Peter W. Reiners, University of Arizona, USA Richard W. Carlson, Carnegie Institution for Science, USA Paul R. Renne, Berkeley Geochronology Center and University of California, USA Kari M. Cooper, University of California, USA Darryl E. Granger, Purdue University, USA Noah M. McLean, University of Kansas, USA Blair Schoene, Princeton University, USA

• Preface ix1 Introduction 11.1 Geo and chronologies 11.2 The ages of the age of the earth 21.3 Radioactivity 71.4 The objectives and significance of geochronology 131.5 References 152 Foundations of radioisotopic dating 172.1 Introduction 172.2 The delineation of nuclear structure 172.3 Nuclear stability 192.3.1 Nuclear binding energy and the mass defect 192.3.2 The liquid drop model for the nucleus 202.3.3 The nuclear shell model 222.3.4 Chart of the nuclides 232.4 Radioactive decay 232.4.1 Fission 232.4.2 Alpha-decay 242.4.3 Beta-decay 252.4.4 Electron capture 252.4.5 Branching decay 252.4.6 The energy of decay 252.4.7 The equations of radioactive decay 272.5 Nucleosynthesis and element abundances in the solar system 302.5.1 Stellar nucleosynthesis 302.5.2 Making elements heavier than iron: s-, r-, p-process nucleosynthesis 312.5.3 Element abundances in the solar system 322.6 Origin of radioactive isotopes 332.6.1 Stellar contributions of naturally occurring radioactive isotopes 332.6.2 Decay chains 332.6.3 Cosmogenic nuclides 332.6.4 Nucleogenic isotopes 352.6.5 Man-made radioactive isotopes 362.7 Conclusions 362.8 References 363 Analytical methods 393.1 Introduction 393.2 Sample preparation 393.3 Extraction of the element to be analyzed 403.4 Isotope dilution elemental quantification 423.5 Ion exchange chromatography 433.6 Mass spectrometry 443.6.1 Ionization 463.6.2 Extraction and focusing of ions 493.6.3 Mass fractionation 503.6.4 Mass analyzer 523.6.5 Detectors 573.6.6 Vacuum systems 603.7 Conclusions 623.8 References 634 Interpretational approaches: making sense of data 654.1 Introduction 654.2 Terminology and basics 654.2.1 Accuracy, precision, and trueness 654.2.2 Random versus systematic, uncertainties versus errors 664.2.3 Probability density functions 674.2.4 Univariate (one-variable) distributions 684.2.5 Multivariate normal distributions 684.3 Estimating a mean and its uncertainty 694.3.1 Average values: the sample mean, sample variance, and sample standard deviation 704.3.2 Average values: the standard error of the mean 704.3.3 Application: accurate standard errors for mass spectrometry 714.3.4 Correlation, covariance, and the covariance matrix 734.3.5 Degrees of freedom, part 1: the variance 734.3.6 Degrees of freedom, part 2: Student’s t distribution 734.3.7 The weighted mean 754.4 Regressing a line 764.4.1 Ordinary least-squares linear regression 764.4.2 Weighted least-squares regression 774.4.3 Linear regression with uncertainties in two or more variables (York regression) 774.5 Interpreting measured data using the mean square weighted deviation 794.5.1 Testing a weighted mean’s assumptions using its MSWD 794.5.2 Testing a linear regression’s assumptions using its MSWD 804.5.3 My data set has a high MSWD—what now? 814.5.4 My data set has a really low MSWD—what now? 814.6 Conclusions 824.7 Bibliography and suggested readings 825 Diffusion and thermochronologic interpretations 835.1 Fundamentals of heat and chemical diffusion 835.1.1 Thermochronologic context 835.1.2 Heat and chemical diffusion equation 835.1.3 Temperature dependence of diffusion 855.1.4 Some analytical solutions 865.1.5 Anisotropic diffusion 865.1.6 Initial infinite concentration (spike) 865.1.7 Characteristic length and time scales 865.1.8 Semi-infinite media 875.1.9 Plane sheet, cylinder, and sphere 885.2 Fractional loss 885.3 Analytical methods for measuring diffusion 895.3.1 Step-heating fractional loss experiments 