Topic 1. Relative abundances

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Tracy Wilkinson
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1 Topic 1 Observational evidence for relative abundances Relative abundances The plot to the right shows the relative abundances of atomic species as a function of atomic mass number. Note that it is a logarithmic plot with everything normalised such that the abundance of Silicon (Si) is 10 6 Here the word abundance refers to atomic abundances i.e. the number of atoms. In this case a relative abundance is the atomic ratio of the element of interest usually with respect to some normalising element such as Silicon Do not confuse this with ratios by mass (concentrations) In this course we will investigate why this plot looks the way it does To do so requires delving into many fields such as cosmology, nuclear physics, particle physics and astrophysics 1

2 Chemical Analysis: Information sources In this topic we will review the experimental evidence for relative abundances from physical sources where chemical analysis can take place Such sources provide very detailed information on composition at the atomic and isotopic level Unfortunately however there are very few such sources and so, here on Earth, we are limited to studying The Earth The Moon (via Moon rocks) Meteorites Understanding the Earth s Composition We know that the Earth is not homogeneous Our understanding of the Earth s structure is that of layers of varying density that increases towards the core Note that we can only directly access the atmosphere, oceans and crust - a mere 0.5% (by mass) of the total! Need a model to extrapolate from our limited observations to overall chemical composition 2

The Blast Furnace Model Based on thermal history Assumes that the Earth formed some 4.5 10 9 years ago At some stage in its early history it was in a molten state Heat from two sources: 1.

3 The Blast Furnace Model Based on thermal history Assumes that the Earth formed some years ago At some stage in its early history it was in a molten state Heat from two sources: 1. Conversion of Gravitational PE (accretion) 2. Radioactive Heating ( 26 Al, 40 K, 235 U, 238 U) We will revisit radioactivity at the end of this topic Under such conditions chemical separation occurs Similar effects seen in blast furnaces Elements group in various compounds of different densities that settle at different levels in a gravitational field Process known as gravitational fractionation / differentiation / separation Blast Furnace Watercolour by Donald K. Lake Chemical Affinities Four groups based on chemical affinities: 1. ATMOPHILES (usually occur as gases) H, C, N and noble gases O is not usually regarded as an atmophile because most oxygen occurs as silicate minerals 2. LITHOPHILES (so-called silicate phase) Li, Na, K, Mg, Si, etc. (Readily form solid oxides) 3. CHALCOPHILES (so-called sulphide phase) Cu, Zn, Hg, Pb, Bi, etc. (Prefer to form sulphides) 4. SIDEROPHILES (iron phase) Fe, Ni, Co, Au, Pd, etc. (Dissolve readily in molten iron) 3

Chemical Affinities The Earth s structure When applied to the Earth we develop a picture where the crust is silicates, the mantle is olivine rock (90% Mg 2 SiO 4, 10% Fe 2 SiO 4 ) and the core is of

4 Chemical Affinities The Earth s structure When applied to the Earth we develop a picture where the crust is silicates, the mantle is olivine rock (90% Mg 2 SiO 4, 10% Fe 2 SiO 4 ) and the core is of solid iron or iron+nickel Supported by evidence such as density, elastic properties and seismic activity Measurements of the Earth s crust show that 98% of it is made up of just 8 elements: O (46.6%), Si (27.7%) Al (8.1%), Fe (5.0%), K (3.6%), Na (2.8%), Ca (2.6%), Mg (2.1%) 4

5 What Earthquakes tell us An earthquake produces body waves and surface waves. By monitoring these we can map the Earth s structure Body waves Travel through the interior of the Earth following ray paths which are deflected by the different densities and compositions in the Earth s structure P waves: longitudinal or compressional waves, travel through any material, travel a little less than twice as fast as S-waves. In air these waves travel as sound waves. P waves cause the ground to be compressed and dilated in the direction of travel of the waves and so are less destructive than S waves and surface waves. P waves travel faster in solids than liquids. Also known as primary waves. S waves: transverse or shear waves, can only travel through solids (fluids do not support shear stresses), travel at a velocity approximately equal to 60% of P waves but with an amplitude several times greater than P waves. S waves cause the ground to be displaced in a direction perpendicular to the wave direction. Also known as secondary waves. Surface waves Analogous to water waves and travel just under the Earth s surface. Low frequency, large amplitude and long duration makes them very destructive Rayleigh waves: cause ground roll like ripples on water Love waves: cause horizontal shears The Moon: Information Sources Main sources of information are: kg of Moon rock samples brought back from the Apollo missions 2. Monitoring seismic activity 3. Physical properties such as Moment of Inertia, Magnetic Field, etc. 5

The Moon s Structure Crust: 60km thick (8% by volume), thinner on side facing the Earth, feldspathic, rich in Al, Ca Mantle/lithosphere: Approximately 90% by volume Core: probably FeS - some debate

