ADVANCED MATERIALS & PROCESSES | OCTOBER 2025 46 INVESTIGATION OF A NEARLY CONTINUOUS PHASE TRANSITION IN SHAPE MEMORY ALLOY AuZn A thorough study of the martensitic phase transition in cryogenic shape memory alloy AuZn offers some surprising insights and promising results for applications involving extreme temperature fluctuations. Zhigang Wu* and John W. Lawson Intelligent Systems Division, NASA Ames Research Center, Moffett Field, California Othmane Benafan, FASM* Materials and Structures Division, NASA Glenn Research Center, Cleveland Shape memory alloys (SMAs) go through a reversible martensitic phase transition between a high-tem- perature, high-symmetry austenite and a low-temperature, low-symmetry martensite phase. Stoichiometric AuZn has a martensitic transition temperature (MTT) around 64–67 K, which is much lower than Nitinol (NiTi)-base and Ru-base SMAs[1-10]. Low-temperature SMAs such as AuZn have found applications in cryogenic conditions as actuators, and thus these cryogenic SMAs can be used to shield equipment (e.g., satellites) from severe damage by extreme temperature fluctuations in space[11]. Compared with the well-studied and well-known NiTi and NiTi-base SMAs, cryogenic SMAs have not been thoroughly investigated. In particular, AuZn has a very low transition temperature. Its martensitic phase transition is nearly continuous (second order)[3,12]. Further, such a transition is the same as Fe-doped NiTi (NiTi-Fex for x < 0.06) and Ni4Ti3, i.e., from the austenite cubic B2 (space group Pm3m) phase to the martensite rhombohedral R (space group P3) phase[7,13-16]. However, the details of this transition remain to be revealed by first principles, especially from the point of view of thermodynamics, as almost all previous theoretical studies were carried out at 0 K[2,12,17-19]. Such zero-K phonon spectra and energetics are useful to elucidate basic physics and predict trends in phase transitions, but they are not able to quantify the transition temperature explicitly or the associated dynamic properties. In this work, researchers employ ab initio molecular dynamics (AIMD) simulations and highly accurate thermodynamics integration to accurately quantify the B2-to-R phase transition. The predicted MTT is in good agreement with the measured data, and the computed small latent heat suggests that the martensitic phase transition is still first order but nearly continuous. This result helps resolve the controversy as to whether the transition is continuous or discontinuous. COMPUTATIONAL METHODS To determine the phase transition temperature, the Gibbs free energies (G) for both the austenite and martensite phases of AuZn were computed: Here, E is the total electronic energy for the reference structure whose volume (V) is optimized at temperature T. The remaining three terms, , , and , are the electronic free energy and the harmonic and anharmonic parts of the phonon free energy, respectively. Lattice vibrations, AIMD simulations, and thermodynamics inte- gration were carried out to evaluate the vibrational free energy contributions to G. For the unstable B2 structure, the authors used the temperature-dependent effective potential (TDEP) method to obtain the phonon spectra at finite temperature[20-22]. Calculations of total energies, lattice vibrations, and the AIMD simulations were performed using the VASP package[23-27]. The Perdew-Burke-Ernzerhof (PBE) functional and the projector augmented wave method (PAW) were used in density functional theory (DFT) calculations[27-29]. The valence ground states of Au and Zn atoms include 5d106s1 and 3d104s2 electrons, respectively. The ABINIT software package was used to compute the phonon distribution of the cubic phase using the linear response theory and the norm-conserving pseudopotentials, which include 5s25p65d106s1 and 3s23p63d104s2 electrons as valence for Au and Zn, respectively[30-32]. RESULTS AND DISCUSSION Phonons at 0 K. The phonon distribution was first computed at 0 K of the cubic B2 phase using VASP as plotted in Fig. 1a. An energy cutoff of 450 eV and a supercell with 432 atoms were used. However, the frequency of the soft phonon mode at (1/3, 1/3, 0) greatly depends on *Member of ASM International FEATURE 10
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