Ab initio Untersuchung von temperaturgetriebenen martensitischen Phasenübergängen: Fallstudie für Erdalkalimetalle
Zusammenfassung der Projektergebnisse
The primary goal of the project was an ab initio based study of temperature-driven martensitic transformations. Ab initio methods are the most fundamental theoretical approaches to materials science, since they are founded on basic physical principles (e.g., quantum mechanics) and do not rely on experimental input. Temperature-driven phase transformations are changes in atomic structure caused by heating or cooling of the respective material. Understanding such transformations is technologically highly important, as it constitutes a main ingredient in advanced materials design. In principle, ab initio methods – particularly density-functional-theory (DFT) – are ideally suited for studying temperature-driven transitions. A practical application faces, however, significant challenges: (1) To manage the huge number of degrees-of-freedom, DFT relies in practice on an approximation to the so-called exchange-correlation (xc) functional of which the quality is difficult to assess. (2) DFT was originally designed for T=0 K and the extension to temperature-driven phenomena is accompanied by large methodological and computational demands. (3) For temperature-driven transformations often very small energy differences are relevant. The crucial question is whether the necessary accuracy is achievable from a principle and a numerical point of view. (4) At high temperatures, many materials show atomic structures which have instabilities at T=0 K (that is, the atoms actually prefer a modified structure) complicating the theoretical treatment. The present “Nachwuchsakademie” project has given important insight into these issues by providing for the first time a complete and extensive DFT study of a prototype temperature-driven martensitic transformation: The fcc-to-bcc transformation in calcium. To accomplish this study, the applicant has successfully extended and applied the methodology that he had originally developed in his PhD thesis prior to the “Nachwuchsakademie” project. In particular, to tackle point (1) the full study was performed with the two currently mostly used approximations to the xc functional (LDA and GGA). This approach had turned out to be very useful in previous studies resulting in an ab initio confidence interval for experimental data. Within the present project, it was possible to extend the confidence interval to similarities in the free energy volume dependence of the two functionals. Knowledge of these similarities allows for instance to extract important general trends for derived thermodynamic properties (e.g., thermal expansion). Point (2) was addressed with a significant amount of effort. On one side, methodological advancements were successfully performed with the goal of increasing the numerical precision. For example, a detailed investigation of the free energy contribution due to electrons allowed the applicant to device a new, physically well-motivated parametrization. This parametrization enabled to capture the electronic contribution with very high accuracy. On the other side, the applicant put effort into optimizing computational performance. This turned out to be a crucial bottleneck and the solution was to implement the applicant’s methods into the currently most efficient DFT code. Since DFT codes are among the most complex computer codes, the implementation was rather challenging. Nonetheless, a running version was implemented relatively fast (≈2 months) and thorough subsequent tests showed the stability and efficiency of the implementation. Based on the work for points (1) and (2), points (3) and (4) could be tackled in a feasible amount of time. As for point (3), the key result is that the temperature dependence of the free energy difference between different atomic structures is described with excellent accuracy (for the prototype Ca system). This result is of crucial importance since free energy differences are directly linked to phase transformations. While the temperature dependence is well described, the present study shows that one must expect an error in the T=0 K energy difference. This insight can be used to design an optimized mixed approach: The T=0 K energy can typically be obtained with modest computational effort and this allows applying more sophisticated but demanding xc functionals. In contrast, the calculation of the temperature dependence can be performed with standard xc functionals. As regards point (4), a detailed investigation revealed a previously unknown instability in the high temperature atomic structure of calcium. More importantly, the applicant showed a proper physical way to treat the instability. A key ingredient thereby is the effect of temperature on the electronic motion, which in turn influences the motion of the atoms leading to a disappearance of the instability. An application of the methodology and experience developed in the present project to an industrially relevant situation is provided directly within the project itself. The highly accurate calculations of the free energies of the various atomic structures allow to extract accurate thermodynamic properties, in particular the heat capacity. The latter is a key input to macroscopic approaches aiming at calculating phase diagrams. Phase diagrams constitute a collection of information on temperature-driven transformations and are therefore of basic importance for industrially relevant materials design. Upon a careful and extensive literature research, the applicant revealed an ambiguous situation for the experimental heat capacity of calcium. In particular, two strongly disagreeing sets of experimental data were found with intolerable differences at high temperatures. From a comparison of these data with the highly accurate ab initio prediction from the present project the applicant was able to single out the more trustful set of experiments. The surprising result is that a popular and for industrial purposes applied thermodynamic database is founded upon the wrong set of experimental data. A reconsideration of the database is suggested. The applicant has already started a continuation and extension of the methods and results achieved in this “Nachwuchsakademie” project in his present work at the LLNL. At LLNL the primary focus is on actinide materials (e.g., uranium or plutonium), which are basic elements in nuclear science. Actinide materials are among the most complex monoatomic materials found in nature with plutonium showing for instance five temperature-driven transformations before the melting point. This complexity poses enormous challenges to a theoretical description, one particular aspect being strong instabilities at T=0 K, which are much more pronounced than for instance in calcium. The methods developed in the “Nachwuchsakademie” project constitute a solid and reliable fundament when tackling the difficulties contained in a theoretical description of the actinide materials.
Projektbezogene Publikationen (Auswahl)
- “Formation energies of point defects at finite temperatures”, Phys. Status Solidi B 248, No. 6, 1295–1308 (2011)
B. Grabowski, T. Hickel, and J. Neugebauer
- “Review: Methodological challenges in combining quantum-mechanical and continuum approaches for materials science applications”, Eur. Phys. J. Plus 126, 101 (2011)
M. Friak, T. Hickel, B. Grabowski, et al.
- “Temperature-driven phase transitions from first principles including all relevant excitations: The fcc-to-bcc transition in Ca”, Phys. Rev. B 84, 2114107 (2011)
B. Grabowski, P. Söderlind, T. Hickel, and J. Neugebauer
- “Topical review: Advancing density functional theory to finite temperatures: methods and applications in steel design”, J. Phys.: Condens. Matter 24, 053202 (2012)
T. Hickel, B. Grabowski, F. Körmann, and J. Neugebauer
(Siehe online unter https://doi.org/10.1088/0953-8984/24/5/053202)
