Meaning
Thermodynamic state functions possessing negative second derivatives with respect to concentration describe systems prone to spontaneous phase separation into distinct stable compositions. In battery electrode materials, free energy curves with local maxima and double energy wells dictate phase behavior during lithium insertion and extraction. A non convex free energy profile indicates that a homogeneous solid solution is energetically unstable across a specific stoichiometry range, driving spinodal decomposition or binodal phase transformation.
Cahn-Hilliard equations utilize the gradient of this free energy functional to model diffuse phase interfaces in lithium iron phosphate and intercalation compounds. Material scientists evaluate non convex free energy parameters to distinguish between single-phase solid-solution materials and two-phase intercalation electrodes.
Phase Instability
Spinodal regions exist within composition domains where the second derivative of free energy with respect to lithium concentration remains strictly negative. Under these thermodynamic conditions, infinitesimal composition fluctuations lower overall energy, causing non convex free energy systems to unmix spontaneously without nucleation barriers. Phase boundaries form dynamically inside active particles during charge and discharge operations.
Phase field models incorporate double-well potential functions to accurately track domain wall movement across active particles.
Voltage Plateau
Open-circuit equilibrium potential curves reflect the chemical potential derivative of host materials as lithium concentration varies. Flat voltage plateaus observed in two-phase electrodes directly result from non convex free energy landscapes where phase coexistence maintains a constant chemical potential across wide state-of-charge intervals. Solid-solution materials display sloping potential profiles because their free energy curves remain strictly convex across all lithium concentrations.
Hysteresis Potential
Energy barriers separating local minima in double-well potentials require extra thermodynamic driving force to trigger phase transitions during cycling.
