{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"8e10b57c1e02799eefb7114743b17beff62f636539d3a950eb30113dd78e1eb3","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["b7c35353fd62dfdca9055b8937766ba6d667e8b06e1798ee63afd4c309993e11","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"f1a74dbce895f22fe920f0392e86cbd589c0450a350f2c41bad6ec236150ee20","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":["ai:gpt-5.5"],"external_id":"cm.crystal-plasticity.inverse-hall-petch","kind":"phenomenon","literature_status":"contested","n":"2","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 $10^{-6}$ to $2 \\times 10^{-6}$ 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":"b7c35353fd62dfdca9055b8937766ba6d667e8b06e1798ee63afd4c309993e11","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":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"b6882512ec3cf87d4a884519b83be904ef5a69c9c4c4a24385b26610381f054e","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"64cb6d1e660307510b86d6fd514d5ab03ec148cdf0c058037f63f2a572ca738e","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"MNu3aZWdGMxl7KckQoD8R2kzM0RuWbp1EV1raBp9DEMBt8ogYpssDBI83SkenuElELstzxVWncEoh_J1nQJAAg"},"schema":"pubphys.envelope/1"},"record_hash":"b6882512ec3cf87d4a884519b83be904ef5a69c9c4c4a24385b26610381f054e","leaf_index":2714}