PGI-1 Seminar: Dr. Fritz Körmann
The influence of magnetic excitations on the phase stability of metals and steels
- 23.May.2012 11:30
MPI für Eisenforschung, Düsseldorf
An ab initio based determination of phase stabilities at finite temperatures requires the explicit description of various kinds of excitation mechanisms. The most challenging contributions - but crucial for many structural materials - are related to the magnetic degrees of freedom. For iron-based materials, the Heisenberg model has proven to yield a sufficiently accurate description of magnetic excitations and to provide an elegant way for a coupling of ground state ab initio calculations with concepts of many-body theory to fully simulate the temperature dependence. We will present a number of analytical and numerical approaches, how this concept can be applied to realistic materials. The discussion will be focused on the specific heat capacity Cp, which provides also a sensitive link to experiments and in addition to empirical CALPHAD simulations.
Our analytical approach to the free energy of the Heisenberg spin system, which is based on the random phase approximation, in combination with vibronic and electronic contributions, allowed us to obtain a remarkably accurate description of the Cp of iron below the critical temperature. For a description of the region above the critical temperature, however, short range correlations need to be taken into account. Classical MC calculations that neglect quantum effects yield significant short comings in the low temperature regime. We have, therefore, derived from an extensive set of quantum and classical Heisenberg model systems a rescaling scheme, which provides the accuracy of QMC calculations at much cheaper numerical costs. This scheme is heavily based on a discovered universal behavior of the thermodynamic properties for the Heisenberg model with respect to the kind of the interaction and the lattice structure.
We have further extended this concept to define effective nearest-neighbor Heisenberg models, for which the QMC approach provides a numerically exact solution. The approach does not only yield for bcc Fe an excellent agreement with experimental Cp(T) data, magnetization curves and free energies. Also the application to the 3d ferromagnets cobalt and nickel, demonstrates its excellent transferability to other magnetic systems containing a single magnetic species. We have, therefore, applied the developed methodology to more complex systems, such as, e.g., cementite (Fe3C) and were able to provide a hitherto not achieved insight into the impact of magnetic contributions to the stability of this phase.
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