Application of Numerical Methods to Study Arrangement and Fracture of Lithium-Ion Microstructure

The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.

We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.

We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.

The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.

Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.

The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.

Experimental Study of Storage Ring Free-Electron Laser with Novel Capabilities

The Duke Free-electron laser (FEL) system, driven by the Duke electron storage ring, has been at the forefront of developing new light source capabilities over the past two decades. In 1999, the Duke FEL demonstrated the first lasing of a storage ring FEL in the vacuum ultraviolet (VUV) region at $194$ nm using two planar OK-4 undulators. With two helical undulators added to the outboard sides of the planar undulators, in 2005 the highest FEL gain ($47.8\%$) of a storage ring FEL was achieved using the Duke FEL system with a four-undulator configuration. In addition, the Duke FEL has been used as the photon source to drive the High Intensity $\gamma$-ray Source (HIGS) via Compton scattering of the FEL beam and electron beam inside the FEL cavity. Taking advantage of FEL's wavelength tunability as well as the adjustability of the energy of the electron beam in the storage ring, the nearly monochromatic $\gamma$-ray beam has been produced in a wide energy range from $1$ to $100$ MeV at the HIGS. To further push the FEL short wavelength limit and enhance the FEL gain in the VUV regime for high energy $\gamma$-ray production, two additional helical undulators were installed in 2012 using an undulator switchyard system to allow switching between the two planar and two helical undulators in the middle section of the FEL system. Using different undulator configurations made possible by the switchyard, a number of novel capabilities of the storage ring FEL have been developed and exploited for a wide FEL wavelength range from infrared (IR) to VUV. These new capabilities will eventually be made available to the $\gamma$-ray operation, which will greatly enhance the $\gamma$-ray user research program, creating new opportunities for certain types of nuclear physics research.

With the wide wavelength tuning range, the FEL is an intrinsically well-suited device to produce lasing with multiple colors. Taking advantage of the availability of an undulator system with multiple undulators, we have demonstrated the first two-color lasing of a storage ring FEL. Using either a three- or four-undulator configuration with a pair of dual-band high reflectivity mirrors, we have achieved simultaneous lasing in the IR and UV spectral regions. With the low-gain feature of the storage ring FEL, the power generated at the two wavelengths can be equally built up and precisely balanced to reach FEL saturation. A systematic experimental program to characterize this two-color FEL has been carried out, including precise power control, a study of the power stability of two-color lasing, wavelength tuning, and the impact of the FEL mirror degradation. Using this two-color laser, we have started to develop a new two-color $\gamma$-ray beam for scientific research at the HIGS.

Using the undulator switchyard, four helical undulators installed in the beamline can be configured to not only enhance the FEL gain in the VUV regime, but also allow for the full polarization control of the FEL beams. For the accelerator operation, the use of helical undulators is essential to extend the FEL mirror lifetime by reducing radiation damage from harmonic undulator radiation. Using a pair of helical undulators with opposite helicities, we have realized (1) fast helicity switching between left- and right-circular polarizations, and (2) the generation of fully controllable linear polarization. In order to extend these new capabilities of polarization control to the $\gamma$-ray operation in a wide energy range at the HIGS, a set of FEL polarization diagnostic systems need to be developed to cover the entire FEL wavelength range. The preliminary development of the polarization diagnostics for the wavelength range from IR to UV has been carried out.