Pre-Orals Review on Isotope Geology

1. Pre-Orals Review on Isotope Geology February 13, 2004 Presented by Allison Franzese

2. General Outline of Presentation • The Basics: • What is an isotope ? • Why are some isotopes stable, and some unstable? • Why do we have unstable isotopes at all; how did they form? • What exactly is radioactive decay? • Applications: why and how are isotopes useful? (Dating, determining rates of processes, tracers) • General principles: dating, mixing, fractionation • Specific isotope systems, and how they are used • Questions (and answers)

3. X A Z Nomenclature “Nuclide” = a particular atom An atom is made up of a nucleus and surrounding electrons The nucleus is made up of protons and neutrons (& other tiny, tiny particles) Z = proton number = # of protons in the nucleus; defines an element N = neutron number = # of neutrons in the nucleus A = mass number = Z + N Notation:

4. So what is an isotope? Isotope = line of equal Z; nuclides with the same # of protons (therefore they are the same element), but variable N; e.g. 12C, 13C, 14C are isotopes Isotone = line of equal N; nuclides with the same # of neutrons, but variable Z; e.g. 11B, 12C, 13N are isotones Isobar = line of equal mass; nuclides with the same mass number, but variable N and Z; e.g. 12C, 12B, 12Be are isobars

5. Nuclear Stability What makes a nucleus stable is something called its “Binding energy” “The whole is less than the sum of its parts” Mass Defect: = Dm = M – (mp + mn + me) Mass and energy are interchangeable (Einstein) E = mc2 EB = Dm c2 (Conversion factor for mass to energy: 1 amu = 931.5 MeV) EB is a measure of nuclear stability: those nuclei with the largest binding energy per nucleon are the most stable.

6. Figure 8.1 shows EB per nucleon as a function of mass. Note that the nucleons of intermediate mass tend to be the most stable.

7. Central path of stability The stability of a nucleus depends on its ratio of N/Z Stable nuclides plot along a central path of stability At low masses, N/Z  1 (Z=N) At high masses, N/Z  3 Has to do with the surface area to volume ratio and the repulsive forces between protons (extra neutron can shield the protons from each other, important for high Z)

8. Some interesting observations & ‘rules’ Mattauch’s rule (1934): Adjacent isobars cannot be stable. 2 stable isobars separated by an unstable daughter. e.g. the isobar where A=40: 40Ar, 40K and 40Ca Even vs. odd Magic #’s: 2, 8, 10, 20, 28, 50, 82, 126 Nuclides with either Z or N = a “magic #” are more likely to be stable

9. Example: even vs. odd & central path

10. Example: even vs. odd & magic #’s

11. Example: Mattauch’s Rule40K is unstable and undergoes a branched decay to both 40Ar and 40Ca

12. “Energy Valleys” Unstable nuclides decay to form nuclides with the lowest energy

13. Types of Isotopes Categories based on how they formed: • Primordial Nuclides: formed when the solar system was formed • Cosmogenic Nuclides: made constantly in earth’s atmosphere • Anthropogenic or “Bomb” Nuclides: • Radiogenic Nuclides: formed as a product of radioactive decay

14. Nucleosynthesis (in short) • Cosmological Nucleosynthesis: • H, He, and Li formed shortly after the big bang • Stellar Nucleosynthesis: Interior of stars • H burning: T ≤ 107 K, • He burning: 107 ≤ T ≤ 108 K, • a-process: occurs when T reaches 109 K • e-process: T > 3 x 109 K • Explosive Nucleosynthesis: Supernovae • s-, r- and p- processes • Galactic Nucleosynthesis: • Formation of Li and Be in interstellar space • Due to spallation of heavy cosmic rays as they hit interstellar gas atoms

15. Radioactive Decay • Unstable nuclides spontaneously decay to form stable nuclides • ‘Radioactivity is the spontaneous transformation of an unstable nuclide, usually involving the emission of particles and energy’ • A radioactive parent decays until a stable daughter nuclide is formed • Conservation of mass and energy apply

