The kinetic anisotropy of lithium ion adsorption and lithium absorption for LixFePO4 olivine nanocrystals is simulated and reported. The kinetics depend on the orientation of the electrolyte/LixFePO4 interface with respect to the far-field ionic flux. As a consequence of these kinetics and a Li miscibility gap in LixFePO4, the particle geometry and orientation also have an effect on the morphology of the two-phase evolution. These processes accompany the charge and discharge behavior in battery microstructures and a direct influence on battery behavior is suggested. A kinetic Monte Carlo (KMC) algorithm based on a cathode particle rigid lattice is used to simulate the kinetics in this system. In these simulations the adsorption kinetics of the electrolyte/electrode interface are treated by coupling the normal flux outside the particle from a continuum numerical simulation of Li-ion diffusion in the electrolyte to the atomistic KMC model within the particle. The interfacial reaction depends on local concentration and the potential drop at the interface via the Butler-Volmer (B-V) relation. The atomic potentials for the KMC simulation are derived from empirical solubility limits (as determined by OCV measurements). The main results show that the galvanostatic lithium-uptake/cellvoltage has three regimes: 1) a decreasing cell potential for Li-insertion into a Li-poor phase; 2) a nearly constant potential after the nucleation of a Li-rich phase Li(1-beta)FePO4; 3) a decreasing cell potential after the Li-poor phase has been evolved into a Li-rich phase. The behavior in the second regime is sensitive to crystallographic orientation.