Subpercent local strains due to the shapes of gold nanorods revealed by data-driven analysis

Analysis of subpercent local strain is important for a deeper understanding of nanomaterials, whose properties often depend on the strain. Conventional strain analysis has been performed by measuring interatomic distances from scanning transmission electron microscopy (STEM) images. However, measuring subpercent strain remains a challenge because the peak positions in STEM images do not precisely correspond to the real atomic positions due to disturbing influences, such as random noise and image distortion. Here, we utilized an advanced datadriven analysis method, Gaussian process regression, to predict the true strain distribution by reconstructing the true atomic positions. As a result, a precision of 0.2% was achieved in strain measurement at the atomic scale. The method was applied to gold nanoparticles of different shapes to reveal the shape dependence of the strain distribution. A spherical gold nanoparticle showed a symmetric strain distribution with a contraction of similar to 1% near the surface owing to surface relaxation. By contrast, a gold nanorod, which is a cylinder terminated by hemispherical caps on both sides, showed nonuniform strain distributions with lattice expansions of similar to 0.5% along the longitudinal axis around the caps except for the contraction at the surface. Our results indicate that the strain distribution depends on the shape of the nanomaterials. The proposed data-driven analysis is a convenient and powerful tool to measure the strain distribution with high precision at the atomic scale