An extended hardness limit in bulk nanoceramics

Abstract Mechanical strengthening by grain refinement is a method whereby a material’s strength and hardness can be increased by decreasing the average crystallite grain size. The empirical Hall–Petch relationship mathematically describes grain boundary strengthening and provides guidance for a straightforward way to produce stronger materials. While the phenomenon has been widely explored in nanocrystalline metals, the difficulty associated with fabricating high-quality dense nanocrystalline ceramics has left unanswered the question of the validity and extent of the relationship in ceramics. Prior studies suggest the occurrence of an inverse Hall–Petch response in ceramics with grain sizes