Katsuyo Thornton

Quantum dot formation on a strain-patterned epitaxial thin film

We model the effect of substrate strain patterning on the self-assembly of quantum dots (QDs). When the surface energy is isotropic, we demonstrate that strain patterning via embedded substrate inclusions may result in ordered, self-organized QD arrays. However, for systems with strong cubic surface energy anisotropy, the same patterning does not readily lead to an ordered array of pyramids at long times. We conclude that the form of the surface energy anisotropy strongly influences the manner in which QDs self-assemble into regular arrays.

Energy Input and Mass Redistribution by Supernovae in the Interstellar Medium

We present the results of numerical studies of supernova remnant evolution and its effects on galactic and globular cluster evolution. We show that parameters such as the density and the metallicity of the environment significantly influence the evolution of the remnant and thus change its effects on the global environment (e.g., globular clusters, galaxies) as a source of thermal and kinetic energy. We conducted our studies using a one-dimensional hydrodynamics code, in which we implemented a metallicity-dependent cooling function. Global time-dependent quantities such as the total kinetic and thermal energies and the radial extent are calculated for a grid of parameter sets. The quantities calculated are the total energy, the kinetic energy, the thermal energy, the radial extent, and the mass. We distinguished between the hot, rarefied bubble and the cold, dense shell, since these two phases are distinct in their roles in a gas-stellar system. We also present power-law fits to those quantities as a function of environmental parameters after the extensive cooling has ceased. The power-law fits enable simple incorporation of improved supernova energy input and matter redistribution (including the effect of the local conditions) in galactic/globular cluster models. Our results for the energetics of supernova remnants in the late stages of their expansion give total energies ranging from ≈ 9 × 1049 to ≈ 3 × 1050 ergs, with a typical case being ≈ 1050 ergs, depending on the surrounding environment. About 8.5 × 1049 ergs of this energy can be found in the form of kinetic energy. Supernovae play an important role in the evolution of the interstellar medium and galaxies as a whole, providing mechanisms for kinetic energy input and for phase transitions of the interstellar medium. However, we have found that the total energy input per supernova is about 1 order of magnitude smaller than the initial explosion energy.

Tracking lithium transport and electrochemical reactions in nanoparticles

Expectations for the next generation of lithium batteries include greater energy and power densities along with a substantial increase in both calendar and cycle life. Developing new materials to meet these goals requires a better understanding of how electrodes function by tracking physical and chemical changes of active components in a working electrode. Here we develop a new, simple in-situ electrochemical cell for the transmission electron microscope and use it to track lithium transport and conversion in FeF(2) nanoparticles by nanoscale imaging, diffraction and spectroscopy. In this system, lithium conversion is initiated at the surface, sweeping rapidly across the FeF(2) particles, followed by a gradual phase transformation in the bulk, resulting in 1-3 nm iron crystallites mixed with amorphous LiF. The real-time imaging reveals a surprisingly fast conversion process in individual particles (complete in a few minutes), with a morphological evolution resembling spinodal decomposition. This work provides new insights into the inter- and intra-particle lithium transport and kinetics of lithium conversion reactions, and may help to pave the way to develop high-energy conversion electrodes for lithium-ion batteries.

Dendrites and Pits: Untangling the Complex Behavior of Lithium Metal Anodes through Operando Video Microscopy

Enabling ultra-high energy density rechargeable Li batteries would have widespread impact on society. However the critical challenges of Li metal anodes (most notably cycle life and safety) remain unsolved. This is attributed to the evolution of Li metal morphology during cycling, which leads to dendrite growth and surface pitting. Herein, we present a comprehensive understanding of the voltage variations observed during Li metal cycling, which is directly correlated to morphology evolution through the use of operando video microscopy. A custom-designed visualization cell was developed to enable operando synchronized observation of Li metal electrode morphology and electrochemical behavior during cycling. A mechanistic understanding of the complex behavior of these electrodes is gained through correlation with continuum-scale modeling, which provides insight into the dominant surface kinetics. This work provides a detailed explanation of (1) when dendrite nucleation occurs, (2) how those dendrites evolve as a function of time, (3) when surface pitting occurs during Li electrodissolution, (4) kinetic parameters that dictate overpotential as the electrode morphology evolves, and (5) how this understanding can be applied to evaluate electrode performance in a variety of electrolytes. The results provide detailed insight into the interplay between morphology and the dominant electrochemical processes occurring on the Li electrode surface through an improved understanding of changes in cell voltage, which represents a powerful new platform for analysis.

