ADVANCED MATERIALS & PROCESSES | OCTOBER 2025 48 using cubic supercells with 128 atoms. Then the computed atomic forces were fitted to obtain the effective force constants of the B2 phase at these temperatures. The resulting phonon distributions are plotted in Fig. 2 based on the TDEP approach. As temperature increases, the magnitude of the frequency of the negative (indicating imaginary) phonon mode at (1/3, 1/3, 0) decreases until the phonon has a positive frequency between 75 and 100 K, suggesting that the cubic phase becomes dynamically stable. Martensitic phase transition. Being dynamically stable, or having no imaginary phonons, is a necessary condition for a phase to exist, but not sufficient. To determine if such a B2-to-R transition would occur, the Gibbs free energies vs. temperature for both phases were computed. Although the B2 phase only has a very weak anharmonicity and the R phase has no imaginary phonons at 0 K, omitting the anharmonic free energies and using the quasi-harmonic approximation leads to an overestimation of MTT to be 166 K, in comparison with the measured values of 64–67 K[1-4]. This is because a tiny energy difference of merely 2.49 meV/atom separates these two phases, and one must evaluate every part of the Gibbs free energy with great care to reach very high accuracy. Therefore, the team ran AIMD simulations and performed thermodynamic integrations for both phases at 25, 50, 75, 100, and 125 K. At each λ (= 0.0, 0.25, 0.50, 0.75, 0.875, 1.0) value in thermodynamic integration, researchers carried out AIMD for 5–10 ps to ensure that the statistical error in is less than 0.05 meV/atom. Three different supercells were also used with 54, 128, and 432 atoms for the B2 phase and 54, 108, and 432 atoms for the R phase, to ensure the convergence with respect to supercell size. The calculated MTTs are 27, 91, and 96 K, respectively, as summarized in Fig. 3. Similar to what was found in NiTi and other binaries, supercells with 128–144 atoms are sufficiently large to obtain numerically nearly converged anharmonic free energy in most SMAs[22,36,37]. Further, the latent heat (q) at MTT was also computed to be 1.24 and 1.05 meV/atom using supercells of 128 (108 for the R phase) and 432 atoms, since ΔE = 2.28 meV/atom at MTT while the corresponding anharmonic energies of the B2 phase are 1.04 and 1.23 meV/atom, respectively[38]. The anharmonic energy in the R phase is negligible. Although the calculated q is very small, merely ~1 meV/atom (~0.7 J/g), it is well above the numerical fluctuation and the statistical standard deviation. Thus, the conclusion is that the B2-to-R martensite phase transition in AuZn is of first order, even though it is very close to a continuous second-order transition. CONCLUSIONS The team carried out a thorough theoretical investigation of the phase transition in low-temperature SMA AuZn. The results confirm that this is a nearly continuous martensitic transition and that the thermodynamic integration based on AIMD can accurately predict the MTTs of SMAs with transition temperature ranging from below 100 K to above 1000 K. Thus, these computational methods and theoretical analysis can be used to help discover novel SMAs applicable in cryogenic or torrid conditions. ~SMST Acknowledgments This work was supported by funding from the NASA Aeronautics Research Mission Directorate’s Trans- formational Tools and Technologies (TTT) project. The authors appreciate insightful discussions with S. Padula, M. Mendelev, and G. Plummer. For more information: Zhigang Wu, AST, Computer Research and Development, Intelligent Systems Division, NASA Ames Research Center, Moffett Field, CA 94035; zhigang.wu@nasa.gov. References 1. T.W. Darling, et al., Elastic and Thermodynamic Properties of the Shape-memory Alloy AuZn, Philos. Mag. B, 82:825-837, 2002. 2. R.D. McDonald, et al., High Magnetic Field Studies of the Shape Memory Alloy AuZn, J. Phys. Chem. Solids, 67:21002105, 2006. 3. J.C. Lashley, et al., Observation of a Continuous Phase Transition in a Shape-Memory Alloy, Phys. Rev. Lett., 101:135703, 2008. 4. B.L. Winn, et al., Structural Phase Transition in AuZn Alloys, J. Phys.: Conf. Ser., 251:012027, 2009. 5. G. Eggeler, Material Science and Engineering of NiTi Shape Memory Alloys: Fundamentals, Microstructure, Processing and Applications, Wiley-VCH, New York, 2020. 6. J. Van Humbeeck, High Temperature Shape Memory Alloys, ASME, J. Eng. Mater. Technol., 121:98-101, 1999. Fig. 3 — Difference in Gibbs free energy (G) between the cubic B2 phase and the rhombohedral R phase vs. temperature using supercells with 54 (violet), 128 (black), and 432 (green) atoms. FEATURE 12
RkJQdWJsaXNoZXIy MTYyMzk3NQ==