16. Types of Radioactive Decay • Alpha decay (a particle = 4He nucleus) • Beta- decay (b- = electron) • Positron emission (b+ = positron) • Electron capture (e = electron) • Nuclear Fission • Gamma emission (g = high energy photon) • If the daughter of any type of decay is left in an excited electron state, it will emit a g ray to release the excess energy (Isomer = metastable state)

17. a- decay • Occurs for unstable nuclides with A  56 (except 5He, 5Li and 6Be) • P  D + 4He + Q ± g (Q = energy) • Conservation of momentum causes the daughter atom to recoil. This is known as a-recoil • The total energy released by a decay includes the KE of the a particle, the recoil energy and the g energy

18. Parent and daughter are isobars • P  D + b- +  + Q ± g ( = antineutrino) • neutron  proton + electron (+ antineutrino) • Neutrino and anti-neutrino were proposed to conserve energy and angular momentum • The b- has a KE continuum Q = max energy of b- particle Q = b- energy +  energy b- decay

19. b+ decay • Analogous to b- decay • proton  neutron + positron (+ neutrino) • P  D + b+ +  + Q ± g ( = neutrino) e capture • Nucleus captures one of its orbiting electrons • electron + proton  neutron + neutrino • P + e- D +  + Q ± g ± x-rays

20. Nuclear Fission • Nucleus splits into 2 or more smaller nuclei plus a, n, Q • Daughter masses range from 30 – 65 (Zn to Tb) • Usually not an even split • Fission products usually have excess neutrons & decay by b- • Spontaneous fission occurs when Z  100; Z2/A too large • Can be induced by neutron bombardment • Release of neutrons as fission products chain reaction • E.g. U: 238U undergoes fission, some of the released neutrons are captured by 235U, 236U in an excited state • In general the concentration of U in nature is not high enough for this sort of thing to happen. • Fission track dating • Fission products have large amounts of KE; travel at very high velocities • They damage the crystal structure through which they pass, producing visible (not to the naked eye!) 'tracks'

21. Oklo natural reactor in central Africa • Found to have an anomalously low 235U/238U ratio, indicating some of the 235U had been ‘burned’ in a nuclear chain reaction. • Natural fission reactor occurred ~1.8 Bya, when the global 235U/238U was much higher than today • Very concentrated U deposit due to special environmental conditions • Water acted as a moderator • Probably lasted ~0.8 Myr

22. Laws of Radioactive Decay -dN/dt = lN N= # atoms of the radioactive nuclide, t = time, l = decay constant = probability that an atom will decay in a unit time N0 = N at t=0 N = N0e-lt Half-life = time it takes for half a sample to decay (t when N = ½N0) t½ = (ln 2) / l = .693/l D* = N0 – N = N0 – N0e-lt = N0 (1- e-lt) D = D0 + N(elt –1) D* = radiogenic daughter = # daughter atoms produced by radioactive decay of a parent, P (D = D0 + D*) Divide by a stable, non-radiogenic isotope of the daughter element to get ratios e.g. for 87Rb 87Sr + b- : 87Sr/86Sr = (87Sr/86Sr)0 + 87Rb/86Sr (elt –1)

23. Growth of Daughter Atoms Decay of Parent Atoms Number of Half-Lives Number of Half-Lives A Pretty Picture of Radioactive Decay

24. Dating We can use the radioactive decay equation to calculate the age of a sample. We can measure the present day ratios and l, but we still have 2 unknowns: R0 and t. What can we do? • 1) Assume zero initial daughter. This approach can be valid if you know something about mineralogy. For example, zircons are often used for U-Pb dating because the mineral incorporates U, but not lead. Therefore any Pb measured is radiogenic. Similarly, micas accept Rb but not Sr. Another example is K-Ar dating of volcanic rocks. Ar, the daughter, is lost upon eruption, and the only Ar present is radiogenic Ar. • 2) Use 2 different isotope systems. For example, if you know what the age should be from a system where you think you know the initial daughter ratio (e.g. U-Pb), you can calculate the initial daughter ratio. • 3) Assume one and calculate the other. If we assume the initial ratio and calculate an age, it is called a “Model Age” • 4) Use an isochron diagram

