<p>Preface ix</p> <p><b>1 </b><b>Introduction 1</b></p> <p>1.1 Geo and chronologies 1</p> <p>1.2 The ages of the age of the earth 2</p> <p>1.3 Radioactivity 7</p> <p>1.4 The objectives and significance of geochronology 13</p> <p>1.5 References 15</p> <p><b>2 </b><b>Foundations of radioisotopic dating 17</b></p> <p>2.1 Introduction 17</p> <p>2.2 The delineation of nuclear structure 17</p> <p>2.3 Nuclear stability 19</p> <p>2.3.1 Nuclear binding energy and the mass defect 19</p> <p>2.3.2 The liquid drop model for the nucleus 20</p> <p>2.3.3 The nuclear shell model 22</p> <p>2.3.4 Chart of the nuclides 23</p> <p>2.4 Radioactive decay 23</p> <p>2.4.1 Fission 23</p> <p>2.4.2 Alpha-decay 24</p> <p>2.4.3 Beta-decay 25</p> <p>2.4.4 Electron capture 25</p> <p>2.4.5 Branching decay 25</p> <p>2.4.6 The energy of decay 25</p> <p>2.4.7 The equations of radioactive decay 27</p> <p>2.5 Nucleosynthesis and element abundances in the solar system 30</p> <p>2.5.1 Stellar nucleosynthesis 30</p> <p>2.5.2 Making elements heavier than iron: <i>s- r-, p-</i>process nucleosynthesis 31</p> <p>2.5.3 Element abundances in the solar system 32</p> <p>2.6 Origin of radioactive isotopes 33</p> <p>2.6.1 Stellar contributions of naturally occurring radioactive isotopes 33</p> <p>2.6.2 Decay chains 33</p> <p>2.6.3 Cosmogenic nuclides 33</p> <p>2.6.4 Nucleogenic isotopes 35</p> <p>2.6.5 Man-made radioactive isotopes 36</p> <p>2.7 Conclusions 36</p> <p>2.8 References 36</p> <p><b>3 </b><b>Analytical methods 39</b></p> <p>3.1 Introduction 39</p> <p>3.2 Sample preparation 39</p> <p>3.3 Extraction of the element to be analyzed 40</p> <p>3.4 Isotope dilution elemental quantification 42</p> <p>3.5 Ion exchange chromatography 43</p> <p>3.6 Mass spectrometry 44</p> <p>3.6.1 Ionization 46</p> <p>3.6.2 Extraction and focusing of ions 49</p> <p>3.6.3 Mass fractionation 50</p> <p>3.6.4 Mass analyzer 52</p> <p>3.6.5 Detectors 57</p> <p>3.6.6 Vacuum systems 60</p> <p>3.7 Conclusions 62</p> <p>3.8 References 63</p> <p><b>4 </b><b>Interpretational approaches: making sense of data 65</b></p> <p>4.1 Introduction 65</p> <p>4.2 Terminology and basics 65</p> <p>4.2.1 Accuracy, precision, and trueness 65</p> <p>4.2.2 Random versus systematic, uncertainties versus errors 66</p> <p>4.2.3 Probability density functions 67</p> <p>4.2.4 Univariate (one-variable) distributions 68</p> <p>4.2.5 Multivariate normal distributions 68</p> <p>4.3 Estimating a mean and its uncertainty 69</p> <p>4.3.1 Average values: the sample mean, sample variance, and sample standard deviation 70</p> <p>4.3.2 Average values: the standard error of the mean 70</p> <p>4.3.3 Application: accurate standard errors for mass spectrometry 71</p> <p>4.3.4 Correlation, covariance, and the covariance matrix 73</p> <p>4.3.5 Degrees of freedom, part 1: the variance 73</p> <p>4.3.6 Degrees of freedom, part 2: Student’s <i>t </i>distribution 73</p> <p>4.3.7 The weighted mean 75</p> <p>4.4 Regressing a line 76</p> <p>4.4.1 Ordinary least-squares linear regression 76</p> <p>4.4.2 Weighted least-squares regression 77</p> <p>4.4.3 Linear regression with uncertainties in two or more variables (York regression) 77</p> <p>4.5 Interpreting measured data using the mean square weighted deviation 79</p> <p>4.5.1 Testing a weighted mean’s assumptions using its MSWD 