WIAS Preprint No. 1425, (2009)

Phase transition and hysteresis in a rechargeable lithium battery revisited


  • Dreyer, Wolfgang
  • Gaberšček, Miran
  • Guhlke, Clemens
  • Huth, Robert
  • Jamnik, Janko

2010 Mathematics Subject Classification

  • 74N20 74A15 74N05 74B99


  • lithium-ion-battery, FePO4, thermodynamics phase transitions, hysteresis, chemical potentials, surface stress, deviatoric stress, elasticity




We revisit a model which describes the evolution of a phase transition that occurs in the cathode of a rechargeable lithium battery during the process of charging/discharging. The model is capable to simulate hysteretic behavior of the voltage - charge characteristics with two voltage plateaus. The cathode consists of small crystalline storage particles. During discharging of the battery, the interstitial lattice sites of the particles are filled up with lithium atoms and these are released again during charging. We show within the context of a sharp interface model for a single particle of core-shell type that two mechanical phenomena go along with the phase transition during supply and removal of lithium. The lithium atoms need more space than is available by the interstitial lattice sites, which leads to a maximal relative change of the crystal volume of about 6%. Furthermore there is an interface between two adjacent phases that has very large curvature of the order of magnitude 108 m-1, which evoke here a discontinuity of the normal component of the stress. In order to simulate the dynamics within a single storage particle we establish a new initial and boundary value problem for a nonlinear PDE system that can be reduced in some limiting case to an ODE system. Furthermore we verify the common assumption of phase nucleation at the external boundary of the particle. In case of quasi static loading inner hysteresis loops in the voltage-charge plots are not contained within the setting of a core-shell model for a single storage particle. The origin of this fact is discussed in detail.

Appeared in

  • European J. Appl. Math., 22 (2011) pp. 267--290.

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