25. The Isochron • The radioactive decay equation is in the form of a line: • D = D0 + P(elt-1) … y = b + xm • Plot D ratio vs. P/D for several comagmatic or cogenetic samples and draw a best fit line through the data • y-intercept = initial D ratio, slope is related to t • This line is called an “Isochron” • Represents true age if: • (1) The system was at isotopic equilibrium at time t = 0. • I.e. all the samples formed with the same initial daughter isotope ratio • (2) Closed system since formation • Whole-rock isochron represents age of formation • Mineral isochron represents age of last metamorphosis

26. Measured data points Isochron Evolution lines Initial Ratios

27. Mixing 2 components, A + B FA = A/(A+B); FB + FA= 1 Elemental concentrations in the mix: Cmix = CAFA + CBFB = CAFA + CB(1 – FA) 2 elements e.g. Sr and Nd: Ndmix = Srmix ( NdA - NdB) / (SrA - SrB) + (NdBSrA – NdASrB) / (SrA - SrB) Y = mx + b plot Nd vs. Sr Isotope compositions of the mix: (87Sr/86Sr)mix = {(87Sr/86Sr)A(SrAFA) + (87Sr/86Sr)B(SrBFB)}/ Srmix Which rearranges to an eq. for hyperbola for 87Sr/86Sr vs. Sr If plot 87Sr/86Sr vs. 1/Sr it becomes a straight line **Mixing is always a straight line if the denominators of the x and y axes are the same**

28. Mixing more stuff 2 elements with IC’s e.g. Sr and Nd: Plot 143Nd/144Nd vs. 87Sr/86Sr get hyperbola Define K = (Nd/Sr)A/ (Nd/Sr)B determines curvature; K>1 concave down; K<1 concave up The farther K is from 1, the more curvature Mixing in this plot is straight only when K=1 and b = 0, i.e. (Nd/Sr)A= (Nd/Sr)B Mixing line can be mistaken for isochron line Mixing and isochron distinguished by checking another isotope system or plotting isotope ratio vs. 1/Concentration

29. Some mixing plots K = 100 K = ½

30. Fractionation (Un-mixing) Elements are fractionated because of different chemical behaviors Crustal extraction from the mantle: Compatible elements stay in the solid residue Incompatible elements go into the melt The Continental Crust is formed from a partial melt, so it is enriched in incompatible elements The Upper Mantle has been left depleted in incompatible elements Mid-Ocean Ridge Basalts (MORB) sample this depleted mantle, and are also depleted Elements can also be fractionated on the earth’s surface due to differences in chemical properties e.g. solubility in H2O

31. A Spidergram

32. Fractionation (More un-mixing) Isotopes of light elements can be fractionated during chemical reactions, phase changes, and biological reactions The bond energy of a molecule depends on the masses of the atoms Bonds between heavier atoms are harder to break. As a reaction occurs, the molecules containing the lighter isotopes will react first (their bonds are easier to break). This will leave the reactant enriched in the heavy isotope, and the product enriched in the lighter isotope (depleted in the heavy isotope) The amount of fractionation depends on the % mass difference i.e. isotopic fractionation is only important for low masses The fractionation factor, a, is defined as the ratio of isotope ratios in two phases: aA-B RA/RB and is related to the equilibrium constant of the reaction

33. Example: Rayleigh distillation When water evaporates, the molecules with lighter isotopes will preferentially go into the vapor phase, while the heavier ones will stay in the liquid phase. (By definition, this means that the lighter molecules have a higher vapor pressure than the heavier ones) When water condenses, the heavier molecules will condense first. If the vapor is removed from the source area before it condenses, we get geographic variations in water isotopes.