895.3.2 Multidomain diffusion 925.3.3 Profile characterization 935.4 Interpreting thermal histories from thermochronologic data 945.4.1 “End-members” of thermochronometric date interpretations 945.4.2 Equilibrium dates 955.4.3 Partial retention zone 955.4.4 Resetting dates 965.4.5 Closure 975.5 From thermal to geologic histories in low-temperature thermochronology: diffusion and advection of heat in the earth’s crust 1055.5.1 Simple solutions for one- and two-dimensional crustal thermal fields 1075.5.2 Erosional exhumation 1085.5.3 Interpreting spatial patterns of erosion rates 1095.5.4 Interpreting temporal patterns of erosion rates 1135.5.5 Interpreting paleotopography 1135.6 Detrital thermochronology approaches for understanding landscape evolution and tectonics 1165.7 Conclusions 1215.8 References 1236 Rb–Sr, Sm–Nd, and Lu–Hf 1276.1 Introduction 1276.2 History 1276.3 Theory, fundamentals, and systematics 1286.3.1 Decay modes and isotopic abundances 1286.3.2 Decay constants 1286.3.3 Data representation 1296.3.4 Geochemistry 1316.4 Isochron systematics 1336.4.1 Distinguishing mixing lines from isochrons 1366.5 Diverse chronological applications 1376.5.1 Dating diagenetic minerals in clay-rich sediments 1376.5.2 Direct dating of ore minerals 1386.5.3 Dating of mineral growth in magma chambers 1406.5.4 Garnet Sm–Nd and Lu–Hf dating 1416.6 Model ages 1436.6.1 Model ages for volatile depletion 1446.6.2 Model ages for multistage source evolution 1466.7 Conclusion and future directions 1486.8 References 1487 Re–Os and Pt–Os 1517.1 Introduction 1517.2 Radioactive systematics and basic equations 1517.3 Geochemical properties and abundance in natural materials 1547.4 Analytical challenges 1547.5 Geochronologic applications 1567.5.1 Meteorites 1567.5.2 Molybdenite 1587.5.3 Other sulfides, ores, and diamonds 1597.5.4 Organic-rich sediments 1617.5.5 Komatiites 1617.5.6 Basalts 1637.5.7 Dating melt extraction from the mantle—Re–Os model ages 1647.6 Conclusions 1677.7 References 1678 U–Th–Pb geochronology and thermochronology 1718.1 Introduction and background 1718.1.1 Decay of U and Th to Pb 1718.1.2 Dating equations 1738.1.3 Decay constants 1738.1.4 Isotopic composition of U 1748.2 Chemistry of U, Th, and Pb 1768.3 Data visualization, isochrones, and concordia plots 1768.3.1 Isochron diagrams 1768.3.2 Concordia diagrams 1778.4 Causes of discordance in the U–Th–Pb system 1788.4.1 Mixing of different age domains 1808.4.2 Pb loss 1808.4.3 Intermediate daughter product disequilibrium 1828.4.4 Correction for initial Pb 1838.5 Analytical approaches to U–Th–Pb geochronology 1848.5.1 Thermal ionization mass spectrometry 1858.5.2 Secondary ion mass spectrometry 1878.5.3 Laser ablation inductively coupled plasma mass spectrometry 1888.5.4 Elemental U–Th–Pb geochronology by EMP 1888.6 Applications and approaches 1888.6.1 The age of meteorites and of Earth 1888.6.2 The Hadean 1928.6.3 P–T–t paths of metamorphic belts 1948.6.4 Rates of crustal magmatism from U–Pb geochronology 1978.6.5 U–Pb geochronology and the stratigraphic record 2008.6.6 Detrital zircon geochronology 2028.6.7 U–Pb thermochronology 2048.6.8 Carbonate geochronology by the U–Pb method 2098.6.9 U–Pb geochronology of baddeleyite and paleogeographic reconstructions 2118.7 Concluding remarks 2128.8 References 2129 The K–Ar and 40Ar/39Ar systems 2319.1 Introduction and fundamentals 2319.2 Historical perspective 2329.3 K–Ar dating 2339.3.1 Determining 40Ar∗ 2339.3.2 Determining 40K 2349.4 40Ar/39Ar dating 2349.4.1 Neutron activation 2349.4.2 Collateral effects of neutron irradiation 2379.4.3 Appropriate materials 2409.5 Experimental approaches and geochronologic applications 2429.5.1 Single crystal fusion 2429.5.2 Intragrain age gradients 2439.5.3 Incremental heating 2439.6 Calibration and accuracy 2489.6.1 40K decay constants 2489.6.2 Standards 2499.6.3 So which is the best calibration? 