University College London A computational study of calcium carbonate Thesis submitted for the degree of Doctor of Philosophy (PhD) by Qi Wang Supervised by Prof. Nora H. de Leeuw University College London Department of Chemistry September 2011 Declaration Declaration I, Qi Wang, confirm that this is my own work and the use of all materials from other sources has been properly indicated in the thesis. ___________________ Qi Wang September 2011 2 Abstract Abstract This thesis presents the results of computer simulation studies of impurity incorporation in calcite and the aggregation of calcite particles, using a combination of classical computational techniques based on interatomic potentials, namely molecular mechanics and molecular dynamics simulations. Firstly, the atomistic simulation techniques have been employed to investigate the thermodynamics of mixing in calcite with seven divalent cationic impurities (Mg2+, Ni2+, Co2+, Zn2+, Fe2+, Mn2+ and Cd2+), based on the calculation of all inequivalent site occupancy configurations in 2 × 2 × 1 and 3 × 3 × 1 supercells of the calcite structure. In addition to the enthalpy of mixing, the configurational entropy and mixing free energy have also been calculated, providing an insight into the mixing behaviour as a function of the temperature for a series of carbonate solid solutions. The calculations have revealed that the solubility of the cationic impurities in calcite is largely related to the cationic coordination distance with oxygen. Secondly, the aggregation process has been investigated implementing classical computational techniques, and especially the interaction of a calcite nanoparticle with the major calcite surfaces, where the adhesion energy and optimised geometries of a typical calcite nanoparticle on different surfaces in vacuum and aqueous environment have been calculated. The results show the orientation of a nanoparticle is a key factor that effects the interactions, besides the size and structure of the nanoparticle. The most stable aggregated configuration occurs when the lattices of the nanoparticle and the surface are perfectly aligned. 3 Abstract Finally, a number of symmetric calcite tilt grain boundaries have been constructed to act as models of two calcite nanoparticles, after collision has occurred but before growth has a chance to commence. Molecular dynamics simulations were then employed to study the stability of these tilt grain boundaries and the growth of a series of calcium carbonate units at the contact points in the pure and hydrated calcite tilt grain boundaries. The calculation have proved that the initial incorporation of a CaCO3 unit is preferential at the obtuse step in a grain boundary, and the growth velocity of the acute step is 1.3 to 2.1 times higher than that of the obtuse step, once the initial growth unit has been deposited on the steps. This study has evaluated the conditions required for the growth of new calcium carbonate materials in the calcite tilt grain boundaries. 4 List of Publications List of Publications The work described in this thesis has been published in the following papers: Qi Wang, Ricardo Grau-Crespo and Nora H. de Leeuw (2011) Mixing thermodynamics of the calcite-structured (Mn,Ca)CO3 solid solution: A computer simulation study. Journal of Physical Chemistry C, accepted. Qi Wang and Nora H. de Leeuw (2009) A computer simulation study of the thermodynamics of mixing in the (Mn,Ca)CO3 solid solution. Geochimica et Cosmochimica Acta, Vol. 73: A1412. Qi Wang and Nora H. de Leeuw (2008) A computer modelling study of CdCO3-CaCO3 solid solutions. Mineralogical Magazine, Vol. 72: 525-529. 5 Acknowledgement Acknowledgement First of all, I would like to thank my supervisor, Prof. Nora H. de Leeuw, for her distinguished guidance and generous support during the past four years. This thesis really wouldn‟t have been possible without her supervision. Particular thanks should go to Dr. Zhimei Du and Dr. Ricardo Grau-Crespo, for their invaluable guidance and helpful discussion throughout this project. I would like to give my acknowledgement to the whole group, where I received lots of help and encouragements. A special thank you to Prof. Steve Parker, who gave me lots of kind help and guidance during my visit in Bath University. I am grateful to the China Scholarship Council (CSC) for financial support and University College London for an Overseas Research Studentship. I also thank the EU-funded “Mineral Nucleation and Growth Kinetics (MIN-GRO) Marie-Curie Research and Training Network” for funding. I also acknowledge the use of the UCL Legion High Performance Computing Facility and associated support services in the completion of this project. Finally, I sincerely thank my grandparents, parents and fiancée Dr. Qiyao Feng for showing concerns, giving loves and support to me during my four years PhD study in UCL. I would like to dedicate this thesis to them. Thank you very much. 6 Table of Contents Table of Contents DECLARATION ....................................................................................................................... 2 ABSTRACT ................................................................................................................................ 3 LIST OF PUBLICATIONS .................................................................................................... 5 ACKNOWLEDGEMENT ...................................................................................................... 6 TABLE OF CONTENTS ........................................................................................................ 7 LIST OF FIGURES ............................................................................................................... 20 LIST OF TABLES ................................................................................................................. 20 LIST OF ABBREVIATIONS ............................................................................................. 20 Chapter 1 Introduction ........................................................................................ 21 1.1 Calcium carbonate ....................................................................................................... 22 1.2 Incorporation of impurities in calcium carbonate ................................................. 24 1.2.1 Heavy metals in nature ........................................................................ 26 1.2.2 Carbonate solid solutions ..................................................................... 27 1.2.3 Experimental studies of carbonate solid solutions ................................ 29 1.2.4 Theoretical studies of carbonate solid solutions.................................... 31 1.3 The growth and dissolution of calcium carbonate ................................................ 34 1.3.1 Nucleation and growth of calcium carbonate........................................ 34 1.3.2 Dissolution of calcite ........................................................................... 37 1.4 Aggregation of calcite nanoparticles ....................................................................... 38 1.5 Aims and overview of the thesis ............................................................................... 41 Chapter 2 Computational Methodology ............................................................. 43 2.1 Molecular mechanics .................................................................................................. 44 2.1.1 Potential energy surface ....................................................................... 44 2.1.2 Energy minimisation algorithm ............................................................ 45 7 Table of Contents 2.1.3 Static lattice optimisation ..................................................................... 48 2.1.4 Surface simulations.............................................................................. 50 2.1.5 Construction of calcite nanoparticles ................................................... 55 2.2 Molecular dynamics .................................................................................................... 56 2.2.1 Finite difference methods..................................................................... 57 2.2.2 Ensembles ........................................................................................... 60 2.2.3 Periodic boundary conditions ............................................................... 61 2.2.4 Running MD simulations ..................................................................... 62 2.2.5 Analysis ............................................................................................... 65 Chapter 3 Potential models.................................................................................. 67 3.1 The Born model of solids ........................................................................................... 68 3.2 The Ewald method ....................................................................................................... 69 3.3 Electronic polarisability ............................................................................................. 70 3.4 Short range potential functions ................................................................................. 72 3.4.1 Buckingham potential function ............................................................ 72 3.4.2 Morse potential function ...................................................................... 73 3.4.3 Lennard-Jones potential function