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The chemical potential of lithium in  Li   x   FePO  4  active cathode nanoparticles and the surface free energy between  Li   x   FePO  4  and electrolyte were determined with the novel thermodynamically consistent application of the regular solution theory. Innovative consideration of crystal anisotropy accounts for the consistent determination of the dependency of the chemical potential on the mechanistically derived enthalpy of mixing and the phase boundary gradient penalty. This enabled the analytic, thermodynamically consistent determination of the phase boundary thickness between  LiFe   P   O  4  and  FePO  4 , which is in good agreement with experimental observations. The obtained explicit functional dependency of the surface free energy on the lithium concentration enables adequate simulation of the initiation of the phase transition from  FePO  4  to  LiFePO  4  at the surface of active cathode particles. To validate the plausibility of the newly developed approaches, lithium intercalation into the  Li   x   FePO  4  nanoparticles from electrolyte was modeled by solving the Cahn-Hilliard equation in a quasi-two-dimensional domain.

Thermodynamically consistent derivation of chemical potential of a battery solid particle from the regular solution theory applied to LiFePO4