Phase discovery with active learning: Application to structural phase transitions in equiatomic NiTi

TL;DR

The paper addresses displacive phase transitions in equiatomic NiTi by developing four on-the-fly trained, machine-learned force fields based on $\text{LDA}$, $\text{PBE}$, $\text{PBEsol}$, and $\text{SCAN}$ DFT functionals. An automated active-learning protocol drives MD simulations and updates the models with DFT data whenever local-energy uncertainty crosses a threshold, providing ab initio-accurate sampling at a fraction of the cost. Across functionals, SCAN uniquely captures the reversible $B2$ to $B19'$ martensitic transition, while $\text{LDA}$, $\text{PBE}$, and $\text{PBEsol}$ predict a distinct low-volume phase $M2$ upon cooling; large-scale MD confirms these pathways and reveals a pressure-stabilized $M2$ region, suggesting a phase diagram where $M2$ is distinct from $B19'$. Overall, the work demonstrates a scalable framework to study complex displacive transformations with high fidelity, and highlights meaningful functional-dependence in NiTi that can only be unveiled through large-scale, data-driven simulations.

Abstract

Nickel titanium (NiTi) is a protypical shape-memory alloy used in a range of biomedical and engineering devices, but direct molecular dynamics simulations of the martensitic B19' -> B2 phase transition driving its shape-memory behavior are rare and have relied on classical force fields with limited accuracy. Here, we train four machine-learned force fields for equiatomic NiTi based on the LDA, PBE, PBEsol, and SCAN DFT functionals. The models are trained on the fly during NPT molecular dynamics, with DFT calculations and model updates performed automatically whenever the uncertainty of a local energy prediction exceeds a chosen threshold. The models achieve accuracies of 1-2 meV/atom during training and are shown to closely track DFT predictions of B2 and B19' elastic constants and phonon frequencies. Surprisingly, in large-scale molecular dynamics simulations, only the SCAN model predicts a reversible B19' -> B2 phase transition, with the LDA, PBE, and PBEsol models predicting a reversible transition to a previously uncharacterized low-volume phase, which we hypothesize to be a new stable high-pressure phase. We examine the structure of the new phase and estimate its stability on the temperature-pressure phase diagram. This work establishes an automated active learning protocol for studying displacive transformations, reveals important differences between DFT functionals that can only be detected in large-scale simulations, provides an accurate force field for NiTi, and identifies a new phase.

Figures (6)

• Figure 1: On-the-fly training of NiTi force fields. (a, d) Snapshots from PBE and SCAN training simulations. Atoms are colored by uncertainty in the local energy prediction. (b, e) Potential energy predictions during the cooling and heating simulations. DFT potential energies are shown in black, with vertical lines indicating changes in temperature. (c, f) Atomic volumes during training. For clarity, a moving average is plotted in dark red and blue.
• Figure 2: Cohesive energy versus volume of $B2$ and $B19'$ NiTi predicted by the four models trained in this work (LDA, black; PBEsol, green; PBE, blue; and SCAN, magenta) and by the MEAM model of Ref. ko2015development (red). DFT cohesive energies are shown as dots for $B2$ and triangles for $B19'$. Experimental estimates of the cohesive energy and atomic volume of $B2$ NiTi derived from Refs. kubaschewski1956reactionkittel1996introductionprokoshkin2004lattice are shown as a gold star.
• Figure 3: Elastic constants of $B19'$ NiTi predicted with the PBE-trained model (dark blue), with PBE DFT (light blue), and with the MEAM model of Ref. ko2015development.
• Figure 4: $B2$ and $B19'$ phonon frequencies predicted with the PBE-trained model (blue), with PBE DFT (dotted), and with the MEAM model of Ref. ko2015development.
• Figure 5: Large-scale MD simulations of phase transitions in equiatomic NiTi at zero pressure. (a) Snapshots of $B2$ NiTi from the SCAN cooling/heating simulation (left) and of $B19'$ NiTi from the SCAN heating simulation (right). (b) Cooling/heating simulation of $B2$ NiTi (dark) and heating simulation of $B19'$ NiTi (light colors). Zero-Kelvin volumes of $B19'$ (triangle) and $M2$ (square) are shown for reference. To avoid overlap in the plot, the PBEsol simulations are reported in Fig. S15.