Open Access

Gregor Golabek

• Die vorliegende Arbeit behandelt das Forschungsthema der Entstehung des flüssigen Eisenkerns im Zentrum unseres Planeten. Dieses bislang wenig verstandene Gebiet ist reich an Fragestellungen, sowohl für Experimentatoren als auch für die Geodynamik. Es gibt sehr viele Arbeiten, die den Bildungsprozess experimentell untersuchen, jedoch wurde in den letzten Jahren die numerische Untersuchung in diesem Gebiet kaum vorangetrieben. Der experimentelle Teil der Arbeit stellt sich hierbei der aktuellen Frage nach der Perkolationsschwelle 1 von Eisenschmelze in der Silikatmatrix der Protoerde, während numerisch die Effekte von Potenzgesetzkriechen, Dissipation und Schmelzsegregation beim Absinken eines Eisendiapirs nach Ausbildung eines ersten flachen Magmaozeans in der Protoerde behandelt werden. Die genauen Fragestellungen könnnen dabei im letzten Abschnitt der Einleitung gefunden werden.
• The diploma thesis 'Formation of Earth's core: Laboratory experiments and numerical models for the percolation mechanism and the Rayleigh-Taylor instability' includes some laboratory experiments and numerical modelling which implement the percolation and Rayleigh-Taylor instability mechanisms. The laboratory experiments have been performed on a fertile peridotite with the addition of iron sulfide by the use of a centrifuge furnace in order to model a percolation flow. In some experiments in-situ performed electrical conductivity measurements have been done in order to access a connectivity of iron sulfide melts. The numerical experiments have been done with the use of a two-dimensional finite difference method applied to the sinking of iron diapirs through a silicate matrix in the case of the temperature and stress-dependent rheology. Peridotite samples containing different amounts of iron sulfide (5-15 vol%) were prepared from powders of the fertile peridotite and chemicals of Fe-FeS of the eutectic composition. They were placed in the centrifuge piston cylinder at the ETH Zürich to determine a percolation velocity of Fe-FeS through the peroditite matrix. It was found that the segregation velocity of Fe-FeS is far too slow in a partially molten silicate matrix to be accounted for the core formation alone. Additionally, the electrical conductivities of samples consisting of fertile peridotite and Fe-FeS were measured in-situ in order to revise the experimental results of Yoshino et al. (2003, 2004). These papers describe an interconnection threshold in a solid silicate matrix at about 5 vol% of iron sulfide. In the present work it was shown that more than 15 vol% Fe-FeS are needed to reach an interconnectivity of Fe-FeS in a peridotite matrix. In the numerical modelling the computer code FDCON was modified and extended to resolve more realistic cases for the evolution of the Rayleigh-Taylor instability at the top of a cold, undifferentiated and less dense protocore. This unstable gravitational configuration was used as a starting point in numerical models. Differing rheologic laws (temperatureindependent, temperature-dependent and power law) were used to explore the parameter space consisting of initial temperature and viscosity of the protocore and the non-dimensional temperature scaling factor of viscosity b to find a realistic scenario in an agreement with the Hf/W isotopic ages of the core in which the core formation is prescribed to be largely completed within the first 33 Ma (Kleine et al., 2002). It was found that only for b <= 10 the iron diapir is able to penetrate fast enough through the protocore and to fullfill the isotopic restrictions. The required central protocore temperature is in an good agreement with the numerical models performed by Merk et al. (2002), which included the heating during the accretion stage and heating due to the radioactive decay of a short-lived isotope 26Al. In a less advanced model without the application of a power law, it is shown that the dissipation plays only a second order role on the sinking depth of a diapir. Numerical experiments including the power law rheology may be useful in order to revise this result for a more realistic case. Finally, it was shown that the introducing of the melt effect in the calculation scheme is relevant to the core formation models due to the intensive development of stress-induced melt channelling in localities surrounding the incipient iron diapir. For simplicity an isothermal model with a temperature independent viscosity of a solid phase and with a rheology depending on a melt-fraction in the partially molten region surrounding a diapir was used. As a result of this model, the intensive development of iron-rich melt channels within a region approximately 2-3 times larger than a diapir size has been observed for sufficiently small melt retention numbers, i.e. the ratio of a Stokes sinking to a Darcy flow velocity. This mechanism enhanced the melt accumulation and accelerated the process of the core formation. The introduction of more realistic temperature profiles, the use of a power-law rheology and a stress-dependent porosity are possible in future numerical models which could lead to a better understanding of the core formation mechanism.