Analysis of the Probability of Synthesizing High-Entropy Alloys in the Systems Ti-Zr-Hf-V-Nb, Gd-Ti-Zr-Nb-Al, and Zr-Hf-V-Nb-Ni

High-entropy alloys (HEAs) are attracting considerable interest as a fundamentally new class of materials. They combine typical characteristics of metal alloys and unique properties of metal ceramics, such as high hardness and softening resistance at high temperatures, precipitation hardening, high-temperature strength, excellent wear and corrosion resistance. Since systematic experiments on a wide range of alloys are complicated and time-consuming, it is reasonable to develop a simple method for preliminary assessment of whether a particular alloy is potentially high-entropy or not. Here we analyze the probability of synthesizing HEAs in the systems Ti-Zr-Hf-V-Nb, Gd-Ti-Zr-Nb-Al, and Zr-Hf-V-Nb-Ni using empirical rules based on two parameters: enthalpy of mixing Δ H mix and atomic size difference δ. It is shown that equiatomic GdTiZrNbAl and ZrHfVNbNi alloys fail to meet both criteria, while equiatomic TiZrHfVNb alloy satisfies the first criterion and is therefore potentially high-entropy. TiZrHfVNb alloy is investigated in detail by thermodynamic modeling with TERRA software. Temperature dependences of the content of solid solution components and thermodynamic characteristics (entropy, enthalpy, internal energy) of the system are modeled. The derived curves are shown to correlate as they kink at the same temperatures, and the kinks are presumably associated with phase transitions. The results obtained can be used to estimate the composition of the condensed and gaseous phases formed during equilibrium heating of the studied systems and to predict material behavior under extreme conditions, which is undoubtedly important for the practical application of such alloys as functional materials.