Table of Contents
List of Figures xiList of Tables xviiPreface xixNotation xxiiPhysical Constants xxv
Chapter 1: Introduction and Overview 11.1 Thermodynamics versus Kinetics 31.2 Chemical Kinetics versus Geochemical Kinetics 61.3 Kinetics of Homogeneous Reactions 71.3.1 Reaction progress parameter x 111.3.2 Elementary versus overall reactions 121.3.3 Molecularity of a reaction 131.3.4 Reaction rate law, rate constant, and order of a reaction 141.3.5 Concentration evolution for reactions of different orders 191.3.6 Dependence of reaction rate constant on temperature; Arrhenius equation 251.3.7 Nonisothermal reaction kinetics 291.3.8 More complicated homogeneous reactions 311.3.9 Determination of reaction rate laws, rate constants, and mechanisms 321.4 Mass and Heat Transfer 361.4.1 Diffusion 371.4.2 Convection 461.5 Kinetics of Heterogeneous Reactions 471.5.1 Controlling factors and'‘reaction laws'’ 481.5.2 Steps in heterogeneous reactions 551.6 Temperature and Pressure Effect on Reaction Rate Coefficients and Diffusivities 581.6.1 Collision theory 591.6.2 Transition state theory 611.7 Inverse Problems 661.7.1 Reactions and diffusion during cooling 661.7.2 Geochronology, closure age, and thermochronology 711.7.3 Geothermometry, apparent equilibrium temperature, and geospeedometry 771.7.4 Geospeedometry using exchange reactions between two or more phases 811.7.5 Concluding remarks 831.8 Some Additional Notes 831.8.1 Mathematics encountered in kinetics 831.8.2 Demystifying some processes that seem to violate thermodynamics 841.8.3 Some other myths 861.8.4 Future research 87Problems 88
Chapter 2: Kinetics of Homogeneous Reactions 952.1 Reversible Reactions 972.1.1 Concentration evolution for first-order reversible reactions 972.1.2 Concentration evolution for second-order reversible reactions 992.1.3 Reversible reactions during cooling 1042.1.4 Fe-Mg order-disorder reaction in orthopyroxene 1132.1.5 Hydrous species reaction in rhyolitic melt 1222.2 Chain Reactions 1302.2.1 Radioactive decay series 1312.2.2 Chain reactions leading to negative activation energy 1442.2.3 Thermal decomposition of ozone 1452.3 Parallel Reactions 1472.3.1 Electron transfer between Fe(II) and Fe(III) in aqueous solution 1472.3.2 From dissolved CO2 to bicarbonate ion 1482.3.3 Nuclear hydrogen burning 1502.4 Some Special Topics 1552.4.1 Photochemical production and decomposition of ozone, and the ozone hole 1552.4.2 Diffusion control of homogeneous reactions 1572.4.3 Glass transition 160Problems 167
Chapter 3: Mass Transfer: Diffusion and Flow 1733.1 Basic Theories and Concepts 1753.1.1 Mass conservation and transfer 1753.1.2 Conservation of energy 1833.1.3 Conservation of momentum 1833.1.4 Various kinds of diffusion 1833.2 Diffusion in a Binary System 1893.2.1 Diffusion equation 1893.2.2 Initial and boundary conditions 1903.2.3 Some simple solutions to the diffusion equation at steady state 1923.2.4 One-dimensional diffusion in infinite or semi-infinite medium with constant diffusivity 1943.2.5 Instantaneous plane, line, or point source 2053.2.6 Principle of superposition 2073.2.7 One-dimensional finite medium and constant D, separation of variables 2093.2.8 Variable diffusion coefficient 2123.2.9 Uphill diffusion in binary systems and spinodal decomposition 2213.2.10 Diffusion in three dimensions; different coordinates 2243.2.11 Diffusion in an anisotropic medium; diffusion tensor 2273.2.12 Summary of analytical methods to obtain solution to the diffusion equation 2313.2.13 Numerical solutions 2313.3 Diffusion of a