Critical Length for Lattice Expansion of SnO₂Nanorods and Nanosheets: Implications for Lithium-Ion Batteries

Lattice expansion and surface stress for tetragonal SnO2 nanorods and nanosheets were systematically investigated using lattice constants determined from in situ synchrotron radiation X-ray powder diffraction of hydrothermal synthesis. A particle size dependence of lattice constants a and c for the nanorods was identical to that for the nanosheets in the same size within experimental uncertainties. The fact suggests the lattice constants of SnO2 nanostructured materials only depend on the particle size parallel to the crystallographic axis. The average atomic volume of the nanorods and nanosheets linearly depends on the ratio of the particle surface area A to volume V in A/V < 0.5 nm-1. The surface stress estimated in A/V < 0.5 nm-1 was -1.7(2) N/m with a reasonable average atomic volume for bulk. Significant deviations from the linear line were observed in A/V > 0.5 nm-1 for the nanorods and nanosheets. A boundary of expansion behavior was found to be the particle size of ∼9 nm. The critical length of 9 nm has an effect on the study of their application for Li-ion batteries since SnO2 nanostructured materials with size from a few nanometers to tens of nanometers have been fabricated and investigated for anodes in lithium-ion batteries.