Computational methods that characterize
the thermodynamic properties
of metal hydrides that operate at high temperatures, i.e., T > 800 K, are desirable for a variety of applications,
including nuclear fuels and energy storage. Ternary hydrides tend
to be less thermodynamically stable than the strongest binary hydride
that forms from the metals. In this paper we use first-principles
methods based on density functional theory, phonon calculations, and
grand potential minimization to predict the isobaric phase diagram
for 0 K ≤ T ≤ 2000 K for the Th–Zr–H
element space, which is of interest given that ThZr2H
x
ternary hydrides have been reported with
an enhanced stability relative to the binary hydrides. We compute
free energies including vibrational contributions for Th, Zr, ThH2, Th4H15, ZrH2, ThZr2, ThZr2H6, and ThZr2H7. We develop a cluster analysis method that efficiently computes
the configurational entropy for ThZr2H6 interstitial
hydride and conclude that the configurational entropy is not a major
driver for the enhanced stability of ThZr2H6 relative to the binary hydrides. Density functional theory (DFT)
predicted thermodynamic stabilities for the hydride phases are in
reasonable agreement with experimental values. ThZr2H6 is stabilized by finite temperature vibrational effects,
and ThZr2H7 is not predicted to be stable at
any studied temperature or pressure.