{"paper":{"title":"Occupation and diffusion of interstitial solutes in dilute alloys in perspective of the Gauss Legendre three square theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Xiaoshuang Wang","submitted_at":"2024-11-24T06:04:21Z","abstract_excerpt":"In the example of the diffusion of C, N, O in dilute ferric iron alloys, it is shown that the polyhedron consisting of equivalent occupation of interstitial solutes in dilute alloys, can be classified into 7 groups altogether, i.e., cube, octahedron, cuboctahedron, truncated octahedron, truncated cube, rhombicuboctahedron and truncated cuboctahedron. No more polyhedron can be found. The notation and the migration paths of C, N, O in dilute alloys are well described by the Gauss Legendre three square theorem. The abstraction of the migration paths gives rise to the Wythoffian operations illustr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15725","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.15725/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}