Size-dependent spinodal and miscibility gaps for intercalation in nano-particles

TL;DR

This paper demonstrates that the spinodal and miscibility gaps in intercalation materials decrease as particle size shrinks to the nanoscale, due to classical and surface effects, impacting high-rate battery performance.

Contribution

It introduces a unified analysis of size-dependent phase stability in nano-particles using a mathematical model, highlighting two mechanisms for phase separation suppression.

Findings

Spinodal and miscibility gaps shrink with decreasing particle size.

Surface effects and geometric confinement suppress phase separation.

Results apply broadly to intercalation materials, exemplified by LiFePO4.

Abstract

Using a recently-proposed mathematical model for intercalation dynamics in phase-separating materials [Singh, Ceder, Bazant, Electrochimica Acta 53, 7599 (2008)], we show that the spinodal and miscibility gaps generally shrink as the host particle size decreases to the nano-scale. Our work is motivated by recent experiments on the high-rate Li-ion battery material LiFePO4; this serves as the basis for our examples, but our analysis and conclusions apply to any intercalation material. We describe two general mechanisms for the suppression of phase separation in nano-particles: (i) a classical bulk effect, predicted by the Cahn-Hilliard equation, in which the diffuse phase boundary becomes confined by the particle geometry; and (ii) a novel surface effect, predicted by chemical-potential-dependent reaction kinetics, in which insertion/extraction reactions stabilize composition gradients near surfaces in equilibrium with the local environment. Composition-dependent surface energy and (especially) elastic strain can contribute to these effects but are not required to predict decreased spinodal and miscibility gaps at the nano-scale.