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We study the  K -state phenomenon in the NiCoCr medium-entropy alloy using first-principles techniques jointly with the efficient Wang–Landau Monte Carlo and simulated annealing algorithms. Our theoretical results successfully explain the existence of the peak around 940 K in the experimental specific heat curve that characterizes the  K -state phenomenon and give a fine picture of its atomic origin. The peak is caused by the maximum change of the local configurations characterized by the short-range-order (SRO) parameters at that temperature. The maximum change in SRO parameters is dominated by the nearest-neighbor interactions of atoms but substantially tuned by the many-body interactions. One surprising aspect revealed by the reciprocal-space SRO parameters is that the Ni–Co pair distribution is not random even above the ordering transition temperature, dramatically different from Ni–Cr and Co–Cr, indicating the system cannot be treated as a pseudo binary alloy. This prototypical example shows the complicated nature of multicomponent alloys, different from binary alloys. Our methods can be directly used to study the important  K -state phenomenon observed in a number of other composition-concentrated alloys regardless of their number of components.

Statistics of the NiCoCr medium-entropy alloy: Novel aspects of an old puzzle