DEVELOPMENT OF LI+ AND NA+ CONDUCTING CERAMICS AND CERAMIC STRUCTURES FOR USE IN SOLID STATE BATTERIES

A solid state lithium metal battery based on a lithium garnet material was developed, constructed and tested. Specifically, a porous-dense-porous trilayer structure was fabricated by tape casting, a roll-to-roll technique conducive to high volume manufacturing. The high density and thin center layer (< 20 μm) effectively blocks dendrites even over hundreds of cycles. The microstructured porous layers, serving as electrode supports, are demonstrated to increase the interfacial surface area available to the electrodes and increase cathode loading. Reproducibility of flat, well sintered ceramics was achieved with consistent powderbed lattice parameter and ball milling of powderbed. Together, the resistance of the LLCZN trilayer was measured at an average of 7.6 ohm-cm2 in a symmetric lithium cell, significantly lower than any other reported literature results. Building on these results, a full cell with a lithium metal anode, LLCZN trilayer electrolyte, and LiCoO2 cathode was cycled 100 cycles without decay and an average ASR of 117 ohm-cm2. After cycling, the cell was held at open circuit for 24 hours without any voltage fade, demonstrating the absence of a dendrite or short-circuit of any type. Cost calculations guided the optimization of a trilayer structure predicted that resulting cells will be highly competitive in the marketplace as intrinsically safe lithium batteries with energy densities greater than 300 Wh/kg and 1000 Wh/L for under $100/kWh. Also in the pursuit of solid state batteries, an improved Na+ superionic conductor (NASICON) composition, Na3Zr2Si2PO12, was developed with a conductivity of 1.9x10-3 S/cm. New super-lithiated lithium garnet compositions, Li7.06La3Zr1.94Y0.06O12 and Li7.16La3Zr1.84Y0.16O12, were developed and studied revealing insights about the mechanisms of conductivity in lithium garnets.

THE STOCHASTIC NAVIER STOKES EQUATIONS FOR HEAT CONDUCTING, COMPRESSIBLE FLUIDS

This dissertation is devoted to the equations of motion governing the evolution of a fluid or gas at the macroscopic scale. The classical model is a PDE description known as the Navier-Stokes equations. The behavior of solutions is notoriously complex, leading many in the scientific community to describe fluid mechanics using a statistical language. In the physics literature, this is often done in an ad-hoc manner with limited precision about the sense in which the randomness enters the evolution equation. The stochastic PDE community has begun proposing precise models, where a random perturbation appears explicitly in the evolution equation. Although this has been an active area of study in recent years, the existing literature is almost entirely devoted to incompressible fluids. The purpose of this thesis is to take a step forward in addressing this statistical perspective in the setting of compressible fluids. In particular, we study the well posedness for the corresponding system of Stochastic Navier Stokes equations, satisfied by the density, velocity, and temperature. The evolution of the momentum involves a random forcing which is Brownian in time and colored in space. We allow for multiplicative noise, meaning that spatial correlations may depend locally on the fluid variables. Our main result is a proof of global existence of weak martingale solutions to the Cauchy problem set within a bounded domain, emanating from large initial datum. The proof involves a mix of deterministic and stochastic analysis tools. Fundamentally, the approach is based on weak compactness techniques from the deterministic theory combined with martingale methods. Four layers of approximate stochastic PDE's are built and analyzed. A careful study of the probability laws of our approximating sequences is required. We prove appropriate tightness results and appeal to a recent generalization of the Skorohod theorem. This ultimately allows us to deduce analogues of the weak compactness tools of Lions and Feireisl, appropriately interpreted in the stochastic setting.