Miscibility Gap Closure, Interface Morphology, and Phase Microstructure of 3D Li_xFePO₄ Nanoparticles from Surface Wetting and Coherency Strain

Abstract

We study the mesoscopic effects which modify phase-segregation in LixFePO4 nanoparticles using a multiphysics phase-field model implement on a high performance cluster. We simulate 3D spherical particles of radii from 3 to 40 nm and examine the equilibrium microstructure and voltage profiles as they depend on size and overall lithiation. The model includes anisotropic, concentration-dependent elastic moduli, misfit strain, and facet dependent surface wetting within a Cahn-Hilliard formulation. We find that the miscibility gap vanishes for particles of radius ∼5 nm, and the solubility limits change with overall particle lithiation. Surface wetting stabilizes minority phases by aligning them with energetically beneficial facets. The equilibrium voltage profile is modified by these effects in magnitude, and the length and slope of the voltage plateau during two-phase coexistence.

Comprehensive analysis of TEM methods for LiFePO4/FePO4 phase mapping: spectroscopic techniques (EFTEM, STEM-EELS) and STEM diffraction techniques (ACOM-TEM)

“…Afterwards, we could confirm many individual nanoparticles with uniform single-crystal like orientation exhibiting both, LFP and FP phases, in agreement with published experimental observations [4,5,14,16] and theoretical modellings [25,26], especially a recent in-situ X-ray study confirmed the coexistence of both phases (LFP+FP) in individual single crystalline particles [27]. Some of the particles in figure 1a containing both phases are shown in detail in figure 2.…”

“…The red color in the ODF corresponds to the largest population of IPB orientations which is normal to [101] crystalline direction. It reveals the most preferred orientation of the LFP/FP interface consistent with the theoretical calculations [25,26]. However, the scatter in the data, even when considering deviations due to projection effects of some boundaries, is too much for a single orientation of all IPBs.…”

“…However, the scatter in the data, even when considering deviations due to projection effects of some boundaries, is too much for a single orientation of all IPBs. In fact, a second local maximum with an IPB orientation close to [010] can also be recognized, while IPBs oriented along [001] have never been observed which is also in agreement with [25,26]. This clearly shows the need for a further statistical analysis of the ACOM-TEM data to develop an appropriate model for the IPBs.…”

Explaining key properties of lithiation in TiO2 -anatase Li-ion battery electrodes using phase-field modeling

“…This is computationally feasible because the phase-interface is taken implicitly into account [9], making it unnecessary to evaluate the phase transition kinetics in every position in an electrode particle. Using phase-field models for LiFePO 4 the observed decreasing miscibility and spinodal gap in nanoparticles [15] has been explained [13,16], the observed transition from a first-order phase transition to a solid solution reaction at high overpotentials [17,18] has been predicted, and the transition from particle by particle to a concurrent mechanism was predicted [11] consistent with observations [19]. Recently, a three-dimensional phase-field model has been presented for LiFePO 4 [16], and crack formation and the effects this causes have also been incorporated [20].…”

A novel model of third phase inclusions on two phase boundaries

“…Furthermore, in order to allow for mobility of these interfaces, and to resolve the physical conditions leading to their evolution, the methods must resolve the volumes away from the interfaces to a similar resolution. The robustness of the diffuse interface models therefore comes at significant computational expense, which can be prohibitive for many 3D applications (Welland et al 2015a). Some savings can be achieved for some models using adaptive solution techniques (i.e., h and/or p refinement), but the overall computational cost remains high, limiting model sizes and integration into multiphysics codes (Provatas et al 2005;Li and Kim 2012).…”