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

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Autori principali: Carvalho, A. M. de M., Furtado, C.
Natura: Preprint
Pubblicazione: 2025
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author Carvalho, A. M. de M.
Furtado, C.
author_facet Carvalho, A. M. de M.
Furtado, C.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2507_03796
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Geometric Modeling of a Line of Alternating Disclinations: Application to Grain Boundaries in Graphene
Carvalho, A. M. de M.
Furtado, C.
General Relativity and Quantum Cosmology
Materials Science
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.
title Geometric Modeling of a Line of Alternating Disclinations: Application to Grain Boundaries in Graphene
topic General Relativity and Quantum Cosmology
Materials Science
url https://arxiv.org/abs/2507.03796