LFP vs LCO Thermodynamic Performance Calculation

What this research found

This is a thermodynamic derivation rather than a new experiment: the theoretical cell voltage and gravimetric capacity of two archetypal lithium-ion cathodes, olivine lithium iron phosphate (LFP) and layered lithium cobalt oxide (LCO), were computed from tabulated reference data against a lithium-metal anode. Every half-reaction, the relation between Gibbs free energy and voltage, and the Faraday arithmetic are worked through explicitly. All computed quantities land within 0.1 volt and a few milliampere-hours per gram of widely reported experimental values.

• Capacity follows purely from stoichiometry: the one-electron olivine reaction gives 169.9 milliampere-hours per gram from a formula mass of 157.76 grams per mole, and the half-lithium layered-oxide reaction gives 136.9, exactly half the 273.9 available if a full lithium could be removed.
• A Hess cycle built from oxide-melt solution calorimetry yields a delithiation enthalpy of +337.2 kilojoules per mole for LFP and therefore a voltage of 3.49 volts. An independent first-principles calculation with a Hubbard correction gives 3.4 volts, against a measured plateau of 3.42 to 3.45 volts.
• For LCO the first-principles reaction free energy of the cobalt(III)/cobalt(IV) couple gives 4.0 volts, corroborated by open-circuit measurements placing the main single-phase region at 3.92 volts and an average of roughly 3.9 volts over the accessible composition window.
• The LCO capacity gap is a materials constraint, not a calculation error. Beyond removing about half the lithium, the lattice becomes progressively less stable, the cobalt 3d band overlaps oxygen 2p states leading to oxygen release, and a sequence of structural transitions fatigues the particles.
• The two chemistries end up close in cathode-level specific energy because the effects nearly cancel: roughly 583 watt-hours per kilogram for LFP at 170 milliampere-hours per gram and 3.43 volts, versus roughly 534 for the reversible LCO reaction at 137 and 3.90 volts. Phosphate covalency pins the LFP voltage near 3.45 volts, while the layered cobalt band sits deeper.

How it was done

Voltages were obtained from the reversible-cell relation between molar Gibbs free-energy change, electrons transferred, and the Faraday constant, using 96,485.332 coulombs per mole. For LFP, oxide-referenced formation enthalpies of the lithiated and delithiated phases from high-temperature oxide-melt solution calorimetry were combined with the standard formation enthalpy of lithia in a thermochemical cycle in which the iron-oxide and phosphate terms cancel. For LCO, where a self-consistent formation enthalpy of the half-delithiated end member is available only by extrapolation, a benchmarked first-principles reaction energy was adopted as the reference datum and cross-checked against calorimetry and open-circuit voltage measurements. Capacities were computed from Faraday's law and formula masses derived from IUPAC standard atomic weights, normalised to the mass of the parent lithiated material.

Data sources

• Iyer et al., Electrochemical and Solid-State Letters 9:A46 (2006) — calorimetric enthalpies of LiFePO4 and delithiated FePO4
• Wang & Navrotsky, Journal of The Electrochemical Society 152:J82 (2005) — formation enthalpy of LixCoO2 for x from 0.5 to 1.0
• Zhou et al., Physical Review B 70:235121 (2004) — first-principles redox potentials with Hubbard correction
• NIST Chemistry WebBook and NIST-JANAF Thermochemical Tables — standard formation enthalpy of lithia
• Ohzuku & Ueda, Journal of The Electrochemical Society 141:2972 (1994) — open-circuit voltage measurements on LixCoO2
• Kawaji et al., Journal of Thermal Analysis and Calorimetry 68:833 (2002) — low-temperature heat capacity of LiCoO2
• CODATA 2018 recommended values of the fundamental physical constants