Size-dependent spinodal and miscibility gaps for intercalation in nanoparticles.

Using a recently proposed mathematical model for intercalation dynamics in phase-separating materials ( Singh , G. K. , Ceder , G. and Bazant , M. Z. Electrochimica Acta 2008 , 53 , 7599. ), we show that the spinodal and miscibility gaps generally shrink as the host particle size decreases to the nanoscale. Our work is motivated by recent experiments on the high-rate Li-ion battery material LiFePO(4); 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 nanoparticles, (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 nanoscale.