{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"551ee488c9210512b8477220571606002fde93d1c72293828056b05e3f45aa3a","created":"2026-10-03T07:17:59Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"0ddcf326084d4ad8fe838cd95c21a87cd42aa86073b6a2b65ed3d6b9061d0920","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":[],"external_id":"cm.crystal-plasticity.inverse-hall-petch","kind":"phenomenon","literature_status":"contested","n":"1","parents":[],"plain":"Metals usually get stronger as their crystal grains shrink, but when grains are only a few dozen atoms across they get weaker again. Where the peak lies and which mechanism takes over is debated.","posed_since":"1989","precise":"Hall-Petch strengthening sigma_y = sigma_0 + k $d$^-1/2 ($d$ the grain size) fails below d of roughly 1e-6 to 2e-6 cm in Cu, Ni and other metals. Determine the critical grain size $d_c$ and the softening mechanism below it (grain-boundary sliding, grain rotation, boundary-mediated dislocation emission, or processing artifacts such as porosity and impurities), and whether boundary relaxation or solute segregation can suppress softening altogether. An answer is $d_c$ and the mechanism from artifact-free samples, matched by simulation.","problem_ref":null,"references":"","settled_by":"Strength measurements on fully dense, impurity-controlled samples spanning $d_{c}$, with in situ observation of the active deformation mechanism.","status_note":"Experiments since about 2017 showed that relaxed or solute-decorated boundaries extend strengthening to smaller grains, leaving the intrinsic limit uncertain.","title":"Grain size of maximum strength in nanocrystalline metals","topic_ref":"01aa4fb74d0c96c5784d789590ab08ed4af0e1bc9234f0d6784e666e779187ae"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"b7c35353fd62dfdca9055b8937766ba6d667e8b06e1798ee63afd4c309993e11","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"5278050bfb6af50427add718e1f0e1980552fd74dc33069fb4ab587e2a956d6f","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"oyKC_sRUN2OrZ1pRaqibeW3TVo6a-emX5aO-ikB6-Cw1BU0TTZdz6kUr8gy-ZFnoyUE_YUkRo_WsaP_7m8QTAw"},"schema":"pubphys.envelope/1"},"record_hash":"b7c35353fd62dfdca9055b8937766ba6d667e8b06e1798ee63afd4c309993e11","leaf_index":924}