in molecular dynamics (MD) simulations. In this work, we develop a model for including electric fields in MD using an atomistic-to-continuum framework. Our model represents the electric potential on a finite element mesh satisfying a Poisson equation with source terms determined by the distribution of the atomic charges. The method is verified using simulations where analytical solutions are known or comparisons can be made to existing techniques. A Calculation of a salt water solution in a silicon nanochannel is performed to demonstrate the method in a target scientific application.

In modeling thermal transport in nanoscale systems, classical molecular dynamics (MD) explicitly represents phonon modes and scattering mechanisms, but electrons and their role in energy transport are missing. Furthermore, the assumption of local equilibrium between ions and electrons often fails at the nanoscale. We have coupled MD (implemented in the LAMMPS MD package) with a partial differential equation based representation of the electrons (implemented using finite elements). The coupling between the subsystems occurs via a local version of the two-temperature model. Key parameters of the model are calculated using the Time Dependent Density Functional Theory with either explicit or implicit energy flow. We will discuss application of this work in the context of the US DOE Center for Integrated Nanotechnologies (CINT).

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We present the results of a three year LDRD project that focused on understanding the impact of defects on the electrical, optical and thermal properties of GaN-based nanowires (NWs). We describe the development and application of a host of experimental techniques to quantify and understand the physics of defects and thermal transport in GaN NWs. We also present the development of analytical models and computational studies of thermal conductivity in GaN NWs. Finally, we present an atomistic model for GaN NW electrical breakdown supported with experimental evidence. GaN-based nanowires are attractive for applications requiring compact, high-current density devices such as ultraviolet laser arrays. Understanding GaN nanowire failure at high-current density is crucial to developing nanowire (NW) devices. Nanowire device failure is likely more complex than thin film due to the prominence of surface effects and enhanced interaction among point defects. Understanding the impact of surfaces and point defects on nanowire thermal and electrical transport is the first step toward rational control and mitigation of device failure mechanisms. However, investigating defects in GaN NWs is extremely challenging because conventional defect spectroscopy techniques are unsuitable for wide-bandgap nanostructures. To understand NW breakdown, the influence of pre-existing and emergent defects during high current stress on NW properties will be investigated. Acute sensitivity of NW thermal conductivity to point-defect density is expected due to the lack of threading dislocation (TD) gettering sites, and enhanced phonon-surface scattering further inhibits thermal transport. Excess defect creation during Joule heating could further degrade thermal conductivity, producing a viscous cycle culminating in catastrophic breakdown. To investigate these issues, a unique combination of electron microscopy, scanning luminescence and photoconductivity implemented at the nanoscale will be used in concert with sophisticated molecular-dynamics calculations of surface and defect-mediated NW thermal transport. This proposal seeks to elucidate long standing material science questions for GaN while addressing issues critical to realizing reliable GaN NW devices.

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Multiscale multiphysics problems arise in a host of application areas of significant relevance to DOE, including electrical storage systems (membranes and electrodes in fuel cells, batteries, and ultracapacitors), water surety, chemical analysis and detection systems, and surface catalysis. Multiscale methods aim to provide detailed physical insight into these complex systems by incorporating coupled effects of relevant phenomena on all scales. However, many sources of uncertainty and modeling inaccuracies hamper the predictive fidelity of multiscale multiphysics simulations. These include parametric and model uncertainties in the models on all scales, and errors associated with coupling, or information transfer, across scales/physics. This presentation introduces our work on the development of uncertainty quantification methods for spatially decomposed atomistic-to-continuum (A2C) multiscale simulations. The key thrusts of this research effort are: inference of uncertain parameters or observables from experimental or simulation data; propagation of uncertainty through particle models; propagation of uncertainty through continuum models; propagation of information and uncertainty across model/scale interfaces; and numerical and computational analysis and control. To enable the bidirectional coupling between the atomistic and continuum simulations, a general formulation has been developed for the characterization of sampling noise due to intrinsic variability in particle simulations, and for the propagation of both this sampling noise and parametric uncertainties through coupled A2C multiscale simulations. Simplified tests of noise quantification in particle computations are conducted through Bayesian inference of diffusion rates in an idealized isothermal binary material system. A proof of concept is finally presented based on application of the present formulation to the propagation of uncertainties in a model plane Couette flow, where the near wall region is handled with molecular dynamics while the bulk region is handled with continuum methods.

