Precision mapping of equilibrium disclination strain in pentagonally twinned nanostructures.

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.