Phase selection rules for cast high entropy alloys: an overview S. Guo* This paper summarises existing phase selection rules for cast high entropy alloys. Essentially, they are almost all based on the parametric approach, utilising various descriptors comprising mixing enthalpy, configuration entropy, mismatch entropy, melting points, atomic size mismatch, electronegativity and valence electron concentration. The overview starts from phase selection rules for solid solutions, intermetallic compounds and the amorphous phase in high entropy alloys. Further discussions are relevant to selection rules for solid solution phases in high entropy alloys, more specifically, for face centred cubic and body centred cubic type solid solutions. Finally, some challenges and future prospects of phase selection rules for high entropy alloys are addressed. Keywords: High entropy alloys, phase selection, Solid solutions, Intermetallic compounds, Amorphous phase This paper is part of a special issue on High entropy alloys Introduction High entropy alloys (HEAs), or multiprincipal element alloys with equiatomic or nearly equiatomic compositions, 1,2 are becoming the new research frontier in the metallic material field. Conceptually, HEAs provide a brand new alloy design strategy to the conventional physical metallurgy that has mainly been working with alloys based on one and two principal elements, for example, Fe, Al, Cu and Ti based alloys and NiAl, TiAl and NiFe based alloys. The compositional space opened by HEAs is enormous, and as a matter of fact, many novel alloys with unique structural and functional properties have been developed in the family of HEAs. 3–7 A very recent and decent example is CoCrFeMnNi, a single phase face centred cubic (fcc) solid solution structured HEA, which showed exceptional damage tolerance with tensile strengths w1 GPa and fracture toughness values exceeding 200 MPa m 1/2 , and simultaneously enhanced strength and ductility at cryogenic temperatures. 8 More excitements from HEAs await further alloy developments and continuous research efforts into this new class of metallic materials. Meanwhile, the rapid development of HEAs also raises opportunities to look into some scientifically intriguing questions on multicomponent alloys, particularly on concentrated multicomponent alloys. The phase selection in HEAs is an outstanding one among those questions and has indeed attracted much attention since the early stage of the development of HEAs. Quite a few works have been done on this topic, and it seems timely at this stage to summarise what are known and what remain to be unknown, a clear understanding of which can benefit further developments of HEAs. Before discussing the phase selection in HEAs, it is important to first clarify the definition of HEAs that is held in the present paper. The simple reason for this clarification is that even the definition of HEAs has been quite controversial. When the term HEAs was coined, HEAs were defined by their compositions in that they are composing of at least five principal metallic elements, each with a concentration between 5 and 35 at-%. 1 The configurational entropies of these compositionally complex alloys, in the liquid or fully random solid solution state, are much higher than those of conven- tional crystalline alloys and even bulk metallic glasses (BMGs), 9 and here comes the name of HEAs. The configuration entropies of alloys are calculated by the Boltzmann equation, on the premise that they are in the liquid or fully random solid solution state 10 : DS mix ¼ 2R X n i¼1 c i lnc i ð1Þ where R is the gas constant, n is the number of alloying elements and c i is the atomic percentage for the ith el- ement. However, this definition has been widely chal- lenged, and the argument is that the phase constitution complexity has to be considered when classifying HEAs. More specifically, the claim is that genuine HEAs are limited to multiprincipal element alloys forming a single phase disordered solid solution. 11–13 This added limi- tation certainly has its ground, as from the entropic point of view, the configurational entropies of the mul- tiprincipal element alloys could be rather low, if inter- metallic compounds form. However, as Miracle et al. pointed out, 14 this more strict definition of HEAs is not trouble free either. In multiprincipal element alloys, it is quite common to see two or more disordered solid sol- utions form, without the formation of intermetallic compounds. 15–18 Furthermore, in some alloys, the amorphous phase with a high configurational entropy is Surface and Microstructure Engineering Group, Department of Materials and Manufacturing Technology, Chalmers University of Technology, SE- 41296, Gothenburg, Sweden, *Corresponding author, email sheng.guo@chalmers.se Ñ 2015 Institute of Materials, Minerals and Mining Published by Maney on behalf of the Institute Received 11 April 2013; accepted 1 August 2013 DOI 10.1179/1743284715Y.0000000018 Materials Science and Technology 2015 VOL 31 NO 10 1223