Dating Martian Lafayette Asteroid with patterns caused by the passaged through the atmosphere. Line on the fusion crust were caused by beads of molten rock. AST111 Lecture 8a Isotopic composition Radioactive dating
Chemical separation Atoms become well mixed in a hot gas. Solid bodies, do not mix well, retaining the molecular composition when they solidified. Melts tend to group with mineralogically compatible counterparts. Condensing gas produces small grains, relatively heterogeneous or homogenous, compared to crystals.
Isotopic fractionation Isotopes are separated from each other by massdependent processes. Lighter molecules tend to escape. Molecular forces: Deuterium preferentially combines with heavy elements, because of a slightly lower energy from deuterium s greater mass. Nuclear processes can also lead to differences in isotope ratios. For example cosmic rays produce different isotopes (like 14 C). Unstable nuclei also decay changing the ratio of isotopes.
Radiometric Dating Formative age is the age since the meteorite was molten or gaseous. Most meteorites have ages of 4.53 to 4.57 10 9 years. These dates are estimated from long lived radioactive isotopes. Types of radioactive decay include β-decay (electron emitted) and α decay (Helium nucleus emitted). For β-decay a neutron is converted to a proton so the atomic number increases by 1. Example: 87 87 Rb Sr For α-decay, the atomic weight is reduced by 4 and the atomic number decreases by 2. Example: 37 38 U 238 234 92 90 Th
N p (t) =N p (t 0 )e (t The decay rate The abundance of a parent species as a function of time t 0)/ m τm decay time constant, depends on the parent nuclide When is Np(t) = Np(t0)/2? At a special time t1/2 from t0 t1/2 is the half-life half left 1/2 =e t 1/2/ m t 1/2 = m ln 2
Long Lived Radioactive nuclides Parent Stable Daughters Half life t 1/2 (Gyr) 40 K 40 Ar, 40 Ca 1.25 87 Rb 87 Sr 48.8 147 Sm 143 Nd, 4 He 106 187 Re 187 Os 46 232 Th 208 Pb, 4 He 14 235 U 207 Pb, 4 He 0.707 238 U 206 Pb, 4 He 4.47
Parent Extinct radioactive nuclides Stable daughters Half life Myr 22 Na 22 Ne 2.6 26 Al 26 Mg 0.72 41 Ca 41 K 0.1 53 Mn 53 Cr 3.6 60 Fe 60 Ni 1.5 107 Pb 107 Ag 6.5 109 I 109 Xe 17
Isotopes of noble gases Some elements decay into noble gases which are trapped in the rock, unless the rock is heated. There is a build up of noble gases in the rock. Gas retention age which can also tell you about cooling history.
Radionuclides, daughters and references Nuclide is the name we use to refer to the nucleus of an isotope of a given element. Radioactivity involves the decay of a radionuclide to a daughter nuclide. Most useful if the daughter is rare. A stable isotope of the daughter species, one which is not involved in radioactivity, serves as the reference nuclide. Suppose that within a given mineral sample, the numbers of these three nuclides are n, d, and s, respectively. Define the relative abundances of radionuclide and daughter: N = n s, D = d s These are independent of the amount of material analyzed, since the amount is proportional to the stable isotope s.
