Lithium-ion batteries are the batteries of choice for diverse applications, especially for those sensitive to size and weight, such as portable electronics and electric cars. At the heart of a Lithium-ion battery is a challenging problem that couples electrochemistry and mechanics. Each electrode in a Lithium-ion battery is a host for Lithium, absorbing or exuding Lithium when the battery is charged and discharged. Repeated lithiation and delithiation induce cyclic deformation and possibly fracture, a mechanism known to cause the capacity of the battery to fade. Lithiation-induced deformation and fracture is a bottleneck in developing batteries of high capacity. This project will develop theory and conduct experiments to study effects of anisotropic insertion, particle size and changing rate. Furthermore, the project will formulate a theory of coupled mass transport and deformation in inelastic hosts, and use the theory to study co-evolution of stress, Lithium concentration, and surface morphology, a phenomenon reported in recent literature.

Given the role of batteries to the society undergoing a profound transformation in its attitude toward environment and resources, the integration of mechanics and electrochemistry is timely. The PIs have already begun to integrate electrochemistry into a course in mechanics, and posted course materials online. The educational impact of this project is already evident from the enthusiasm of the graduate students in the PIs' groups. Their imagination is captured by this unique opportunity to bring the discipline of mechanics to the heart of a technology that will transform society.

Project Report

This project is a joint experimental and theoretical study on the stress and deformation caused by insertion reactions in lithium ion batteries. Lithium ion batteries, owing to their high energy densities, have rapidly become the batteries of choice for portable electronics. Companies worldwide are racing to develop lithium ion batteries for electric cars. At the heart of a lithium ion battery is a challenging mechanics problem. The battery works by insertion reactions, by which electrodes absorb a large amount of lithium. When the battery is being charged, lithium ions are extracted from the positive electrode and inserted into the negative electrode. When the battery is being discharged, the process goes in the opposite direction, performing usable work. A large number of charge/discharge cycles are needed for the battery to be economically viable. The insertion and extraction cause the electrodes to swell or contract, which may lead to fracture, a mechanism for capacity fading. An understanding of how an electrode sustains a large swelling without degradation holds great promise for the future of high-density batteries. The objective of this project, then, is to understand the mechanisms of deformation, stress development, and fracture associated with lithiation reactions in electrodes of Li ion batteries based on theoretical and experimental studies. To achieve these goals, a continuum model was developed that couples chemistry and mechanics and that enables quantitative predictions about the deformations and stresses that develop during lithiation of the electrodes in the battery. This model demonstrates that using a soft material can effectively mitigate the fracture of electrodes. The model also predicts a critical feature size below which no fracture occurs and that this feature size decreases with increasing charge rate. Several different anode designs have been analyzed: hollow core-shell nanostructures and one-dimensional nanofibers. In both cases, experimentally observed fracture modes are in good agreement with theoretical predictions. The model is generally valid if transport of lithium in the electrode is controlled by diffusion. In the special case of an electrode that consists of crystalline silicon, the initial lithiation process is controlled by a reaction in which silicon is amorphized and lithiated at the same time. This process is described by a model of concurrent reaction and plasticity. Experiments then confirmed that the lithiation of crystalline silicon is indeed reaction-controlled as opposed to diffusion-controlled under the usual experimental conditions, and that silicon undergoes significant plastic deformation upon lithiation. Plasticity at room temperature in a brittle material is very unusual. To better understand this process a first-principles study was performed to elucidate the mechanism by which this happens. This study demonstrated that when four Li atoms surround a single Si-Si bond the covalent bond readily breaks and the two Si dangling bonds are essentially saturated by the formation of weak bonds with the nearby Li atoms. Plasticity then occurs by a dynamic process of lithium-mediated breaking and reforming of Si bonds. When single-crystalline silicon is lithiated, the silicon expands at different rates in different directions. This study demonstrated that this anisotropic expansion is a consequence, not of anisotropic diffusion as assumed in the past, but of an anisotropic reaction rate. Both experiments and a first-principles study were conducted to confirm this observation. Finally, experiments were performed to measure material parameters such as stiffness, flow stress, and resistance to fracture. These parameters along with the coupled field theory allow quantitative predictions of the behavior of silicon anodes. The results of this study were published in fourteen archival journal papers and were presented at several conferences, companies and academic institutions by the Principal Investigators and their graduate students. The results were also presented on iMechanica, a popular web site for mechanicians that was founded by one of the Principal Investigators.

National Science Foundation (NSF)
Division of Civil, Mechanical, and Manufacturing Innovation (CMMI)
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Thomas Siegmund
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Harvard University
United States
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