{"paper":{"title":"Atomic-scale phase-field modeling with dopants: Stochastic self-consistent harmonic approximation with fractional site occupancy","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Kairi Masuda, Yu Kumagai","submitted_at":"2026-07-27T07:46:13Z","abstract_excerpt":"Phase-field modeling has achieved great success in predicting pattern formation in materials, such as the formation of ferroelectric domains. However, because it is typically based on continuum mechanics, conventional phase-field modeling cannot be straightforwardly applied to atomic-scale pattern formation, such as dopant segregation and vacancy ordering, which are driven by chemical potentials. Here, we extend the phase-field concept to the atomic scale by formulating the free energy of atomic systems within stochastic self-consistent harmonic approximation (SSCHA) theory to allow fractional"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24107","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/2607.24107/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"}