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Using a recently-proposed mathematical model for intercalation dynamics inphase-separating materials [Singh, Ceder, Bazant, Electrochimica Acta 53, 7599(2008)], we show that the spinodal and miscibility gaps generally shrink as thehost particle size decreases to the nano-scale. Our work is motivated by recentexperiments on the high-rate Li-ion battery material LiFePO4; this serves asthe basis for our examples, but our analysis and conclusions apply to anyintercalation material. We describe two general mechanisms for the suppressionof phase separation in nano-particles: (i) a classical bulk effect, predictedby the Cahn-Hilliard equation, in which the diffuse phase boundary becomesconfined by the particle geometry; and (ii) a novel surface effect, predictedby chemical-potential-dependent reaction kinetics, in whichinsertion/extraction reactions stabilize composition gradients near surfaces inequilibrium with the local environment. Composition-dependent surface energyand (especially) elastic strain can contribute to these effects but are notrequired to predict decreased spinodal and miscibility gaps at the nano-scale.

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