Grain size of maximum strength in nanocrystalline metals
In plain words
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.
Precise statement
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.
What would settle it
Strength measurements on fully dense, impurity-controlled samples spanning $d_{c}$, with in situ observation of the active deformation mechanism.
Status in the literature
Experiments since about 2017 showed that relaxed or solute-decorated boundaries extend strengthening to smaller grains, leaving the intrinsic limit uncertain.