University College London Computational studies of magnetite Fe3O4 and related spinel-structured materials Thesis submitted for the degree of Doctor of Philosophy (PhD) by David Santos Carballal Supervised by Prof. Nora H. de Leeuw University College London Department of Chemistry March 2015 Declaration I, David Santos Carballal, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. David Santos Carballal March 2015 2 Abstract This thesis presents the results of ab initio based simulation studies of magnetite (Fe3O4) and related FeM2X4 (thio)spinels with M = Cr, Mn, Fe, Co and Ni and X = O and S. Using density functional theory with long-range dispersion correction and on- site Coulomb interactions (DFT + U – D2), we have investigated a number of properties of these materials. Firstly, we present a study of the inversion degree and its relevance in the electronic structure and magnetic properties of the spin filter candidates FeM2X4, which are one of the key devices in spintronic applications. We also analyze the role played by the size of the ions and by the crystal field stabilization effects in determining the equilibrium inversion degree. Secondly, we present the calculations of the elastic constants and other macroscopic mechanical properties by applying elastic strains on the unit cell of Fe3O4, which is the main component in different types of catalysts used in myriad of industrial processes. Thirdly, we calculate the geometries and surface free energies of a number of Fe3O4 surfaces at different compositions, including the non- dipolar stoichiometric plane, and those with a deficiency or excess of oxygen atoms. We propose a morphology in thermodynamic equilibrium conditions for the nanocrystals of this compound. We also present the simulated scanning tunnelling microscopy images of the different terminations of the surfaces shown on the Fe3O4 morphology. Finally, we investigate the initial oxidation stages of the greigite (Fe3S4) (001) surface induced by water. Fe3S4 is a mineral widely identified in anoxic aquatic environments and certain soils, which can be oxidised by these environments 3 Abstract producing and extremely acid solution of sulfur-rich wastewater called acid mine drainage (AMD). We propose a number of mechanisms involving one or two water molecules and one OH group to explain the replacement of one sulfur by one oxygen atom in this mineral. The findings presented in this thesis provides a theoretical insight into various bulk and surface properties of this group of compounds. 4 Table of contents Declaration ···················································································· 2 Abstract ························································································ 3 Table of contents ············································································· 5 Acknowledgments ············································································ 9 List of publications ·········································································· 10 List of abbreviations ········································································ 11 List of tables ·················································································· 14 List of figures ················································································· 17 Chapter 1: Magnetite Fe3O4 and related spinel-structured materials ············ 23 1.1 Introduction ···················································································· 23 1.2 Natural occurrence and synthesis ························································· 24 1.2.1 Rocks, ores and soils ····································································· 24 1.2.2 Organisms ·················································································· 26 1.2.3 Synthetic preparation ····································································· 27 1.3 Crystal structure and morphology of spinels ··········································· 30 1.3.1 Crystal structure of spinels ······························································ 30 1.3.2 Morphology of spinel crystals ··························································· 31 1.4 Magnetic and electric properties of spinels ·············································· 33 1.5 Catalytic applications of Fe3O4 ····························································· 34 1.5.1 Haber-Bosch process for the production of ammonia ······························· 35 1.5.2 Fischer-Tropsch synthesis ······························································· 36 1.5.3 Water gas shift reaction ·································································· 38 1.5.4 Other applications of Fe3O4 and the (thio)spinels ···································· 40 1.6 Objectives of the thesis ······································································· 42 Chapter 2: Methods for materials modelling ·········································· 43 2.1 Introduction ···················································································· 43 2.2 The Schrödinger equation ·································································· 44 2.3 Density functional theory ··································································· 46 5 Table of contents 2.3.1 The Hohenberg-Kohn theorems ························································· 46 2.3.2 Kohn-Sham equations ···································································· 47 2.3.3 Exchange-correlation functionals: LDA and GGA ··································· 48 2.4 DFT + U method ·············································································· 50 2.5 Hybrid functionals ············································································ 52 2.6 The electronic problem in periodic solids ················································ 53 2.6.1 Bloch’s theorem ··········································································· 53 2.6.2 Plane-wave expansion of the wavefunctions ·········································· 54 2.7 Pseudopotentials ·············································································· 55 2.7.1 The projector augmented-wave method ··············································· 56 2.8 Dispersion interaction correction methods ·············································· 57 2.9 Geometry optimizations ····································································· 59 2.9.1 Optimisation of ionic positions: the conjugate gradients method ·················· 60 2.9.2 Relaxation of cell parameters: Pulay stress and equation of state method ········ 63 2.9.3 Transition states ··········································································· 64 2.10 Analysis of optimized grometries ························································ 65 2.10.1 Vibrational frequencies ································································· 65 2.10.2 Density of states ········································································· 66 2.10.3 Bader analysis of the charges ·························································· 66 Chapter 3: Inversion thermodynamics and electronic structure of FeM2X4 (thio)spinels (M = Cr, Mn, Fe, Co, Ni; X = O, S) ······································ 68 3.1 Introduction ···················································································· 68 3.2 Computational methods ····································································· 73 3.2.1 Calculation details ········································································ 73 3.2.2 Configurational free energy of inversion ·············································· 80 3.3 Equilibrium structures ······································································ 81 3.4 Equilibrium inversion degrees ····························································· 81 3.5 Size of ions and crystal field stabilization effects ······································· 88 3.6 Atomic spin moments and charges ························································ 90 3.7 Electronic density of states ·································································· 95 3.7.1 FeCr2X4 ····················································································· 95 3.7.2 FeMn2X4 ···················································································· 98 6 Table of contents 3.7.3 Fe3X4 ······················································································· 100 3.7.4 FeCo2X4 ··················································································· 101 3.7.5 FeNi2X4 ···················································································· 103 3.8 Chapter conclusions ········································································· 105 Chapter 4: Mechanical properties of magnetite····································· 108 4.1 Introduction ··················································································· 108 4.2 Computational details ······································································· 110 4.3 Structural properties ········································································ 113 4.4 Mechanical properties ······································································ 115 4.5 Chapter conclusions ·········································································