9 research outputs found
Size-dependent spinodal and miscibility gaps for intercalation in nano-particles
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