A uniform rule between hardness and structure hierarchy of ceramics in both direct and inverse Hall-Petch regimes

The MicroStructure Hierarchy Descriptor (mu$\umu$SHD) has built a bridge in linking the structure hierarchy and properties of ceramic materials. Here, a new variable Asc$Asc$, which stands for the average of scales present in a ceramic microstructure, based on the mu$\umu$SHD, is constructed and calibrated. It is found that the Asc$Asc$ is not only related to the size scales, but also the morphological features in microstructures, due to an inheritance from the mu$\umu$SHD. The Asc$Asc$ is positively linear correlated with the average grain size d, but the relationship changes to be nonlinear when the morphology of grains is considered. In the Hall-Petch regime, the Vickers hardness H-V of both, ZrO2-SiC composite ceramics and a class of high entropy metallic borides, is found to increase with the decrease of Asc$Asc$ index. For the case study of ZrO2 ceramic, a uniform rule is found to be valid in both the direct and inverse Hall-Petch regimes that the Asc$Asc$ varies in an opposite trend as the H-V varies with d.

Automated summary

The MicroStructure Hierarchy Descriptor (muμSHD) has established a connection between the structure hierarchy and properties of ceramic materials. A new variable, AscAsc, has been constructed and calibrated based on muμSHD, which represents the average of scales in a ceramic microstructure. It is found that AscAsc is related to both the size scales and morphological features in microstructures. In the Hall-Petch regime, the Vickers hardness (H-V) of ZrO2-SiC composite ceramics and high entropy metallic borides is found to increase with the decrease of AscAsc index. For ZrO2 ceramics, a uniform rule is identified in both direct and inverse Hall-Petch regimes, where AscAsc varies in the opposite trend as H-V varies with grain size (d).