| At present,the commercial applications of LiFeP04 material with orthorhombic olivine structure are being vigorously pursued.Due to its inherent advantages of low toxicity,inexpensive,long cycle ability and environmentally benign,the crystal has become an important electrode material for lithium-ion rechargeable battery.During the discharging and charging process of the electrode,the electrochemical reactions basically involve the migration of lithium ions,and lithium-ions can be electrochemically intercalated and deintercalated from this crystal many times without changing the olivine topology.Using olivine LiFePO4 as model system,the phase-field model proposed by Federmann et al.is studied theoretically and numerically.This dissertation mainly focuses on the following problems:1.The phase-field model without the elastic energy consists of a nonlinear parabolic equation of order parameter coupled to a linear parabolic equation of lithium concentration.Using the Galerkin method and the Aubin-Lions lemma,we shall study the existence of global-in-time solutions to the initial-boundary value problem with the homogeneous Dirichlet boundary conditions.2.The phase-field model with the elastic energy consists of the equations of linear elliptic equations and the nonlinear parabolic equations.Applying the method of continuation of local solutions,we shall study the existence and the regularity of global-in-time solutions to the initial-boundary value problem with the homogeneous Dirichlet boundary conditions.3.The phase-field model is based on the second model,in which a thermodynamically relevant potential p(c)is considered for the chemical free energy.Invoking the method of continuation of local solutions,we shall study the existence and the regularity of global-intime solutions to the initial-boundary value problem with the Dirichlet and the Neumann boundary conditions.4.Different numerical implementations of these three phase-field models are then performed to simulate the evolution of lithium concentration and of phase interfaces.During electrochemical cycling the fundamental behavior of the crystal is the diffusion of lithium which controls the movement of the phase boundary without changing the olivine topology.Simulations show that lithium-ions fill successive channels of fast diffusion in the crystal along the[010]direction and the phase boundary moves in the[100]direction. |
