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arXiv · 2507.03796

Geometric Modeling of a Line of Alternating Disclinations: Application to Grain Boundaries in Graphene

A. M. de M. Carvalho·C. Furtado
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Abstract

We develop a conformal geometric model for grain boundaries in graphene based on a periodic line of alternating disclinations. Within the framework of (2+1)-dimensional gravity, we solve a reduced form of the Einstein equations to determine the conformal factor, from which the induced metric, scalar curvature, and holonomy are obtained analytically. Each pentagon-heptagon pair is modeled as a disclination dipole, forming a continuous distribution that captures the geometric signature of experimentally observed 5-7 grain boundaries. We show that the curvature is localized near the defect line and that the geometry becomes asymptotically flat, with trivial holonomy at large distances. This construction provides a tractable and physically consistent realization of the Katanaev-Volovich framework, connecting topological defect theory with atomistic features of graphene.

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A. M. de M. Carvalho, C. Furtado. 2025-07-04. Geometric Modeling of a Line of Alternating Disclinations: Application to Grain Boundaries in Graphene. https://arxiv.org/abs/2507.03796

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