Abstract
Pentatwinned nanostructures are key to understanding the mechanical, chemical, and structural behavior of nanomaterials owing to their unique fivefold symmetry and lattice strain from a 7.35° disclination gap between {111} twin boundaries. However, the precise equilibrium strain distributions have remained unclear because of heterogeneity among individual particles, requiring statistical analysis across large sample populations. Here, we use nanobeam four-dimensional scanning transmission electron microscopy (4D-STEM) to extract averaged strain profiles from uniformly sized, shape-identical particles, achieving high-resolution, statistically robust insights beyond single-particle noise. The strain profiles reveal how tensile, shear, and rotational components collectively compensate for the angular deficit, with particle shape-dependent local variations highlighting the importance of morphological control in synthesis. By integrating in situ heating with 4D-STEM, we captured a previously unobserved strain relaxation pathway involving the formation of periodic partial dislocations that stabilizes the strain-relieved equilibrium state. This study establishes a quantitative framework for equilibrium strain in fivefold-twinned nanostructures and offers strain engineering strategies for tailored properties.