Prediction of phase, hardness and density of high entropy alloys based on their electronic structure and average radius Articles uri icon


  • Calvo Dahlborg, M.
  • Mehraban, S.
  • Lavery, N. P.
  • Brown, S. G.R.
  • Cullen, J.
  • Cieslak, J.
  • Leong, Z.
  • Goodall, R.
  • Dahlborg, U.

publication date

  • June 2021

start page

  • 1

end page

  • 8


  • 865

International Standard Serial Number (ISSN)

  • 0925-8388

Electronic International Standard Serial Number (EISSN)

  • 1873-4669


  • According to a recent Hume-Rothery approach, the electron concentration, e/a, and the average radius can be used to identify the domain of stability of HEAs and to estimate the phases that may occur in the alloy. The present study investigates the influence of the electronic structure and the average radius on the hardness for a series of HEA alloys. The alloys investigated in this work all contained Co, Fe and Ni as base elements. To this base system one or more elements were added, including Al, Cr, Cu, Sn, Pd, Ru, Ti, and V in different proportions. For comparison, data on phases identified and hardness have been taken from a wide range of bibliography for other types of alloys in the systems Co-Cr-Fe-Cu-A-B-C-D-E-F, with A, B, C, D, E, F = Al, Ti, V, Nb, Cu, Mo, Mn, B, Si, Y, Sc, Ru, Re, Gd, Dy, Ho, Lu, Tb, Er, Tm, La, W, Ta, Hf, Zr. In order to predict the occurrence of mainly fcc, bcc and hcp phases, the average atomic radius is preferable over to the average radius for a 12 nearest atoms neighbourhood. Based on this [e/a; radius] system, it is shown that the hardness of the HEA composition can be predicted. By using this classification, it is possible to determine compositions of HEA alloys with adequate range of hardness, density and phases present. The consequences of such predictions when modelling the structure and mechanical behaviour of HEAs is fundamental for their application.


  • Materials science and engineering


  • density; design; hardness; high entropy alloys; phases