Universität Stuttgart
Accurate thermodynamic data of the unary refractory or titanium-group systems are a requisite, for example, when used as end members for phase diagrams of high entropy alloys. With the newly developed direct-upsampling method, which provides a five-fold increase in efficiency compared to previous state-of-the-art methods, we are now in a position where we can calculate highly converged thermodynamic properties with full DFT accuracy. We have applied the method to the five bcc refractory elements V, Nb, Ta, Mo and W, and present well-converged Gibbs energy surfaces with stable second-derivative properties such as the heat capacity, thermal expansion coefficient and bulk modulus. We show their convergence with respect to fitting polynomial order and volume-temperature-grid density. For all five elements, both anharmonic and electronic contributions are large, the latter including a strong coupling with the thermal vibrations. In contrast, the contribution from thermal vacancies, which we have also included, is very small. Taking all relevant contributions into account, there is a strong agreement with experimental data from the literature. In addition, we also present results for the group IV elements Ti, Zr and Hf in their hpc and bcc structures. Also here, the anharmonic contribution and electronic contribution, including its coupling to vibrations, are crucial to the strong agreement seen with existing experimental data.
Abstract
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