Radiogenic Isotopes In Igneous Petrology Francis, 2013
N P P N Tin P = 50 Proton No. Neutron No.
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
Radioactive Decay + ray Parent Isotope + ray + ray
4He2+ + γ Alpha decay Beta decay P+ + e- + ue No • P+ → No + e+ + ue • Beta capture
-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
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
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
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.
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
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.
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.
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.
Sm - Nd: 147Sm 143Nd + 4He + 143Nd = 143Ndi + 147Sm × (eλt-1) During partial melting, Liquid (Sm / Nd) < Residue (Sm / Nd) KSm > KNd
Nd isotopic evolution 143Nd/144Nd = (143Nd/144Nd)i + (147Sm/144Nd) × (eλt-1)
εNd and Model Ages MORB εNd(t)= ((143Nd/144NdSample(t)) / (143Nd/144NdChur(t)) - 1) × 104
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
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.
Continental flood Basalts Continental flood Basalts
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.
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.
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
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
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?
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.
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.
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.
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
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.
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
Contamination and Assimilation
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