1. Radiogenic Isotopes In Igneous Petrology Francis, 2013

2. Proton No. Neutron No. P P N N Tin P = 50

4. Beta decay: Beta Capture : (positron emission): Alpha decay: 87 Rb  87 Sr + e - + +  t 1/2 = 5.2  10 10 years = 1.42  10 -11 / yr 147 Sm  143 Nd + 4 He +  t 1/2 = 1.06  10 10 years = 6.54  10 -12 / yr 26 Al  26 Mg + e + + +  t 1/2 = 0.72  10 6 years = 9.8  10 -7 / yr Conversion of protons to neutrons and vice versa – Weak Nuclear Force Loss of alpha particles – residual Strong Nuclear Force Radioactive Decay

5. +  ray Parent Isotope +  ray Radioactive Decay

6. P + → N o + e + +  e Beta capture Beta decay P + + e - +  e N o 4 He 2+ + γ Alpha decay

7. -δN / δ t = λ × N N = N o × e -λt -δN / N = λ × δ t ln(N) = -λ × t + N o D* = N o - N D* = N × (e λt – 1) D = D o + D* D = D o + N × (e λt – 1) t 1/2 = ln 2/λ Law of Radioactivity Rutherford and Soddy, 1902

8. Some Useful Radioactive Decay Schemes: Beta decay: 182 Hf  182 W + e - + +  t 1/2 = 9  10 6 years = 7.7  10 -8 /yr 129 I  129 Xe + e - + +  t 1/2 = 16  10 6 years = 4.3  10 -8 / yr 176 Lu  176 Hf + e - + +  t 1/2 = 3.5  10 10 years = 1.94  10 -11 / yr 187 Re  187 Os + e - + +  t 1/2 = 4.56  10 10 years = 1.52  10 -11 / yr 87 Rb  87 Sr + e - + +  t 1/2 = 5.2  10 10 years = 1.42  10 -11 / yr Beta Capture (positron emission): 26 Al  26 Mg + e + + +  t 1/2 = 0.72  10 6 years = 9.8  10 -7 / yr 53 Mn  53 Cr + e + + +  t 1/2 = 3.7  10 6 years = 1.9  10 -7 / yr 40 K  40 Ar + e + + +  = 0.581  10 -10 / yr 40 K  40 Ca + e - + +  t 1/2 = 1.250  10 9 years = 4.962  10 -10 / yr Alpha decay: 146 Sm  142 Nd + 4 He +  t 1/2 = 103  10 6 years = 147 Sm  143 Nd + 4 He +  t 1/2 = 1.06  10 10 years = 6.54  10 -12 / yr 235 U  207 Pb + 7 4 He + 4e - +  t 1/2 = 0.7038  10 9 years = 9.8485  10 -10 / yr 232 Th  208 Pb + 6 4 He + 4e - +  t 1/2 = 14.010  10 9 years = 4.9475  10 -11 / yr 238 U  206 Pb + 8 4 He + 6e - +  t 1/2 = 4.468  10 10 years = 1.55125  10 -10 / yr combined

9. Summary Radioactive Decay Schemes: Beta decay: 87 Rb  87 Sr + e - + +  t 1/2 = 5.2  10 10 yrs = 1.42  10 -11 / yr Alpha decay: 147 Sm  143 Nd + 4 He +  t 1/2 = 1.06  10 10 yrs = 6.54  10 -12 / yr 235 U  207 Pb + 7 4 He + 4e - +  t 1/2 = 0.7038  10 9 yrs = 9.8485  10 -10 / yr 232 Th  208 Pb + 6 4 He + 4e - +  t 1/2 = 14.010  10 9 yrs = 4.9475  10 -11 / yr 238 U  206 Pb + 8 4 He + 6e - +  t 1/2 = 4.468  10 10 yrs = 1.55125  10 -10 / yr

10. Rb – Sr System 87 Rb  87 Sr + e - + +  t 1/2 = 5.2  10 10 years = 1.42  10 -11 / yr Rb + substitutes for K + in the large W site of phases such as feldspar, mica, and amphibole, whereas Sr 2+ substitutes for Ca 2+ in feldspars. In-grown 86 Sr thus sits in a site that is not only too large for it, but which may have been damaged by the decay process. As a result, Rb-Sr isochrons are relatively easily disturbed. This situation is aggravated by the fact that both Rb and Sr are relatively soluble in aqueous solutions leading to the mobility of Rb and Sr during secondary processes such as weathering and metamorphism. Not useful in old metamorphosed rocks.