6 The Moon s Structure Crust: 60km thick (8% by volume), thinner on side facing the Earth, feldspathic, rich in Al, Ca Mantle/lithosphere: Approximately 90% by volume Core: probably FeS - some debate here Density of the Moon is 3500 kg.m -3 compared with 5500 kg.m -3 for the Earth (densest of the planets) Moment of inertia indicates uniform density No magnetic field now probably not a pure iron core Elemental Content of Moon Rock No water so no terrestrial type sedimentary rocks no minerals formed by hydration no weathering No atmosphere = no oxides Igneous rocks form by direct crystallization out of a silicate melt Lower density rocks frothed up to the surface as the molten Moon cooled More abundant on the Moon: Lithophiles, U, Ti, Zr, REE Less abundant on the Moon: C, N, O, Cl, siderophiles, chalcophiles, Iron The higher the boiling point of an element the more abundant it is on Earth Nothing to indicate that Earth and Moon do not have common origin The Moon has two distinct topographical areas: Maria ( seas ) Highlands Highlands: Oldest rocks ( yr) Lighter in appearance - lacking iron-rich basalts Maria Younger ( yr) Volcanic outflows Rocks like oceanic crust on Earth Evidence of Titanium rich lavas that have rapidly cooled 6

Moon s Moment of Inertia From measurements of Doppler tracking of the Lunar Prospector spacecraft Place the satellite in a low (~100 km altitude) circular polar orbit Measure line-of-sight velocity

7 Moon s Moment of Inertia From measurements of Doppler tracking of the Lunar Prospector spacecraft Place the satellite in a low (~100 km altitude) circular polar orbit Measure line-of-sight velocity via Doppler shift Accurate at 10-7 level Measured normalised moment of inertia I/MR 2 = ± Moment of Inertia (Solid Sphere) We write where z = r sinθ dv so I = ρ I = z 2 dm dm = ρ dv = r 2π π R R I = 5 r π π ρ sinθ dr dθ dφ 3 sin θ dr dθ dφ 3 sin θ dθ dφ 7

8 Moment of Inertia (Solid Sphere) Using π 0 sin 3 θ dθ π 2 = ( sin θ sin θ cos θ ) π [ ] = 3 cos θ cos θ = 0 and so I = 4R5 ρ 2π dφ = 8πR5 ρ substituting ρ = M gives V = M 4 I = 3 πr3 0 dθ 2 5 MR2 Results from Lunar Prospector How do we interpret the results from the Lunar Prospector? Note that MoI for a Hollow Sphere is: So a normalised MoI < 0.4 implies a small solid core For MoI = then core radius and fractional Moon mass is r = 320 m = km(fe) %(Fe) r = 510 m = km(fes) %(FeS) I = 2 3 MR2 8

Meteorites Definitions: Meteoroid: before entering Earth s atmosphere.

lands on Earth Some facts about meteorites: Estimated 79,000 tonnes per year on Earth (includes

Antarctica The Meteorite Family Tree I Iron Also known as siderites Mainly Fe and Ni <1% pop.

2% falls 6% finds Stony 75-90% silicate content Many different sources ~5% pop.

9 Meteorites Definitions: Meteoroid: before entering Earth s atmosphere. Meteor: becomes incandescent to frictional drag with atmosphere (20km/s, deceleration) Meteorite: lands on Earth Some facts about meteorites: Estimated 79,000 tonnes per year on Earth (includes microscopic dust, etc) Only 1 meteorite per 10 6 km 2 per year has a mass > 500g Lots are found in Antarctica The Meteorite Family Tree I Iron Also known as siderites Mainly Fe and Ni <1% pop. 6% falls 54% finds Stony-Iron Complex silicate-metal Minerals (siderolites) <1% pop. 2% falls 6% finds Stony 75-90% silicate content Many different sources ~5% pop. 92% falls 40% finds Next slide Hexahedrites < 6% Nickel Octahedrites 6-15% Nickel Ataxites > 16-20% Nickel Mesosiderites Asteroid Collision? Pallasites Asteroid core mantle boundary 9

10 Meteorite Family Tree II From last slide Stony 75-90% silicate content Many different sources ~5% pop. 92% falls 40% finds Achondrites Rarer class of stony meteorites Only account for 8% of all meteorite falls Mainly asteroidal in origin but some, e.g. from the Moon or Mars Made of rock that has crystallised from a molten state and typically lack chondrules Chemically similar to basalts Due to melting on Earth, Moon, asteroids, etc. Silicate-rich differentiated meteorites, products of heating and separation Chondrites 84% of all known falls Originate in sources that have never undergone differentiation Almost all contain chondrules - small (0.1mm to 2.0mm) glass spheroids of once molten silicates With the exception of volatiles such as H, He chondrites are largely thought to have a composition closely matching that of the original solar nebula Carbonaceous chondrites contain carbon, evidence of H 2 O and sometimes volatiles Meteors, falls and finds Meteor Type (%) Meteor Population (%) Meteorite Falls (%) Meteorite Finds (%) Cometary ~95% 0% 0% Iron 6% 54% Stony-iron <1% 2% 6% Achondrites 8% 3% Chondrites ~5% 84% 37% Meteor sources include: Comets (most prevalent, frozen methane, ammonia, water, etc.) Differentiated asteroids (stratification due to high temps) Asteroids Differentiated planetoids (e.g. lunar ejecta) 10

