### Achievement

We develop a novel data-driven framework to construct effective Hamiltonian for the study of thermodynamics in HEAs using a data-driven approach. Compared to traditional DFT methods, the use of the linear-scaling LSMS greatly improves the calculation speed, allowing the use of a relatively larger DFT dataset and the direct evaluation of the configurations from Monte Carlo simulation. By using the effective pair interactions as the features and adopting the regularized Bayesian regression, the learned effective Hamiltonians demonstrate excellent robustness. By systematically adding data from the Monte Carlo samples, the representativeness of the datasets is greatly improved and the obtained effective Hamiltonian demonstrates very high predicted accuracy, with the test RMSEs as small as 0.019, 0.044, and 0.099 mRy respectively for MoNbTaW, MoNbTaVW, and MoNbTaTiW. These small errors are particularly critical for the study of low-temperature phases and order-disorder transition in thermodynamics.

Using the learned effective Hamiltonian, we investigate the evolution of the specific heats and short-range order parameters through canonical Monte Carlo simulation. For all the studied materials, we demonstrate that there are two major order-disorder transitions, one occurring near room temperature and another one at a higher temperature. We identify that the first transition is caused by W and Nb, while the second one is due to the other elements. We conclude that these results provide an explanation for the stress-strain relations found in the experiment. For example, the addition of V introduces strong pair interactions, which significantly increases the temperature of the second order-disorder transition. As a result, the abundance of second-phase precipitates in a wide temperature range reduces the ductility of the MoNbTaVW, as compared to MoNbTaW and MoNbTaTiW. Moreover, the first order-disorder transition in the materials also helps explain the experimental phenomenon of ductility increase after room temperature. These findings will provide useful guidance and insight to the future design of HEAs.

**Publication**:

- Xianglin Liu, Jiaxin Zhang*, Junqi Yin, Sirui Bi, Markus Eisenbach, Yang Wang. "Monte Carlo simulation of order-disorder transition in refractory high entropy alloys: a data-driven approach."
, 2020. arXiv:2011.00698**Computational Materials Science**

### Significance and Impact

- A novel data-driven approach to study the thermodynamics of HEAs is introduced, with pair interactions adopted as the machine learning features, and active learning applied to improve the representativeness of the dataset.

- Using this method, highly accurate effective Hamiltonians are obtained. The test error is 0.019, 0.044, and 0.099 mRy for MoNbTaW, MoNbTaVW, and MoNbTaTiW, respectively.

- From the calculated specific heats and short-range order parameters, two major order-disorder transitions are identified and their origins are revealed.

- By comparing with the experiment, the results demonstrate that the order-disorder transitions provide an explanation for the temperature dependence of strength and ductility in HEAs.

Last Updated: January 14, 2021 - 11:16 am