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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 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