79</p> <p>4.5.2 Testing a linear regression’s assumptions using its MSWD 80</p> <p>4.5.3 My data set has a high MSWD—what now? 81</p> <p>4.5.4 My data set has a really low MSWD—what now? 81</p> <p>4.6 Conclusions 82</p> <p>4.7 Bibliography and suggested readings 82</p> <p><b>5 </b><b>Diffusion and thermochronologic interpretations 83</b></p> <p>5.1 Fundamentals of heat and chemical diffusion 83</p> <p>5.1.1 Thermochronologic context 83</p> <p>5.1.2 Heat and chemical diffusion equation 83</p> <p>5.1.3 Temperature dependence of diffusion 85</p> <p>5.1.4 Some analytical solutions 86</p> <p>5.1.5 Anisotropic diffusion 86</p> <p>5.1.6 Initial infinite concentration (spike) 86</p> <p>5.1.7 Characteristic length and time scales 86</p> <p>5.1.8 Semi-infinite media 87</p> <p>5.1.9 Plane sheet, cylinder, and sphere 88</p> <p>5.2 Fractional loss 88</p> <p>5.3 Analytical methods for measuring diffusion 89</p> <p>5.3.1 Step-heating fractional loss experiments 89</p> <p>5.3.2 Multidomain diffusion 92</p> <p>5.3.3 Profile characterization 93</p> <p>5.4 Interpreting thermal histories from thermochronologic data 94</p> <p>5.4.1 “End-members” of thermochronometric date interpretations 94</p> <p>5.4.2 Equilibrium dates 95</p> <p>5.4.3 Partial retention zone 95</p> <p>5.4.4 Resetting dates 96</p> <p>5.4.5 Closure 97</p> <p>5.5 From thermal to geologic histories in low-temperature thermochronology: diffusion and advection of heat in the earth’s crust 105</p> <p>5.5.1 Simple solutions for one- and two-dimensional crustal thermal fields 107</p> <p>5.5.2 Erosional exhumation 108</p> <p>5.5.3 Interpreting spatial patterns of erosion rates 109</p> <p>5.5.4 Interpreting temporal patterns of erosion rates 113</p> <p>5.5.5 Interpreting paleotopography 113</p> <p>5.6 Detrital thermochronology approaches for understanding landscape evolution and tectonics 116</p> <p>5.7 Conclusions 121</p> <p>5.8 References 123</p> <p><b>6 </b><b>Rb–Sr, Sm–Nd, and Lu–Hf 127</b></p> <p>6.1 Introduction 127</p> <p>6.2 History 127</p> <p>6.3 Theory, fundamentals, and systematics 128</p> <p>6.3.1 Decay modes and isotopic abundances 128</p> <p>6.3.2 Decay constants 128</p> <p>6.3.3 Data representation 129</p> <p>6.3.4 Geochemistry 131</p> <p>6.4 Isochron systematics 133</p> <p>6.4.1 Distinguishing mixing lines from isochrons 136</p> <p>6.5 Diverse chronological applications 137</p> <p>6.5.1 Dating diagenetic minerals in clay-rich sediments 137</p> <p>6.5.2 Direct dating of ore minerals 138</p> <p>6.5.3 Dating of mineral growth in magma chambers 140</p> <p>6.5.4 Garnet Sm–Nd and Lu–Hf dating 141</p> <p>6.6 Model ages 143</p> <p>6.6.1 Model ages for volatile depletion 144</p> <p>6.6.2 Model ages for multistage source evolution 146</p> <p>6.7 Conclusion and future directions 148</p> <p>6.8 References 148</p> <p><b>7 </b><b>Re–Os and Pt–Os 151</b></p> <p>7.1 Introduction 151</p> <p>7.2 Radioactive systematics and basic equations 151</p> <p>7.3 Geochemical properties and abundance in natural materials 154</p> <p>7.4 Analytical challenges 154</p> <p>7.5 Geochronologic applications 156</p> <p>7.5.1 Meteorites 156</p> <p>7.5.2 Molybdenite 158</p> <p>7.5.3 Other sulphides, ores, and diamonds 159</p> <p>7.5.4 Organic-rich sediments 161</p> <p>7.5.5 Komatiites 161</p> <p>7.5.6 Basalts 163</p> <p>7.5.7 Dating melt extraction from