Radioactivity Some nuclides are radioactive, and will transmute into other nuclides over time. If one starts with a bunch of groups of a given nuclide, each group having a total of n 0 atoms at t = 0, then after a time t the average number remaining in a group is N 2 0 λt 0 divide by s 0 n = n e ##### N = N e λt 0 1 2 1 2 1 2 = N e = λt t = λt s=a stable isotope of daughter where λ is the decay rate for the radionuclide, a quantity that has usually been measured accurately in the laboratory. λ is related to the commonly-quoted half-life: ln 2 ln 2. λ,
Important example: the Rb-Sr system Rubidium is an alkali; it can replace the much-more-abundant sodium and potassium in minerals (e.g. feldspars). It has one stable isotope, 87 Rb and one long-lived radioisotope 85 Rb Strontium is an alkaline, and can replace magnesium and calcium in feldspars. It has four stable isotopes: 84 Sr, 86 Sr, 87 Sr, 88 Sr 87 Rb beta decays into 87 Sr 87 87 Rb Sr + e + ν e + energy Commonly used: N 87 87 = n Rb d Sr, D. s = 86 86 Sr = s = Sr
The use of radionuclides to find out how long ago an igneous rock was last melted There are many radioisotopes, with halflives spread from thousands to billions of years, all accurately and precisely measured in the laboratory. We can measure the abundances of stable and radioactive nuclides simply by taking rocks apart into the minerals of which they are made, and in turn taking the minerals apart into atoms, counting the number for each element and isotope in a mass spectrometer. This gives values of N and D, a pair for each mineral. Plot the Ds against the Ns: the slope of the resulting line depends upon how many halflives have passed since it froze, and the intercept depends upon the initial relative abundance of the daughter nuclide. 12
The use of radionuclides to find out how long ago an igneous rock was last melted (continued) D (e.g. 87 86 Sr! Sr " # Minerals after aging by a fixed number of half lives W Molten rock X Y Minerals after freezing 87 86 N (e.g. Rb Sr) Measure slope and intercept to find age and initial relative abundance of the daughter nuclide. Z! All the same " D, since daughter " # and stable ref. " are chemically " $ identical. 13
A two-mineral system The initial relative abundances N 0 and D 0 The relative abundance of daughter nuclides as a function of time is: amount decayed ( ) ( ) D = D0 + N0 N = D0 + N e λt 1. Suppose we have a rock consisting of two minerals, A and B, with equal initial relative abundances of the daughter nuclide. We can measure the present abundances of A and B: ( λt 1 ), ( λt 1) D = D + N e D = D + N e A 0 A B 0 B Two equations, two unknowns: D 0 and t. This can be solved for t, in terms of measurable quantities: t 1 " D ln A DB # = % + 1 &. λ ' NA NB ( 14
Example two-mineral system The rate at which 87 Rb decays into 87 Sr is λ 87 86 Rb 11-1 = 1.39 10 yr Samples of two different minerals from the same plutonic rock from northern Ontario are analyzed in a mass spectrometer, with these results: Sample How old is the rock? Sr 87 86 Sr Sr A N A =0.0755 D A =0.7037 B N B= 0.3280 D B =0.7133 15
Example two-mineral system (continued) Solution: 1 # D ln A DB $ t = % + 1 & λ ' NA NB ( 1 = 11-1 1.39 10 yr # 0.7133 0.7037 $ ln % + 1& ' 0.328 0.0755 ( 9 = 2.7 10 yr. D = 87 Sr/ 86 Sr 0.712 0.708 D 0.704 0.700 A B 0 0.1 0.2 0.3 0.4 N = 87 Rb/ 86 Sr The y intercept gives the value of D that the rock had at the 87 86 time it froze: D0 = d s = Sr Sr = 0.7008. 16
Results for Earth and Moon The Moon began to solidify about 4.5 billion years ago. The highlands are clearly older than the maria, as the cratering record also shows. The Moon solidified long before the Earth did. Figure from Jay Frogel.
Dating rocks containing radioactive isotopes Consider both the abundance of the parent and daughter species ( t t0 ) / τ m N ( t) = e N ( t ) p 0 p 0 ( t t0 ) / τ m Nd ( t) = Nd ( t0) + (1 e ) N p( t0) We have two unknowns: t t0, the age and N ( t ), the initial amount of daughter species d
Different ratios of parent daughter nuclides To break the uncertainty caused by the two unknowns, different samples of rock from the same meteor are used. Each crystal has a different ratio of elements. Compare the ratio of parent and daughter elements to another nuclide which is stable and not changing. Use another isotope of the same element as the daughter nuclide. The initial isotope ratios should be the same in the different rock samples.
N s is a stable isotope of N d Slope which only depends on the decay time. ( t t ) / τ d s d 0 s p 0 s N ( t) / N = N ( t ) / N + (1 e 0 m ) N ( t ) / N Original daughter isotope ratio. Should be the same in all crystals. Original parent ratio which depends on the crystal. Observed daughter ratio, depends on decay. Since intercepts and slopes should be the same, points from different crystals should all fall on a line. The slope of the line determines the age of the rock.
