Influence of Al substitution for Sc on thermodynamic properties of HCP high entropy alloy Hf0.25Ti0.25Zr0.25Sc0.25-xAlx from first-principles investigation
Introduction
In recent years, high-entropy alloy (HEA) as a new concept of alloy design is proposed, which contains five or more principal elements with concentration of each element in the range of 5–35 at.% [[1], [2], [3], [4]]. Naturally the configuration space of HEAs exceeds considerably over one of conventional alloys comprised of one and rarely two base elements [5]. Due to high configuration entropy, multicomponent HEAs usually form random solid solution phases and possess four core effects [6,7]: high entropy of mixing, sluggish diffusion of atoms, severe lattice distortion and cocktail effect. Hence, HEAs have superior properties, such as high strength [8], high toughness [9,10], good wear and corrosion resistance [11], high structural thermal stability and stronger resistance to thermal softening [12], and special electromagnetic properties [13]. These properties show great potentials in a widespread range of structural and functional applications [14]. So the new high-entropy alloys have been attracting great research interesting in modern material science.
With rapid development of HEA field, more and more HEAs are synthesized. So far, most HEAs possess FCC and BCC structures, while hexagonal close-packed (HCP) HEAs are very rare and mainly composed of rare-earth (RE) elements [11], hence the development of more HCP HEAs is hot topic. On the other hand, intense efforts in HEAs field have been devoted to exploring various potential applications. Since most HEAs have high densities which impede their practical applications to some extent, thus researchers have gradually focused on explorations of low-density HEAs [15]. Based on development tendency above, investigation of low-density HCP HEAs, especially less or no RE HCP HEAs, is frontier topic. Moreover, mechanical strength and/or hardness of HCP HEAs are presumably stronger originating from the distinct structural feature from FCC and BCC structures [16]. Recently, Lukasz et al. [17] have reported a novel HCP HfScTiZr HEA system, with lower density and excellent mechanical properties, good fatigue resistance characteristics, superior thermal stability and design flexibility, etc. In more recent study [17], Al as typical additive is introduced into the novel HCP HfScTiZr and substituted for Sc. It is found that the crucial mechanical properties such as strength/hardness and ductility are improved with Al content less than 15 at.%, even higher Al content lead to formation of superstructure. To promote the high temperature structural applications of high entropy alloys Hf0.25Ti0.25Zr0.25Sc0.25-xAlx, it is very necessary and valuable to study deeply the influences of Al content on thermodynamic properties of Hf0.25Ti0.25Zr0.25Sc0.25-xAlx.
Since the experimental research is time-consuming and high cost, theoretical study is more convenient, and becomes a power tool in modern material science. In this study, the investigations of thermodynamic properties of Hf0.25Ti0.25Zr0.25Sc0.25-xAlx (x ≤ 15 at.%) are performed from first-principles employing the exact muffin-tin orbitals (EMTO) method in combination with the coherent potentials approximation (CPA) and quasi-harmonic Debye-Grüneisen model. The influences of Al content on temperature dependence of crucial thermodynamic properties are studied in detail. Present investigations are significant for understanding, optimization and applications of novel HCP HEAs Hf0.25Ti0.25Zr0.25Sc0.25-xAlx.
Section snippets
Computational methods
The present theoretical calculations were performed using density functional theory (DFT) via EMTO-CPA method in which the Perdew-Burke-Ernzerhof (PBE) version of generalized gradient approximation (GGA) [18] were employed, because EMTO-CPA approach has been proven to be an effective tool to investigate the equilibrium properties of HEAs [19,20]. The EMTO basis set included s, p, d, and f orbitals, and the Green's function was calculated for 16 complex energy points distributed exponentially on
Structural stability
To judging the solid solution phase formation of high entropy Hf0.25Ti0.25Zr0.25Sc0.25-xAlx (x ≤ 15 at.%), the atomic size difference is one of most crucial parameters, which is defined asWhere with ri and ci being respectively the atomic radius and atomic percentage of the individual alloy components, and n is the number of components. The obtained results are shown in Fig. 1. It can be seen that with substitution of Al for Sc, the atomic size difference of Hf0.25
Conclusions
In this work, thermodynamic properties of HCP Hf0.25Ti0.25Zr0.25Sc0.25-xAlx (x ≤ 15 at.%) HEAs has been studied by ab initio calculations in conjunction with the quasi-harmonic Debye-Grüneisen model. Noticeably, substitution of Al for Sc has significant influence on structural and thermodynamic properties of HCP Hf0.25Ti0.25Zr0.25Sc0.25-xAlx (x ≤ 15 at.%). With increasing Al content, bulk modulus is appreciably enhanced in spite of similar softening trend, so addition of Al is beneficial to
CRediT authorship contribution statement
Guo-Yong Gan: Methodology, Software, Formal analysis, Writing - original draft. Li Ma: Data curation, Resources. Dong-Ming Luo: Visualization, Formal analysis. Shan Jiang: Software, Validation. Bi-Yu Tang: Conceptualization, Supervision, Writing - review & editing.
Acknowledgments
The authors gratefully acknowledge the financial support from National Natural Sciences Foundation of China under Grant no. 51461002, Key Project of Guangxi Scientific Foundation under Grant no. 2018GXNSFDA281010 and Guangxi Key Laboratory of Processing for Nonferrous Metals and Featured Materials, Guangxi University under Grant no. 2019GXYSOF07.
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