Fig. 4: Monte Carlo atomistic simulations employing a machine learning potential developed to capture CSRO in CrCoNi²⁹.

a Direct comparison of ΔH_CSRO between simulations and experiments. The \(\varDelta {H}_{{{\rm {CSRO}}}}\) can be understood as \({H}_{{{\rm {CSRO}}}}^{{T}}-{H}_{{{\rm {CSRO}}}}^{748\,{\rm {K}}}\), or in other words, as the difference in enthalpy between the sample at a temperature T and the equilibrium state at 748 K. b Enthalpic contribution stemming from CSRO as a function of temperature (blue) and Cr–Cr Warren–Cowley parameter \({\alpha }_{{{\rm {Cr}}}-{{\rm {Cr}}}}^{m=1}\) (green) for first neighbors. At temperatures above 748 K, the figure shows the enthalpy is higher (or more positive), meaning that there is heat absorption by the system to destroy CSRO. Good agreement between the experimental and simulated values is seen only above 873 K because only at this temperature do the kinetics of the system allow the system to reach equilibrium within the experimental timescale. Below this temperature, the experimentally measured ΔH_CSRO is expected to be lower than simulations because experiments do not achieve the equilibrium CSRO due to slow kinetics, while simulations always predict equilibrium values. A 4.3% error was considered for the experimental data as explained in the “Methods” section, also further details on the calculation of the experimental curve are given in Supplementary Information Fig. 6.