Knowledge of the elastic properties of Li–Si alloys as a function of Li concentration is crucial in the development of reliable deformation and fracture mechanics models for Si anodes in Li-ion batteries. Here, we have studied these properties using first-principles calculations for both amorphous and crystalline phases observed during lithiation of Si anodes. In the case of crystalline alloys, we present the anisotropic elastic tensors as well as the homogenized Young's, shear, and bulk moduli and the Poisson's ratios. We find that while these moduli decrease in an approximately linear manner with increasing Li concentration leading to significant elastic softening (by about one order of magnitude) in both crystalline and amorphous systems, the Poisson's ratios remain in the range of 0.05–0.20 and 0.20–0.30 in the case of crystalline and amorphous systems, respectively. Further, for a given Li concentration, we find that the amorphous structures are elastically somewhat softer than their crystalline counterparts, the difference being more significant (about 30–40%) in Li-poor phases. Our results underscore the importance of including the concentration dependence of elastic constants in the analysis of stress and deformation fields during lithiation and de-lithiation of Si anodes.

http://ma.ecsdl.org/content/MA2010-02/11/1135.full.pdf

Elastic Softening of Amorphous and Crystalline Li-Si Phases with Increasing Li Concentration: A First-Principles Study

Li deposition is observed and measured on a solid electrolyte in the vicinity of a metallic current collector. Four types of ion-conducting, inorganic solid electrolytes are tested: Amorphous 70/30 mol% Li2S-P2S5, polycrystalline β-Li3PS4, and polycrystalline and single-crystalline Li6La3ZrTaO12 garnet. The nature of lithium plating depends on the proximity of the current collector to defects such as surface cracks and on the current density. Lithium plating penetrates/infiltrates at defects, but only above a critical current density. Eventually, infiltration results in a short circuit between the current collector and the Li-source (anode). These results do not depend on the electrolytes shear modulus and are thus not consistent with the Monroe–Newman model for “dendrites.” The observations suggest that Li-plating in pre-existing flaws produces crack-tip stresses which drive crack propagation, and an electrochemomechanical model of plating-induced Li infiltration is proposed. Lithium short-circuits through solid electrolytes occurs through a fundamentally different process than through liquid electrolytes. The onset of Li infiltration depends on solid-state electrolyte surface morphology, in particular the defect size and density.

Mechanism of Lithium Metal Penetration through Inorganic Solid Electrolytes

http://ma.ecsdl.org/content/MA2011-02/17/1343.full.pdf

Stress Mitigation during the Lithiation of Patterned Amorphous Si Islands for Li-Ion Batteries

Status and challenges facing representative anode materials for rechargeable lithium batteries

Monitoring in real time the stress state in high capacity electrodes during charge-discharge processes is pivotal to the performance assessment and structural optimization of advanced batteries. The wafer curvature measurement technique broadly employed in thin-film industry, together with stress analysis using the Stoney equation, has been successfully adopted to measure in situ the stress in thin film electrodes. How large plastic deformation or interfacial delamination during electrochemical cycles in such electrodes affects the applicability of Stoney equation remains unclear. Here we develop a robust electrochemical-mechanical coupled numerical procedure to investigate the influence of large plastic deformation and interfacial failure on the measured stress in thin film electrodes. We identify how the constitutive behavior of electrode materials and film-substrate interfacial properties affect the measured stress-capacity curves of electrodes, and hence establish the relationship of electrode material parameters with the characteristics of stress-capacity curves. Using Li-ions batteries as examples, we show that plastic deformation and interfacial delamination account for the asymmetric stress-capacity loops seen in in situ stress measurements. The methods used here, along with the finite-element code in the supplementary material, may be used to model the electrode behavior as a function of the state of charge.

Stress evolution in elastic-plastic electrodes during electrochemical processes: A numerical method and its applications

Silicon nanotube anodes are notably promising for high-performance lithium-ion batteries due to their outstanding structural stability, but fundamental understanding about their structural evolution during lithiation still remains unclear. Here, the expansion and fracture behavior of lithiated silicon nanotubes is investigated, and the influences of the crystal phase, crystal orientation, inner radius, wall thickness, and thickness–radius ratio are demonstrated. Experiments and simulations demonstrate anisotropic expansion and outer-surface fractures of crystalline silicon nanotubes and isotropic expansion of amorphous ones. The inner holes of nanotubes undergo much less expansion than the outside. The fracture ratio and the maximum hoop stress are positively correlated with both wall thickness and inner radius for crystalline silicon nanotubes. Their competition gives rise to an optimal thickness–outer radius ratio of about 2/3, and the critical diameter reaches 700 nm correspondingly. This research provides significant insight into the lithiation behavior of silicon nanotubes, which could help to design improved silicon anodes.

Anisotropic expansion and size-dependent fracture of silicon nanotubes during lithiation

Precise understanding on the temperature and time-dependent deformation in lithium-metal anode is of compelling need for durable service of Li-based batteries. Due to both temporal and spatial intertwined thermal agitations and the scarcity of experiments, faithful deformation map of Li-metal covering a broad range of service condition is still lacking. Here we design a physics-driven machine learning (PD-ML) algorithm to map the temperature, stress and rate-dependent deformation in Li-metal. We demonstrate that the PD-ML model, fed with limited experimental results, can predict the mechanical response of Li-metal in a wide span of temperature and deformation rate, and help to realize a deformation map of Li-metal with high fidelity. A finite element (FE) procedure based on the PD-ML constitutive model is then developed. The integration of PD-ML with FE procedure inherits the power of FE analysis and the accuracy originated from PD-ML in describing temperature, stress and rate-dependent mechanical response of Li-metal. The method introduced here paves a new way for constitutive modelling to capture the complex deformation in solids involving multi-field and multiscale mechanics.

Jici Wen

Papers

Stress evolution in elastic-plastic electrodes during electrochemical processes: A numerical method and its applications

Anisotropic expansion and size-dependent fracture of silicon nanotubes during lithiation

Physics-driven machine learning model on temperature and time-dependent deformation in lithium metal and its finite element implementation

Examining the validity of Stoney-equation for in-situ stress measurements in thin film electrodes using a large-deformation finite-element procedure

Linear correlation between state-of-health and incremental state-of-charge in Li-ion batteries and its application to SoH evaluation