Principles of Radiometric Dating

Preface xi
Acknowledgments xiii
1. Basics 1
1.1 Nuclear Size and Constituents 1
1.2 Fundamental Forces 2
1.3 Nuclear Mass 3
1.4 Equivalence of Mass and Energy 3
1.5 Periodic Table 4
1.6 Nuclear Composition and Stability 6
1.7 Nuclear Binding Energy 8
1.8 Cosmic Abundances 9
2. Nuclear Transformations 12
2.1 Introduction 12
2.2 Spontaneous Nuclear Transformations 12
2.3 Induced Nuclear Transformations 15
2.4 Induced Nuclear Transformations in the Laboratory and Nature 16
2.5 Role of Natural Radioactivity in Geodynamics and Geochronology 17
2.6 Statistical Aspect of Radioactivity 18
2.7 Binomial Distribution for Radioactive Disintegrations 21
2.8 Poisson Distribution 21
3. Nucleosynthesis 23
3.1 Introduction 23
3.2 Stellar Nucleosynthesis 24
4. Isotopics 33
4.1 Introduction 33
4.2 Isotopic Abundance 33
4.3 Isotope Effect in the Nuclear and Atomic Domains 34
4.4 Notation of Isotopic Abundances 34
4.5 Mixtures of Isotopically Different Components 36
5. Radioactivity and Radiometric Dating 40
5.1 Introduction 40
5.2 Radioactive and Radiogenic Isotope Dating 43
5.3 Long-lived Parent-daughter Couples used in Radiometric Dating 48
5.4 Short-lived Parent-daughter Couples used in Radiometric Dating 53
5.5 Interpretation of t, Radioactive Decay Interval 58
5.6 Isochron Concept, Isotope Equilibration, and Closure Temperature 58
5.7 Termination of a Single Stage Growth in the Past 61
5.8 Recognition of Events Causing Isotopic Equilibration on Different Scales 63
5.9 Projection of Present Day Isotopic Composition Back in Time 64
5.10 Reservoir Ages 66
5.11 Coupling Two Different, But Chemically Identical Parent-daughter Systems 67
5.12 Concordia and Discordia 71
5.13 Coupling Two Chemically Different Decay Systems 74
5.14 Chemical and Half-life Diversity of Parent-daughter Pairs 76
5.15 Radiometric Dating by Indirect Radiogenic Effects 77
5.16 Conclusion 79
6. Mass Spectrometry and Isotope Geochemistry 80
6.1 Introduction 80
6.2 Principles of Mass Spectrometry 81
6.3 Ion Detectors 82
6.4 Sequential vs Simultaneous Detection of Ion Beams 83
6.5 Improved Mass Spectrometers 85
6.6 Types of Ion Sources Used in Isotope Geochemistry 86
6.7 Typical Commercial Mass Spectrometers Using Different Ion Sources 88
6.8 Mass Fractionation in Mass Spectrometers 91
6.9 Absolute Abundance of an Isotope 92
6.10 Sample Size Requirements 93
6.11 Mass Spectrometry vs Decay Counting 93
6.12 Accelerator Mass Spectrometer 94
7. Error Analysis 96
7.1 Introduction 96
7.2 Systematic and Random Errors 97
7.3 Measurement of Random Data 97
7.4 Population Mean and Sample Mean 98
7.5 Propagation of Measurement Uncertainties 101
7.6 Standard Deviation of the Mean of n Measurements 102
7.7 Joint Variation of Two or More Random Variables 103
7.8 Regression Analysis 105
7.9 York’s Solution 106
7.10 Measure of Goodness-of-fit 109
8. Meteorites: Link between Cosmo- and Geochemistry 110
8.1 Introduction 110
8.2 Nucleocosmochronology 111
8.3 Extinct Nuclides and Formation Interval 112
8.4 Meteorites 114
8.5 Nebular condensation 117
8.6 Planetary Accretion 118
8.7 Isotope Abundances in the Solar Nebula 119
9. Chronology of Meteorite History 121
9.1 Introduction 121
9.2 Stage 1: Formation Intervals from Extinct Isotopes 124
9.3 Stages 2 through 4: Formation Ages of Meteorites 127
9.4 Rb-Sr, Sm-Nd and U-Pb Ages of Meteorites 129
9.5 Very High Precision Model Ages 131
9.6 Meteorite Ages Much Younger than 4.5 Ga 134
9.7 Stage 5: Gas Retention Ages and Post-Formational Cooling and Heating Histories 134
9.8 Stage 6: Duration of Meteorites as Small Independent Objects in Space 137
9.9 Stage 7: Terrestrial Residence Time of Meteorite Finds 139
10. Chemical Evolution of the Earth 140
10.1 Composition of Terrestrial Planets and Chondritic Meteorites 140
10.2 Energetic Processes During the Final Stages of Earth Accretion 141
10.3 Element Segregation: Some Geochemical Rules 142
10.4 Segregation of Major and Trace Elements During Melting or Igneous Processes 143
10.5 Graphical Representation of Inter-Element Variations in Compatibility 145
10.6 Melting and Crystallization Models 146
10.7 Combined Partial Melting and Recrystallization 150
10.8 Observational Constraints on the Structure and Composition of the Modern Mantle 151
10.9 Earth as a Large Geochemical System 155
10.10 Elemental Chemistry of Mid-Ocean-Ridge Basalts, Ocean-Island Basalts and Continental Crust 157
11. Chronology of Earth History 161
11.1 Introduction 161
11.2 Early Siderophile-Lithophile Segregation and Timing of Core Formation 163
11.3 Early Lithophile-Atmophile Separation and Timing of the Primitive Atmosphere 165
11.4 Lithophile-Lithophile Separation and Timing of the Early Crust 168
11.5 142Nd Evolution in the Earth’s Mantle 171
11.6 143Nd Evolution in the Earth’s Mantle 172
11.7 87Sr Evolution in the Earth’s Mantle 175
11.8 Coupling Neodymium and Strontium Data 176
11.9 206Pb, 207Pb Evolution in the Earth’s Mantle 180
11.10 Evolution of 176Hf in the Earth’s Mantle 182
11.11 Evolution of 187Os in the Earth’s Mantle 182
11.12 Evolution of Strontium and Neodymium Isotope Ratios in Seawater 183
11.13 Magma Sources in the Mantle 185
11.14 Evolution of Radioactive Daughter Isotopes 188
11.15 Giant Impact Hypothesis 191
References 192
Index 203