Theory of Coherent Nucleation in Phase-Separating Nanoparticles

Abstract

The basic physics of nucleation in solid 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. Thus 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 LiXFePO4, 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 shows how to tailor the elastic and surface properties of a solid nanostructure to achieve desired phase behavior.

Nanoscale visualization of redox activity at lithium-ion battery cathodes

“…The lowest currents (o10 pA), which comprise ca. 98% of the sampled surface, are mainly owing to the Pt substrate, whereas the broad current distribution at higher values can be attributed to the LiFePO 4 nanoparticles that are reasonably expected to have different crystal orientations 36 and phases 37 . This result ties closely to the activity images of secondary particles, discussed above (for example, Fig.…”

Rate-Dependent Morphology of Li2O2 Growth in Li–O2 Batteries

“…When the film thickness approaches 5 nm, the active surfaces become passivated, as electronic resistance increases with thickness [24]. In this Letter we model the rate-dependent morphological transition in Li 2 O 2 growth, using the recently developed variational theory of electrochemical kinetics [25][26][27][28][29][30] applied to classical surface-growth models [31][32][33]. The theory predicts a transition starting in the first monolayer from particle growth to film growth when the current exceeds the exchange current for the oxygen reduction reaction, consistent with experimental observations.…”

“…We describe the current density profile I(x, t) using generalized Butler-Volmer kinetics based on nonequilibrium thermodynamics, recently developed by Bazant et al [25] and applied to intercalation dynamics in Li-ion batteries [26][27][28][29][30]48]. Here, we apply the theory for the first time to surface growth, using a different model for the Li 2 O 2 chemical potential,…”

Cahn-Hilliard Reaction Model for Isotropic Li-ion Battery Particles

“…It has become clear that a more realistic particle model must account for crystal anisotropy [22,2,24], coherency strain [9,8] and reaction limitation in nanoparticles [22,2,14] in nanoparticles. In larger, micron-sized particles, however, the shrinking-core model may still have some relevance due to solid diffusion limitation and defects (such as dislocations and micro cracks) that can reduce coherency strain.…”

“…For reaction-limited anisotropic LFP nanoparticles, the general theory can be reduced to the Allen-Cahn reaction (ACR) equation for the depth-averaged ion concentration [22,2], which has been applied successfully to predict experimental data, using generalized Butler-Volmer kinetics and accounting for coherency strain [9,8,3]. An important prediction of the ACR model is the dynamical suppression of phase separation [2,9].…”