34. Rubidium-Strontium First decay system to be widely used 87Rb 87Sr + b- t½ = 48.8 Gyr l = 1.42 x 10-11 yr-1 87Sr/86Sr = (87Sr/86Sr)0 + 87Rb/86Sr (elt –1) Incompatibility: Rb > Sr Crust Rb/Sr, 87Sr/86Sr > mantle Rb/Sr, 87Sr/86Sr Isotope evolution diagram: a closed reservoir will evolve along a line whose slope is proportional to the parent-daughter ratio, in this case 87Rb/86Sr

35. Rb-Sr Dating • Isochron method used to date igneous and metamorphic rocks, and authigenic sedimentary minerals (e.g.glauconite) • Pros: • Large range in Rb/Sr ratio in crustal rocks (several orders of magnitude)  large range in 87Sr/86Sr • High concentrations of Rb and Sr make it easy to measure • Minerals are “reset” by metamorphism but whole rock composition is not so we can get dates of igneous formation and dates of last metamorphic event • Cons: • Rb and Sr are soluble and may be mobile • Low decay energy has made precise determination of l difficult

36. other Rb-Sr uses • Provenance: • Identify geologic source of sediments by their 87Sr/86Sr and/or Rb/Sr model age • Seawater Sr: • Sr is soluble in seawater and has a very long residence time (~2.5 x 106 yr) relative to the ocean (~103 yr)  Sr is well-mixed in the oceans • 87Sr/86Sr depends on the relative proportion of continental and hydrothermal inputs. The ratio of these will vary with mean spreading rate, erosion rates (relative proportion of carbonate vs. silicate weathering), and plate geometry. • Calcite and gypsum incorporate Sr from seawater, and exclude Rb, so (87Sr/86Sr)0 is preserved - compare to global SW curve to get an age

37. Age (Ma) Seawater Sr Himalayan Uplift

38. { } (143Nd/144Nd)sample eNd= - 1 x 104 (143Nd/144Nd)CHUR Samarium-Neodymium 147Sm 143Nd + a- t½ = 106 Gy 143Nd /144Nd = (143Nd/144Nd)0 + 147Sm/144Nd (elt –1) ‘Opposite of Rb-Sr’ Incompatibility: Sm < Nd Crust has low Sm/Nd, low 143Nd/144Nd,eNd <0 Depleted mantle has high Sm/Nd, high 143Nd/144Nd, eNd >0 Isotope evolution diagram: a closed reservoir will evolve along a line whose slope is proportional to the parent-daughter ratio, in this case 87Rb/86Sr

39. Sm-Nd Dating Isochron used to date igneous and metamorphic rocks Cons: requires more precise measurements due to small range in Sm/Nd ratio and lower concentrations in most crustal samples Pros: Sm and Nd are relatively immobile during metamorphic, diagenetic, weathering and transport processes; can “see through” • a metamorphic event • Sm-Nd age can be viewed as a “Crustal Residence” age • Model Ages: TCHUR and TDM

40. other Sm-Nd uses • Assessing the rates of crustal growth and mantle depletion • Sediment Provenance • Water mass tracer: • Short residence time (300yrs) compared with mixing time of oceans leads to heterogeneity • The eNd depends on source of weathering products (old continental crust or young volcanics) • Measured in Fe-Mn nodules, crusts and particles which co-precipitate Nd (SW Nd conc 3 ppt; Fe-Mn Nd conc is hundreds of ppm) and phosphate fossils e.g. fish teeth, which scavenge Nd from SW shortly after death

41. Rb-Sr-Sm-Nd The “Mantle Array”

42. Uranium-Thorium-Lead 238U 206Pb, t½ = 4.47 Gyr 235U 207Pb, t½ = 0.70 Gyr 232Th208Pb, t½ = 14.0 Gyr No longer in pseudolinear decay regime • 238U/235U = 137.88 • everywhere (today) • m = 238U/204Pb • k = 232Th/235U ~ 4.0 • (chondrites) Can derive equations relating the Pb isotopes – useful because don’t need to measure parents Plot 207Pb/204Pb vs. 206Pb/204Pb Line = isochron if it passes through initial ratios Steeper slope = older age Evolution lines depend on m

