We perform a comprehensive first-principles statistical mechanical study of the thermodynamic and kinetic properties of two separate materials systems with very different applications using a collection of reliable computational methods.
Anatase TiO2 can be lithiated to LixTiO2 and has thus been a candidate material for Li-ion battery electrodes for quite some time. We establish that the experimentally observed step in the voltage vs lithium composition curve between x = 0.5 and 0.6 is due to Li ordering. Furthermore, we predict that full lithiation of anatase TiO2 is thermodynamically possible at positive voltages but that there is an enormous difference in Li diffusion coefficients in the dilute and fully lithiated forms of TiO2, providing an explanation for the limited capacity in large electrode particles. We also predict that Li diffusion in the ordered phase (Li0.5TiO2) is strictly one-dimensional. The TiO2 to Li0.5TiO2 phase transition has much in common with shape memory alloys. Crystallographically, it can support strain invariant interfaces separating TiO2 and Li0.5TiO2 within the same particle. The strain invariant interfaces are parallel to the one-dimensional diffusion direction in Li0.5TiO2, which, we argue, has important consequences for the role of particle shape on achievable capacity, charge and discharge rates, and hysteresis.
The titanium-aluminum alloy system has many important structural applications in the automotive and aerospace realms. Variations in alloy concentration or the degree of short or long range order affect the vacancy concentration and thereby the mobility of the constituents of the alloy. Here we develop statistical mechanical methods to predict the thermodynamic properties of vacancies within multi-component solids from first principles. We introduce a coarse graining procedure that enables the prediction of very dilute vacancy concentrations and their associated thermodynamic properties with Monte Carlo simulations. We apply this approach to a study of vacancies in HCP based Ti-Al binary alloys to explore the role of variations in both short range and long range order on the equilibrium vacancy concentration. We find a strong dependence of the equilibrium vacancy concentration on Al concentration and degree of long range order, especially at low temperature.PhDMaterials Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/110441/1/aabelak_1.pd
