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Computational and Experimental Studies of Solids in the Ammonia COMPUTATIONAL AND EXPERIMENTAL STUDIES OF SOLIDS IN THE AMMONIA – WATER SYSTEM A thesis submitted to the University of London for the degree of Doctor of Philosophy by Andrew Fortes Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, United Kingdom January 2004 1 ABSTRACT This thesis reports the results of first-principles computational studies of thirteen crystalline structures in the H2O-NH3 system. This includes eight low- and high- pressure polymorphs of pure water ice, two polymorphs of solid ammonia, and three low-pressure stoichiometric ammonia hydrates. These simulations have been used to determine the athermal equation of state (EoS) of each phase. Where empirical data was lacking, experiments have been undertaken. Hence, this thesis also reports the results of time-of-flight neutron scattering studies of deuterated ammonia dihydrate powders down to 4 K, and up to a maximum pressure of 8.6 GPa. In addition, I have developed a flexible and accurate planetary model that can be used to calculate the triaxial shape and gravitational field of any object, regardless of size or composition, given an assumed mineralogical constitution and provided the EoS of said minerals are known. The EoS parameters found in this work have therefore been used to model the structure and thermal evolution of icy moons orbiting Saturn in anticipation of the Cassini spacecraft arriving at Saturn in mid-2004. Models of Rhea, Saturn’s second largest moon, suggest that its volatile component is likely to contain > 3 weight percent ammonia, but that one is unlikely to be able to constrain the bulk chemistry of the ice mantle from Cassini flyby data. 2 ACKNOWLEDGEMENTS I would like to acknowledge the UCL Graduate School for financial support awarded in the form of a Postgraduate Scholarship. My Ph.D Supervisors, Dr Lidunka Vočadlo, Dr Ian Wood, and Dr John Brodholt, provided me with the perfect mix of expertise and support throughout my studentship. Dr Vočadlo has pushed me forwards, despite my futile resistance, since I began my full- time undergraduate studies here seven years ago, championing my first publication and exhorting me to go to meetings and give talks and lectures, etc. All of which has been very good for me. The following individuals have also provided support, advice, or helpful criticism: Prof. David Price (UCL), Prof. John Guest (UCL), Dr Hilary Downs (Birkbeck), Dr Ian Crawford (UCL), Dr H. Donald Jenkins (Warwick), Dr Maria Alfredsson (UCL/RI), and Dr Francis Nimmo (UCL/UCLA). From ISIS, I thank Dr Kevin Knight and Bill Marshall for their great efforts and patience during my experimental time on the HRPD and PEARL instruments. I would also like to thank John Dreyer and his technical staff at ISIS. Prof. Claudio Vita-Finzi has provided me with unswerving friendship and tutelage, for which I am most grateful. His efforts to curtail the flowery verbiage in my writing have met with mixed contrafibularity. I’d like to thank my fellow postgraduate students, who have shared a blast furnace….I mean office….over the past three years and kept me from being a total stranger to human interaction; namely Louise Bishop, Peter Grindrod, Roberto Bugiolacchi, Terry Hackwill, Joyce Vetterlein, Dr Matt Balme, and the remarkable Dr Emma Bowden. I cannot even begin to thank my parents for their love and support in spite of their own troubles. This work is dedicated to my Mum, who passed away in November 2002 after a long illness. 3 Contents CONTENTS Title……………………………………………………………………………………….. 1 Abstract…………………………………………………………………………………… 2 Acknowledgements……………………………………………………………………….. 3 Contents…………………………………………………………………………………… 4 List of figures……………………………………………………………………………... 10 List of tables………………………………………………………………………………. 15 Chapter 1: Icy moons and the ammonia-water system 1 Introduction…………………………………………………………………………….. 17 1.1 Justification for studying the ammonia-water system……………………………. 17 1.1.1 The hydrogen bond……………………………………………………….. 18 1.1.2 The icy bodies of our solar system……………………………………….. 21 1.1.2.1 Models of icy moon formation……………………………………... 23 1.1.2.2 Atmospheric spectroscopy…………………………………………. 25 1.1.2.3 Surface spectroscopy………………………………………………. 26 1.1.2.4 Geomorphology…………………………………………………….. 27 1.1.2.5 Summary of the evidence for ammonia in icy moons……………… 32 1.2 Methods to satisfy the goals of this thesis………………………………………… 32 1.2.1 Computer simulation……………………………………………………… 33 1.2.2 Neutron diffraction………………………………………………………... 35 1.3 Work done towards this thesis……………………………………………………. 38 1.3.1 Pure H2O solids…………………………………………………………… 39 1.3.2 Pure NH3 solids…………………………………………………………… 39 1.3.3 Mixed H2O – NH3 solids………………………………………………….. 39 1.3.4 Planetary modelling………………………………………………………. 