The Case Against Hall-Petch Hardening in High Entropy Carbide Ceramics

Abstract

Grain size is often used with the Hall-Petch relationship to justify differences in hardness in ceramic materials. Herein, hardness does not vary systematically with grain-size for fully dense, single-phase (Cr,Mo,Ta,V,W)C1-δ high entropy carbide ceramics for grain sizes that varied by a factor of three. Fully dense, single-phase ceramics with grain sizes from 9.3+/-0.3 to 28.8+/-0.7 microns exhibited a pronounced indentation size effect, with Vickers hardness decreasing from ~28-30 GPa at 0.49 N to ~20-21 GPa at 9.81 N, and Berkovich nanohardness ranging from 26 to 30 GPa at 10 mN. However, at a given load, hardness remained within a narrow range across the grain-size series, and no consistent Hall-Petch dependence was resolved. The lack of grain-size dependence likely indicates that the deformation volume sampled by the indenter was not controlled by grain-boundary interactions; instead, hardness was governed primarily by indentation load and local response of the rock salt carbide matrix.