Abstract:A method for rapidly predicting the formation and stability of undiscovered single phase high-entropy alloys (SPHEAs) is provided. Our software implementation of the algorithm uses data for 73 metallic elements and rapidly combines them -4, 5 or 6 elements at a time -using the Miedema semi-empirical methodology to yield estimates of formation enthalpy. Approximately 186,000,000 compositions of 4, 5 and 6 element alloys were screened, and ~1,900 new equimolar SPHEAs predicted. Of the 185 experimentally reported HEA systems currently known, the model correctly predicted the stability of the SPHEA structure in 177. The other sixteen were suggested to actually form a partially ordered solid solution -a finding supported by other recent experimental and theoretical work. The stability of each alloy at a specific temperature can also be predicted, allowing precipitation temperatures (and the likely precipitate) to be forecast. This combinatorial algorithm is described in detail, and its software implementation is freely accessible through a webservice allowing rapid advances in the design, development and discovery of new technologically important alloys. , and re-iterated by others since then [1,12], defines a HEA as any alloy consisting of 5 or more elements between 5 -35 at. %. As such, this type of HEA will usually possess a microstructure consisting of two or more distinct phases, some of which are likely to be brittle intermetallic compounds. Although, multiphase strengthening is sometimes desirable in alloys, a large amount of any brittle phase will generally make an alloy unusable as a structural material and such HEAs are therefore mundane. However, as will be discussed shortly, in a few special cases, the additional entropy of the multi-element composition will stabilise a microstructure consisting of either (i) a single solid solution having one of the simple close-packed crystal structures (FCC, HCP or BCC) or (ii) a duplex microstructure consisting of two such simple solid solutions. Generally, it is these non-trivial examples of HEA that interest investigators.This is because the resulting random solid solution(s) will exhibit a combination of ductility coupled with significant solid solution hardening. We recommend use of the term single 2 phase high-entropy alloy (SPHEA) as a more restrictive term to differentiate the rare and desirable single phase type of HEA from generic examples of multiphase HEAs.Combining Yeh's compositional limits [7] with the requirement for a single phase solid solution, we can define a SPHEA as an alloy with  4 alloying elements, at least 4 of which with a molar ratio between 0.33 -1 to that of the highest contributing element. These alloys must be able to display a single phase of simple, random, close-packed structure below the solidus.We return now to the factors that might stabilise a SPHEA. The prevailing hypotheses were (i) that the simple crystal structure or structures are thermodynamically stabilised, relative to possible intermetallic compounds, by the inc...