Coherency strain and the kinetics of phase separation in LiFePO4

A theoretical investigation of the effects of elastic coherency on the thermodynamics, kinetics, and morphology of intercalation in single LiFePO4 nanoparticles yields new insights into this important battery material. Anisotropic elastic stiffness and misfit strains lead to the unexpected prediction that low-energy phase boundaries occur along {101} planes, while conflicting reports of phase boundary orientations are resolved by a partial loss of coherency in the {100} direction. Elastic relaxation near surfaces leads to the formation of a striped morphology, whose characteristic length scale is predicted by the model and yields an estimate of the interfacial energy. The effects of coherency strain on solubility and galvanostatic discharge are studied with a reaction-limited phase-field model, which quantitatively captures the influence of misfit strain, particle size, and temperature on solubility seen in experiments. Coherency strain strongly suppresses phase separation during discharge, which enhances rate capability and extends cycle life. The effects of elevated temperature and the feasibility of nucleation are considered in the context of multi-particle cathodes

Theory of Nucleation in Phase-separating Nanoparticles

The basic physics of nucleation in solid \hl{single-crystal} nanoparticles is revealed by a phase-field theory that includes surface energy, chemical reactions and coherency strain. In contrast to binary fluids, which form arbitrary contact angles at surfaces, complete "wetting" by one phase is favored at binary solid surfaces. Nucleation occurs when surface wetting becomes unstable, as the chemical energy gain (scaling with area) overcomes the elastic energy penalty (scaling with volume). The nucleation barrier thus decreases with the area-to-volume ratio and vanishes below a critical size, and nanoparticles tend to transform in order of increasing size, leaving the smallest particles homogeneous (in the phase of lowest surface energy). The model is used to simulate phase separation in realistic nanoparticle geometries for \ce{Li_XFePO4}, a popular cathode material for Li-ion batteries, and collapses disparate experimental data for the nucleation barrier, with no adjustable parameters. Beyond energy storage, the theory generally shows how to tailor the elastic and surface properties of a solid nanostructure to achieve desired phase behavior.Comment: 7 pages, 4 fig

Size-dependent phase morphologies in LiFePO4 battery particles

Lithium iron phosphate (LiFePO$_4$) is the prototypical two-phase battery material, whose complex patterns of lithium ion intercalation provide a testing ground for theories of electrochemical thermodynamics. Using a depth-averaged (a-b plane) phase-field model of coherent phase separation driven by Faradaic reactions, we reconcile conflicting experimental observations of diamond-like phase patterns in micron-sized platelets and surface-controlled patterns in nanoparticles. Elastic analysis predicts this morphological transition for particles whose a-axis dimension exceeds the bulk elastic stripe period. We also simulate a rich variety of non-equilibrium patterns, influenced by size-dependent spinodal points and electro-autocatalytic control of thermodynamic stability

Thermodynamic phase-field model for microstructure with multiple components and phases: the possibility of metastable phases

A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition gradient energy to capture solute trapping, and is therefore suited for studying phenomena where the width of the interface plays an important role. Derivation of the inhomogeneous free energy functional from a Taylor expansion of homogeneous free energy reveals how the interfacial properties of each component and phase may be specified under a mass constraint. A diffusion potential for components was defined away from the dilute solution limit, and a multi-obstacle barrier function was used to constrain phase fractions. The model was used to simulate solidification via nucleation, premelting at phase boundaries and triple junctions, the intrinsic instability of small particles, and solutal melting resulting from differing diffusivities in solid and liquid. The shape of metastable free energy surfaces is found to play an important role in microstructure evolution and may explain why some systems premelt at phase boundaries and phase triple junctions while others do not.Comment: 14 pages, 8 figure