11 Why Meteorites are important To date all meteorites that have been dated have ages within a 16Myr interval of the age of the solar system (4.53 ±0.02) Gyr Some meteorites show evidence for the presence of water and amino acids Meteorites are believed to have elemental abundances that best represent that at the start of the solar system In order to age meteorites the relative amounts of certain radioactive compounds are measured In the next slides we will revise the basics of radioactivity The Allende Meteorite A huge carbonaceous chondrite meteorite fell near to Pueblito de Allende in Mexico in 1969 To date more than 2 tons of fragments have been collected and examined As well as chondrules the meteorite contains microscopic diamonds which are older than the solar system and may be extra-solar in origin, possibly from a supernova 11

12 The Allende Meteorite Highly unequilibrated many inclusions chondrules grains of minerals with apparent different chemical histories Likely that the material formed in a high temperature environment, no equilibration with residual gas (i.e. no condensation in thermal equilibrium) Some isotopic anomalies may be explained by inclusion of material from a nearby Supernova, supported by analysis of heavy Oxygen isotopes 17 O and 18 O Some inclusions show isotopic anomalies for very many elements. Possibly unmodified stellar ejecta incorporated into the solar nebula in solid form The role of Radioactivity We have already seen that radioactive elements play a role in the formation of the Earth Similarly, radioactive elements can be used to date materials such as meteorites, the most famous technique is carbon dating Shortly we will look at how this dating is done, first of all let s quickly revise some basics of radioactivity 12

13 Radioactive Decay A radioactive element is one which spontaneously (and randomly) undergoes a change within its nuclear makeup There are 3 basic types of radioactivity: 1. Decays with emission of nucleons 2. Different modes of beta decay 3. Transitions between states of the same nucleus 1. Examples: α-decay, neutron emission, proton emission, spontaneous fission 2. Examples: β-decay, inverse β-decay, electron capture 3. Examples: γ-decay, internal conversion Lifetime, Half-life, Decay Constant When a radioactive isotope decays it does so in a random, unpredictable way However over time the original amount of the radioactive material (N 0 ) decays exponentially according to expression N = N 0 exp (-t / τ) Where N is the amount left after time t and τ is the lifetime Alternatively we can write N = N 0 exp (-λt) where λ is the decay constant Another quantity used is the half-life t 1/2 which is the time t at which N=N 0 /2. From this we see that t 1/2 = τ ln(2) 13

14 Case Study: Ageing a Meteorite The assumptions that are made: Amongst meteorites all chondrites have a similar chemical composition. One way in which they do change is via the decay of radioactive isotopes This can be used to determine their date of formation. One problem is that there will have been an unknown amount of the parent and daughter isotopes at the time of the meteorite s formation Need to normalise against some stable isotope The problem: Consider the radioactive decay 87 Rb 87 Sr + e - + ν e which has a decay constant 1.4 x yr -1 The isotopic ratios of two different meteorite samples have been measured (below) Use this information to estimate the age of the meteorites assuming they originated in the same event meteorite ( 87 Sr/ 86 Sr) now ( 87 Rb/ 86 Sr) now A B Meteorite Ageing: Solution After time t the amount of the parent nuclide remaining is: P t = P 0 exp(-λt) and so the amount of the parent nuclide that has decayed into daughter nuclide is given by: P 0 [1 - exp(-λt)] = P t [exp(λt) - 1] and so the amount of the daughter nuclide at time t is given by: D t = D 0 + P 0 [1 - exp(-λt)] = D 0 + P t [exp(λt) - 1] where P 0 is the original amount of the parent nuclide P t is the current amount of the parent nuclide D 0 is the original amount of the daughter nuclide D t is the current amount of the daughter nuclide However D 0 is unknown and so we need to normalize by dividing by another element that must be another stable isotope of D which is assumed to remain constant and orignally incorporated in the meteorite samples in the same proportion as D. In this case the equation above becomes: (D/S) t = (D/S) 0 + (P/S) t [exp(λt) - 1] which we identify with y = mx+c and use the data in the table to get t=4.45x10 9 yr 14

15 Summary A lot of information on elemental abundances can be gained from direct measurement of samples acquired from the Earth Moon Meteorites Whilst there are some differences the basic picture is always very similar In the next topic we will look at abundances from the spectra of stars 15

Formation of the Earth and Solar System

Formation of the Earth and Solar System a. Supernova and formation of primordial dust cloud. NEBULAR HYPOTHESIS b. Condensation of primordial dust. Forms disk-shaped nubular cloud rotating counterclockwise.