Search

Abstract: Recent experimental developments reveal that nanoscale lithium iron phosphate (LiFePO4) olivine particles exhibit very different phase transition behavior from the bulk olivine phase. A crystalline-to-amorphous phase transition has been observed in nanosized particles in competition with the equilibrium phase transition between the lithium-rich and lithium-poor olivine phases. Here we apply a diffuse-interface (phase-field) model to study the kinetics of the different phase transition pathways in nanosized LiFePO4 particles upon delithiation. We find that the nucleation and growth kinetics of the crystalline-to-crystalline and crystalline-to-amorphous phase transformations are sensitive to the applied electrical overpotential and particle size, which collectively determine the preferred phase transition pathway. While the crystalline-to-crystalline phase transition is favored by either faster nucleation or growth kinetics at low or high overpotentials, particle amorphization dominates at intermediate overpotentials. Decreasing particle size expands the overpotential region in which amorphization is preferred. The asymmetry in the nucleation energy barriers for amorphization and recrystallization results in a phase transition hysteresis that should promote the accumulation of the amorphous phase in electrodes after repeated electrochemical cycling. The predicted overpotential- and size-dependent phase transition behavior of nanoscale LiFePO4 particles is consistent with experimental observations. [ABSTRACT FROM AUTHOR]

The thermodynamics and kinetics of phase transformations in electrochemical systems are reviewed. Phase transitions in Li MPO4 ( M = Fe, Mn, Ni, Co) olivines are highlighted. The phase transformation phenomena in Li MPO4 are diverse and include thermodynamic effects of particle size and applied overpotential, the appearance of metastable phases, and the effects of defects from atomic disorder and aliovalent doping. Such phenomena also include kinetic effects such as interface motion and diffusion of Li-electron complexes. The nature of phase transitions directly influences electrode performance in battery applications. Reduced particle size and doping can reduce or eliminate room-temperature Li miscibility gaps, which in turn affect characteristics of state of charge versus voltage and the elastic energy due to volume mismatches between phases. Near the conditions for a phase transition, Li diffusion coefficients are reduced. Nucleation and growth kinetics produce a series of phase transition sequences, which can result in the accumulation of noncrystalline phases during electrochemical cycling. [ABSTRACT FROM AUTHOR]

The Wulff construction yields the equilibrium shape of a particle of fixed volume embedded in a single phase at constant temperature. When the particle attaches to an interface (boundary) between two distinct phases or grains of the same phase, the Wulff construction must be modified to account for the abutment of Wulff shapes at the boundary as well as the boundary energy that is replaced by the particle. If the boundary is non-deformable, a portion of the particle interface is constrained to replace the image (i.e. the exact position) of the boundary that is removed, and the Winterbottom construction yields the equilibrium particle shape. If the boundary can deform, the particle is not constrained to replace the image of removed boundary, and the particle shape is determined by a more general modification of the Wulff construction. In two dimensions, the particle attaches to an initially flat boundary and creates two disjoint segments that remain flat at equilibrium. In three dimensions, the boundary surrounding the particle is contiguous, and numerical calculations show that such a boundary is not necessarily flat but maintains a constant mean curvature of zero at equilibrium. [ABSTRACT FROM AUTHOR]

Diffusion-induced phase transitions typically change the lattice symmetry of the host material. In battery electrodes, for example, Li ions (diffusing species) are inserted between layers in a crystalline electrode material (host). This diffusion induces lattice distortions and defect formations in the electrode. The structural changes to the lattice symmetry affect the host material's properties. Here, we propose a 2D theoretical framework that couples a Cahn-Hilliard (CH) model, which describes the composition field of a diffusing species, with a phase-field crystal (PFC) model, which describes the host-material lattice symmetry. We couple the two continuum models via coordinate transformation coefficients. We introduce the transformation coefficients in the PFC method to describe affine lattice deformations. These transformation coefficients are modeled as functions of the composition field. Using this coupled approach, we explore the effects of coarse-grained lattice symmetry and distortions on a diffusion-induced phase transition process. In this paper, we demonstrate the working of the CH-PFC model through three representative examples: First, we describe base cases with hexagonal and square symmetries for two composition fields. Next, we illustrate how the CH-PFC method interpolates lattice symmetry across a diffuse phase boundary. Finally, we compute a Cahn-Hilliard type of diffusion and model the accompanying changes to lattice symmetry during a phase transition process. [ABSTRACT FROM AUTHOR]

We propose a theoretical framework to derive thermodynamically consistent equilibrium equations and kinetic driving forces to describe the time evolution for electrically and magnetically active materials. This procedure starts from the combined statement of the first and second laws of thermodynamics, naturally incorporates Maxwell’s equations, and accommodates the description of continuous phase transformations for conserved and non-conserved order parameters. The kinetics of conserved and non-conserved ordered parameters are introduced, the adequate gradient flow is identified, thus the appropriate kinetics (e.g., Allen–Cahn, Cahn–Hilliard) are derived. Example applications of this theory include the electromechanical fields of piezoelectric materials and the wave equation in the limit of chemically homogeneous solids. Moreover, we derive a thermodynamically consistent set of partial differential equations which describe the transport of charged species in conductive, non-polarizable, magnetizable solids, and in polarizable, electrically insulating, non-magnetizable solids. [Copyright &y& Elsevier]

An objective in battery development for higher storage energy density is the design of compounds that can accommodate maximum changes in ion concentration over useful electrochemical windows. Not surprisingly, many storage compounds undergo phase transitions in situ, including production of metastable phases. Unique to this environment is the frequent application of electrical over- and underpotentials, which are the electrical analogs to undercooling and superheating. Surprisingly, overpotential effects on phase stability and transformation mechanisms have not been studied in detail. Here we use synchrotron X-ray diffraction performed in situ during potentiostatic and galvanostatic cycling, combined with phase-field modeling, to reveal a remarkable dependence of phase transition pathway on overpotential in the model olivine Li1-xFePO4. For a sample of particle size ∼113 nm, at both low (e.g., 75 mV) overpotentials a crystal-to-crystal olivine transformation dominates, whereas at intermediate overpotentials a crystalline-to-amorphous phase transition is preferred. As particle sizes decrease to the nanoscale, amorphization is further emphasized. Implications for battery use and design are considered. [ABSTRACT FROM AUTHOR]