the mantle—Re–Os model ages 164</p> <p>7.6 Conclusions 167</p> <p>7.7 References 167</p> <p><b>8 </b><b>U–Th–Pb geochronology and thermochronology 171</b></p> <p>8.1 Introduction and background 171</p> <p>8.1.1 Decay of U and Th to Pb 171</p> <p>8.1.2 Dating equations 173</p> <p>8.1.3 Decay constants 173</p> <p>8.1.4 Isotopic composition of U 174</p> <p>8.2 Chemistry of U, Th, and Pb 176</p> <p>8.3 Data visualization, isochrones, and concordia plots 176</p> <p>8.3.1 Isochron diagrams 176</p> <p>8.3.2 Concordia diagrams 177</p> <p>8.4 Causes of discordance in the U–Th–Pb system 178</p> <p>8.4.1 Mixing of different age domains 180</p> <p>8.4.2 Pb loss 180</p> <p>8.4.3 Intermediate daughter product disequilibrium 182</p> <p>8.4.4 Correction for initial Pb 183</p> <p>8.5 Analytical approaches to U–Th–Pb geochronology 184</p> <p>8.5.1 Thermal ionization mass spectrometry 185</p> <p>8.5.2 Secondary ion mass spectrometry 187</p> <p>8.5.3 Laser ablation inductively coupled plasma mass spectrometry 188</p> <p>8.5.4 Elemental U–Th–Pb geochronology by EMP 188</p> <p>8.6 Applications and approaches 188</p> <p>8.6.1 The age of meteorites and of Earth 188</p> <p>8.6.2 The Hadean 192</p> <p>8.6.3 <i>P–T–t </i>paths of metamorphic belts 194</p> <p>8.6.4 Rates of crustal magmatism from U–Pb geochronology 197</p> <p>8.6.5 U–Pb geochronology and the stratigraphic record 200</p> <p>8.6.6 Detrital zircon geochronology 202</p> <p>8.6.7 U–Pb thermochronology 204</p> <p>8.6.8 Carbonate geochronology by the U–Pb method 209</p> <p>8.6.9 U–Pb geochronology of baddeleyite and paleogeographic reconstructions 211</p> <p>8.7 Concluding remarks 212</p> <p>8.8 References 212</p> <p><b>9 </b><b>The K–Ar and <sup>40</sup>Ar/<sup>39</sup>Ar systems 231</b></p> <p>9.1 Introduction and fundamentals 231</p> <p>9.2 Historical perspective 232</p> <p>9.3 K–Ar dating 233</p> <p>9.3.1 Determining <sup>40</sup>Ar<sup>∗</sup> 233</p> <p>9.3.2 Determining 40K 234</p> <p>9.4 <sup>40</sup>Ar/<sup>39</sup>Ar dating 234</p> <p>9.4.1 Neutron activation 234</p> <p>9.4.2 Collateral effects of neutron irradiation 237</p> <p>9.4.3 Appropriate materials 240</p> <p>9.5 Experimental approaches and geochronologic applications 242</p> <p>9.5.1 Single crystal fusion 242</p> <p>9.5.2 Intragrain age gradients 243</p> <p>9.5.3 Incremental heating 243</p> <p>9.6 Calibration and accuracy 248</p> <p>9.6.1 <sup>40</sup>K decay constants 248</p> <p>9.6.2 Standards 249</p> <p>9.6.3 So which is the best calibration? 250</p> <p>9.6.4 Interlaboratory issues 252</p> <p>9.7 Concluding remarks 252</p> <p>9.7.1 Remaining challenges 252</p> <p>9.8 References 253</p> <p><b>10 </b><b>Radiation-damage methods of geochronology and thermochronology 259</b></p> <p>10.1 Introduction 259</p> <p>10.2 Thermal and optically stimulated luminescence 259</p> <p>10.2.1 Theory, fundamentals, and systematics 259</p> <p>10.2.2 Analysis 260</p> <p>10.2.3 Fundamental assumptions and considerations for interpretations 264</p> <p>10.2.4 Applications 265</p> <p>10.3 Electron spin resonance 266</p> <p>10.3.1 Theory, fundamentals, and systematics 266</p> <p>10.3.2 Analysis 267</p> <p>10.3.3 Fundamental assumptions and considerations for interpretations 268</p> <p>10.3.4 Applications 269</p> <p>10.4 Alpha decay, alpha-particle haloes, and alpha-recoil tracks 