Geometry and physics in the deformations of crystalline caps

TL;DR

This paper explores how stress and geometry interact in crystalline caps on spheres, revealing unique curvature screening, fracture behaviors, and stress engineering strategies that enhance understanding of frustrated crystalline structures.

Contribution

It uncovers a novel curvature screening mechanism, characterizes fracture morphologies in plastic regimes, and proposes vacancy-based stress engineering in crystalline caps.

Findings

Partial, uniform substrate curvature screening by induced curvature.

Fracture morphologies unique to spherical crystalline caps.

Vacancy strategies for stress and fracture control.

Abstract

Elucidating the interplay of stress and geometry is a fundamental scientific question arising in multiple fields. In this work, we investigate the geometric frustration of crystalline caps confined on the sphere in both elastic and plastic regimes. Based on the revealed quasi-conformal ordering, we discover the partial, but uniform screening of the substrate curvature by the induced curvature underlying the inhomogeneous lattice. This scenario is fundamentally different from the conventional screening mechanism based on topological defects. In the plastic regime, the yield of highly stressed caps leads to fractures with featured morphologies not found in planar systems. We also demonstrate the strategy of engineering stress and fractures by vacancies. These results advance our general understanding on the organization and adaptivity of geometrically-frustrated crystalline order.