Multi-component high-entropy alloys (MHAs) are expected to be one of the emerging structural materials, which are designed by the strategy of equal/near-equal atomic ratio and high entropy of mixing, (DS mix ). [1][2][3] MHAs generally have at least five principal elements with the concentrations of each of them being between 5 and 35 at.%. Their particular microstructure and properties offer many potential applications, such as tools, molds, and mechanical parts, etc. [4] Many kinds of MHAs have been studied on their microstructure and properties since the concept was first proposed. [5] Some MHAs have complex microstructures including many intermetallic compounds as its main phases, which makes them brittle and difficult in processing and analyses. [6] However, for some other MHAs, only body-centered cubic (BCC) or face-centered cubic (FCC) solid-solution phase forms rather than intermetallics, and the total number of phases is well below the maximum equilibrium number allowed by the Gibbs phase rule. [2,4,5,[7][8][9] This kind of particular microstructure makes them possess excellent properties, such as high strength, high plasticity, and so on. [2,4,8,9] Thus, for the MHAs, solid solution phase formation rules remain a common interesting scientific problem.Up to now, the existing solid-solution-formation rules are mainly based on alloys with one or two principal components, and there are no any detailed solid-solution formation rules for the MHAs. The purpose of this paper is, by summarizing the microstructure characteristics of the reported MHAs in terms of their atomic-size difference and enthalpy of mixing, to predict the solid-solution formation in various MHAs.From the thermodynamics of materials, solid solution generally forms at the terminal side of the phase diagram, while the ordered intermediate-phase forms at the center of the phase diagram. According to the Hume-Rothery rules for high degree of solubility in binary alloy systems, [10] two factors are mentioned, which would affect the formation of the solid solution in alloys. The first is the size effects of component atoms. For alloys whose component atomic-size differences are over 15 %, it's most improbable to form a substitution solid solution. The second is the chemical compatibility between components, i.e., the electro-negativity difference, or the enthalpy of mixing. The larger the electro-negativity difference (or the more negative of the enthalpy of mixing), the more likely the alloys form compounds rather than solid solutions.In MHAs, however, the case is quite different. As there are many more principal components than common alloys, the component atoms have the same probability to occupy the COMMUNICATIONS 534
