A thermodynamic model for the FePO 4 -LiFePO 4 olivine join has been developed in order to provide support for the understanding of the charge transport behaviour within the cathode material during the battery operation. The Gibbs energy model for the olivine solution is based on the compound energy formalism with long-range-order and has been calibrated using the CALPHAD method, permitting the computation of phase equilibria by Gibbs energy minimization techniques. The model can simultaneously reproduce the reported eutectoid reaction, the 3 low-temperature miscibility gaps, the enthalpy of mixing, and the change of the voltage plateau with temperature during the delithiation process, in agreement with the available experimental data. The spinodal decomposition, which is possibly associated with fast charge transport within the cathode material, involves up to two sub-spinodal decompositions. Hence, the unique low-temperature miscibility gap of this system is considered as a blend of the two sub-miscibility gaps.

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A new thermodynamically self-consistent (TSC) method, based on the quasi-harmonic approximation (QHA), is used to obtain the Debye temperatures of LiFePO4 (LFP) and FePO4 (FP) from available experimental specific heat capacities for a wide temperature range. The calculated Debye temperatures show an interesting critical and peculiar behavior so that a steep increase in the Debye temperatures is observed by increasing the temperature. This critical behavior is fitted by the critical function and the adjusted critical temperatures are very close to the magnetic phase transition temperatures in LFP and FP. Hence, the critical behavior of the Debye temperatures is correlated with the magnetic phase transitions in these compounds. Our first-principle calculations support our conjecture that the change in electronic structures, i.e. electron density of state and electron localization function, and consequently the change in thermophysical properties due to the magnetic transition may be the reason for the observation of this peculiar behavior of the Debye temperatures.