Thermodynamic Properties as a Function of Temperature of AlMoNbV, NbTaTiV, NbTaTiZr, AlNbTaTiV, HfNbTaTiZr, and MoNbTaVW Refractory High-Entropy Alloys from First-Principles Calculations

Abstract

Refractory high-entropy alloys (RHEAs) are strong candidates for use in high-temperature engineering applications. As such, the thermodynamic properties as a function of temperature for a variety of RHEA systems need to be studied. In the present work, thermodynamic quantities such as entropy, enthalpy, heat capacity at constant volume, and linear thermal expansion are calculated for three quaternary and three quinary single-phase, BCC RHEAs: AlMoNbV, NbTaTiV, NbTaTiZr, AlNbTaTiV, HfNbTaTiZr, and MoNbTaVW. First-principle calculations based on density functional theory are used for the calculations, and special quasirandom structures (SQSs) are used to represent the random solid solution nature of the RHEAs. A code for the finite temperature thermodynamic properties using the Debye-Grüneisen model is written and employed. For the first time, the finite temperature thermodynamic properties of all 24 atomic configuration permutations of a quaternary RHEA are calculated. At most, 1.7% difference is found between the resulting properties as a function of atomic configuration, indicating that the atomic configuration of the SQS has little effect on the calculated thermodynamic properties. The behavior of thermodynamic properties among the RHEAs studied is discussed based on valence electron concentration and atomic size. Among the quaternary RHEAs studied, namely AlMoNbV, NbTaTiZr, and NbTaTiV, it is found that the presence of Zr contributes to higher entropy. Additionally, at lower temperatures, Zr contributes to higher heat capacity and thermal expansion compared to the alloys without Zr, possibly due to its valence electron concentration. At higher temperatures, Al contributes to higher heat capacity and thermal expansion, possibly due its ductility. Among the quinary systems, the presence of Mo, W, and/or V causes the RHEA to have a lower thermal expansion than the other systems studied. Finally, when comparing the systems with the NbTaTi core, the addition of Al increases thermal expansion, while the removal of Zr lowers the thermal expansion.