Coupled phase field crystal method and Cahn–Hilliard model for phase separation in battery electrode particles

Dr. Karthik Chockalingam
Institute for Applied and Numerical Mathematics, Department of Mathematics,
Karlsruhe Institute of Tenchnology, Karlsruhe

Abstract
A Lithium ion-battery is an electrical device composed of two electrodes
(anode and cathode) separated by an electrolyte. While the battery is in
discharge mode lithium-ions migrate from the anode to cathode. During the
insertion of lithium-ions into the active electrode cathode particles, the host
material exhibit phase change resulting in a lithium-rich phase and a lithium-
depleted phase. This phase change in the electrode particles is captured by
the Cahn-Hilliard (CH) equation. A logarithmic multi-well potential is used
in the bulk material.
Manganese Oxide, which is a commonly used electrode particle that has
a cubic lattice structure, is modeled using the phase field crystal (PFC)
method. The evolution of the phase-field crystal system is coupled to the
Cahn-Hilliard equation via a composition-dependent Laplacian. The Lapla-
cian includes the change in lattice structure due to lithiation of the particle.
The numerical scheme employed here to solve this coupled PFC-CH
system is based on a finite element approach. The PFC- and CH-equation
evolves on two different time scales. It was found that lithiation accelerates
grain boundary migration in the electrode particle.

Vortrag am 27.01.2020