Jishnu Bhattacharya

Understanding Li Diffusion in Li-Intercalation Compounds

Intercalation compounds, used as electrodes in Li-ion batteries, are a fascinating class of materials that exhibit a wide variety of electronic, crystallographic, thermodynamic, and kinetic properties. With open structures that allow for the easy insertion and removal of Li ions, the properties of these materials strongly depend on the interplay of the host chemistry and crystal structure, the Li concentration, and electrode particle morphology. The large variations in Li concentration within electrodes during each charge and discharge cycle of a Li battery are often accompanied by phase transformations. These transformations include order-disorder transitions, two-phase reactions that require the passage of an interface through the electrode particles, and structural phase transitions, in which the host undergoes a crystallographic change. Although the chemistry of an electrode material determines the voltage range in which it is electrochemically active, the crystal structure of the compound often plays a crucial role in determining the shape of the voltage profile as a function of Li concentration. While the relationship between the voltage profile and crystal structure of transition metal oxide and sulfide intercalation compounds is well characterized, far less is known about the kinetic behavior of these materials. For example, because these processes are especially difficult to isolate experimentally, solid-state Li diffusion, phase transformation mechanisms, and interface reactions remain poorly understood. In this respect, first-principles statistical mechanical approaches can elucidate the effect of chemistry and crystal structure on kinetic properties. In this Account, we review the key factors that govern Li diffusion in intercalation compounds and illustrate how the complexity of Li diffusion mechanisms correlates with the crystal structure of the compound. A variety of important diffusion mechanisms and associated migration barriers are sensitive to the overall Li concentration, resulting in diffusion coefficients that can vary by several orders of magnitude with changes in the lithium content. Vacancy clusters, groupings of vacancies within the crystal lattice, provide a common mechanism that mediates Li diffusion in important intercalation compounds. This mechanism emerges from specific crystallographic features of the host and results in a strong decrease of the Li diffusion coefficient as Li is added to an already Li rich host. Other crystallographic and electronic factors, such as the proximity of transition metal ions to activated states of hops and the occurrence of electronically induced distortions, can result in a strong dependence of the Li mobility on the overall Li concentration. The insights obtained from fundamental studies of ionic diffusion in electrode materials will be instrumental for physical chemists, chemical engineers, synthetic chemists, and materials and device designers who are developing these technologies.

Linking the electronic structure of solids to their thermodynamic and kinetic properties

Predicting measurable thermodynamic and kinetic properties of solids from first-principles requires the use of statistical mechanics. A major challenge for materials of technological importance arises from the fact that first-principles electronic structure calculations of elementary excited states are computationally very demanding. Hence statistical mechanical averaging over the spectrum of excited states must rely on the use of effective Hamiltonians that are parameterized by a limited number of first-principles electronic structure calculations, but nevertheless predict energies of excited states with a high level accuracy. Here we review important effective Hamiltonians that account for vibrational and configurational degrees of freedom in multi-component crystalline solids and show how they can be used to predict phase stability as a function of composition and temperature as well as kinetic transport constants such as diffusion coefficients in non-dilute crystalline solids.

Designing the next generation high capacity battery electrodes

Much of current research in electrochemical energy storage is devoted to new electrode chemistries and reaction mechanisms that promise substantial increases in energy density. Unfortunately, most high capacity electrodes exhibit an unacceptably large hysteresis in their voltage profile. Using a first-principles multi-scale approach to examine particle level dynamics, we identify intrinsic thermodynamic and kinetic properties that are responsible for the large hysteresis exhibited by many high capacity electrodes. Our analysis shows that the hysteresis in the voltage profile of high capacity electrodes that rely on displacement reactions arises from a difference in reaction paths between charge and discharge. We demonstrate that different reaction paths are followed (i) when there is a large mismatch in ionic mobilities between the electrochemically active species (e.g. Li) and displaced ionic species and (ii) when there is a lack of a thermodynamic driving force to redistribute displaced ions upon charging of the electrode. These insights motivate the formulation of design metrics for displacement reactions in terms of fundamental properties determined by the chemistry and crystallography of the electrode material, properties that are now readily accessible with first-principles computation.

Relative stability of normal vs. inverse spinel for 3d transition metal oxides as lithium intercalation cathodes

Spinel oxides represent an important class of cathode materials for Li-ion batteries. Two major variants of the spinel crystal structure are normal and inverse. The relative stability of normal and inverse ordering at different stages of lithiation has important consequences in lithium diffusivity, voltage, capacity retention and battery life. In this paper, we investigate the relative structural stability of normal and inverse structures of the 3d transition metal oxide spinels with first-principles DFT calculations. We have considered ternary spinel oxides LixM2O4 with M = Ti, V, Cr, Mn, Fe, Co and Ni in both lithiated (x = 1) and delithiated (x = 0) conditions. We find that for all lithiated spinels, the normal structure is preferred regardless of the metal. We observe that the normal structure for all these oxides has a lower size mismatch between octahedral cations compared to the inverse structure. With delithiation, many of the oxides undergo a change in stability with vanadium in particular, showing a tendency to occupy tetrahedral sites. We find that in the delithiated oxide, only vanadium ions can access a +5 oxidation state which prefers tetrahedral coordination. We have also calculated the average voltage of lithiation for these spinels. The calculated voltages agree well with the previously measured and calculated values, wherever available. For the yet to be characterized spinels, our calculation provides voltage values which can motivate further experimental attention. Lastly, we observe that all the normal spinel oxides of the 3d transition metal series have a driving force for a transformation to the non-spinel structure upon delithiation.

An Enthalpy Model for Simulation of Dendritic Growth

In this article we present an enthalpy-based simulation for the evolution of equiaxial dendrites, growing in an undercooled melt of a pure substance. The enthalpy formulation, which is used extensively for macroscale modeling of solidification, is modified appropriately by combining relevant macroscale and microscale features. An implicit finite-volume method is employed for the numerical solution of continuum equations (mass, momentum, and energy conservation equations). Microscale effects such as anisotropy, surface tension, and noise are incorporated through empirical rules, as implemented in existing cellular automaton models in the literature. In two dimensions, two problems are studied separately: The first is a diffusion-dominated case of dendrite growth, while the second consists of combined convection-diffusion effects. In order to illustrate the model capabilities, simulation results for dendritic growth under various conditions are presented. The results are compared with those employing other models found in the literature, and good qualitative agreement is observed.

Time-resolved spectral analysis of prompt emission from long gamma-ray bursts with GeV emission

We performed detailed time-resolved spectroscopy of bright long gamma-ray bursts (GRBs) which show significant GeV emissions (GRB 080916C, GRB 090902B and GRB 090926A). In addition to the standard Band model, we also use a model consisting of a black body and a power law to fit the spectra. We find that for the latter model there are indications of an additional soft component in the spectra. While previous studies have shown that such models are required for GRB 090902B, here we find that a composite spectral model consisting of two blackbodies and a power law adequately fits the data of all the three bright GRBs. We investigate the evolution of the spectral parameters and find several interesting features that appear in all three GRBs, like (a) temperatures of the blackbodies are strongly correlated with each other, (b) fluxes in the black body components are strongly correlated with each other, (c) the temperatures of the black body trace the profile of the individual pulses of the GRBs, and (d) the characteristics of power law components like the spectral index and the delayed onset bear a close similarity to the emission characteristics in the GeV regions. We discuss the implications of these results and the possibility of identifying the radiation mechanisms during the prompt emission of GRBs.