Using first-principles calculations, we study the effect of cation substitution on the transition-metal sublattice in phospho-olivines, with special attention given to the ${\text{Li}}_x\left({\text{Fe}}_{1-y}{\text{Mn}}_y\right){\text{PO}}_4$ system. We use a cluster expansion model derived from first-principles with Monte Carlo simulations to calculate finite-$T$ phase diagrams, voltage curves, and solubility limits of the system. The phase diagram of ${\text{Li}}_x\left({\text{Fe}}_{1-y}{\text{Mn}}_y\right){\text{PO}}_4$ shows two low-temperature miscibility gaps separated by a solid solution phase centered at Li composition $x\approx y$, which corresponds to a state where most Fe ions are oxidized and most Mn are not. This intermediate low-$T$ solid solution is stabilized by the dilution of phase-separating interactions caused by the disorder of redox potentials on the transition-metal sites. The calculated voltage curves show two plateaus at $\sim 4–4.2\text{V}$ and $\sim 3.5–3.7\text{V}$, corresponding to the ${\text{Mn}}^{3+}/{\text{Mn}}^{2+}$ and ${\text{Fe}}^{3+}/{\text{Fe}}^{2+}$ redox couples, respectively, with an extended sloping region in between corresponding to the low-$T$ solid solution phase. In agreement with experiment, we find that the ${\text{Mn}}^{3+}/{\text{Mn}}^{2+}$ $\left({\text{Fe}}^{3+}/{\text{Fe}}^{2+}\right)$ voltage is decreased (increased) by Fe (Mn) substitution. We explain this by considering the energy of the solid solution which is the discharged (charged) state for these redox couples and argue that such changes are generic to all mixed olivine systems. We also find reduced phase transformation polarization on both plateaus which we attribute to the decreased composition difference between the oxidized and reduced state for each redox couple

• Received 7 April 2009

DOI:https://doi.org/10.1103/PhysRevB.79.214201