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.
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BibTeX
@misc{sarikhani2026case,
title = {{The Case Against Hall-Petch Hardening in High Entropy Carbide Ceramics}},
author = {Ali Sarikhani and Ana C. Feltrin and Gregory E. Hilmas and David W. Lipke and Douglas E. Wolfe and Stefano Curtarolo and Shen J. Dillon and William G. Fahrenholtz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15717},
eprint = {2609.15717},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15717},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Case Against Hall-Petch Hardening in High Entropy Carbide Ceramics
AU - Ali Sarikhani
AU - Ana C. Feltrin
AU - Gregory E. Hilmas
AU - David W. Lipke
AU - Douglas E. Wolfe
AU - Stefano Curtarolo
AU - Shen J. Dillon
AU - William G. Fahrenholtz
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15717
UR - https://arxiv.org/abs/2609.15717
AB - 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.
ER -