First Principles Modeling of the Thermodynamic and Kinetic Properties of Anatase LixTiO2 and the Ti-Al Alloy System With Dilute Vacancies.

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

Kinetics of Anatase Electrodes: The Role of Ordering, Anisotropy, and Shape Memory Effects

We perform a comprehensive first-principles statistical mechanical study of the thermodynamic and kinetic properties of lithiated anatase Li_<i>x</i>TiO₂. We establish that the experimentally observed step in the voltage vs lithium composition curve between <i>x</i> = 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 (Li_0.5TiO₂) is strictly one-dimensional. The TiO₂ to Li_0.5TiO₂ phase transition has much in common with shape memory alloys. Crystallographically, it can support strain invariant interfaces separating TiO₂ and Li_0.5TiO₂ within the same particle. The strain invariant interfaces are parallel to the one-dimensional diffusion direction in Li_0.5TiO₂, which, we argue, has important consequences for the role of particle shape on achievable capacity, charge and discharge rates, and hysteresis

Kinetics of Anatase Electrodes: The Role of Ordering, Anisotropy, and Shape Memory Effects

We perform a comprehensive first-principles statistical mechanical study of the thermodynamic and kinetic properties of lithiated anatase Li_<i>x</i>TiO₂. We establish that the experimentally observed step in the voltage vs lithium composition curve between <i>x</i> = 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 (Li_0.5TiO₂) is strictly one-dimensional. The TiO₂ to Li_0.5TiO₂ phase transition has much in common with shape memory alloys. Crystallographically, it can support strain invariant interfaces separating TiO₂ and Li_0.5TiO₂ within the same particle. The strain invariant interfaces are parallel to the one-dimensional diffusion direction in Li_0.5TiO₂, which, we argue, has important consequences for the role of particle shape on achievable capacity, charge and discharge rates, and hysteresis

Financial aggregates for identifying the recessions in the financial market

В статье проведено обобщение финансовых агрегатов, идентифицирующих снижения устойчивости финансового рынка. На основе пробит-анализа выявлены финансовые агрегаты, которые наилучшим образом идентифицируют рецессию в финансовом секторе экономики.The financial aggregates identifying decrease in stability of the financial market are summarized. Based on probit analysis the financial aggregates that are the best for identifying the recession in the financial sector are extracted

Thermodynamics of Lithium in TiO₂(B) from First Principles

We use first-principles density functional theory (DFT) calculations combined with statistical mechanical techniques based on the cluster expansion method and Monte Carlo simulations to predict the lithium site occupancies, voltage curves, and phase diagram for TiO₂(B), a candidate anode material for lithium ion batteries. We find that Li intercalation is thermodynamically favorable up to a Li/Ti ratio of 1.25, higher than the theoretical maximum usually assumed for TiO₂. The calculated phase diagram at 300 K contains three first-order phase transformations corresponding to major changes in the favored intercalation sites at increasing Li concentrations. Calculations based on DFT predict the stability of a new Li site at high Li concentrations in TiO₂(B) and the occurrence of a dramatic site-inversion as Li is added to the host

Thermodynamics of Lithium in TiO₂(B) from First Principles

We use first-principles density functional theory (DFT) calculations combined with statistical mechanical techniques based on the cluster expansion method and Monte Carlo simulations to predict the lithium site occupancies, voltage curves, and phase diagram for TiO₂(B), a candidate anode material for lithium ion batteries. We find that Li intercalation is thermodynamically favorable up to a Li/Ti ratio of 1.25, higher than the theoretical maximum usually assumed for TiO₂. The calculated phase diagram at 300 K contains three first-order phase transformations corresponding to major changes in the favored intercalation sites at increasing Li concentrations. Calculations based on DFT predict the stability of a new Li site at high Li concentrations in TiO₂(B) and the occurrence of a dramatic site-inversion as Li is added to the host

Thermodynamics of Lithium in TiO₂(B) from First Principles

We use first-principles density functional theory (DFT) calculations combined with statistical mechanical techniques based on the cluster expansion method and Monte Carlo simulations to predict the lithium site occupancies, voltage curves, and phase diagram for TiO₂(B), a candidate anode material for lithium ion batteries. We find that Li intercalation is thermodynamically favorable up to a Li/Ti ratio of 1.25, higher than the theoretical maximum usually assumed for TiO₂. The calculated phase diagram at 300 K contains three first-order phase transformations corresponding to major changes in the favored intercalation sites at increasing Li concentrations. Calculations based on DFT predict the stability of a new Li site at high Li concentrations in TiO₂(B) and the occurrence of a dramatic site-inversion as Li is added to the host