Geochemical Kinetics

List of Figures xi List of Tables xvii Preface xix Notation xxii Physical Constants xxv Chapter 1: Introduction and Overview 1 1.1 Thermodynamics versus Kinetics 3 1.2 Chemical Kinetics versus Geochemical Kinetics 6 1.3 Kinetics of Homogeneous Reactions 7 1.3.1 Reaction progress parameter x 11 1.3.2 Elementary versus overall reactions 12 1.3.3 Molecularity of a reaction 13 1.3.4 Reaction rate law, rate constant, and order of a reaction 14 1.3.5 Concentration evolution for reactions of different orders 19 1.3.6 Dependence of reaction rate constant on temperature; Arrhenius equation 25 1.3.7 Nonisothermal reaction kinetics 29 1.3.8 More complicated homogeneous reactions 31 1.3.9 Determination of reaction rate laws, rate constants, and mechanisms 32 1.4 Mass and Heat Transfer 36 1.4.1 Diffusion 37 1.4.2 Convection 46 1.5 Kinetics of Heterogeneous Reactions 47 1.5.1 Controlling factors and"reaction laws" 48 1.5.2 Steps in heterogeneous reactions 55 1.6 Temperature and Pressure Effect on Reaction Rate Coefficients and Diffusivities 58 1.6.1 Collision theory 59 1.6.2 Transition state theory 61 1.7 Inverse Problems 66 1.7.1 Reactions and diffusion during cooling 66 1.7.2 Geochronology, closure age, and thermochronology 71 1.7.3 Geothermometry, apparent equilibrium temperature, and geospeedometry 77 1.7.4 Geospeedometry using exchange reactions between two or more phases 81 1.7.5 Concluding remarks 83 1.8 Some Additional Notes 83 1.8.1 Mathematics encountered in kinetics 83 1.8.2 Demystifying some processes that seem to violate thermodynamics 84 1.8.3 Some other myths 86 1.8.4 Future research 87 Problems 88 Chapter 2: Kinetics of Homogeneous Reactions 95 2.1 Reversible Reactions 97 2.1.1 Concentration evolution for first-order reversible reactions 97 2.1.2 Concentration evolution for second-order reversible reactions 99 2.1.3 Reversible reactions during cooling 104 2.1.4 Fe-Mg order-disorder reaction in orthopyroxene 113 2.1.5 Hydrous species reaction in rhyolitic melt 122 2.2 Chain Reactions 130 2.2.1 Radioactive decay series 131 2.2.2 Chain reactions leading to negative activation energy 144 2.2.3 Thermal decomposition of ozone 145 2.3 Parallel Reactions 147 2.3.1 Electron transfer between Fe2yFE and Fe3yFE in aqueous solution 147 2.3.2 From dissolved CO2 to bicarbonate ion 148 2.3.3 Nuclear hydrogen burning 150 2.4 Some Special Topics 155 2.4.1 Photochemical production and decomposition of ozone, and the ozone hole 155 2.4.2 Diffusion control of homogeneous reactions 157 2.4.3 Glass transition 160 Problems 167 Chapter 3: Mass Transfer: Diffusion and Flow 173 3.1 Basic Theories and Concepts 175 3.1.1 Mass conservation and transfer 175 3.1.2 Conservation of energy 183 3.1.3 Conservation of momentum 183 3.1.4 Various kinds of diffusion 183 3.2 Diffusion in a Binary System 189 3.2.1 Diffusion equation 189 3.2.2 Initial and boundary conditions 190 3.2.3 Some simple solutions to the diffusion equation at steady state 192 3.2.4 One-dimensional diffusion in infinite or semi-infinite medium with constant diffusivity 194 3.2.5 Instantaneous plane, line, or point source 205 3.2.6 Principle of superposition 207 3.2.7 One-dimensional finite medium and constant D, separation of variables 209 3.2.8 Variable diffusion coefficient 212 3.2.9 Uphill diffusion in binary systems and spinodal decomposition 221 3.2.10 Diffusion in three dimensions; different coordinates 224 3.2.11 Diffusion in an anisotropic medium; diffusion tensor 227 3.2.12 Summary of analytical methods to obtain solution to the diffusion equation 231 3.2.13 Numerical solutions 231 3.3 Diffusion of a