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High entropy alloys (HEAs) are a series of novel materials that demonstratemany exceptional mechanical properties. To understand the origin of theseattractive properties, it is important to investigate the thermodynamics andelucidate the evolution of various chemical phases. In this work, we introducea data-driven approach to construct the effective Hamiltonian and study thethermodynamics of HEAs through canonical Monte Carlo simulation. The maincharacteristic of our method is to use pairwise interactions between atoms asfeatures and systematically improve the representativeness of the dataset usingsamples from Monte Carlo simulation. We find this method produces highly robustand accurate effective Hamiltonians that give less than 0.1 mRy test error forall the three refractory HEAs: MoNbTaW, MoNbTaVW, and MoNbTaTiW. Using replicaexchange to speed up the MC simulation, we calculated the specific heats andshort-range order parameters in a wide range of temperatures. For all thestudied materials, we find there are two major order-disorder transitionsoccurring respectively at $T_1$ and $T_2$, where $T_1$ is near room temperaturebut $T_2$ is much higher. We further demonstrate that the transition at $T_1$is caused by W and Nb while the one at $T_2$ is caused by the other elements.By comparing with experiments, {\color{black} the results provide insight intothe role of chemical ordering in the strength and ductility of HEAs.

Monte Carlo simulation of order-disorder transition in refractory high entropy alloys: a data-driven approach