Geochronometry-Isotope tracing-Age of the Earth

1. Geochronometry-Isotope tracing-Age of the Earth • Geochronometry (methods) • Nuclear synthesis • Meteorites • Age of the Earth accretion • Pb • Formation of the core • Formation of the core (energy considerations) • Formation of crust • Plate tectonics starts

2. Geochronometry • Radiogenic isotopes • Decay mechanisms (α decay, β decay, electron capture) • Main isotopic systems for dating • Rb-Sr • K-Ar • U-Pb • Th-Pb • Other isotopes used mainly for “tracing” (Sm-Nd, Re-Os, …)

5. Geochronometry (hypotheses) • Parent -> daughter decay probability λ • Mineral closes at temperature (depends on type: zircons 800 deg, feldspars 350, …) • No daughter present at closure (or it can be accounted for) • No loss or gain of parent or daughter after mineral closes • Counting P/D gives the time that elapsed since the system closed

6. Geochronometry (particulars) • K->Ar is a branching decay K40 -> Ar 40 or Ca 40 • U -> Pb two different isotopes of same element give two independent age estimates (must be concordant) • Rb/Sr requires different minerals with variable Rb/Sr ratios (same for Sm-Nd). Methods yield initial isotopic ratio of Sr87/Sr86 (important for tracing)

7. Same equations and method for other systems (U-Pb, Sm-Nd)

10. K-Ar • No Ar initially • But problem of atmospheric contamination • Correction based on Ar36 • Also Ar is easily lost • Retrace loss by step heating of samples and Ar-Ar ages

14. Dating the synthesis of elements

16. Meteorite samples achondrite chondrite Iron

18. Xe129 • Xe129 product of short half life I129 • Meteorites formed shortly after nucleosynthesis. • Xe129 in earth atmosphere (I129 in primitive earth) comes from degasing of mantle • Earth and meteorites have ~ same age

21. Meteorites • All meteorites have about the same age 4.55 Ga • Some meteorites that have younger ages come from the moon. They were ejected after impact. • A few are much younger (1.1 Ga). They are assumed to have been ejected by Mars after a large impact

22. Martian meteorites (?)

27. Moon samples Nasa has collected samples for dating Ages range between 3.0 and 4.5 Ga (see PDF document)

28. Time series of a Moon-forming impact simulation. Results are shown looking down onto the plane of the impact at times t = 0.3, 0.7, 1.4, 1.9, 3, 3.9, 5, 7.1, 11.6, 17 and 23 hours (from left to right); the last frame is t = 23 hours viewed on-edge. Colour scales with internal energy (shown on the colour bar in units of 6.67 times 108 erg g-1), so that blue and dark green represents condensed matter, and red particles signify either the expanded phase or a hot, high-pressure condensed phase; pressures at intermediate energies are computed by an interpolation between the Tillotson15 condensed and expanded phases. We form initial impactors and targets in hydrostatic equilibrium by pre-colliding smaller bodies together at zero incidence, resulting in realistically evolved internal energies, stratified densities (basalt mantle + iron core) and consistent pressures. Each particle's internal energy is evolved due to the effects of expansion/compression and shock dissipation, with the latter represented by artificial viscosity terms that are linear and quadratic in the velocity divergence of converging particles; effects of mechanical strength and radiative transfer are ignored. The momentum of each particle is evolved due to pressure, viscous dissipation and gravity. Gravity is computed using a binary tree algorithm, reducing the N2 calculation of particle–particle attractions into an NlogN calculation25. We use a beta spine kernel to define the spatial distribution of material represented by each SPH particle. The scale of each particle, h, is automatically adjusted to cause overlap with a minimum of 40 other particles, ensuring a 'smoothed' distribution of material even in low-density regions. The code is explicit, requiring a Courant-limited timestep Deltat < (c/h) where c is the sound speed. For a full description of the technique, see ref. 26, from whose efforts our present algorithm derives.

29. Rappel • Geochronometry hypotheses • Nucleosynthesis (6 to 4.6 Ga) • Age of meteorites 4.55 Ga • Meteorites follow shortly end of nucleosynthesis • Earth followed shortly end of nucleosynthesis • Moon samples 3.2 to 4.5 Ga • Oldest rock on Earth 4 Ga • Age of Earth from Pb 4.55 Ga

32. Dating core formation • Hafnium Hf and Tungsten W • Hf182 -> W182 (half life 9 Myears) • Hf180 reference • Hf stays in mantle • W goes in core • Initial ratio Hf182/Hf180 in solar system different from that of mantle

33. εw values of carbonaceous chondrites compared with those of the Toluca iron meteorite and terrestrial samples analysed in this study. The values for Toluca, Allende, G1-RF and IGDL-GD are the weighted averages of four or more independent analyses. Also included are data from ref. 16 (indicated by a), ref. 30 (b), and ref. 2 (c). For the definition of εw see Table 1. The vertical shaded bar refers to the uncertainty in the W isotope composition of chondrites. Terrestrial samples include IGDL-GD (greywacke), G1-RF (granite) and BB and BE-N (basalts).

34. εw versus 180Hf/184W for different fractions of the H chondrites Ste Marguerite (a) and Forest Vale (b). NM-1, NM-2 and NM-3 refer to different nonmagnetic fractions, M is the magnetic fraction. We interpret the positive correlation of εw with 180Hf/184W as an internal Hf–W isochron whose slope corresponds to the initial 182Hf/180Hf ratio at the time of closure of the Hf–W system.

35. Time of core formation in Myr after CAI condensation for Vesta, Mars, Earth and Moon versus planet radius as deduced from Hf–W systematics. For the Moon, the two data points refer to the endmember model ages. The Moon plots distinctly to the left of the correlation line defined by Vesta, Mars and Earth, suggesting a different formation process.

36. Timing of core formation. The Earth formed through accretion, absorbing planetesimals (lumps of rock and ice) through collisions. Did the Earth accrete undifferentiated material that then separated into shell and core — in which case, did the planet reach its present mass before differentiating, or was it a more gradual process? Alternatively, core formation might have happened rapidly inside growing planetesimals, so that the Earth's core is a combination of these previously formed cores. Isotopic evidence supports the latter model, and now Yoshino et al.1 demonstrate a mechanism for the physical process.

37. Core formation (conservation laws) • Gravitational potential energy decreases when core forms • Moment of inertia decreases • Angular velocity of rotation increases • Rotational energy increases • Increase in energy of rotation < Decrease in gravitational potential energy • Total energy must be conserved • Difference goes into heat • Estimates: Core formation -> 1000-2000K temperature increase

42. He • It is assumed that volatiles were lost during accretion • Very little He in atmosphere (too light, lost to space) • He in mantle • He3 is primitive, He4 primitive + decay of radioelements • He4/He3 ratio (initial ratio same as that of universe) • He4/He3 ratio grows with time • Some degasing • Shows mantle is not well mixed

44. Tracing with isotopes • Crust • Rb/Sr high • Sm/Nd low • Sr87/Sr86 increases • Nd143/Nd144 decreases compared with mantle • Mantle • Rb/Sr low • Sm/Nd high