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arXiv · 2003.07826

A simple, general criterion for onset of disclination disorder on curved surfaces

Siddhansh Agarwal·Sascha Hilgenfeldt
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Abstract

Determining the positions of lattice defects on elastic surfaces with Gaussian curvature is a non-trivial task of mechanical energy optimization, particularly for surfaces with boundaries. We introduce a simple way to predict the onset of disclination disorder from the shape of bounded surfaces. The criterion fixes the value of a weighted integral Gaussian curvature to a universal constant and proves accurate across a great variety of shapes, even when previously suggested criteria fail. It is an easy avenue to improved understanding of the limitations to crystalline order in many materials.

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Siddhansh Agarwal, Sascha Hilgenfeldt. 2020-03-17. A simple, general criterion for onset of disclination disorder on curved surfaces. https://doi.org/10.1103/physrevlett.125.078003

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