Multispecies Component 2363.3.1 Diffusion of water in silicate melts 2383.3.2 Diffusion of CO2 component in silicate melts 2453.3.3 Diffusion of oxygen in melts and minerals 2493.4 Diffusion in a Multicomponent System 2513.4.1 Effective binary approach 2523.4.2 Modified effective binary approach 2543.4.3 Multicomponent diffusivity matrix (concentration-based) 2553.4.4 Multicomponent diffusivity matrix (activity-based) 2633.4.5 Concluding remarks 2633.5 Some Special Diffusion Problems 2653.5.1 Diffusion of a radioactive component 2663.5.2 Diffusion of a radiogenic component and thermochronology 2673.5.3 Liesegang rings 2703.5.4 Isotopic ratio profiles versus elemental concentration profiles 2713.5.5 Moving boundary problems 2733.5.6 Diffusion and flow 2803.6 Diffusion Coefficients 2843.6.1 Experiments to obtain diffusivity 2853.6.2 Relations and models on diffusivity 298Problems 317
Chapter 4: Kinetics of Heterogeneous Reactions 3254.1 Basic Processes in Heterogeneous Reactions 3314.1.1 Nucleation 3314.1.2 Interface reaction 3424.1.3 Role of mass and heat transfer 3504.1.4 Dendritic crystal growth 3614.1.5 Nucleation and growth of many crystals 3624.1.6 Coarsening 3664.1.7 Kinetic control for the formation of new phases 3714.1.8 Some remarks 3724.2 Dissolution, Melting, or Growth of a Single Crystal, Bubble, or Droplet Controlled by Mass or Heat Transfer 3734.2.1 Reference frames 3754.2.2 Diffusive crystal dissolution in an infinite melt reservoir 3784.2.3 Convective dissolution of a falling or rising crystal in an infinite liquid reservoir 3934.2.4 Diffusive and convective crystal growth 4064.2.5 Diffusive and convective bubble growth and dissolution 4124.2.6 Other problems that can be treated similarly 4174.2.7 Interplay between interface reaction and diffusion 4174.3 Some Other Heterogeneous Reactions 4184.3.1 Bubble growth kinetics and dynamics in beer and champagne 4184.3.2 Dynamics of explosive volcanic eruptions 4234.3.3 Component exchange between two contacting crystalline phases 4264.3.4 Diffusive reequilibration of melt and fluid inclusions 4304.3.5 Melting of two crystalline phases or reactions between them 4344.4 Remarks About Future Research Needs 439Problems 441
Chapter 5: Inverse Problems: Geochronology,Thermochronology, and Geospeedometry 4455.1 Geochronology 4475.1.1 Dating method 1: The initial number of parent nuclides may be guessed 4495.1.2 Dating method 2: The initial number of atoms of the daughter nuclide may be guessed 4615.1.3 Dating method 3: The isochron method 4685.1.4 Dating method 4: Extinct nuclides for relative ages 4805.1.5 Requirements for accurate dating 4835.2 Thermochronology 4855.2.1 Closure temperature and closure age 4865.2.2 Mathematical analyses of diffusive loss and radiogenic growth 4905.2.3 More developments on the closure temperature concept 5055.2.4 Applications 5125.3 Geospeedometry 5165.3.1 Quantitative geospeedometry based on homogeneous reactions 5175.3.2 Cooling history of anhydrous glasses based on heat capacity measurements 5295.3.3 Geospeedometry based on diffusion and zonation in a single phase 5315.3.4 Geospeedometry based on diffusion between two or more phases 5415.3.5 Cooling history based on other heterogeneous reactions 5475.3.6 Comments on various geospeedometers 553Problems 555
Appendix 1 Entropy Production and Diffusion Matrix 561Appendix 2 The Error Function and Related Functions 565Appendix 3 Some Solutions to Diffusion Problems 570Appendix 4 Diffusion Coefficients 580Answers to Selected Problems 587References 593Subject Index 623