Designing the next generation high capacity battery electrodes

Much of current research in electrochemical energy storage is devoted to new electrode chemistries and reaction mechanisms that promise substantial increases in energy density. Unfortunately, most high capacity electrodes exhibit an unacceptably large hysteresis in their voltage profile. Using a first-principles multi-scale approach to examine particle level dynamics, we identify intrinsic thermodynamic and kinetic properties that are responsible for the large hysteresis exhibited by many high capacity electrodes. Our analysis shows that the hysteresis in the voltage profile of high capacity electrodes that rely on displacement reactions arises from a difference in reaction paths between charge and discharge. We demonstrate that different reaction paths are followed (i) when there is a large mismatch in ionic mobilities between the electrochemically active species (e.g. Li) and displaced ionic species and (ii) when there is a lack of a thermodynamic driving force to redistribute displaced ions upon charging of the electrode. These insights motivate the formulation of design metrics for displacement reactions in terms of fundamental properties determined by the chemistry and crystallography of the electrode material, properties that are now readily accessible with first-principles computation.

Extended smoothed boundary method for solving partial differential equations with general boundary conditions on complex boundaries

In this paper, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A continuous function, the domain parameter, is used to modify the original differential equations such that the equations are solved in the region where a domain parameter takes a specified value while boundary conditions are imposed on the region where the value of the domain parameter varies smoothly across a short distance. The mathematical derivations are straightforward and applicable to a wide variety of partial differential equations. To demonstrate the general applicability of the approach, we provide four examples herein: (1) the diffusion equation with both Neumann and Dirichlet boundary conditions; (2) the diffusion equation with both surface diffusion and reaction; (3) the mechanical equilibrium equation; and (4) the equation for phase transformation with the presence of additional boundaries. The solutions for several of these cases are validated against numerical solutions of the corresponding sharp-interface equations. The potential of the approach is demonstrated with five applications: surface-reaction?diffusion kinetics with a complex geometry, Kirkendall-effect-induced deformation, thermal stress in a complex geometry, phase transformations affected by substrate surfaces and relaxation of a droplet on irregular surfaces.

Theory of grain boundary diffusion induced by the Kirkendall effect

A set of coupled diffusion equations is numerically solved to demonstrate that grain boundary diffusion is significantly enhanced when diffusing atomic species have dissimilar atomic hop frequencies in the bulk. The model is based on a rigorous treatment of two-component substitutional diffusion where vacancies are treated as an additional species. By examining the concentration fields and the eigenvalues of the diffusivity matrix, the origin of the enhanced grain boundary diffusion is explained in terms of the Kirkendall effect.

Electrochemical Stability Window of Imidazolium-Based Ionic Liquids as Electrolytes for Lithium Batteries

This paper presents the computational assessment of the electrochemical stability of a series of alkyl methylimidazolium-based ionic liquids for their use as lithium battery electrolytes. The oxidation and reduction potentials of the constituent cation and anion of each ionic liquid with respect to a Li(+)/Li reference electrode were calculated using density functional theory following the method of thermodynamic cycles, and the electrochemical stability windows (ESW)s of these ionic liquids were obtained. The effect of varying the length of alkyl side chains of the methylimidazolium-based cations on the redox potentials and ESWs was investigated. The results show that the limits of the ESWs of these methylimidazolium-based ionic liquids are defined by the oxidation potential of the anions and the reduction potential of alkyl-methylimidazolium cations. Moreover, ionic liquids with [PF6](-) anion have a wider ESW. In addition to characterizing structure-function relationships, the accuracy of the computational approach was assessed through comparisons of the data against experimental measurements of ESWs. The potentials calculated by the thermodynamic cycle method are in good agreement with the experimental data while the HOMO/LUMO method overestimates the redox potentials. This work demonstrates that these approaches can provide guidance in selecting ionic liquid electrolytes when designing high-voltage rechargeable batteries.

The Kirkendall effect in the phase field crystal model

The Kirkendall effect stems from unequal mobilities of atomic species, which give rise to a net flux of vacancies during interdiffusion in substitutional alloys. In this work, we study a simple binary phase field crystal model to include unequal atomic mobilities and demonstrate that the model captures many phenomena associated with the Kirkendall effect, including the center of mass motion, vacancy supersaturation that can lead to pore formation, and enhanced vacancy concentration near grain boundaries.

The topology and morphology of bicontinuous interfaces during coarsening

We investigate the late-stage coarsening of three-dimensional two-phase mixtures via conserved dynamics over a range of volume fractions. We find that the phases remain bicontinuous at volume fractions as low as 36%. The morphologies of these bicontinuous structures depend on the volume fraction, and they differ from the corresponding structure of a symmetric mixture coarsening via nonconserved dynamics. However, these structures have nearly the same scaled genus of approximately 0.13, possibly indicating a universality in the topology of bicontinous structures undergoing self-similar coarsening.