Phase Field Crystal Modeling of Coherent Interfaces in Lithium Batteries

Abstract

The aim is to study the role of material crystallography in the formation of coherent interfaces in lithium ferrous phosphate (LFP) electrodes. In a typical LFP electrode, lithiated crystals with different orientations nucleate heterogeneously and little is known about how they interact to form coherent interfaces. The current work provides insights on how lithiated crystals interact, and the effects of coherency stresses at interface and grain boundaries. A key limitation of the battery performance is the structural instability of the electrodes with continuous usage, resulting in its failure [1]. In a battery cycle the electrode microstructures typically operate in a two-phase window that comprises of a moving coherent interface. Theoretical studies [2-4] indicate that a moving coherent interface causes anisotropic expansion of electrode [2], and affects Li-ion kinetics [4]. These factors affect battery performance, and it is therefore important to explore how interfaces form. In recent years, phase field models have been developed to describe microstructures in electrodes, and use Li-ion concentration as the order parameter [3-6]. While these models reveal insights on nucleation barrier [4] and stress generation at the coherent interface [6], the anisotropic properties arising from material crystallography is not captured. This limits understanding on the role of coherent interfaces on in-situ battery operation. In the present study, we apply a phase field crystal (PFC) model to investigate the formation of coherent interfaces in LFP electrodes [7,8]. PFC models offer the advantage of describing crystal growth on atomic scales, while solving diffusive time equations [7]. This modeling method has been applied to describe grain boundary melting [9], graphene defect structures [8], and has been well established to solve for a range of crystal symmetries. Here, we define a two-dimensional spatial density field, ψ, of a group of atoms to represent the orthorhombic (rectangular in 2D) symmetry of LFP crystals. A challenge here is to model ψ (order parameter) as a function of Li-ion concentration to differentiate the lithiated and unlithiated phases of the electrode. The free energy of the system is then described as a function of ψ, and is equal to the sum of bulk and excess energy terms [8]. The excess energy terms incorporate the two-point and the three-point interactions, which set the lattice spacings (a = 6.008Å, c = 10.334Å), and the lattice symmetry [10]. Finally, we control the evolution of the density field by a generalized equation of motion for conserved fields [8]. The coherency stresses and diffusion barriers at interfaces are captured by the PFC simulation. The results provide insights and strategies for doping electrode materials so as to reduce coherency stresses in electrodes.