Background and problem

The iron-rich region of the Fe-Si phase diagram is of interest both to the planetology community and the materials engineering community. Indeed, the planet Mercury has a solid inner core that consists predominantly of iron, with some nickel, and a selection of lighter elements. Mercury surface spectra and the thought formation conditions suggest that silicon could perhaps be the dominant light element [Nittler 2018, Fisher 2012]. Understanding in which phase this Fe-Si alloy appears – at the relevant pressure and temperature of the Mercury core – is mandatory before one can even attempt to predict important properties such as the elastic behavior of the core. In a very different context, iron-rich Fe-Si alloys are used on Earth by electrical engineers as transformer cores. They are called ‘electrical steels’ for that reason (https://en.wikipedia.org/wiki/Electrical_steel). The ideal resistivity for this application is reached above 6 mass % of silicon, yet at that concentration the alloy is too brittle for cold rolling. Electrical steels in actual use have therefor only half of the ideal amount of silicon. Here too, understanding the phase diagram better is a route towards improving the properties (i.c. the silicon content) of electrical steels.

The standard phase diagram for Fe-Si is the one by Kubaschewski (1982). In the iron-rich region, the dominant phases are a-Fe (0 at.% Si), DO3 (a1, 25 at.% Si) and B20 (e, 50 at.% Si). a and a1 have the bcc lattice as underlying lattice, and a1 consists of an ordered replacement of one quarter of the Fe atoms by Si. The similarity between a and a1 means that there is not a clear division between these two phases. Much of the confusion  in the interpretation of this phase diagram is related to a lack of insight in the details of the long-range and short-range order of the Si-sublattice.

Figure 1: structure of the planet Mercury

Goal

You will take a look at the Fe-Si phase diagram at the atomic scale. Density-functional theory – the work horse of computational materials physics – is ideally suited to inspect the stability of a systematic family of ordered silicon sublattices at several concentrations. In order to take large and complex silicon sublattices into account – more complex than is suitable for DFT calculations – DFT can be combined with Monte Carlo simulations or with artificial intelligence (machine learning potentials). Once you have determined which phases in this family are stable, you will establish a new – predicted – phase diagram. This can be extended as a function of pressure, in the range relevant for the Mercury core. Phonon calculations – with DFT or with machine learning potentials – will extend the phase diagram to the high temperatures relevant for the Mercury core. For those phases that appear to be relevant either for Mercury or for electrical steels, predictions of elastic properties will be performed. X-ray diffraction patterns can be predicted as well, to compare with experimental data.

Collaboration with company

Epotentia (epotentia.com) for machine learning support