Radiogenic Isotopes In Igneous Petrology

1. Radiogenic Isotopes In Igneous Petrology Francis, 2013

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

4. Radioactive Decay Conversion of protons to neutrons and vice versa – Weak Nuclear Force Beta decay: 87Rb 87Sr + e- +  +  t1/2 = 5.2 1010 years= 1.42  10-11/ yr Beta Capture: (positron emission): 26Al 26Mg + e+ +  +  t1/2 = 0.72 106 years = 9.8  10-7/ yr Loss of alpha particles – residual Strong Nuclear Force Alpha decay: 147Sm 143Nd + 4He +  t1/2 = 1.06 1010 years = 6.54  10-12/ yr

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

6. 4He2+ + γ Alpha decay Beta decay P+ + e- + ue No • P+ → No + e+ + ue • Beta capture

7. -δN / δt= λ × N Law of Radioactivity Rutherford and Soddy, 1902 -δN / N = λ × δt ln(N) = -λ × t + No N = No× e-λt D* = No - N D* = N × (eλt – 1) D = Do + D* D = Do + N × (eλt – 1) t1/2 = ln 2/λ

8. Some Useful Radioactive Decay Schemes: Beta decay: 182Hf 182W + e- +  + t1/2 = 9 106 years = 7.7  10-8/yr 129I 129Xe + e- +  + t1/2 = 16 106 years = 4.3  10-8/ yr 176Lu 176Hf + e- +  +  t1/2 = 3.5 1010 years = 1.94  10-11/ yr 187Re 187Os + e- +  + t1/2 = 4.56 1010 years = 1.52  10-11/ yr 87Rb 87Sr + e- +  + t1/2 = 5.2 1010 years= 1.42  10-11/ yr Beta Capture (positron emission): 26Al 26Mg + e+ +  + t1/2 = 0.72 106 years = 9.8  10-7/ yr 53Mn 53Cr + e+ +  + t1/2 = 3.7 106 years = 1.9  10-7/ yr 40K 40Ar + e+ +  + = 0.581  10-10/ yr 40K 40Ca + e- +  + t1/2 = 1.250 109 years = 4.962  10-10/ yr Alpha decay: 146Sm 142Nd + 4He +  t1/2 = 103 106 years = 147Sm 143Nd + 4He +  t1/2= 1.06 1010 years = 6.54  10-12/ yr 235U 207Pb + 7 4He + 4e- + t1/2 = 0.7038 109 years = 9.8485  10-10/ yr 232Th 208Pb + 6 4He + 4e- + t1/2 = 14.010 109 years = 4.9475  10-11/ yr 238U 206Pb + 8 4He + 6e- +  t1/2 = 4.468 1010 years = 1.55125  10-10/ yr combined

9. Summary Radioactive Decay Schemes: Beta decay: 87Rb 87Sr + e- +  + t1/2 = 5.2 1010 yrs= 1.42  10-11/ yr Alpha decay: 147Sm 143Nd + 4He +  t1/2 = 1.06 1010 yrs = 6.54  10-12/ yr 235U 207Pb + 7 4He + 4e- + t1/2 = 0.7038 109 yrs = 9.8485  10-10/ yr 232Th 208Pb + 6 4He + 4e- + t1/2 = 14.010 109 yrs = 4.9475  10-11/ yr 238U 206Pb + 8 4He + 6e- +  t1/2 = 4.468 1010 yrs = 1.55125  10-10/ yr

10. Rb – Sr System 87Rb 87Sr + e- +  +  t1/2 = 5.2 1010 years= 1.42  10-11/ yr Rb+ substitutes for K+ in the large W site of phases such as feldspar, mica, and amphibole, whereas Sr2+ substitutes for Ca2+ in feldspars. In-grown 86Sr 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. D = Do + N × (eλt – 1) 87Sr = 87Sri + 87Rb × (eλt-1) 87Sr/86Sr = (87Sr/86Sr)i + (87Rb/86Sr) × (eλt-1) 2 unknowns: t = Time (87Sr/86Sr)i Y = Yi + a × X a = (eλt-1) i

12. The Effect of Metamorphism

13. Rb – Sr System 87Rb 87Sr + e- +  +  During partial melting, Liquid (Rb / Sr) > Residue (Rb / Sr) KRb < KSr 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.

