Geometric frustration arises when geometry prevents the simultaneous satisfaction of local interactions, producing pseudosymmetry and emergent behaviors. Pseudosymmetric features in crystalline nanomaterials are known to appear as local strain and distortion, but how these features depend on particle size and govern structural stability remains unclear. Here we present the first study of a particle size-dependent crossover in pseudosymmetry of multi-twinned gold nanoparticles (NPs) by nanoscale strain mapping based on 4D scanning transmission electron microscopy. Analysis of 26 decahedral NPs (edge length: 20-55 nm) reveals the manifestation of pronounced heterogeneity in multiple modes of in-plane strain and displacement field in small NPs, caused by geometric gap closing of the five tetrahedral grains. As particle size increases, the strain fields in NPs homogenize across grains and local phases shift from predominantly lower-symmetry body-centered tetragonal to face-centered cubic character, approaching bulk gold. We identify a crossover particle size of ∼35 nm, well below the bulk, which is also correlated to a transition from modified-Wulff particles to pentagonal bipyramids, consistent with finite element predictions. The particle size-dependent strain and pseudosymmetry at the nanoscale can extend to other geometrically frustrated nanostructures, guiding design and control of crystalline solids and phase transformation for catalysis, photonics, electronics, and energy storage.
Lin et al. (2026) studied this question.