6 research outputs found
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<sub><i>x</i></sub>TiO<sub>2</sub>. 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 TiO<sub>2</sub> 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 TiO<sub>2</sub>, providing an explanation
for the limited capacity in large electrode particles. We also predict
that Li diffusion in the ordered phase (Li<sub>0.5</sub>TiO<sub>2</sub>) is strictly one-dimensional. The TiO<sub>2</sub> to Li<sub>0.5</sub>TiO<sub>2</sub> phase transition has much in common with shape memory
alloys. Crystallographically, it can support strain invariant interfaces
separating TiO<sub>2</sub> and Li<sub>0.5</sub>TiO<sub>2</sub> within
the same particle. The strain invariant interfaces are parallel to
the one-dimensional diffusion direction in Li<sub>0.5</sub>TiO<sub>2</sub>, 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<sub><i>x</i></sub>TiO<sub>2</sub>. 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 TiO<sub>2</sub> 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 TiO<sub>2</sub>, providing an explanation
for the limited capacity in large electrode particles. We also predict
that Li diffusion in the ordered phase (Li<sub>0.5</sub>TiO<sub>2</sub>) is strictly one-dimensional. The TiO<sub>2</sub> to Li<sub>0.5</sub>TiO<sub>2</sub> phase transition has much in common with shape memory
alloys. Crystallographically, it can support strain invariant interfaces
separating TiO<sub>2</sub> and Li<sub>0.5</sub>TiO<sub>2</sub> within
the same particle. The strain invariant interfaces are parallel to
the one-dimensional diffusion direction in Li<sub>0.5</sub>TiO<sub>2</sub>, 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
Π ΡΡΠ°ΡΡΠ΅ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ΠΎ ΠΎΠ±ΠΎΠ±ΡΠ΅Π½ΠΈΠ΅ ΡΠΈΠ½Π°Π½ΡΠΎΠ²ΡΡ
Π°Π³ΡΠ΅Π³Π°ΡΠΎΠ², ΠΈΠ΄Π΅Π½ΡΠΈΡΠΈΡΠΈΡΡΡΡΠΈΡ
ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΠΈ ΡΠΈΠ½Π°Π½ΡΠΎΠ²ΠΎΠ³ΠΎ ΡΡΠ½ΠΊΠ°. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΏΡΠΎΠ±ΠΈΡ-Π°Π½Π°Π»ΠΈΠ·Π° Π²ΡΡΠ²Π»Π΅Π½Ρ ΡΠΈΠ½Π°Π½ΡΠΎΠ²ΡΠ΅ Π°Π³ΡΠ΅Π³Π°ΡΡ, ΠΊΠΎΡΠΎΡΡΠ΅ Π½Π°ΠΈΠ»ΡΡΡΠΈΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠΌ ΠΈΠ΄Π΅Π½ΡΠΈΡΠΈΡΠΈΡΡΡΡ ΡΠ΅ΡΠ΅ΡΡΠΈΡ Π² ΡΠΈΠ½Π°Π½ΡΠΎΠ²ΠΎΠΌ ΡΠ΅ΠΊΡΠΎΡΠ΅ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΠΊΠΈ.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 TiO<sub>2</sub>(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 TiO<sub>2</sub>(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 TiO<sub>2</sub>. 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 TiO<sub>2</sub>(B) and the occurrence of a dramatic site-inversion as Li is added to the host
Thermodynamics of Lithium in TiO<sub>2</sub>(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 TiO<sub>2</sub>(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 TiO<sub>2</sub>. 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 TiO<sub>2</sub>(B) and the occurrence of a dramatic site-inversion as Li is added to the host
Thermodynamics of Lithium in TiO<sub>2</sub>(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 TiO<sub>2</sub>(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 TiO<sub>2</sub>. 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 TiO<sub>2</sub>(B) and the occurrence of a dramatic site-inversion as Li is added to the host