Dynamically stabilized phases with full ab initio accuracy: Thermodynamics of Ti, Zr, Hf with a focus on the hcp-bcc transition

JH Jung and A Forslund and P Srinivasan and B Grabowski, PHYSICAL REVIEW B, 108, 184107 (2023).

DOI: 10.1103/PhysRevB.108.184107

Certain systems feature phases that are dynamically unstable at 0 K but are stabilized by vibrations at higher temperatures. Treatment of these phases by conventional 0-K methods is not feasible and effective harmonic models introduce approximations. Here, we significantly advance the direct upsampling methodology npj Comput. Mater. 9, 3 (2023) to obtain free energies including the anharmonic contribution to full ab initio accuracy also for such dynamically stabilized phases. The centerpiece behind the procedure is accurate machinelearning potentials (moment tensor potentials) which are used to efficiently scan the volume-temperature space to uncover the stability regime and to perform thermodynamic integration on a dense grid within the stable window. We apply the methodology to the prototype systems Ti, Zr, and Hf and calculate hcp-bcc transition properties and thermodynamic properties of both phases. We find a very good agreement for the heat capacities with existing experimental/CALPHAD data, and an overall best agreement for Ti. The transition properties agree well on a relative temperature axis, where the temperature is scaled with respect to the transition temperature. Anharmonic free energies increase the transition temperature by up to one thousand kelvin. Electronic effects are smaller and bring down the transition temperature by as much as 172 K. We establish a new definition of the 0-K energy-volume curve for the dynamically stabilized bcc phase. Instead of using static lattice ab initio values, an extrapolation of the high-temperature high-accuracy free-energy surface to 0 K provides a physically more meaningful description. With this effective 0-K definition, discrepancies existing in the literature between CALPHAD and ab initio values are addressed.

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