Materials science communication
Prediction of high-entropy stabilized solid-solution in multi-component alloys

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Abstract

Phase formation for the multi-component alloys has been predicted by calculating parameter Ω and δ for typical multi-component alloys reported. Here, Ω is defined as a parameter of the entropy of mixing timing the average melting temperature of the elements over the enthalpy of mixing, δ is the mean square deviation of the atomic size of elements. It shows that the high-entropy (HE) stabilized solid-solution is located at Ω  1.1 and δ  6.6%.

Highlights

► A parameter Ω is defined for predicting the solid-solution formation. ► The parameters Ω and δ are calculated for typical multi-component alloys reported. ► A new criterion for forming solid-solution phase is proposed.

Introduction

In recent years, high-entropy alloys (HEAs) have attracted increasing attentions, because they have been reported to exhibit unique microstructures and special properties [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35]. According to Yeh et al. [2], [3], [6], HEAs are defined as alloys that generally have at least 5 major metallic elements, each of which has an atomic percentage between 5% and 35%.

It has been reported that HEAs usually intend to form FCC and/or BCC solid solutions rather than intermetallic compounds or other complex ordered phases owing to HE of mixing [2], [11]. This HE stabilized solid-solution is a very strong solution, and we cannot know which one is the solvent atom and which ones are solute atoms.

People are usually interested in prediction what the phases and micro/nano structures will be formed for the multi-component HEAs before doing the experiments. However, up to now, only a few studies have been carried out on phase formation rule for multi-component HEAs because of the absence of information about multi-component alloys in phase diagrams. Zhang et al. [15] proposed that small atomic size differences and near-zero values of the absolute enthalpy of mixing facilitate the formation of solid-solutions for multi-component alloys, that is, the atomic size differences should be less than 6.5%, the enthalpy of mixing should be in the range of −15 to 5 kJ mol−1 and the entropy of mixing should be in the range of 12–17.5 J K−1 mol−1.

However, as a wide range of new multi-component HEAs systems have been explored lately, these proposed phase formation rules should be revised accordingly. Hence, further investigation is necessary to obtain a more precise phase formation rule for multi-component HEAs.

In the present study, a literature search of microstructure in various multi-component alloy systems has been carefully conducted, and the corresponding atomic size differences, enthalpy of mixing and entropy of mixing have been calculated. On the basis of all available data, a solid-solution formation rule for multi-component HEAs has been proposed in this paper.

Section snippets

Theory analysis and discussion

As reported previously [10], [36], [37], besides solid-solutions phases, multi-component HEAs may form intermetallic compounds and amorphous phases. Simple solid-solution phases are most expected to form in multi-component HEAs owing to their promising properties [2], [16]. In order to predict the solid-solution formation rule in multi-component alloys, Gibbs free energy for multi-component alloy systems has been considered firstly.

For the analysis of solidification, the difference in Gibbs

Results

Table 1 presents the values of δ, ΔHmix, ΔSmix, Tm and Ω, which are calculated based on Eqs. (2), (3), (4), (5), (6), for the reported typical multi-component HEAs. It is necessary to point out that only the multi-component HEAs which are synthesized by normal casting or casting into copper mould are shown in the table in order to lower the influence of dynamic factors. The number of the phases and their structures also depend on processing conditions besides δ and Ω, such as the splat

Conclusions

A parameter Ω, defined as TmΔSmix/ǀΔHmixǀ, has been proposed to estimated solid-solution formation ability in multi-component alloy systems. By calculating parameters of δ and Ω for typical multi-component HEAs reported, a solid-solution formation rule for multi-component HEAs has been proposed, and Ω  1.1, δ  6.6% should be expected as the criteria for forming HE stabilized solid-solution phase.

Acknowledgments

The authors would like to acknowledge financial support by the National Natural Science Foundation of China (NNSFC, no. 50971019).

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