Effect of stoichiometry on sintering shrinkage and grain growth in binary and high-entropy carbides during spark plasma sintering

Ultrafine-grained (UFG) ceramic materials exhibit improved reliability compared with coarse-grained ceramics due to the higher density of grain boundaries. This increases the crack propagation path during intergranular fracture, which is particularly beneficial for composite materials where intergranular fracture typically dominates. The formation of a UFG structure requires a detailed understanding of the sintering behavior and grain growth mechanisms in ceramic materials. In this study, submicron single-phase powders (150–350 nm) of binary and high-entropy carbides (HECs) of stoichiometric (C/Me = 1) and non-stoichiometric (C/Me = 0.8) compositions were obtained by the calcium-carbothermic synthesis. The powders were  consolidated by spark plasma sintering (SPS) at temperatures of 1350–1950 °C with holding times of 0–20 min. The effect of SPS temperature and powder stoichiometry on grain growth, sintering shrinkage, and the activation energy of sintering and grain coarsening was investigated. The behavior of high-entropy carbides was compared with that of tantalum carbide. The results show that carbide stoichiometry  significantly affects sintering behavior. A decrease in stoichiometry, corresponding to an increased concentration of carbon vacancies, reduces the activation energy of sintering and grain coarsening and increases the shrinkage rate. The onset of grain growth was found to be independent of stoichiometry and occurs at a relative  density of ~0.90÷0.95. In highly dense ceramics (>0.95), grain growth proceeds most intensively in stoichiometric carbides, which is observed both in HECs and in TaC.

1. Zhu Y., Chai J., Wang Z., Sheng T., Niu L., Li S., Jin P., Zhang H., Li J., Cui M. Microstructural damage evolution of (WTiVNbTa)C5 high-entropy carbide ceramics induced by self-ions irradiation. Journal of the European Ceramic Society. 2022;42(6):2567–2576. https://doi.org/10.1016/j.jeurceramsoc.2022.01.061

2. Liu Y., Zhu Z., Tang Z., Yu H., Zhuang L., Chu Y. Unraveling lattice-distortion hardening mechanisms in high-entropy carbides. Small. 2024;20(38):2403159. https://doi.org/https://doi.org/10.1002/smll.202403159

3. Hu J., Yang Q., Zhu S., Zhang Y., Yan D., Gan K., Li Z. Superhard bulk high-entropy carbides with enhanced toughness via metastable in-situ particles. Nature Communications. 2023;14(1):5717. https://doi.org/10.1038/s41467-023-41481-6

4. Wen Z., Liu Y., Yang J., Chen Y., Fu Y., Zhuang L., Yu H., Chu Y. Exceptional oxidation resistance of high-entropy carbides up to 3600 °C. Advanced Materials. 2025;37(34):2507254. https://doi.org/https://doi.org/10.1002/adma.202507254

5. Sulaiman S., Izman S., Uday M.B., Omar M.F. Review on grain size effects on thermal conductivity in ZnO thermoelectric materials. RSC Advances. 2022;12(9):5428–5438. https://doi.org/10.1039/d1ra06133j

6. Dong H., Wen B., Melnik R. Relative importance of grain boundaries and size effects in thermal conductivity of nanocrystalline materials. Scientific Reports. 2014;4:7037. https://doi.org/10.1038/srep07037

7. Alsabbagh A., Valiev R.Z., Murty K.L. Influence of grain size on radiation effects in a low carbon steel. Journal of Nuclear Materials. 2013;443(1-3):302–310. https://doi.org/10.1016/j.jnucmat.2013.07.049

8. Kalita P., Ghosh S., Gutierrez G., Rajput P., Grover V., Sattonnay G., Avasthi D.K. Grain size effect on the radiation damage tolerance of cubic zirconia against simultaneous low and high energy heavy ions: Nano triumphs bulk. Scientific Reports. 2021;11(1):10886. https://doi.org/10.1038/s41598-021-90214-6

9. Wang F., Zhang X., Yan X., Lu Y., Nastasi M., Chen Y., Cui B. The effect of submicron grain size on thermal stability and mechanical properties of high-entropy carbide ceramics. Journal of the American Ceramic Society. 2020;103(8):4463–4472. https://doi.org/10.1111/jace.17103

10. Feng L., Chen W.T., Fahrenholtz W.G., Hilmas G.E. Strength of single-phase high-entropy carbide ceramics up to 2300 °C. Journal of the American Ceramic Society. 2021;104(1):419–427. https://doi.org/10.1111/jace.17443

11. Sun J., Zhao J., Chen Y., Wang L., Yun X., Huang Z. Toughening in low-dimensional nanomaterials high-entropy ceramic nanocomposite. Composites. Part B: Engineering. 2022;231:109586. https://doi.org/10.1016/j.compositesb.2021.109586

12. Liu Y., Guo W.M., Xu L., Sun S.K., Lin H.T. Low-temperature sintered (Ti, Zr, Nb, Ta, Mo)C-based composites toughened with damage-free SiCw. Journal of the European Ceramic Society. 2023;43(4):1740–1745. https://doi.org/10.1016/j.jeurceramsoc.2022.11.051

13. Mao H.R., Dong E.T., Jin S.B., Qiu X.M., Shen P. Ultrafast high-temperature synthesis and densification of high-entropy carbides. Journal of the European Ceramic Society. 2022;42(10):4053–4065. https://doi.org/10.1016/j.jeurceramsoc.2022.03.054

14. Feng L., Fahrenholtz W.G., Hilmas G.E. Low-temperature sintering of single-phase, high-entropy carbide ceramics. Journal of the American Ceramic Society. 2019; 102(12):7217–7224. https://doi.org/10.1111/jace.16672

15. Volodko S., Moskovskikh D., Yudin S., Kuskov K., Kuzmin A., Guryanov A., Alimov I., Kasimtsev A. Synthesis of nano- and ultra-fine refractory carbide powders by low-temperature calcium-carbothermic process and their grain growth during sintering. Ceramics International. 2024;50(12):22141–22148. https://doi.org/10.1016/j.ceramint.2024.03.327

16. Nisar A., Ariharan S., Balani K. Densification kinetics and mechanical properties of tantalum carbide. International Journal of Refractory Metals and Hard Materials. 2018;73:221–230. https://doi.org/10.1016/j.ijrmhm.2018.02.013

17. Sygnatowicz M., Cutler R.A., Shetty D.K. Processing of dense ζ-Ta4C3–x by reaction sintering of Ta and TaC powder mixture. Journal of the American Ceramic Society. 2014;97(12):3826–3834. https://doi.org/10.1111/jace.13254

18. Wang J., Raj R. Estimate of the activation energies for boundary diffusion from rate‐controlled sintering of pure alumina, and alumina doped with zirconia or titania. Journal of the American Ceramic Society. 1990;73(5):1172–1175. https://doi.org/10.1111/j.1151-2916.1990.tb05175.x

19. Wang J., Raj R. Activation energy for the sintering of two‐phase alumina/zirconia ceramics. Journal of the American Ceramic Society. 1991;74(8):1959–1963. https://doi.org/10.1111/j.1151-2916.1991.tb07815.x