Quantum Mechanical First Principles Calculations of the Electronic and Magnetic Structure of Fe-bearing Rock-forming Silicates

Abstract

The focus of this thesis is the study of the electronic and magnetic structure of three representative members of Fe-bearing rock-forming silicates, viz. orthoferrosilite (Fe²⁺₂Si₂O₆), almandine (Fe²⁺₃Al₂(SiO₄)₃) and andradite (Ca₃Fe³⁺₂(SiO₄)₃). These minerals have attracted significant attention due to their abundance in the Earth's crust and mantle, and because crystallised silicates are main components of cosmic dust which is the most abundant raw material in the Universe. For this purpose quantum mechanical first principles electronic structure calculations are performed by the most efficient DFT method in the local spin-density approximation for calculating spectroscopic data: the spin-polarized self consistent charge Xa method.

The specific feature and strength of these investigations consist in the theoretical characterization of these complex systems based on experimental results. This means that, on one hand, experimental spectroscopic and crystallographic data are being used to judge the reliability of the calculations, whereas, on the other hand, experimental data are interpreted and explained by the theoretical results.

This work comprises seven chapters. After a brief introduction (Chapter 1) Chapter 2 describes the theoretical bases, ideas, approximations and advantages of the SCC- Xa method and basics of the art of cluster construction. Chapter 3 considers physical bases of crystal field theory, absorption, Mossbauer spectroscopy and magnetic interactions, as well as the calculation of spectroscopic data within the frame of the SCC-Xa method. In addition, tetragonally, trigonally and angularly distorted octahedral sites with various degrees of the distortions are calculated and analyzed. The electronic and magnetic structures of orthoferrosilite, almandine and andradite are described in the following chapters. In the case of orthoferrosilite the magnetic interactions between the iron spins within the ribbons and between neighboring ribbons are characterized. Two identical interpenetrating magnetic sublattices of circles of 10 edge-shared dodecahedra are revealed and characterized in almandine. The calculated spin structure explains and solves the controversy in the interpretation of the Mossbauer spectra of almandine below the Neel temperature. For andradite a model of the magnetic structure is proposed based on geometrical considerations and the calculated spin coupling constants for the various interaction pathways. According to this model, the magnetic structure of andradite consists of two frustrated equivalent magnetic sublattices. The spins of the Fe ions within each sublattice are coupled antiferromagnetically. The derived spin pattern explains two sextets in the Mossbauer spectra of andradite below the Neel temperature. Finally, the main results are summarized in Chapter 7.