Publications

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This report describes an Engineering Sciences Research Foundation (ESRF) project to characterize and understand fracture processes via molecular dynamics modeling and atom-to-continuum methods. Under this aegis we developed new theory and a number of novel techniques to describe the fracture process at the atomic scale. These developments ranged from a material-frame connection between molecular dynamics and continuum mechanics to an atomic level J integral. Each of the developments build upon each other and culminated in a cohesive zone model derived from atomic information and verified at the continuum scale. This report describes an Engineering Sciences Research Foundation (ESRF) project to characterize and understand fracture processes via molecular dynamics modeling and atom-to-continuum methods. The effort is predicated on the idea that processes and information at the atomic level are missing in engineering scale simulations of fracture, and, moreover, are necessary for these simulations to be predictive. In this project we developed considerable new theory and a number of novel techniques in order to describe the fracture process at the atomic scale. Chapter 2 gives a detailed account of the material-frame connection between molecular dynamics and continuum mechanics we constructed in order to best use atomic information from solid systems. With this framework, in Chapter 3, we were able to make a direct and elegant extension of the classical J down to simulations on the scale of nanometers with a discrete atomic lattice. The technique was applied to cracks and dislocations with equal success and displayed high fidelity with expectations from continuum theory. Then, as a prelude to extension of the atomic J to finite temperatures, we explored the quasi-harmonic models as efficient and accurate surrogates of atomic lattices undergoing thermo-elastic processes (Chapter 4). With this in hand, in Chapter 5 we provide evidence that, by using the appropriate energy potential, the atomic J integral we developed is calculable and accurate at finite/room temperatures. In Chapter 6, we return in part to the fundamental efforts to connect material behavior at the atomic scale to that of the continuum. In this chapter, we devise theory that predicts the onset of instability characteristic of fracture/failure via atomic simulation. In Chapters 7 and 8, we describe the culmination of the project in connecting atomic information to continuum modeling. In these chapters we show that cohesive zone models are: (a) derivable from molecular dynamics in a robust and systematic way, and (b) when used in the more efficient continuum-level finite element technique provide results that are comparable and well-correlated with the behavior at the atomic-scale. Moreover, we show that use of these same cohesive zone elements is feasible at scales very much larger than that of the lattice. Finally, in Chapter 9 we describe our work in developing the efficient non-reflecting boundary conditions necessary to perform transient fracture and shock simulation with molecular dynamics.

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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.

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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 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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