Isochron diagrams Animation by Jon Fleming
Isochron diagram
Radiometric dating assumption Ratio of original daughter isotope to stable isotope of daughter, D0 is independent of solidification, crystallization and cooling. No ``fractionation"
Extinct nuclide dating Search for rare daughter products of short lived nuclides. For example, Xenon is fairly rare, much rarer than Iodine. 129 I beta decays to 129 Xe with a half life of 17 million years. The total amount of Xenon in the meteor is related to the initial amount of radioactive 129 I.
The interval between nucleosynthesis and condensation In a supernovae r-process elements are produced when there is a high flux of energetic neutrons. The unstable nuclei do not necessarily have time to β-decay before they gain another neutron. The r-process produces a particular nuclide distribution. Unstable r-process elements including 129 I decay after formation. The amount of 129 I inferred in the rock (by looking at the amount of present Xenon) gives a timescale between the supernova and the condensation of the solar nebula. --- The protosolar nebula was probably condensed only 80 million years after a supernova enriched the gas which was incorporated into the solar nebula.
Light elements with short half lives There is a correlation in chondrites between Al abundance and 26 Mg/ 24 Mg ratio. This cannot be a result of mass dependent fractionation because 25 Mg/ 24 Mg is normal. So probably 26 Al beta decays into 26 Mg, 26 Al half life is 720,000 years. Since Al is abundant, this could have provided a substantial amount of energy for melting planetesimals. Supernova, nearby enriching protosolar nebula. The decay also produces a gamma ray which is detected from the Galaxy.
Cosmic ray exposure ages Galactic cosmic rays (energy above 1Gev, mostly protons) penetrate to 1m or so in asteroids. The amount of cosmic rays a meteor has been exposed to indicates how long it was in space. Rare isotopes only produced by this process must be identified. Such as 21 Ne and 38 Ar, or 10 Be. Abundance varies with depth so this must be estimated independently. Typical cosmic ray exposure ages range from 10 6 years for carbonaceous chondrites to 10 7 for stones, to 10 8 for stony irons and 10 9 for irons. To explain this dependence: There could be a tendency for weaker materials to erode. Also the Yarkovski force has a weaker effect on denser materials.
Chondrites Abundances of chondrites are very regular, being almost exactly solar in composition with the exception of the loss of some volatile elements, and those resulting from radioactive decay. Are there any anomalies due to other processes? Chondrites have not been melted for 4.56 billion years but they are not uniform. Chondrites also contain Chondrules and CAI inclusions (calcium and aluminum rich). Chondrites include 0-80% of mass in chondrules.
Solar System Abundances Ir=77
Chondrules Chondrules 0.1-2mm, must have cooled on order of 10 minutes to a few hours to explain their crystalline properties. Correlations between size and composition are difficult to explain, but must have been formed before becoming part of larger bodies.
The matrix The matrix consists of smaller grains, a lot of olivine and pyroxine (also seen in IR spectra of extra-solar debris disks and comets) Can also have grains from other stars mixed in (including diamonds).
Clues to formation of the solar system The Allende CV3 meteorite is 4.563±0.004 10 9 years old. This pretty much dates the solar system. Moon rocks are younger (3--4.45 10 9), so have melted since then. Terrestrial rocks are less than 4 10 9 years old. Differences in composition tell you about where they formed (mass fractionation), nuclear decay, processing by melting and water and cosmic rays.
Meteorites from differentiated bodies Excess 60 Ni which is a stable decay product of 60 Fe suggest that some rocks differentiated within 10 7 years after nuclear synthesis. Retention of noble gases can also be related to a cooling history. A cooling history depends on the size of the body. There is a consensus that some smaller bodies <100km melted.
Origin of Chondrules and CAIs Possible scenarios: Drag during passage through an accretion shock. X-wind acceleration followed by cooling in a shaded region. Lightning Nebular shock waves
D/H ratio Some organic material in carbonaceous chondrites contain high D/H ratios more than 1000 times solar. Some fractionation could occur in the solar nebula due to temperature differences as a function of radius, and high D/H at large radii (factor of 10). Cold interstellar clouds, however are needed to produce such a large variation (factor of 1000). Interstellar grains probably were processed into the proto-solar nebula.
Summary Isotopic fractionation. Long lived and short lived nuclides. Radioactive dating and how to do it. Cosmic ray exposure times. Time between nucleo-synthesis and condensation.