We present a material frame formulation analogous to the spatial frame formulation developed by Hardy, whereby expressions for continuum mechanical variables such as stress and heat flux are derived from atomic-scale quantities intrinsic to molecular simulation. This formulation is ideally suited for developing an atomistic-to-continuum correspondence for solid mechanics problems. We derive expressions for the first Piola-Kirchhoff (P-K) stress tensor and the material frame heat flux vector directly from the momentum and energy balances using localization functions in a reference configuration. The resulting P-K stress tensor, unlike the Cauchy expression, has no explicit kinetic contribution. The referential heat flux vector likewise lacks the kinetic contribution appearing in its spatial frame counterpart. Using a proof for a special case and molecular dynamics simulations, we show that our P-K stress expression nonetheless represents a full measure of stress that is consistent with both the system virial and the Cauchy stress expression developed by Hardy. We also present an expanded formulation to define continuum variables from micromorphic continuum theory, which is suitable for the analysis of materials represented by directional bonding at the atomic scale. © 2009 Elsevier Inc.

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Understanding charge transport processes at a molecular level using computational techniques is currently hindered by a lack of appropriate models for incorporating anistropic electric fields in molecular dynamics (MD) simulations. An important technological example is ion transport through solid-electrolyte interphase (SEI) layers that form in many common types of batteries. These layers regulate the rate at which electro-chemical reactions occur, affecting power, safety, and reliability. In this work, we develop a model for incorporating electric fields in MD using an atomistic-to-continuum framework. This framework provides the mathematical and algorithmic infrastructure to couple finite element (FE) representations of continuous data with atomic data. In this application, the electric potential is represented on a FE mesh and is calculated from a Poisson equation with source terms determined by the distribution of the atomic charges. Boundary conditions can be imposed naturally using the FE description of the potential, which then propagates to each atom through modified forces. The method is verified using simulations where analytical or theoretical solutions are known. Calculations of salt water solutions in complex domains are performed to understand how ions are attracted to charged surfaces in the presence of electric fields and interfering media.

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Materials with characteristic structures at nanoscale sizes exhibit significantly different mechanical responses from those predicted by conventional, macroscopic continuum theory. For example, nanocrystalline metals display an inverse Hall-Petch effect whereby the strength of the material decreases with decreasing grain size. The origin of this effect is believed to be a change in deformation mechanisms from dislocation motion across grains and pileup at grain boundaries at microscopic grain sizes to rotation of grains and deformation within grain boundary interface regions for nanostructured materials. These rotational defects are represented by the mathematical concept of disclinations. The ability to capture these effects within continuum theory, thereby connecting nanoscale materials phenomena and macroscale behavior, has eluded the research community. The goal of our project was to develop a consistent theory to model both the evolution of disclinations and their kinetics. Additionally, we sought to develop approaches to extract continuum mechanical information from nanoscale structure to verify any developed continuum theory that includes dislocation and disclination behavior. These approaches yield engineering-scale ex-pressions to quantify elastic and inelastic deformation in all varieties of materials, even those that possess highly directional bonding within their molecular structures such as liquid crystals, covalent ceramics, polymers and biological materials. This level of accuracy is critical for engineering design and thermo-mechanical analysis is performed in micro- and nano systems. The research proposed here innovates on how these nanoscale deformation mechanisms should be incorporated into a continuum mechanical formulation, and provides the foundation upon which to develop a means for predicting the performance of advanced engineering materials.