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

Klemen Zelič; Tomaž Katrašnik

doi:10.1038/s41598-019-38635-2

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

Sci Rep. 2019 Feb 14;9(1):2123. doi: 10.1038/s41598-019-38635-2.

Authors

Klemen Zelič¹, Tomaž Katrašnik²

Affiliations

¹ University of Ljubljana, Faculty of Mechanical Engineering, Laboratory for Internal Combustion Engines and Electromobility, Ljubljana, SI-1000, Slovenia. klemen.zelic@fs.lj-uni.si.
² University of Ljubljana, Faculty of Mechanical Engineering, Laboratory for Internal Combustion Engines and Electromobility, Ljubljana, SI-1000, Slovenia.

Abstract

The chemical potential of lithium in Li_xFePO₄ active cathode nanoparticles and the surface free energy between Li_xFePO₄ 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_PO₄ and FePO₄, 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 FePO₄ to LiFePO₄ at the surface of active cathode particles. To validate the plausibility of the newly developed approaches, lithium intercalation into the Li_xFePO₄ nanoparticles from electrolyte was modeled by solving the Cahn-Hilliard equation in a quasi-two-dimensional domain.