Lithium dendrite (filament) propagation through ceramic electrolytes, leading to short-circuits at high rates of charge, is one of the greatest barriers to realising high energy density all-solidstate lithium anode batteries. Utilising in-situ X-ray computed tomography coupled with spatially mapped X-ray diffraction, the propagation of cracks and the propagation of lithium dendrites through the solid electrolyte have been tracked in a Li/Li6PS5Cl/Li cell as a function of the charge passed. On plating, cracking initiates with spallation, conical "pothole"-like cracks that form in the ceramic electrolyte near the surface with the plated electrode. The spallations form predominantly at the lithium electrode edges where local fields are high. Transverse cracks then propagate from the spallations across the electrolyte from the plated to the stripped electrode. Lithium ingress drives the propagation of the spallation and transverse cracks by widening the crack from the rear, i.e. the crack front propagates ahead of the Li. As a result, cracks traverse the entire electrolyte before the Li arrives at the other electrode and therefore before a short-circuit occurs.

This paper presents a study of the nonequilibrium relaxation process of chemically reactive systems using steepest-entropy-ascent quantum thermodynamics (SEAQT). The trajectory of the chemical reaction, i.e., the accessible intermediate states, is predicted and discussed. The prediction is made using a thermodynamic-ensemble approach, which does not require detailed information about the particle mechanics involved (e.g., the collision of particles). Instead, modeling the kinetics and dynamics of the relaxation process is based on the principle of steepest-entropy ascent (SEA) or maximum-entropy production, which suggests a constrained gradient dynamics in state space. The SEAQT framework is based on general definitions for energy and entropy and at least theoretically enables the prediction of the nonequilibrium relaxation of system state at all temporal and spatial scales. However, to make this not just theoretically but computationally possible, the concept of density of states is introduced to simplify the application of the relaxation model, which in effect extends the application of the SEAQT framework even to infinite energy eigenlevel systems. The energy eigenstructure of the reactive system considered here consists of an extremely large number of such levels (on the order of 10^{130}) and yields to the quasicontinuous assumption. The principle of SEA results in a unique trajectory of system thermodynamic state evolution in Hilbert space in the nonequilibrium realm, even far from equilibrium. To describe this trajectory, the concepts of subsystem hypoequilibrium state and temperature are introduced and used to characterize each system-level, nonequilibrium state. This definition of temperature is fundamental rather than phenomenological and is a generalization of the temperature defined at stable equilibrium. In addition, to deal with the large number of energy eigenlevels, the equation of motion is formulated on the basis of the density of states and a set of associated degeneracies. Their significance for the nonequilibrium evolution of system state is discussed. For the application presented, the numerical method used is described and is based on the density of states, which is specifically developed to solve the SEAQT equation of motion. Results for different kinds of initial nonequilibrium conditions, i.e., those for gamma and Maxwellian distributions, are studied. The advantage of the concept of hypoequilibrium state in studying nonequilibrium trajectories is discussed.

This paper presents a nonequilibrium thermodynamic model for the relaxation of a local, isolated system in nonequilibrium using the principle of steepest entropy ascent (SEA), which can be expressed as a variational principle in thermodynamic state space. The model is able to arrive at the Onsager relations for such a system. Since no assumption of local equilibrium is made, the conjugate fluxes and forces, which result, are intrinsic to the subspaces of the system's state space and are defined using the concepts of hypoequilibrium state and nonequilibrium intensive properties, which describe the non-mutual equilibrium status between subspaces of the thermodynamic state space. The Onsager relations are shown to be a thermodynamic kinematic feature of the system independent of the specific details of the micro-mechanical dynamics. Two kinds of relaxation processes are studied with different constraints (i.e., conservation laws) corresponding to heat and mass diffusion. Linear behavior in the near-equilibrium region as well as nonlinear behavior in the far-from-equilibrium region are discussed. Thermodynamic relations in the equilibrium and nearequilibrium realm, including the Gibbs relation, the Clausius inequality, and the Onsager relations, are generalized to the far-from-equilibrium realm. The variational principle in the space spanned by the intrinsic conjugate fluxes and forces is expressed via the quadratic dissipation potential. As an application, the model is applied to the heat and mass diffusion of a system represented by a single particle ensemble, which can also be applied to a simple system of many particles. Phenomenological transport coefficients are also derived in near-equilibrium realm.

Li-ion batteries have revolutionized the portable electronics industry and empowered the electric vehicle (EV) revolution. Unfortunately, traditional Li-ion chemistry is approaching its physicochemical limit. The demand for higher density (longer range), high power (fast charging), and safer EVs has recently created a resurgence of interest in solid state batteries (SSB). Historically, research has focused on improving the ionic conductivity of solid electrolytes, yet ceramic solids now deliver sufficient ionic conductivity. The barriers lie within the interfaces between the electrolyte and the two electrodes, in the mechanical properties throughout the device, and in processing scalability. In 2017 the Faraday Institution, the UK’s independent institute for electrochemical energy storage research, launched the SOLBAT (solid-state lithium metal anode battery) project, aimed at understanding the fundamental science underpinning the problems of SSBs, and recognising that the paucity of such understanding is the major barrier to progress. The purpose of this Roadmap is to present an overview of the fundamental challenges impeding the development of SSBs, the advances in science and technology necessary to understand the underlying science, and the multidisciplinary approach being taken by SOLBAT researchers in facing these challenges. It is our hope that this Roadmap will guide academia, industry, and funding agencies towards the further development of these batteries in the future.