270</p> <p>10.4.1 Theory, fundamentals, and systematics 270</p> <p>10.5 Fission tracks 273</p> <p>10.5.1 History 273</p> <p>10.5.2 Theory, fundamentals, and systematics 273</p> <p>10.5.3 Analyses 274</p> <p>10.5.4 Fission-track age equations 276</p> <p>10.5.5 Fission-track annealing 278</p> <p>10.5.6 Track-length analysis 280</p> <p>10.5.7 Applications 281</p> <p>10.6 Conclusions 284</p> <p>10.7 References 285</p> <p><b>11 </b><b>The (U–Th)/He system 291</b></p> <p>11.1 Introduction 291</p> <p>11.2 History 291</p> <p>11.3 Theory, fundamentals, and systematics 292</p> <p>11.4 Analysis 294</p> <p>11.4.1 “Conventional” analyses 294</p> <p>11.4.2 Other analytical approaches 306</p> <p>11.4.3 Uncertainty and reproducibility in (U–Th)/He dating 307</p> <p>11.5 Helium diffusion 310</p> <p>11.5.1 Introduction 310</p> <p>11.5.2 Apatite 311</p> <p>11.5.3 Zircon 322</p> <p>11.5.4 Other minerals 332</p> <p>11.5.5 A compilation of He diffusion kinetics 334</p> <p>11.6 <sup>4</sup>He/<sup>3</sup>He thermochronometry 342</p> <p>11.6.1 Method requirements and assumptions 346</p> <p>11.7 Applications and case studies 348</p> <p>11.7.1 Tectonic exhumation of normal fault footwalls 348</p> <p>11.7.2 Paleotopography 349</p> <p>11.7.3 Orogen-scale trends in thermochronologic dates 350</p> <p>11.7.4 Detrital double-dating and sediment provenance 353</p> <p>11.7.5 Volcanic double-dating, precise eruption dates, and magmatic residence times 353</p> <p>11.7.6 Radiation-damage-and-annealing model applied to apatite 355</p> <p>11.8 Conclusions 355</p> <p>11.9 References 356</p> <p><b>12 </b><b>Uranium-series geochronology 365</b></p> <p>12.1 Introduction 365</p> <p>12.2 Theory and fundamentals 367</p> <p>12.2.1 The mathematics of decay chains 367</p> <p>12.2.2 Mechanisms of producing disequilibrium 369</p> <p>12.3 Methods and analytical techniques 369</p> <p>12.3.1 Analytical techniques 369</p> <p>12.4 Applications 372</p> <p>12.4.1 U-series dating of carbonates 372</p> <p>12.4.2 U-series dating in silicate rocks 378</p> <p>12.5 Summary 389</p> <p>12.6 References 390</p> <p><b>13 </b><b>Cosmogenic nuclides 395</b></p> <p>13.1 Introduction 395</p> <p>13.2 History 395</p> <p>13.3 Theory, fundamentals, and systematics 396</p> <p>13.3.1 Cosmic rays 396</p> <p>13.3.2 Distribution of cosmic rays on Earth 396</p> <p>13.3.3 What makes a cosmogenic nuclide detectable and useful? 397</p> <p>13.3.4 Types of cosmic-ray reactions 398</p> <p>13.3.5 Cosmic-ray attenuation 399</p> <p>13.3.6 Calibrating cosmogenic nuclide-production rates in rocks 400</p> <p>13.4 Applications 401</p> <p>13.4.1 Types of cosmogenic nuclide applications 401</p> <p>13.4.2 Extraterrestrial cosmogenic nuclides 401</p> <p>13.4.3 Meteoric cosmogenic nuclides 402</p> <p>13.5 Conclusion 415</p> <p>13.6 References 416</p> <p><b>14 </b><b>Extinct radionuclide chronology 421</b></p> <p>14.1 Introduction 421</p> <p>14.2 History 422</p> <p>14.3 Systematics and applications 423</p> <p>14.3.1 <sup>26</sup>Al–<sup>26</sup>Mg 423</p> <p>14.3.2 <sup>53</sup>Mn–<sup>53</sup>Cr chronometry 425</p> <p>14.3.3 <sup>107</sup>Pd–<sup>107</sup>Ag 428</p> <p>14.3.4 <sup>182</sup>Hf–<sup>182</sup>W 430</p> <p>14.3.5 I–Pu–Xe 433</p> <p>14.3.6 <sup>146</sup>Sm–<sup>142</sup>Nd 436</p> <p>14.4 Conclusions 441</p> <p>14.5 References 441</p> <p>Index 445</p>