{"paper":{"title":"Spatio-temporal distribution of nucleation events during crystal growth","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Claudio Castellano, Paolo Politi","submitted_at":"2001-02-12T18:35:58Z","abstract_excerpt":"We consider irreversible second-layer nucleation that occurs when two adatoms on a terrace meet. We solve the problem analytically in one dimension for zero and infinite step-edge barriers, and numerically for any value of the barriers in one and two dimensions. For large barriers, the spatial distribution of nucleation events strongly differs from $\\rho^2$, where $\\rho$ is the stationary adatom density in the presence of a constant flux. The probability $Q(t)$ that nucleation occurs at time $t$ after the deposition of the second adatom, decays for short time as a power law [$Q(t)\\sim t^{-1/2}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0102212","kind":"arxiv","version":2},"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"}