Interaction between diffusion and stresses in composition-gradient electrodes

• Interaction between diffusion and stresses is investigated.
• The spherical composition-gradient electrodes are considered.
• Decreasing form of partial molar volume reduces the stresses.

Composition-gradient electrode material is one of the most promising materials in lithium-ion battery resulting from its inhomogeneous mechanical and electrochemical properties. The present work studies the interaction between stresses and diffusion in spherical composition-gradient electrodes. The large deformation theory is adopted to establish the mechanical equations, and the stress-induced diffusion is adopted to establish the diffusion equations. Compared with the interaction effects on lithium-ion distributions and stress distributions in homogeneous electrodes, the results in composition-gradient electrodes may show differences. Three inhomogeneous factors are investigated here—diffusion coefficient, elastic modulus and partial molar volume. When elastic modulus and diffusion coefficient are inhomogeneous, the interaction effects increase the magnitudes of radial stresses initially and then reduce the magnitudes of radial stresses, whose variations are same as the hoop stresses at the electrode center. On the other hand, the interaction effects can reduce the magnitudes of hoop stresses at electrode surface throughout the process of charge. However, when partial molar volume is inhomogeneous, the interaction effects show totally different influences on lithium-ion concentration distributions and stress distributions compared with those in homogeneous electrodes. The interaction effects play a positive role for the decreasing form of partial molar volume Ω(R), while the opposite conclusion hold for the increasing form of partial molar volume Ω(R). The results can guide the design of composition-gradient electrode materials.