43. The Geochron The Geochron is the Pb-Pb isochron with a slope corresponding to T=4.56 Ga that passes through the composition of primordial Pb - reflects closed system evolution of lead in solar system • Plot data from several meteorites, which define a line • Initial ratio determined by the Canyon Diablo troilite (FeS, incorporates Pb,but not U; initial Pb isotope ratios are preserved) which plots along the geochron • If U/Pb, sample is right of geochron • If U/Pb, sample is left of geochron

44. The Lead Paradox U, Th more incompatible than Pb Paradox: U/Pb has increased in both the crust and the mantle • There must be a reservoir with extra Pb to balance the earth - possibilities are: • In the core (lead sulfides) • Lower crust (crustal metamorphism expels fluids, U to upper crust, excess Pb remains in lower crust) • Hidden reservoir

45. Concordia/Discordia • Plot 207Pb*/238U vs. 206Pb*/235U • All points with the same age form a curve = Concordia; • If the data fall along a line instead = Discordia • Use zircons; exclude Pb, all Pb is radiogenic • Discordia beneath Concordia = Pb loss (usually) or U gain • Discordia above Concordia = U loss • Most rocks are discordant and can be explained by Pb loss • Intersection of Discordia line with Concordia curve gives age of formation and age of Pb loss

46. Other U-Series Uses • Dating marine corals by 234U - 238U disequilibria and / or 230Th - 238U disequilibria (238U 234U  230Th) • Seawater 234U/238U >1 (~1.14) due to alpha recoil and preferential leaching of the daughter at the damaged site. Once incorporated into a coral, the U will slowly return to secular equilibrium. Measure d234U and calculate the time since it was precipitated from seawater. • 230Th - 238U Disequilibria can also be used for: • Dating the initial crystallization of lavas • Sedimentation rates and sediment focussing • Th /Pa on sediments for ocean circulation rates • Short-lived isotopes used for mixing rates and scavenging rates in the ocean, rivers, or groundwater

47. Potassium - Argon • Ar = Ar* (often) because: • – K common component of rocks • – Rocks usually form with no initial Ar (noble gas) • 40K branched decay to 40Ar and 40Ca • Must measure K and Ar on different sample splits; • introduces error; instead use Ar-Ar dating • Irradiate samples: 39K + n 39Ar + p • 39Ar is stable over the analysis time • Plot inverse isochron- mixing line • Slope = 40Ar/39Ar • x intercept gives radiogenic Ar, proportional to age

48. Ar - Ar uses (besides dating) • Various minerals have different closure temperatures • When temp. is below closure temp. the “clock” starts • Different Ar ages from different minerals can show real processes, e.g. cooling rate • Can examine contact metamorphism, and plot age vs distance from contact • Flat areas of graph represent true ages

49. Extinct Nuclides Primordial nuclides with half-lives so short that they have decayed away and no longer exist in nature Overabundance of daughter shows that a sample formed before the parent was extinct 182Hf 182W, t½ = 9 Ma – Hf left in mantle, but W absorbed to core – W found in mantle shows earth’s core formed during first 30 Ma of the solar system 26Al 26Mg, t½ = 730,000 years – 26Al existed in early solar system, so we see an overabundance of 26Mg/24Mg in Al-rich phases – Because 26Al only formed in supernovae (explosive nucleosynthesis), implies that supernova material was injected into the solar nebula

50. Cosmogenic Nuclides • Cosmogenic Nucleosynthesis: Formation of isotopes in earth’s atmosphere by interaction with cosmic rays • 3H, 10Be, 14C, 26Al, 32Si, 36Cl, 39Ar, and 81Kr • Dating using these gives date of last contact with atmosphere or extent of time in contact w/atm. (“exposure age”)