Multispecies Component 236 3.3.1 Diffusion of water in silicate melts 238 3.3.2 Diffusion of CO2 component in silicate melts 245 3.3.3 Diffusion of oxygen in melts and minerals 249 3.4 Diffusion in a Multicomponent System 251 3.4.1 Effective binary approach 252 3.4.2 Modified effective binary approach 254 3.4.3 Multicomponent diffusivity matrix (concentration-based) 255 3.4.4 Multicomponent diffusivity matrix (activity-based) 263 3.4.5 Concluding remarks 263 3.5 Some Special Diffusion Problems 265 3.5.1 Diffusion of a radioactive component 266 3.5.2 Diffusion of a radiogenic component and thermochronology 267 3.5.3 Liesegang rings 270 3.5.4 Isotopic ratio profiles versus elemental concentration profiles 271 3.5.5 Moving boundary problems 273 3.5.6 Diffusion and flow 280 3.6 Diffusion Coefficients 284 3.6.1 Experiments to obtain diffusivity 285 3.6.2 Relations and models on diffusivity 298 Problems 317 Chapter 4: Kinetics of Heterogeneous Reactions 325 4.1 Basic Processes in Heterogeneous Reactions 331 4.1.1 Nucleation 331 4.1.2 Interface reaction 342 4.1.3 Role of mass and heat transfer 350 4.1.4 Dendritic crystal growth 361 4.1.5 Nucleation and growth of many crystals 362 4.1.6 Coarsening 366 4.1.7 Kinetic control for the formation of new phases 371 4.1.8 Some remarks 372 4.2 Dissolution, Melting, or Growth of a Single Crystal, Bubble, or Droplet Controlled by Mass or Heat Transfer 373 4.2.1 Reference frames 375 4.2.2 Diffusive crystal dissolution in an infinite melt reservoir 378 4.2.3 Convective dissolution of a falling or rising crystal in an infinite liquid reservoir 393 4.2.4 Diffusive and convective crystal growth 406 4.2.5 Diffusive and convective bubble growth and dissolution 412 4.2.6 Other problems that can be treated similarly 417 4.2.7 Interplay between interface reaction and diffusion 417 4.3 Some Other Heterogeneous Reactions 418 4.3.1 Bubble growth kinetics and dynamics in beer and champagne 418 4.3.2 Dynamics of explosive volcanic eruptions 423 4.3.3 Component exchange between two contacting crystalline phases 426 4.3.4 Diffusive reequilibration of melt and fluid inclusions 430 4.3.5 Melting of two crystalline phases or reactions between them 434 4.4 Remarks About Future Research Needs 439 Problems 441 Chapter 5: Inverse Problems: Geochronology, Thermochronology, and Geospeedometry 445 5.1 Geochronology 447 5.1.1 Dating method 1: The initial number of parent nuclides may be guessed 449 5.1.2 Dating method 2: The initial number of atoms of the daughter nuclide may be guessed 461 5.1.3 Dating method 3: The isochron method 468 5.1.4 Dating method 4: Extinct nuclides for relative ages 480 5.1.5 Requirements for accurate dating 483 5.2 Thermochronology 485 5.2.1 Closure temperature and closure age 486 5.2.2 Mathematical analyses of diffusive loss and radiogenic growth 490 5.2.3 More developments on the closure temperature concept 505 5.2.4 Applications 512 5.3 Geospeedometry 516 5.3.1 Quantitative geospeedometry based on homogeneous reactions 517 5.3.2 Cooling history of anhydrous glasses based on heat capacity measurements 529 5.3.3 Geospeedometry based on diffusion and zonation in a single phase 531 5.3.4 Geospeedometry based on diffusion between two or more phases 541 5.3.5 Cooling history based on other heterogeneous reactions 547 5.3.6 Comments on various geospeedometers 553 Problems 555 Appendix 1 Entropy Production and Diffusion Matrix 561 Appendix 2 The Error Function and Related Functions 565 Appendix 3 Some Solutions to Diffusion Problems 570 Appendix 4 Diffusion Coefficients 580 Answers to Selected Problems 587 References 593 Subject Index 623