11. 87 Sr = 87 Sr i + 87 Rb × (e λt -1) 87 Sr/ 86 Sr = ( 87 Sr/ 86 Sr) i + ( 87 Rb/ 86 Sr) × (e λt -1) Y = Y i + a × X a = (e λt -1) 2 unknowns: t = Time ( 87 Sr/ 86 Sr) i i D = D o + N × (e λt – 1)

12. The Effect of Metamorphism

13. Rb – Sr System 87 Rb  87 Sr + e - + +  K Rb < K Sr Liquid (Rb / Sr) > Residue (Rb / Sr) Small degrees partial melting fractionates the Parent / Daughter ratio Rb/Sr, such that liquids have higher parent / daughter ratios and residues have lower parent / daughter ratios. During partial melting,

14. Sm - Nd System 147 Sm  143 Nd + 4 He +  t 1/2 = 1.06  10 10 years = 6.54  10 -12 / yr Both Sm 3+ and Nd 3+ substitute for Al 3+ in clinopyroxene, amphibole, and are also preferentially up taken by apatite. The Sm-Nd isotopic system is significantly more robust than the Rb/Sr system because both the parent and daughter are happy in similar crystallographic sites, and both are relatively insoluble and thus immobile. The similar chemical properties of Sm and Nd, however, means that it is more difficult to find enough spread in the parent/daugther ratio to yield a good isochron. 143 Nd = 143 Nd i + 147 Sm × (e λt -1) 143 Nd / 144 Nd = 143 Nd/ 144 Nd i + ( 147 Sm/ 144 Nd) × (e λt -1) D = D o + N × (e λt – 1)

15. Oldest Age on the Moon

16. Sm - Nd System 147 Sm  143 Nd + 4 He +  Liquid (Sm / Nd) < Residue (Sm / Nd) 143 Nd = 143 Nd i + 147 Sm × (e λt -1) In contrast to the Rb/Sr system, in the Sm-Nd system partial melts have lower parent /daughter ratios and the solid residue of partial melting has higher parent daughter ratios. Note: this is the reverse of the situation in the Rb/Sr isotopic system. K Sm > K Nd

17. Sm - Nd: 147 Sm  143 Nd + 4 He +  K Sm > K Nd Liquid (Sm / Nd) < Residue (Sm / Nd) 143 Nd = 143 Nd i + 147 Sm × (e λt -1) During partial melting,

18. 143 Nd/ 144 Nd = ( 143 Nd/ 144 Nd) i + ( 147 Sm/ 144 Nd) × (e λt -1) Nd isotopic evolution

19. ε Nd(t) = (( 143 Nd/ 144 Nd Sample(t) ) / ( 143 Nd/ 144 Nd Chur(t) ) - 1) × 10 4 MORB ε Nd and Model Ages

20. Mantle Extraction Ages: It is important to distinguish between crystallisation age and mantle extraction age of the continental crust. This problem has been addressed by DePaolo using a combination of zircon crystallization ages and Nd model mantle extraction ages. His results indicate that 80% of the Earth's continental crust was formed by 1.6 Ga. Many younger crustal rocks must thus represent reworked older crust. ε Nd(t) = (( 143 Nd/ 144 Nd Sample(t) ) / ( 143 Nd/ 144 Nd Chur(t) ) - 1) × 10 4 MORB

21. Mantle Array

23. Long-term depleted source that has been recently enriched.

24. 2 types of Enrichment The incompatible trace element enrichment of E-MORB is associated with elevated 87 Sr/ 86 Sr and 143 Nd/ 144 Nd isotopic ratios compared to N- MORB, opposite to the correlation observed at many hot spots, such as Hawaii.

26. Continental flood Basalts Continental flood Basalts

28. Calc-Alkaline Arcs

30. U, Th, and Pb Isotopic Systems 235 U  207 Pb + 74 He + 4e- +  t 1/2 = 0.7038  10 9 yrs = 9.8485  10 -10 / yr 232 Th  208 Pb + 64 He + 4e- +  t 1/2 = 14.010  10 9 yrs = 4.9475  10 -11 / yr 238 U  206 Pb + 84 He + 6e- +  t 1/2 = 4.468  10 10 yrs = 1.55125  10 -10 / yr U 3-6+, Th 4+, and Pb 2-4+ are highly incompatible in most rock forming minerals (K << 1), with Th and U being more incompatible than Pb, leading to a crust with high U/Pb ratios. Furthermore, Th and U are lithophile and preferentially partition into large sites in accessory phases such as zircon, apatite, perovskite, and baddelyeite. Pb, on the other hand, is largely excluded from zircon and is significantly chalcophile, partitioning preferentially into sulfides. Both U and Pb are relatively easily mobilized and the use of these radiogenic isotopes as tracers is largely restricted to modern, unaltered igneous rocks. Th, on the other hand, is relatively immobile, and has been successfully used as a tracer in older metamorphosed rocks.

