Differentiation of Earth

Introduction

  • Earth: third planet from the Sun; 5th5^{th} largest in the Solar System and largest terrestrial planet by diameter, mass and density.
  • Galactic context: Milky Way → Local Group cluster → Virgo Super-cluster.
  • Only confirmed location of life.
  • Formed extca.4.6  Gaext{ca. }4.6\;\text{Ga} (giga-annum) in an initially molten state, setting the stage for internal chemical and physical re-organisation (differentiation).

Core Ideas & Vocabulary

  • Differentiation: Gravitational separation of materials according to density while the planet is partially or wholly molten.
    • Produces a concentric, density-stratified structure (core → mantle → crust).
  • Accretion: Growth of a planet by collision and sticking of solid particles and larger bodies.
    • Two working models: Homogeneous accretion vs Heterogeneous accretion.
  • Planetesimal: Km-scale precursor body in the protoplanetary disk.

Chronology of Differentiation

  • Onset: soon after accretion began, ∼4.56  Ga\sim 4.56\;\text{Ga}.
  • Must pre-date oldest known lunar crustal rocks (anorthosites) at 4.47  Ga4.47\;\text{Ga}.
  • Therefore Earth’s interior became layered within the first ∼90  Ma\sim 90\;\text{Ma} of Solar-System history.

Energy Sources Driving Melting

  • Impact heating
    • Continuous high-velocity collisions; a single gigantic impact (Theia hypothesis) likely formed the Moon, tilted Earth’s spin axis and injected additional heat.
  • Radioactive decay
    • Short-lived nuclides (e.g.
    26Al,  60Fe^{26}\text{Al},\;^{60}\text{Fe}) & long-lived nuclides ( 238U,  235U,  232Th,  40K^{238}\text{U},\;^{235}\text{U},\;^{232}\text{Th},\;^{40}\text{K} ).
    • Greater heat production early on (exponential decay law Q(t)=Q0e−λtQ(t)=Q_0 e^{-\lambda t}).
  • Gravitational/adiabatic compression
    • Conversion of potential energy to thermal energy during self-compaction.

Accretion Models

  • Homogeneous Accretion
    • All incoming material chemically similar.
    • Initial state: cold, mechanically coherent aggregate.
    • Progressive internal heating → partial/total melt → metallic iron droplets segregate downward.
    • Produces a sequential internal layering after accretion.
  • Heterogeneous Accretion
    • Dust/ice gradient in protoplanetary disk yields compositionally graded infall.
    • Early infall: refractory, metal-rich; later infall: volatile, silicate-rich.
    • Layering develops during accretion.
  • Reality: likely hybrid; early Earth plausibly transitioned from heterogeneous to homogeneous style as impactor composition evolved.

Physical Mechanisms of Differentiation

  • Density-Driven Segregation in molten/partially-molten body:
    • ρ<em>Fe-Ni≈7.8  g cm−3\rho<em>{\text{Fe-Ni}} \approx 7.8\;\text{g\,cm}^{-3} sinks. • ρ</em>silicate melt≈2.7!–!3.5  g cm−3\rho</em>{\text{silicate melt}} \approx 2.7!\text{--}!3.5\;\text{g\,cm}^{-3} rises.
  • Chemical Partitioning
    • Molten metal scavenges siderophile (Fe-loving) and chalcophile elements; melt becomes ‘compatible’ for these.
    • Coexisting silicate melt enriched in ‘incompatible’ lithophile elements (K, Na, U, Th, etc.).
  • Magma-Ocean Hypothesis
    • Large-scale silicate melt layer forms; convective overturn expedites metal percolation (‘iron rain’).
    • Upon cooling, forms basaltic protocrust; repeated impact-induced re-melting resets crust multiple times.

Present-Day Internal Stratigraphy

  • (Dimensions from surface radius R⊕≈6378  kmR_\oplus \approx 6378\;\text{km})

    • Crust – variable thickness ≈10!–!70  km\approx 10!\text{–}!70\;\text{km}.
    – Oceanic: ρ≈3.0!–!3.3  g cm−3\rho \approx 3.0!\text{–}!3.3\;\text{g\,cm}^{-3}; basaltic.
    – Continental: ρ≈2.7!–!3.0  g cm−3\rho \approx 2.7!\text{–}!3.0\;\text{g\,cm}^{-3}; granitic.
    • Lithosphere – crust + rigid uppermost ∼100  km\sim 100\;\text{km} of mantle.
    • Asthenosphere – ductile, partially molten upper mantle at ∼150!–!400  km\sim 150!\text{–}!400\;\text{km} depth.
    • Mantle – ∼2900  km\sim 2900\;\text{km} thick; Fe-Mg silicates, ρ=3.3!–!5.7  g cm−3\rho=3.3!\text{–}!5.7\;\text{g\,cm}^{-3}.
    • Outer Core – ∼2300  km\sim 2300\;\text{km} thick, liquid Fe-Ni alloy; ρ=9.9!–!12.2  g cm−3\rho=9.9!\text{–}!12.2\;\text{g\,cm}^{-3}; convective motions generate geodynamo.
    • Inner Core – ∼1200  km\sim 1200\;\text{km} radius, solid Fe-Ni; ρ=12.6!–!13.0  g cm−3\rho=12.6!\text{–}!13.0\;\text{g\,cm}^{-3}; growth releases latent heat and light elements.

