Elsevier

Intermetallics

Volume 86, July 2017, Pages 134-146
Intermetallics

Prediction of structure and elastic properties of AlCrFeNiTi system high entropy alloys

https://doi.org/10.1016/j.intermet.2017.03.014Get rights and content

Highlights

  • The mixing enthalpy would be a common criterion for evaluating the elastic isotropy of HEAs.

  • There is a combination bonding of metallic, covalent and ionic nature in AlCrFeNiTiX alloy.

  • The ductility of AlCrFeNiTiX HEAs weakens with increasing mixing enthalpy.

Abstract

The effect of alloy compositions on structure and elastic properties of single-phase AlCrFeNiTi and AlCrFeNiTiX (X = V, Mn, Co, Zn, Zr, Nb, Mo and La) high entropy alloys was investigated by calculating solid solution characteristics of alloys combining with the first principles method. The obtained formation enthalpy, cohesive energy and mechanical stability indicated AlCrFeNiTi and AlCrFeNiTiX (X = V, Mn, Co, Nb and Mo) HEAs adopt the body centered cubic structure instead of face centered cubic structure. There is a rather good agreement between theoretical structure predictions and the classic criteria of valence electron concentration VEC. A detailed investigation on electronic structure of AlCrFeNiTi and AlCrFeNiTiX alloys revealed the bonding behavior of alloys. In addition, the calculated results of polycrystalline elastic parameters confirmed the ductility of AlCrFeNiTiX alloys would weaken with increasing mixing enthalpy ΔHmix (or decreasing atomic size difference δ), and the increase in ΔHmix is predicted to decrease the elastic anisotropy. Furthermore, we predicted that the present high entropy alloys should be more elastically isotropic when the corresponding the mixing enthalpy ΔHmix has a larger value.

Introduction

High entropy alloys (HEAs), which are composed of more than four metallic elements with equal or near equal atomic ratio, have attracted widespread concerns and become one class of emerging structural materials with greater development potential due to its outstanding high mechanical strength, excellent corrosion and wear resistance and unique electromagnetic properties [1], [2], [3]. Based on the traditional theory of high mixing entropy, the formation of multiple and complex intermetallic compounds are avoided in HEAs, and high entropy alloys usually form simple solid solutions with body centered cubic (BCC) or face centered cubic (FCC) structures [4], [5], [6], [7], [8]. The formation of solid solutions in HEAs is the main reason that these alloys present excellent properties. Hence, the relationship between composition design and property prediction for HEAs has become an important focus in recent years.

The statistical method is usually adopted to predict the structures of HEAs from the view of some solid solution characteristics of alloys. The atomic size difference and chemical compatibility are widely used as criteria for HEAs to estimate the structures of alloys. Yang et al. [9] predicted the formation ability of solid solutions, ordered solid solutions, intermetallics and bulk metallic glasses in multi-component alloy systems by calculating parameters including atomic size difference (δ) and the ratio of entropy to enthalpy (Ω), it was found that when δ ≤ 6.6% and Ω ≥ 1.1 are satisfied, there are stabilized solid-solution phases forming in HEAs. The valance electron concentration (VEC) was introduced to evaluate the structure stability of HEAs by Guo et al. [10], the results showed that a higher and a lower value of VEC correspond to the formation of FCC and BCC phases in HEAs, respectively. In addition, the artificial neural network method was also successfully applied to predict the structures of HEAs by the current authors [11], using these solid solution characteristics mentioned above. These research results all indicate the formation of structures in HEAs is closely related to the atomic size difference and chemical compatibility. Hence, it brings out the light on the structure prediction for HEAs.

On the other hand, despite of these theoretical efforts, the investigation on property prediction connected to alloy compositions of HEAs is still very limited. The first principles method, which is an effective tool to predict the physical and mechanical properties of materials from atomic level description, is also applied to investigate the structural stability and elastic property of HEAs. Li et al. [12] used the supercell model combined with first principle calculations to reveal the bonding features of Al2CrCoNiFe HEAs with body centered cubic (BCC) structure, it was reported that there is somewhat ionic bonding between Al and other metal elements. Based on the Ab initio calculations, the bulk properties of CuNiCoFeCrTix (x = 0.0–1.0) HEAs were investigated by Tian et al. [13], which indicated that the addition of Ti would improve the ductility of CuNiCoFeCr alloys while the isotropy feature would be less. These authors also calculated the single-phase TiZrNbMoVx (x = 0–1.5) HEAs by the Ab initio method [14], the results verified the correlation between the VEC and the elastic properties, and provided a range of VEC for these HEAs with better elastically isotropy.

