Ab initio design of elastically isotropic TiZrNbMoVx high-entropy alloys

Significance Statement

High Entropy Alloys (HEAs) are crystalline solid solutions containing at least 5 elements in equal (or nearly equal) atomic fractions. They form an exciting new class of engineering materials showing great promise for various applications. Compared to other extended solid solutions, the High Entropy Alloys show excellent mechanical properties, corrosion resistance and thermal stability.

The first High Entropy Alloys , synthesized more than ten years ago by J.-W. Yeh[1], were based on 3d transition metals. A few years after the initial discovery, O. N. Senkov[2] and coworkers designed HEAs based on refractory transition metals, as potential candidates for high-temperature applications. Motivated by these pioneering works, the number of scientific publications on the subject matter increased nearly exponentially during the last decade.

Today the search for new High Entropy Alloys is based on a substantial amount of accumulated knowledge on composition-processing-property correlations. So far these correlations were established mostly by trial-and-error methods. Despite these efforts, the knowledge of the microstructure and the main deformation mechanisms in High Entropy Alloys is still far from satisfactory, which limits the reliability of the modeling of their properties. In order to turn the composition-processing-property correlations more ‘intelligent’ one should look inside the High Entropy Alloys , to the networks of atoms and reveal the various interactions between them. In recent years, it has become clear that in the search for advanced alloys, multi-scale modelling built on first-principles quantum theory is going to play an increasingly important role.

Recently, we used first-principles alloy theory to investigate the atomic-level properties of High Entropy Alloys composed of 3d metals,[3] and refractory elements.[4] Our study3 provided the first ab initio phase diagram for the 3d-HEAs doped with Al, and confirms the previously established experimentaland estimated phase selection rules. Furthermore, we show that the face centered cubic solid solutions are typically highly anisotropic, whereas the body centered cubic solid solutions made of refractory elementsturn completely isotropic when the valence electron concentration becomes~4.72 (figure).These findings illustrate how first-principles quantum theory combined with modern alloy theory can promote our understanding about the complex chemical and magnetic interactions in novel High Entropy Alloys


[1] Jien-Wei Yeh, US patent, 2002/0159914A1; J. W. Yeh, et al., Adv. Eng. Mater. 6, 299 (2004).

[2]O.N. Senkov, et al., Intermetallics 18, 1758 (2010).

[3] F. Tian, et al., Phys. Rev. B 87, 075144 (2013); Ibid Phys. Rev. B 88, 085128 (2013).

[4] F. Tian, et al., J. Alloys and Comp. 599, 19 (2014).


Figure Legend Characteristic surface of the Young’s modulus E for TiZrNbMoxVyHigh Entropy Alloys.

Characteristic surface of the Young’s modulus E for TiZrNbMoxVy High Entropy Alloys.

Journal Reference

Journal of Alloys and Compounds, Volume 599, 25 June 2014, Pages 19-25.

Fuyang Tian, Lajos Karoly Varga, Nanxian Chen, Jiang Shen, Levente Vitos.

Applied Materials Physics, Department of Materials Science and Engineering, Royal Institute of Technology, Stockholm SE-100 44, Sweden and

Institute for Applied Physics, University of Science and Technology Beijing, Beijing 100083, China and

Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary and

Department of Physics, Tsinghua University, Beijing 100084, China and

Department of Physics and Astronomy, Division of Materials Theory, Uppsala University, Box 516, SE-751210 Uppsala, Sweden.


The TiZrVNb and TiZrNbMoVx (x   = 0–1.5) high-entropy alloys (HEAs) are single-phase solid solutions having the body centered cubic crystallographic structure. Here we use the ab initio   exact muffin-tin orbitals method in combination with the coherent potential approximation to study the equilibrium bulk properties of the above refractory HEAs. We provide a detailed investigation of the effect of alloying elements on the electronic structure and elastic parameters. Our results indicate that vanadium enhances the anisotropy of TiZrNbMoVx. As an application of the present theoretical database, we verify the often quoted correlation between the valence electron concentration (VEC) and the micro-mechanical properties in the case of multi-component alloys. Furthermore, we predict that the present HEAs become elastically isotropic forVEC∼4.72.


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