Thermal & Rheological Boundaries

  • Moho (Mohorovičić Discontinuity) – crust/upper-mantle seismic velocity jump ≈35!–!10  km\approx 35!\text{–}!10\;\text{km} depth (oceanic vs continental).
  • Gutenberg Discontinuity – mantle/outer-core boundary at d≈2890  kmd\approx 2890\;\text{km}; contrast in V<em>P,V</em>SV<em>P,V</em>S due to solid→liquid change.
  • Lehmann Discontinuity – outer-/inner-core transition at d≈5150  kmd\approx 5150\;\text{km} (liquid→solid).

Quantitative Thermal Profile (approx.)

  • Surface T≈0∘CT \approx 0^\circ\text{C} → Moho T≈870∘CT \approx 870^\circ\text{C} → CMB T≈3700∘CT \approx 3700^\circ\text{C} → ICB T≈4300∘CT \approx 4300^\circ\text{C} → centre T≈7200∘CT \approx 7200^\circ\text{C}.

Lunar Evidence & Its Significance

  • Why the Moon? Earth’s earliest record erased by plate tectonics and erosion; lunar surface preserves >4\;\text{Ga} history.
  • Key observations:
    1. Anorthositic Highlands – require global or near-global magma ocean; plagioclase floatation formed ∼50  km\sim 50\;\text{km} crust.
    2. Age Window (4.4!–!3.2  Ga4.4!\text{–}!3.2\;\text{Ga}) – abundant radiometric ages bracket end of lunar differentiation and mare volcanism; contrasts with sparse terrestrial record >3.8\;\text{Ga}.
    3. Gravity & Magnetism – implied early whole-Moon melt; absence of large Fe core today suggests limited metal or later core crystallisation.
  • Implication: Earth, being larger, must have undergone at least equally extensive, and likely more rapid, differentiation.

Comparative Planetology

  • Other terrestrial bodies (Mars, Mercury, differentiated asteroids like Vesta) show evidence for core/mantle segregation, supporting universality of density-driven differentiation in rocky planets.

Ethical, Philosophical & Practical Implications

  • Understanding differentiation informs:
    • Resource exploration: localisation of siderophile and lithophile elements.
    • Geomagnetic field origin → radiation shielding crucial for biosphere; highlights planetary habitability factors.
    • Planetary defence & origin‐of‐life narratives: giant impacts both destroy and create environments.
    • Exoplanet studies: internal layering influences plate tectonics, magnetic fields, atmosphere retention.

Key Numerical & Formula Summary

  • Timeframe of main differentiation: 4.56  Ga−4.47  Ga4.56\;\text{Ga} - 4.47\;\text{Ga}.
  • Density contrast drives gravitational potential energy release: ΔE∼35GM2R(Δρρ)\Delta E \sim \frac{3}{5}G\frac{M^2}{R}\left(\frac{\Delta \rho}{\rho}\right) (order-of-magnitude).
  • Radioactive heat production: Q(t)=Q<em>0e−λtQ(t)=Q<em>0 e^{-\lambda t}; half-life t</em>1/2=ln⁡2λt</em>{1/2}=\frac{\ln 2}{\lambda}.

Process Flow (Simplified)

  1. Accretion → assembly of planetesimals.
  2. Heating (impacts + radioactivity + compression) → partial/complete melting.
  3. Metal-silicate segregation (‘iron rain’) → core formation.
  4. Silicate magma ocean crystallisation → primitive basaltic crust & depleted upper mantle.
  5. Ongoing internal cooling → inner-core solidification, mantle convection, plate tectonics.
  6. Surface evolution & recycling obscure earliest rock record.

Study Tips & Connections

  • Link differentiation to plate tectonics: compositional layering sets up thermal convection cells.
  • Recall periodic table groups: siderophile vs lithophile behaviour explains geochemical reservoirs.
  • Compare Earth–Moon system for understanding giant impact hypothesis and angular momentum conservation.

Closing Points

  • Earth’s layered architecture is an inevitable outcome of early high-energy conditions and universal physical laws (gravity, thermodynamics, phase equilibria).
  • Present-day observations (seismic, geomagnetic, geochemical) are fingerprints of these primordial processes.
  • Continuous research (high-pressure experiments, isotope geochemistry, space missions) refines timelines and mechanisms.

References (from original slides)

  • Don L. Eicher, “History of Earth,” Prentice-Hall (1980) pp. 8–26.
  • M. W. McElhinny, “The Earth: Its Origin, Structure and Evolution,” Academic Press (1979) pp. 2–53.
  • C. M. R. Fowler, “The Solid Earth,” Cambridge Univ. Press (1990) pp. 4–30.
  • Online: www.google.com,  www.wikipedia.com\text{www.google.com},\;\text{www.wikipedia.com}