2509.6.4 Interlaboratory issues 2529.7 Concluding remarks 2529.7.1 Remaining challenges 2529.8 References 25310 Radiation-damage methods of geochronology and thermochronology 25910.1 Introduction 25910.2 Thermal and optically stimulated luminescence 25910.2.1 Theory, fundamentals, and systematics 25910.2.2 Analysis 26010.2.3 Fundamental assumptions and considerations for interpretations 26410.2.4 Applications 26510.3 Electron spin resonance 26610.3.1 Theory, fundamentals, and systematics 26610.3.2 Analysis 26710.3.3 Fundamental assumptions and considerations for interpretations 26810.3.4 Applications 26910.4 Alpha decay, alpha-particle haloes, and alpha-recoil tracks 27010.4.1 Theory, fundamentals, and systematics 27010.5 Fission tracks 27310.5.1 History 27310.5.2 Theory fundamentals and systematics 27310.5.3 Analyses 27410.5.4 Fission-track age equations 27610.5.5 Fission-track annealing 27810.5.6 Track-length analysis 28010.5.7 Applications 28110.6 Conclusions 28410.7 References 28511 The (U–Th)/He system 29111.1 Introduction 29111.2 History 29111.3 Theory, fundamentals, and systematics 29211.4 Analysis 29411.4.1 “Conventional” analyses 29411.4.2 Other analytical approaches 30611.4.3 Uncertainty and reproducibility in (U–Th)/He dating 30711.5 Helium diffusion 31011.5.1 Introduction 31011.5.2 Apatite 31111.5.3 Zircon 32211.5.4 Other minerals 33211.5.5 A compilation of He diffusion kinetics 33411.6 4He/3He thermochronometry 34211.6.1 Method requirements and assumptions 34611.7 Applications and case studies 34811.7.1 Tectonic exhumation of normal fault footwalls 34811.7.2 Paleotopography 34911.7.3 Orogen-scale trends in thermochronologic dates 35011.7.4 Detrital double-dating and sediment provenance 35311.7.5 Volcanic double-dating, precise eruption dates, and magmatic residence times 35311.7.6 Radiation-damage-and-annealing model applied to apatite 35511.8 Conclusions 35511.9 References 35612 Uranium-series geochronology 36512.1 Introduction 36512.2 Theory and fundamentals 36712.2.1 The mathematics of decay chains 36712.2.2 Mechanisms of producing disequilibrium 36912.3 Methods and analytical techniques 36912.3.1 Analytical techniques 36912.4 Applications 37212.4.1 U-series dating of carbonates 37212.4.2 U-series dating in silicate rocks 37812.5 Summary 38912.6 References 39013 Cosmogenic nuclides 39513.1 Introduction 39513.2 History 39513.3 Theory, fundamentals, and systematics 39613.3.1 Cosmic rays 39613.3.2 Distribution of cosmic rays on Earth 39613.3.3 What makes a cosmogenic nuclide detectable and useful? 39713.3.4 Types of cosmic-ray reactions 39813.3.5 Cosmic-ray attenuation 39913.3.6 Calibrating cosmogenic nuclide-production rates in rocks 40013.4 Applications 40113.4.1 Types of cosmogenic nuclide applications 40113.4.2 Extraterrestrial cosmogenic nuclides 40113.4.3 Meteoric cosmogenic nuclides 40213.5 Conclusion 41513.6 References 41614 Extinct radionuclide chronology 42114.1 Introduction 42114.2 History 42214.3 Systematics and applications 42314.3.1 26Al–26Mg 42314.3.2 53Mn–53Cr chronometry 42514.3.3 107Pd–107Ag 42814.3.4 182Hf–182W 43014.3.5 I–Pu–Xe 43314.3.6 146Sm–142Nd 43614.4 Conclusions 44114.5 References 441Index 445

"Geochronology and Thermochronology is an excellent textbook that delivers on the difficult balance between having an appropriate level of detail to be useful for an upper undergraduate to graduate-level class or research reference text without being too esoteric for a more general audience, with content and descriptions that are understandable and enlightening to the non-specialist. I would recommend this textbook for anyone interested in the history, principles, and mechanics of geochronology and thermochronology."—American Mineralogist, 2021