{"paper":{"title":"Rigid Unit Modes in $sp$-$sp^2$ Hybridized Carbon Systems: Origin of Negative Thermal Expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Cheol-Woon Kim, Seoung-Hun Kang, Young-Kyun Kwon","submitted_at":"2015-07-20T16:53:52Z","abstract_excerpt":"Using density functional theory combined with quasi-harmonic approximation, we investigate the thermal expansion behaviors of three different types ({\\alpha}, {\\beta}, and {\\gamma}) of graphyne which is a two-dimensional carbon allotrope composed of sp and $sp^2$ bonds. For each type of graphyne, we obtain the temperature dependent area variation by minimizing its free energy as a function of temperature, which is calculated by considering all the phonon modes in the whole Brillouin zone. We find that all three types of graphyne exhibit negative in-plane thermal expansion up to $T\\lesssim1000$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05562","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}