Deformation and fracture of silicon electrodes in lithium-ion batteries

We have performed a number of experiments to examine the mechanical behavior of amorphous silicon -electrodes of lithium-ion batteries. In particular, we have measured the fracture energy of lithiated silicon thin-film electrodes as a function of lithium concentration. The fracture energy is found to be similar to that of pure silicon and essentially independent of the concentration of lithium. Thus, although lithiated silicon can flow plastically, it appears to fracture in a brittle manner. We have also varied the rate of lithiation of amorphous silicon thin films while -simultaneously measuring stresses. Increasing the rate of lithiation resulted in a corresponding increase in the flow stress. These observations indicate that rate-sensitive plasticity occurs in a-Li × Si electrodes at room temperature and at charging rates typically used in lithium-ion batteries. Using a simple mechanical model, we have extracted material parameters from our experiments, finding a good fit to a power law relationship between the plastic strain rate and the stress. The observations of rate-sensitivity provide insight into the unusual ability of a-Li × Si to flow plastically while fracturing in a brittle manner. Moreover, the results have direct ramifications concerning the rate capabilities of silicon electrodes: faster charging rates (i.e., strain rates) result in larger stresses and hence larger driving forces for fracture

Diffusion, Deformation, and Damage in Lithium-Ion Batteries and Microelectronics

This thesis explores mechanical behavior of microelectronic devices and lithium-ion batteries. We first examine electromigration-induced void formation in solder bumps by constructing a theory that couples electromigration and creep. The theory can predict the critical current density below which voids do not form. Due to the effects of creep, this quantity is found to be independent of the solder size and decrease exponentially with increasing temperature, different from existing theories.Engineering and Applied Science

Variation of stress with charging rate due to strain-rate sensitivity of silicon electrodes of Li-ion batteries

Silicon is a promising anode material for lithium-ion batteries due to its enormous theoretical energy density. Fracture during electrochemical cycling has limited the practical viability of silicon electrodes, but recent studies indicate that fracture can be prevented by taking advantage of lithiation-induced plasticity. In this paper, we provide experimental insight into the nature of plasticity in amorphous LixSi thin films. To do so, we vary the rate of lithiation of amorphous silicon thin films and simultaneously measure stresses. An increase in the rate of lithiation results in a corresponding increase in the flow stress. These observations indicate that rate-sensitive plasticity occurs in a-LixSi electrodes at room temperature and at charging rates typically used in lithium-ion batteries. Using a simple mechanical model, we extract material parameters from our experiments, finding a good fit to a power law relationship between the plastic strain rate and the stress. These observations provide insight into the unusual ability of a-LixSi to flow plastically, but fracture in a brittle manner. Moreover, the results have direct ramifications concerning the rate-capabilities of silicon electrodes: faster charging rates (i.e., strain rates) result in larger stresses and hence larger driving forces for fracture.Engineering and Applied Science

ART-Owen Scrambling

We present a novel algorithm for implementing Owen-scrambling, combining the generation and distribution of the scrambling bits in a single self-contained compact process. We employ a context-free grammar to build a binary tree of symbols, and equip each symbol with a scrambling code that affects all descendant nodes. We nominate the grammar of adaptive regular tiles (ART) derived from the repetition-avoiding Thue-Morse word, and we discuss its potential advantages and shortcomings. Our algorithm has many advantages, including random access to samples, fixed time complexity, GPU friendliness, and scalability to any memory budget. Further, it provides two unique features over known methods: it admits optimization, and it is invertible, enabling screen-space scrambling of the high-dimensional Sobol sampler.Comment: To appear at SIGGRAPH Asia 202

A Generalized Ray Formulation For Wave-Optics Rendering

Under ray-optical light transport, the classical ray serves as a local and linear "point query" of light's behaviour. Such point queries are useful, and sophisticated path tracing and sampling techniques enable efficiently computing solutions to light transport problems in complex, real-world settings and environments. However, such formulations are firmly confined to the realm of ray optics, while many applications of interest, in computer graphics and computational optics, demand a more precise understanding of light. We rigorously formulate the generalized ray, which enables local and linear point queries of the wave-optical phase space. Furthermore, we present sample-solve: a simple method that serves as a novel link between path tracing and computational optics. We will show that this link enables the application of modern path tracing techniques for wave-optical rendering, improving upon the state-of-the-art in terms of the generality and accuracy of the formalism, ease of application, as well as performance. Sampling using generalized rays enables interactive rendering under rigorous wave optics, with orders-of-magnitude faster performance compared to existing techniques.Comment: For additional information, see https://ssteinberg.xyz/2023/03/27/rtplt

Microstructural evolution induced by micro-cracking during fast lithiation of single-crystalline silicon

h i g h l i g h t s Lithiation of Si results in various microstructures depending of crystal orientation. A complex vein-like microstructure of Li x Si was observed in {100} oriented Si. Micro-cracks provide a fast path for Li diffusion and cause a non-uniform lithiation. Crystalline Li x Si plays an important role in micro-crack generation. a r t i c l e i n f o t r a c t We report observations of microstructural changes in {100} and {110} oriented silicon wafers during initial lithiation under relatively high current densities. Evolution of the microstructure during lithiation was found to depend on the crystallographic orientation of the silicon wafers. In {110} silicon wafers, the phase boundary between silicon and Li x Si remained flat and parallel to the surface. In contrast, lithiation of the {100} oriented substrate resulted in a complex vein-like microstructure of Li x Si in a crystalline silicon matrix. A simple calculation demonstrates that the formation of such structures is energetically unfavorable in the absence of defects due to the large hydrostatic stresses that develop. However, TEM observations revealed micro-cracks in the {100} silicon wafer, which can create fast diffusion paths for lithium and contribute to the formation of a complex vein-like Li x Si network. This defect-induced microstructure can significantly affect the subsequent delithiation and following cycles, resulting in degradation of the electrode