Insertion-induced breakage of materials

Extensive experiments have shown the breakage of active materials, such as Sn and Si, after several charging and discharging in the development of rechargeable Li-ion batteries. To understand the breakage behavior due to the insertion and deinsertion of lithium into the active materials, the effect of surface mechanics and the insertion-induced deformation is examined within the theory of linear elasticity. An approach is presented whereby the average size of the fragment pieces due to the insertion of lithium into a spherical particle is governed by the equilibrium of the system energies before and after the breakage, in which the contribution of the insertion-induced deformation to both the total stored strain energy and the total surface energy is included in the calculation of free energy. The ratio of the average size of the fragment pieces to the radius of the spherical particle is relatively independent of the particle size in the range of millimeter to micrometer, and the ratio is a function of material properties and the volume expansion due to the lithium-insertion.