A new empirical rule to form single phase solid solution structured high entropy alloys was proposed by integrating three dependent parameters, i.e. atomic size difference δ, mixing enthalpy Δ Hmix and valence electron concentration VEC. It was found that the single phase face centred cubic solid solution will form if δ < 4.27, − 7.27 kJ mol− 1 < Δ Hmix < 4 kJ mol− 1 and VEC>8, while the single phase body centred cubic solid solution will form in the case of δ < 4.27, − 7.27 kJ mol− 1 < Δ Hmix < 4 kJ mol− 1 and VEC < 6.87. This empirical rule was verified by typical high entropy alloys that have been reported.

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