40 Chapter 2: Computational methods: VASP and DFT 2 Introduction…………………………………………………………………………….. 41 2.1 The theoretical background to density functional theory…………………………. 42 2.1.1 The Schrödinger equation………………………………………………… 42 2.1.2 The Born-Oppenheimer approximation…………………………………... 43 2.1.3 Electron interactions: exchange and correlation………………………….. 44 2.1.4 Solutions. I. Wavefunction theories……………………………………… 45 2.1.4.1 The variational principle……………………………………………. 45 4 Contents 2.1.4.2 The Hartree and Hartree-Fock approximations…………………….. 46 2.1.4.3 Basis functions: STO's and GTO's…………………………………. 47 2.1.4.4 Electron correlation in the Hartree-Fock approximation…………… 48 2.1.4.5 Summary of wavefunction theories………………………………… 49 2.1.5 Solutions. II. Density functional theory………………………………….. 50 2.1.5.1 The Hohenberg-Kohn theorems……………………………………. 50 2.1.5.2 The Kohn-Sham equations…………………………………………. 51 2.1.5.3 The local-density approximation…………………………………… 53 2.1.5.4 The generalised gradient approximation…………………………… 54 2.1.5.5 Summary of density functional theory……………………………... 55 2.1.6 Quantum Monte Carlo…………………………………. 56 2.2 The practical application of density functional theory……………………………. 57 2.2.1 Vienna Ab-initio simulation package……………………………………... 57 2.2.1.1 Inputs and outputs………………………………………………….. 57 2.2.1.2 Plane-waves as basis functions…………………………………….. 58 2.2.1.3 Pseudopotentials……………………………………………………. 59 v 2.2.1.4 k -point sampling…………………………………………………... 61 2.2.1.5 Ionic relaxation…………………………………………………….. 61 2.2.2 Application to hydrogen bonded systems………………………………… 63 2.2.2.1 Hydrogen bonds, dispersion forces and the GGA. Why PW91?…... 63 2.2.2.2 The quantum nature of the hydrogen atom…………………………. 64 2.2.2.3 Tests on H2O and NH3 monomers………………………………….. 65 2.3 From total energy to equation of state……………………………………………. 66 2.4 Summary………………………………………………………………………….. 69 Chapter 3: Water ices at high-pressure: ices VIII, X and beyond 3 High-pressure water ices……………………………………………………………….. 70 3.1 Ice VIII……………………………………………………………………………. 73 3.1.1 Computational detail……………………………………………………… 73 3.1.2 Equation of state of ice VIII……………………………………………… 76 3.1.3 Structure of ice VIII………………………………………………………. 78 3.1.4 Hydrogen bonding in ice VIII…………………………………………….. 79 3.2 Ice X………………………………………………………………………………. 81 3.2.1 The transition from ice VIII to ice X……………………………………... 81 3.3 Post-ice X polymorphs…………………………………………………………… 83 3.3.1 The d-hcp structure……………………………………………………….. 84 5 Contents 3.3.2 The antifluorite structure………………………………………………….. 85 3.3.3 The CaCl2 and α-PbO2 structures………………………………………… 86 3.4 Summary………………………………………………………………………….. 87 Chapter 4: Water ices at low-pressure: ices II and XI 4 Low-pressure water ices………………………………………………………………… 88 4.1 Ice XI……………………………………………………………………………… 88 4.1.1 Phase relations…………………………………………………………….. 88 4.1.2 The structure of ice XI……………………………………………………. 89 4.1.3 Computational details…………………………………………………….. 90 4.1.4 Equation of state of ice XI………………………………………………... 90 4.1.5 The simulated structure of ice XI…………………………………………. 94 4.1.6 Summary………………………………………………………………….. 95 4.2 Ice II………………………………………………………………………………. 96 4.2.1 Phase relations…………………………………………………………….. 96 4.2.2 The structure of ice II……………………………………………………... 97 4.2.3 Computational method……………………………………………………. 99 4.2.4 Equation of state of ice II…………………………………………………. 100 4.2.5 Structural changes under pressure………………………………………… 101 4.3 Summary………………………………………………………………………….. 104 Chapter 5: Simulation of solid ammonia: Phases I and IV 5 Introduction……………………………………………………………………………... 106 5.1 Ammonia I and IV………………………………………………………………... 107 5.1.1 Structure and phase relations……………………………………………... 107 5.1.2 Previous computational studies…………………………………………… 108 5.1.3 Computational method…………………………………………………… 109 5.2 Results…………………………………………………………………………….. 109 5.2.1 Macroscopic elastic properties……………………………………………. 109 5.2.1.1 Equation of state……………………………………………………. 109 5.2.2 Microscopic bonding phenomena………………………………………… 112 5.2.2.1 Crystal structure and hydrogen bonding……………………………. 112 5.2.2.2 Hydrogen-bond symmetrisation……………………………………. 117 5.3 Summary………………………………………………………………………….. 119 6 Contents Chapter 6: Simulation of ammonia monohydrate and ammonia hemihydrate 6 Introduction…………………………………………………………………………….. 120 6.1 Ammonia monohydrate (NH3·H2O) and ammonium hydroxide (NH4OH)………. 120 6.1.1 Computational detail……………………………………………………… 121 6.1.2 Equation of state………………………………………………………….. 122 6.1.3 Structure of AMH I……………………………………………………….. 125 6.1.4 Structure of NH4OH………………………………………………………. 127 6.1.5 Thermodynamics………………………………………………………….. 130 6.1.6 Summary………………………………………………………………….. 134 6.2 Ammonia hemihydrate (2NH3·H2O)……………………………………………… 134 6.2.1 Computational detail……………………………………………………… 135 6.2.2 Equation
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