Slow Voltage Relaxation\nof Silicon Nanoparticles with\na Chemo-Mechanical Core–Shell Model

Silicon presents itself as a high-capacity anode material\nfor lithium-ion\nbatteries with a promising future. The high ability for lithiation\ncomes along with massive volume changes and a problematic voltage\nhysteresis, causing reduced efficiency, detrimental heat generation,\nand a complicated state-of-charge estimation. During slow cycling,\namorphous silicon nanoparticles show a larger voltage hysteresis than\nafter relaxation periods. Interestingly, the voltage relaxes for at\nleast several days, which has not been physically explained so far.\nWe apply a chemo-mechanical continuum model in a core–shell\ngeometry interpreted as a silicon particle covered by the solid-electrolyte\ninterphase to account for the hysteresis phenomena. The silicon core\n(de)lithiates during every cycle while the covering shell is chemically\ninactive. The visco-elastoplastic behavior of the shell explains the\nvoltage hysteresis during cycling and after relaxation. We identify\na logarithmic voltage relaxation, which fits with the established\nGarofalo law for viscosity. Our chemo-mechanical model describes the\nobserved voltage hysteresis phenomena and outperforms the empirical\nPlett model. In addition to our full model, we present a reduced model\nto allow for easy voltage profile estimations. The presented results\nsupport the mechanical explanation of the silicon voltage hysteresis\nwith a core–shell model and encourage further efforts into\nthe investigation of the silicon anode mechanics.