Shrinking Core Model for the Discharge of a Metal Hydride Electrode

Abstract

A shrinking core model is presented for the galvanostatic discharge of a metal hydride particle. A quantitative criterion for when the shrinking core can be completely neglected or approximated by a pseudosteady-state solution is presented. The effect of shrinking of the core on the discharge behavior of a metal hydride particle is also studied.

Characterisation of charge and discharge behaviour of lithium ion batteries with olivine based cathode active material

“…This effect is characteristic not only for the intercalation of Li ions in lattices of various materials. Subramanian et al report this effect also to take place during the admission of hydrogen molecules into electrodes of NiMH cells [10].…”

“…With the shrinking core theory (Subramanian et al [10]) it is possible to develop an intuitive approach for the microscopic processes during two-phase transition of intercalation compounds. It is assumed that electrodes are consisting of spherical particles covered with a substance having an ideal conductivity.…”

Simulations of Lithium-Magnetite Electrodes Incorporating Phase Change

“…The concentration distributions agree well with experimental observations; however, the results are highly dependent on the use of a representation of the free energy of the system (often arising from regular solution theory and developed based on experimental observations), which often results in poor agreement between simulations and electrochemical performance data [33][34][35][36][37]. Other attempts to simulate 5 the electrochemical performance of a material which undergoes phase change have utilized a "shrinking-core" model, which tracks the boundary separating the highand low-lithium phases as it progresses from the surface of a crystal to the center during lithiation [38][39][40]. These models agree well with electrochemical data; however, they often only simulate the battery during lithiation of the electrode because modeling the subsequent delithiation is difficult due to the existence of multiple moving boundaries.…”

Analytical solutions for composition and stress in spherical elastic–plastic lithium-ion electrode particles containing a propagating phase boundary

“…These can be divided into two broad groups: in one approach, the particle geometry is approximated as a sphere, with a core consisting of one phase encapsulated within a shell of the second phase (Subramanian and White, 2001;Subramanian et al, 2000;Zhang and White, 2007;Srinivasan and Newman, 2004;Park et al, 2011;Deshpande et al, 2011;Renganathan et al, 2010). In this case, analytical expressions can often be obtained for stresses and Li concentration distributions within the particle.…”

“…Equilibrium conditions in sharp-interface models can be calculated by straightforward energy minimization: for example, Meethong et al (2007) use energy arguments to determine the influence of elasticity on phase equilibria and nucleation of a second phase in Olivine based cathode particles. Modeling the transient conditions that develop during Li insertion is more challenging, but has been treated in several studies (Subramanian and White, 2001;Subramanian et al, 2000;Zhang and White, 2007;Srinivasan and Newman, 2004;Park et al, 2011;Deshpande et al, 2011;Renganathan et al, 2010). These have focused primarily on understanding the influence of the moving phase boundary on the transient evolution of concentration in the particle, and in some cases also consider the resulting effects on the behavior of a full cell.…”