31. U/Pb

33. U – Pb Concordia Diagrams 235 U  207 Pb + 74 He + 4e - +  t 1/2 = 0.7038  10 9 years = 9.8485  10 -10 / yr 238 U  206 Pb + 84 He + 6e - +  t 1/2 = 4.468  10 10 years = 1.55125  10 -10 / yr The difference in geochemical behaviour of Pb versus Th and U works to our advantage in using zircons for dating. The low levels of common Pb in zircon, combined with zircons high resistance to alteration make U-Pb isotopes in zircon an excellent geochronometer of the past.

35. U – Pb Concordia Diagrams 235 U  207 Pb + 74 He + 4e - +  t 1/2 = 0.7038  10 9 years = 9.8485  10 -10 / yr 238 U  206 Pb + 84 He + 6e - +  t 1/2 = 4.468  10 10 years = 1.55125  10 -10 / yr Mississippi River Zircons Mackenzie River Zircons Amazon River Zircons Zircons in the Sands of Major Rivers

36. Pb Isochrons and the Age of the Solar System

37. Pb – Pb Isochron Diagrams 235 U  207 Pb + 74 He + 4e - +  t 1/2 = 0.7038  10 9 years = 9.8485  10 -10 / yr 238 U  206 Pb + 84 He + 6e - +  t 1/2 = 4.468  10 10 years = 1.55125  10 -10 / yr

38. Future Ages, Mixing Lines, & Pseudo-Isochrons? The apparent future ages of MORB and OIB can be explained by multi-stage fractionations, but the Pb paradox remains. The first Pb Paradox : virtually all mantle reservoirs plot to the right of the Geochron, where are the complimentary reservoirs required for mass balance? MORB

43. The lavas within many OIB suites define approximately linear arrays between two chemical and isotopic components, one relatively depleted and the other relatively enriched. Originally these were thought to correlate with the MORB source and primitive mantle respectively. However, it rapidly became apparent that these linear arrays were different in different OIB suites.

44. There are thus many "flavours" of OIB suites, and at least five different components are required to explain them. Furthermore, there are geographic correlations in the isotopic characteristics of OIB suites. For example, the DUPAL anomaly in the south Pacific is defined by the abundance of EM II OIB suites that appears to correlate with a lower mantle seismic tomography anomaly.

45. Mantle Components / Reservoirs Bulk Silicate Earth (BSE) or Primitive Mantle (PM) 87 Sr/ 86 Sr =.7045, 143 Nd/ 144 Nd =.5126, chondrite-defined Depleted MORB Mantle (DMM) lava characteristics: low 87 Sr/ 86 Sr 0.5130), low 206 Pb/ 204 Pb (~18) source time integrated: low Rb/Sr, high Sm/Nd, low U/Pb nature: Primitive mantle minus continental crust or small degree melt. Enriched Mantle I (EM 1): lava characteristics: moderate 87 Sr/ 86 Sr (~0.7050), lowest 143 Nd/ 144 Nd (~0.5124), Pitcairn Is., Tristan de Cunha low 206 Pb/ 204 Pb (< 17) Hawaii source time integrated: moderate Rb/Sr, low Sm/Nd, low U/Pb nature: subducted lower continental crust and/or lithospheric mantle, pelagic sediments? Enriched Mantle II (EM 2): lava characteristics: highest 87 Sr/ 86 Sr (>0.7080), low 143 Nd/ 144 Nd (~.5125), 206 Pb/ 204 Pb (~19) Samoa, Society Islands source time integrated: high Rb/Sr, low Sm/Nd, low U/Pb Dupal anomaly nature: subducted upper continental crust and/or sediments, also similar to Group II kimberlites and some olivine lamproites HIMU (high U/Pb): lava characteristics: low 87 Sr/ 86 Sr, (~ 0.7030), high 143 Nd/ 144 Nd (~0.5129), St. Helena Is., Austral Is., Azores highest 206 Pb/ 204 Pb (>20), high Ca source time integrated: low Rb/Sr, high Sm/Nd, high U/Pb nature: subducted oceanic crust that has lost Pb because of seawater alteration.

