Electronic Moment Tensor Potentials (eMTP): Application to Refractories and Shape-Memory Alloys

We present the electronic moment tensor potentials (eMTPs), a class of machine-learning interatomic models and a generalization of the classical MTPs, reproducing both the electronic and vibrational degrees of freedom, up to the accuracy of <i>ab initio</i> calculations (Srinivasan et al., 2023). Following the original polynomial interpolation idea of the MTPs, the eMTPs are defined as polynomials of vibrational and electronic degrees of freedom, corrected to have a finite interatomic cutoff. Practically, an eMTP is constructed from the classical MTPs fitted to a training set, whose energies and forces are calculated with electronic temperatures corresponding to the Chebyshev nodes on a given temperature interval. The eMTP energy is hence a Chebyshev interpolation of the classical MTPs. With eMTPs, one can access the temperature-dependent electronic and vibrational free energies and the coupling between the two, separately.<br/><br/>The performance is demonstrated on two classes of systems: (1) refractory Nb and TaVCrW high-entropy alloy, and (2) equiatomic Nickel-Titanium (NiTi) shape-memory alloy (SMA). The refractories demonstrate a significant electronic, vibrational, and coupling contribution to the free energy, all of which get captured accurately by performing a thermodynamic integration (Jung et al., 2022) to the eMTPs. We are able to reach full density-functional theory accuracy in thermodynamic properties all the way to the melting point without any further <i>ab initio</i> calculations.<br/><br/>The NiTi SMA is considerably more challenging to model owing to several energetically competing phases (body-centered cubic B2, monoclinic B19’, orthorhombic B19 and base-centered orthorhombic B33). We train an eMTP to obtain the thermodynamic phase stability including all relevant contributions. The experimentally observed low-temperature martensitic (B19’) and high-temperature austenitic (B2) phases get entropically stabilized. Both the vibrational and electronic contributions also significantly affect the B2-B19’ phase transformation, bringing the behavior much closer to experiments. The eMTP-thermodynamic integration approach enables us to analyze the accuracy of different exchange correlation functionals and <i>ab initio</i> parameters. Lastly, to investigate kinetic effects, we perform large-scale molecular dynamics simulations using the eMTP to model the stress-induced and temperature-induced phase transformation.<br/><br/><u><b>References</b></u><br/>[1] Srinivasan P., Demuriya D., Grabowski B., Shapeev A.V.: preprint at research square https://doi.org/10.21203/rs.3.rs-2643432/v1, 2023<br/>[2] Jung J.H., Srinivasan P., Forslund A., Grabowski, B.: npj Computational Materials <b>9</b>, 3 (2023)