Geometric Modeling of a Line of Alternating Disclinations: Application to Grain Boundaries in Graphene
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909675892506624 |
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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 |