Refining a metal’s grain size can result in dramatic increases in strength, and the magnitude of this strengthening increment can be estimated using the Hall–Petch equation. Since the Hall–Petch equation was proposed, there have been many experimental studies supporting its applicability to pure metals, intermetallics and multi-phase alloys. In this article, we gather the grain-size strengthening data from the Hall–Petch studies on pure metals and use this aggregated data to calculate best estimates of these metals’ Hall–Petch parameters. We also use this aggregated data to re-evaluate the various models developed to physically support the Hall–Petch scaling.

Metal Manipulation: Reducing the grain size below 100 micrometers can vastly improve the properties of a metal. However, these nanocrystalline metals are not thermally stable; at elevated temperatures the grains will grow and merge. Alloying with a second metal to slow grain growth can slow down this process, which has shown some success on a trial-and-error basis. Chookajorn et al. (p. 951 ; see the Perspective by Weertman ) now provide a theoretical framework to create stability maps to identify potential alloys with the greatest thermal stability. For tungsten, counterintuitively, the theory suggests that atoms with the largest size differential or lowest solubility are not the best alloying choice. Indeed, an alloy of tungsten and titanium was processed more easily than pure nanocrystalline tungsten and also showed better stability at high temperatures.

Shape Memory Ceramics: Shape memory materials convert heat into strain and vice versa. These materials are often made from metal alloys, which can generate large stresses with small shape changes. Ceramics have certain characteristics that underlie shape memory transformation, but generally crack under strain. Lai et al. (p. 1505 ; see the Perspective by Faber ) introduce a modified ceramic structure with limited crystal grains that can withstand comparable cyclic strains to shape memory metals.