46. Focal Zone (FOZO: The apparent point of convergence of the linear isotopic arrays of many OIB suites, thus possibly representing a mantle component that is common to all. It has a relatively depleted composition compared to primitive mantle in terms of Sr and Nd isotopes, but moderately radiogenic Pb isotopes. It is thus not the asthenospheric mantle (DMM), and not primitive mantle. It may be the figment of a fertile imagination. It is important to remember that not only is the identity of these different mantle components a matter of debate, there is little constraint on their physical location, They are typically hidden in the deep mantle

47. General Mixing Equation: AX + BXY + CY + D = 0 A = a 2 b 1 Y 2 – a 1 b 2 Y 1 B = a 1 b 2 – a 2 b 1 C = a 2 b 1 X 1 – a 1 b 2 X 2 D = a 1 b 2 X 2 Y 1 – a 2 b 1 X 1 Y 2 a i = denominator of Y i b i = denominator of X i r = a 1 b 2 / a 2 b 1 Open Systems: Bulk Contamination : Two data points 1 and 2 may be related by a mixing curve between 2 end-members M and N provided the following relationship holds: Mixing lines are hyperbolic curves whose curvature is proportional to r. The asymptotes of mixing curves with large or small r’s can be used to define some of the ratios of the unseen end- members.

48. Mixing in Ratio – Ratio Plots: AX + BXY + CY + D = 0 A = a 2 b 1 Y 2 – a 1 b 2 Y 1 B = a 1 b 2 – a 2 b 1 C = a 2 b 1 X 1 – a 1 b 2 X 2 D = a 1 b 2 X 2 Y 1 – a 2 b 1 X 1 Y 2 a i = denominator of Y i b i = denominator of X i R = a 1 b 2 / a 2 b 1 Mixing lines are hyperbolic curves Two data points may be related by a mixing curve provided the following relationship holds: Mixing lines are hyperbolic curves whose curvature is proportional to r

49. Contamination and Assimilation

50. Assimilation Fractional Crystallization (AFC) C i liq = C i o × F -z + (r × C i a × (1-F -z )) / ((r-1) × z × C i o ) z = (r + D i - 1) / (r-1) DePaolo, 1981 r = assimilation rate / crystallization rate, ≤ 1 for closed system heat budget Parent Liquid + Contaminant Daughter Liquid + Crystal Cumulates Analytical solution for constant D i Open Systems:

51. Open System: Compatible Elements Daughter Liquid (1-X) × Parent Liquid - X × Crystal Cumulates + r ×X × Contaminant Computer Models:

52. Open System: Incompatible Elements Daughter Liquid (1-X) × Parent Liquid - X × Crystal Cumulates + r ×X × Contaminant Computer Models:

53. 87 Sr/ 86 Sr in AOB & Hy-Norm Basalts Armstrong’s Granitoid Lines > 0.707 < 0.705 Hf FS Ra Ed CC OMB CPB IMB YT Within the northern Canadian Cordillera, there is a clear correlation between isotopic composition and the tectonic belt within which recent alkaline magmas erupt that mirrors that observed in Mesozoic granitoids and late Cretaceous shoshonites. All the alkaline basalts of the Omenica Belt are have more radiogenic Sr and Pb isotopes and less radiogenic Nd isotopes than their equivalents in the Intermontane Belt. This clearly indicates the involvement of lithospheric mantle and/or crust in their origin.

54. Mixing in Ratio - Element Plots: AX + BXY + CY + D = 0 A = a 2 Y 2 – a 1 Y 1 B = a 1 – a 2 b = 1 C = a 2 X 1 – a 1 X 2 D = a 1 X 2 Y 1 – a 2 X 1 Y 2 a i = denominator of Y i b i = denominator of X i = 1 R = a 1 / a 2 Mixing lines are still hyperbolic curves maybe No

55. Mixing in Element -Element Plots: AX + BXY + CY + D = 0 A = Y 2 – Y 1 B = 0 C = X 1 – X 2 D = X 2 Y 1 – X 1 Y 2 a i = denominator of Y i = 1 b i = denominator of X i = 1 r = 1 Mixing lines are straight lines

56. EM1 EM2 HIMU PM DMM PM EM1 HIMU EM2 The many "flavours" of OIB suites suggest the lower mantle is “blobby” and contains at least 5 different components. PM DMM EM1 Fe-Ni Core continent ocean

58. There is typically a systematic increase in 143 Nd/ 144 Nd and decrease in 87 Sr/ 86 Sr and Pb isotopes with decreasing Si, from Hy norm basalts through to nephelinites. The values of nephelinites approach those of MORB. Ol- Neph Hy-Norm

59. EM1 EM2 HIMU PM DMM PM EM1 HIMU EM2 The many "flavours" of OIB suites suggest the lower mantle is “blobby” and contains at least 5 different components. PM DMM EM1 Fe-Ni Core continent ocean