@article{Bustamante2026, 
author = {Michael E. Bustamante and Gabriel Bustamante and Kristina Lilova},
title = {Volatility sets high-entropy carbide service life above 3000 K, and both wall temperature and propellant chemistry set the required hafnium fraction},
year = {2026},
journal = {Extreme Materials},
volume = {2},
number = {3},
keywords = {Ultra high-temperature ceramics, High entropy carbides, Extreme environments, Oxide volatility, Recession, Lifetime prediction, Thermodynamic screening, Rocket propulsion},
url = {https://www.sciopen.com/article/10.1016/j.exm.2026.100047},
doi = {10.1016/j.exm.2026.100047},
abstract = {Bulk phase stability does not determine the service life of high entropy carbides in rocket applications; oxidation and recession of the surface oxide scale do. A screening methodology combining a regular solution stability model, equilibrium thermochemistry, and recession kinetics is applied to (Hf,Zr,Ti,Ta,Nb)C. No compositional spinodal is predicted, so selection falls to the oxide scale; every candidate oxide is molten at a throat, so volatility, not melting temperature, controls recession. Loss is bracketed between dissociative vaporization (floor) and a steam hydroxide channel (ceiling), second order in water vapor, which raises throat recession over two orders of magnitude at a hydrogen engine. The wall temperature controls recession exponentially, and a 55 flight life needs it below about 1870 K. At fixed wall temperature the dominant lever is the water vapor pressure; exchanging the steam loadings of hydrogen and kerosene engines changes recession 22 fold, against 1.4 fold for their 105 K gas temperature difference. Hafnium enrichment is worth 8.8 fold on the dissociation channel but only 1.06 fold with hydroxides. Against an adopted 100 µm/h criterion, five of seven candidates clear a leading edge and none clears a hydrogen engine throat; the hafnium and zirconium rich carbide ranks first in both.}
}