However, in order to predict elastic properties of HEAs by using the first principles method, there are still two important core problems which are needed to be discussed. The first one is the selection of a reasonable crystal structure for multi-component alloys. That is because HEAs are usually disordered solid solutions, and all alloying atoms have no fixed positions and tendency of long range ordering in lattice. Aiming at this, crystal structures for the HEAs suggested by researchers [13], [15], [16] are employed by building a simple supercell (SC) based on BCC or FCC unit cells, in which all alloying elements are distributed and neighbors to each other. Although this structure also shows the feature of long-range order, it is a rather small effect on the elastic properties of alloys [17]. Hence, it is appropriate to adopt this ordered crystal structure to investigate the elastic properties of HEAs by the first principle calculations. In addition, the first principle method is only suitable for calculating the electronic and elastic properties of single-phase structure, which is an intrinsic disadvantage. Regarding HEAs, it is confirmed by experiments that single-phase solid solution only forms in a few and special alloy systems, and mixed structures including FCC + BCC, disordered and ordered BCC, or two FCC are usually observed in most of systems [1], [2], [3], [4], [5], [6]. It is seem that it is not feasible to predict the mechanical property of HEAs by using this first principles method. Fortunately, although there are two or even more solid solutions with different alloy compositions forming in most of HEAs system, every single solid solution can be seen as a single-phase structure and would be calculated by first principles. Hence, the elastic properties of each solid solution phase in HEAs, which can provide guidance for the prediction of the mechanical property to a certain degree, also play an important role on alloy design.

In the present paper, in order to explore the relationship between alloy compositions and elastic properties of HEAs, firstly, the first principle calculations were applied to investigate the theoretical elastic properties of HEAs, and alloy compositions were represented in the form of the atomic size difference and chemical compatibility. Then the effect of solid solution characteristics on elastic properties was deeply discussed. A series of single-phase AlCrFeNiTiX (X = V, Mn, Co, Zn, Zr, Nb, Mo and La) (or one phase in HEAs) were chosen as the research systems. This result will provide a direction of the alloy design for HEAs.

Section snippets

Computational details

The atomic size difference δ, mixing enthalpy ΔHmix, electronegativity difference Δχ and valence electron concentration VEC were introduced in this work to investigate the solid solution characteristics of single-phase AlCrFeNiTiX HEAs. The atomic size difference δ, which is related to the formation of the substitution solid solution, is usually calculated as [18]:δ=100i=1Nci(1ri/r¯)2,r¯=i=1nciriwhere ci is atomic percentage of the ith component, and ri is the corresponding atomic radius.

Equilibrium volume and structural stability

According to the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method [29] of structure optimization, the equilibrium volumes and corresponding lattice constants for single-phase AlCrFeNiTiX (X = V, Mn, Co, Zn, Zr, Nb, Mo and La) HEAs were obtained. Based on the assumption about the structural modelings mentioned above, each unit cell in supercell maintains orthorhombic structure characteristic, thus it was found in this calculation that similar lattice constants a, b and c for respective unit cells

Conclusions

In conclusions, the first principle calculations have been introduced to investigate the relationship between solid solution characteristics and elastic properties of single-phase AlCrFeNiTi and AlCrFeNiTiX (X = V, Mn, Co, Zn, Zr, Nb, Mo and La) HEAs. The calculated equilibrium lattice constants have the same change rule with the atomic size difference δ. AlCrFeNiTi and AlCrFeNiTiX (X = V, Mn, Co, Nb and Mo) HEAs are predicted to adopt the BCC structure instead of FCC structure based on the

Acknowledgments

This research was supported the Doctor Startup Foundation of Liaoning Province, China (No. 201501079) and the National Natural Science Foundation of China (No. 51401099). The authors would also like to thank the Harbin Institute of Technology for providing the research facilities.

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