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.

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A cohesive zone, finite element fracture analysis is based upon a traction-separation relation. Our recent work has used molecular dynamics simulations to derive general traction-separation relationships for interfacial fracture between two brittle materials under mix-mode loading conditions. Here we apply our method to explore the effects of elastic constants of the two materials on the traction-separation relationship. A comparison and discussion of our results will be provided.

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 mechani-cal responses from those predicted by conventional, macroscopic continuum theory. For example,nanocrystalline metals display an inverse Hall-Petch effect whereby the strength of the materialdecreases with decreasing grain size. The origin of this effect is believed to be a change in defor-mation mechanisms from dislocation motion across grains and pileup at grain boundaries at mi-croscopic grain sizes to rotation of grains and deformation within grain boundary interface regionsfor nanostructured materials. These rotational defects are represented by the mathematical conceptof disclinations. The ability to capture these effects within continuum theory, thereby connectingnanoscale 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 ofdisclinations and their kinetics. Additionally, we sought to develop approaches to extract contin-uum mechanical information from nanoscale structure to verify any developed continuum theorythat 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 thatpossess highly directional bonding within their molecular structures such as liquid crystals, cova-lent ceramics, polymers and biological materials. This level of accuracy is critical for engineeringdesign and thermo-mechanical analysis is performed in micro- and nanosystems. The researchproposed here innovates on how these nanoscale deformation mechanisms should be incorporatedinto a continuum mechanical formulation, and provides the foundation upon which to develop ameans for predicting the performance of advanced engineering materials.4 AcknowledgmentThe authors acknowledge helpful discussions with Farid F. Abraham, Youping Chen, Terry J.Delph, Remi Dingreville, James W. Foulk III, Robert J. Hardy, Richard Lehoucq, Alejandro Mota,Gregory J. Wagner, Edmund B. Webb III and Xiaowang Zhou. Support for this project was pro-vided by the Enabling Predictive Simulation Investment Area of Sandia's Laboratory DirectedResearch and Development (LDRD) program.5

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