A phase-field study of ternary multiphase microstructures

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2010.Cataloged from PDF version of thesis.Includes bibliographical references.A diffuse-interface model for microstructures with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and applied to the study of ternary eutectic phase transformations. Gradients in composition and phase were included in the free energy functional, and a generalized diffusion potential equal to the chemical potential at equilibrium was defined as the driving force for diffusion. Problematic pair-wise treatment of phases at interfaces and triple junctions was avoided, and a cutoff barrier was introduced to constrain phase fractions to physically meaningful values. Parameters in the model were connected to experimentally measurable quantities. Numerical methods for solving the phase-field equations were investigated. Explicit finite difference suffered from stability problems while a semi-implicit spectral method was orders of magnitude more stable but potentially inaccurate. The source of error was found to be the rich temporal dynamics of spinodal decomposition combined with large timesteps and a first-order time integrator. The error was addressed with a second-order semi-implicit Runge-Kutta time integrator and adaptive timestepping, resulting in two orders of magnitude improvement in efficiency. A diffusion-limited growth instability in multiphase thin-film systems was discovered, highlighting how ternary systems differ from binary systems, and intricate asymmetries in the processes of solidification and melting were simulated. A nucleation barrier for solidification was observed and prompted development of a Monte-Carlo-like procedure to trigger nucleation. However when solid was heated from below the melting point, premelting was observed first at phase triple junctions and then at phase boundaries with stable liquid films forming under certain conditions. Premelting was attributed to the shape and position of the metastable liquid curve, which was found to affect microstructure by creating low energy pathways through composition space. Slow diffusivity in solid relative to liquid was shown to produce solutal melting of solid below the melting point. Finally, the multiphase method was used to produce the first reported simulation of the entire transient liquid phase bonding process. The model shows promise for optimizing the bonding process and for simulating non-planar solidification interfaces.by Daniel A. Cogswell.Ph.D

Current-induced transition from particle-by-particle to concurrent intercalation in phase-separating battery electrodes

Many battery electrodes contain ensembles of nanoparticles that phase-separate on (de)intercalation. In such electrodes, the fraction of actively intercalating particles directly impacts cycle life: a vanishing population concentrates the current in a small number of particles, leading to current hotspots. Reports of the active particle population in the phase-separating electrode ​lithium iron phosphate (​LiFePO4; ​LFP) vary widely, ranging from near 0% (particle-by-particle) to 100% (concurrent intercalation). Using synchrotron-based X-ray microscopy, we probed the individual state-of-charge for over 3,000 ​LFP particles. We observed that the active population depends strongly on the cycling current, exhibiting particle-by-particle-like behaviour at low rates and increasingly concurrent behaviour at high rates, consistent with our phase-field porous electrode simulations. Contrary to intuition, the current density, or current per active internal surface area, is nearly invariant with the global electrode cycling rate. Rather, the electrode accommodates higher current by increasing the active particle population. This behaviour results from thermodynamic transformation barriers in ​LFP, and such a phenomenon probably extends to other phase-separating battery materials. We propose that modifying the transformation barrier and exchange current density can increase the active population and thus the current homogeneity. This could introduce new paradigms to enhance the cycle life of phase-separating battery electrodes

Suppression of Phase Separation in LiFePO4 Nanoparticles During Battery Discharge

Using a novel electrochemical phase-field model, we question the common belief that LixFePO4 nanoparticles separate into Li-rich and Li-poor phases during battery discharge. For small currents, spinodal decomposition or nucleation leads to moving phase boundaries. Above a critical current density (in the Tafel regime), the spinodal disappears, and particles fill homogeneously, which may explain the superior rate capability and long cycle life of nano-LiFePO4 cathodes.Comment: 27 pages, 8 figure

HIV-1 Nef Induces Proinflammatory State in Macrophages through Its Acidic Cluster Domain: Involvement of TNF Alpha Receptor Associated Factor 2

Background: HIV-1 Nef is a virulence factor that plays multiple roles during HIV replication. Recently, it has been described that Nef intersects the CD40 signalling in macrophages, leading to modification in the pattern of secreted factors that appear able to recruit, activate and render T lymphocytes susceptible to HIV infection. The engagement of CD40 by CD40L induces the activation of different signalling cascades that require the recruitment of specific tumor necrosis factor receptor-associated factors (i.e. TRAFs). We hypothesized that TRAFs might be involved in the rapid activation of NF-kappa B, MAPKs and IRF-3 that were previously described in Nef-treated macrophages to induce the synthesis and secretion of proinflammatory cytokines, chemokines and IFN beta to activate STAT1, -2 and -3. Methodology/Principal Findings: Searching for possible TRAF binding sites on Nef, we found a TRAF2 consensus binding site in the AQEEEE sequence encompassing the conserved four-glutamate acidic cluster. Here we show that all the signalling effects we observed in Nef treated macrophages depend on the integrity of the acidic cluster. In addition, Nef was able to interact in vitro with TRAF2, but not TRAF6, and this interaction involved the acidic cluster. Finally silencing experiments in THP-1 monocytic cells indicate that both TRAF2 and, surprisingly, TRAF6 are required for the Nef-induced tyrosine phosphorylation of STAT1 and STAT2. Conclusions: Results reported here revealed TRAF2 as a new possible cellular interactor of Nef and highlighted that in monocytes/macrophages this viral protein is able to manipulate both the TRAF/NF-kappa B and TRAF/IRF-3 signalling axes, thereby inducing the synthesis of proinflammatory cytokines and chemokines as well as IFN beta