The mechanism of Li intercalation in olivine LiFePO₄ is a subject of intensive study in recent years. The formation of metastable solid solution is now recognized as an important factor in enabling the excellent high-rate performance of this material. On the other hand, phase separation occurs at low to moderate charge/discharge rates or during rest, leading to the domain structures of coexisting LiFePO₄ and FePO₄ phases. As defects such as cracks and dislocations are frequently nucleated at domain boundaries, understanding the domain formation phenomenon has significant implications for predicting the degradation of olivine cathode.

Despite numerous studies, the formation mechanism, morphology and stability of domain structure in olivine remain to be further elucidated. Previously, a notable experimental observation by Chen et al. [1] reveal intriguing ordered LiFePO₄/FePO₄ domains separated by parallel (100) phase boundaries in chemically delithiated LiFePO₄ particles. However, the absence of (010) phase boundaries in this structure is puzzling since the strongly anisotropic Li diffusivity should prefer a facile phase separation in the [010] direction. While 2D depth-averaged models have been employed to explain the observed domain structure [2], more detailed three-dimensional simulations are required to shed light on this issue.

In this work, we carried out 3D phase-field simulations and domain energy calculations to examine the phase separation and domain formation mechanism in free-standing, partially (de)lithiated olivine particles. The employed phase-field model quantitatively captures the effects of Li diffusion anisotropy, interface charge transfer kinetics, coherency stress and stress relaxation at particle surface. Our calculations expose the intricate interplay between thermodynamic driving force and kinetic constraints in the domain formation process, and lead to the following findings:

1) Li exchange between [010] diffusion channels crucially influences domain morphology. When such exchange is negligible, a novel, metastable checkboard pattern containing both (100) and (010) phase boundaries emerges from spontaneous phase separation (or spinodal decomposition) along [010]. In comparison, the stripe pattern reported by Chen et al. is thermodynamically more favorable by eliminating the (010) boundaries, but its formation is kinetically viable only when Li transport between [010] channels is allowed by two possible mechanisms, i.e. i) [100] lattice hopping enabled by the presence of defects and ii) inter-channel exchange through electrolyte. Under the circumstance where inter-channel Li transport has a much larger characteristic time than Li diffusion in the [010] direction, we predict that the checkboard structure will exist as an intermediate structure that can be observed experimentally.

2) Periodic domain structure in free-standing olivine particles is a kinetically stabilized feature. When the volume expansion of olivine particles is not severely constrained by their surrounding, theoretical calculations show that both elastic and interface energy stored in a particle decreases monotonically with domain length, dictating that the thermodynamic equilibrium domain structure should have only one phase boundary in the particle. However, the domain structure can be effectively “frozen” at a finite length scale due to the increasingly sluggish domain coarsening kinetics. Simulations show that the kinetically stabilized domain size is proportional to [010] particle thickness, which is consistent with experiment. The metastability of the periodic domain pattern explains why it is not universally observed in olivine particles prepared under similar conditions [3].  

This study shows the important role of kinetic constraints in domain structure evolution in LiFePO₄, which provides new insights on potential avenues to improve control of domain morphology via engineering the kinetic properties of olivine materials.

References:

1. Chen, G.; Song, X.; Richardson, T. J. Electron Microscopy Study of the LiFePO₄ to FePO₄ Phase. Electrochem. Solid-State Lett. 2006, 9 (6), A295-A298.
2. Cogswell, D. A.; Bazant, M. Z. Coherency Strain and the Kinetics of Phase Separation in LiFePO₄ Nanoparticles. ACS Nano 2012, 6, 2215-2225.
3. Yu, Y.S.; Kim, C.; et al. Dependence on Crystal Size of the Nanoscale Chemical Phase Distribution and Fracture in Li_xFePO₄. Nano Letters 2015, 15, 4282-4288.