Size-dependent fracture of silicon nanoparticles during lithiation

Lithiation of individual silicon nanoparticles was studied in real time with in situ transmission electron microscopy. A strong size dependence of fracture was discovered; that is, there exists a critical particle diameter of ∼150 nm, below which the particles neither cracked nor fractured upon first lithiation, and above which the particles initially formed surface cracks and then fractured due to lithiation-induced swelling. The unexpected surface cracking arose owing to the buildup of large tensile hoop stress, which reversed the initial compression, in the surface layer. The stress reversal was attributed to the unique mechanism of lithiation in crystalline Si, taking place by movement of a two-phase boundary between the inner core of pristine Si and the outer shell of amorphous Li-Si alloy. While the resulting hoop tension tended to initiate surface cracks, the small-sized nanoparticles nevertheless averted fracture. This is because the stored strain energy from electrochemical reactions was insufficient to drive crack propagation, as dictated by the interplay between the two length scales, that is, particle diameter and crack size, that control the fracture. These results are diametrically opposite to those obtained previously from single-phase modeling, which predicted only compressive hoop stress in the surface layer and thus crack initiation from the center in lithiated Si particles and wires. Our work provides direct evidence of the mechanical robustness of small Si nanoparticles for applications in lithium ion batteries.