Phase transition in a rechargeable lithium battery

We discuss the lithium storage process within a single-particle cathode of a lithium-ion battery. The single storage particle consists of a crystal lattice whose interstitial lattice sites may be empty or reversibly filled with lithium atoms. The resulting evolution equations describe diffusion with mechanical coupling and incorporate volume changes, phase transitions and surface tension. In order to simulate the dynamics, we assume spherical symmetry and fast bulk diffusion of the lithium atoms, which lead to a core shell model. We verify the common assumption of phase nucleation at the external boundary of the particle. This model is capable to predict voltage-capacity behaviour. For slow charging rates, we compare the results with experimental voltage-capacity plots exhibiting hysteretic behaviour. We observe that hysteresis cannot be described within the setting of a single-particle cathode. The origin of this fact is discussed in detail. The result is of enormous importance because single-particle models, in particular core shell models, up to now are very popular in the chemical literature.