14. Sm - Nd System 147Sm 143Nd + 4He +  t1/2 = 1.06 1010 years = 6.54  10-12/ yr 143Nd = 143Ndi + 147Sm × (eλt-1) D = Do + N × (eλt – 1) 143Nd /144Nd = 143Nd/144Ndi + (147Sm/144Nd) × (eλt-1) Both Sm3+ and Nd3+ substitute for Al3+ 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.

15. Oldest Age on the Moon

16. Sm - Nd System 147Sm 143Nd + 4He +  143Nd = 143Ndi + 147Sm × (eλt-1) KSm > KNd Liquid (Sm / Nd) < Residue (Sm / Nd) 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.

17. Sm - Nd: 147Sm 143Nd + 4He +  143Nd = 143Ndi + 147Sm × (eλt-1) During partial melting, Liquid (Sm / Nd) < Residue (Sm / Nd) KSm > KNd

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

19. εNd and Model Ages MORB εNd(t)= ((143Nd/144NdSample(t)) / (143Nd/144NdChur(t)) - 1) × 104

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. MORB εNd(t)= ((143Nd/144NdSample(t)) / (143Nd/144NdChur(t)) - 1) × 104

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 87Sr/86Sr and 143Nd/144Nd 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 235U 207Pb + 74He + 4e- + t1/2 = 0.7038 109 yrs = 9.8485  10-10/ yr 232Th 208Pb + 64He + 4e- + t1/2 = 14.010 109 yrs = 4.9475  10-11/ yr 238U 206Pb + 84He + 6e- +  t1/2 = 4.468 1010 yrs = 1.55125  10-10/ yr U3-6+, Th4+, and Pb2-4+ 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 235U 207Pb + 74He + 4e- + t1/2 = 0.7038 109 years = 9.8485  10-10/ yr 238U 206Pb + 84He + 6e- +  t1/2 = 4.468 1010 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 235U 207Pb + 74He + 4e- + t1/2 = 0.7038 109 years = 9.8485  10-10/ yr 238U 206Pb + 84He + 6e- +  t1/2 = 4.468 1010 years = 1.55125  10-10/ yr Zircons in the Sands of Major Rivers Mackenzie River Zircons Mississippi River Zircons Amazon River Zircons

36. Pb Isochrons and the Age of the Solar System

37. Pb – Pb Isochron Diagrams 235U 207Pb + 74He + 4e- +  t1/2 = 0.7038 109 years = 9.8485  10-10/ yr 238U 206Pb + 84He + 6e- +  t1/2 = 4.468 1010 years = 1.55125  10-10/ yr

38. Future Ages, Mixing Lines, & Pseudo-Isochrons? MORB 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?

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) 87Sr/86Sr = .7045, 143Nd/144Nd = .5126, chondrite-defined Depleted MORB Mantle (DMM)lava characteristics: low 87Sr/86Sr <0.7025), high 143Nd/144Nd (>0.5130), low 206Pb/204Pb (~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 87Sr/86Sr (~0.7050), lowest 143Nd/144Nd (~0.5124), Pitcairn Is., Tristan de Cunha low 206Pb/204Pb (< 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 87Sr/86Sr (>0.7080), low 143Nd/144Nd (~.5125), 206Pb/204Pb (~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 87Sr/86Sr, (~ 0.7030), high 143Nd/144Nd (~0.5129), St. Helena Is., Austral Is., Azores highest 206Pb/204Pb (>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. Open Systems: Bulk Contamination: General Mixing Equation: 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: AX + BXY + CY + D = 0 A = a2b1Y2 – a1b2Y1 B = a1b2 – a2b1 C = a2b1X1 – a1b2X2 D = a1b2X2Y1 – a2b1X1Y2 ai = denominator of Yi bi = denominator of Xi r = a1b2 / a2b1 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: Two data points may be related by a mixing curve provided the following relationship holds: AX + BXY + CY + D = 0 A = a2b1Y2 – a1b2Y1 B = a1b2 – a2b1 C = a2b1X1 – a1b2X2 D = a1b2X2Y1 – a2b1X1Y2 ai = denominator of Yi Mixing lines are hyperbolic curves bi = denominator of Xi R = a1b2 / a2b1 Mixing lines are hyperbolic curves whose curvature is proportional to r

49. Contamination and Assimilation

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