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06 February 2016 The Deep Earth Practical Assessment: Carbon in the core (5%) 1. What are the origins of magnetism in a material? Unpaired electrons with spin up(down) and long-range order (large domains) 2. Write down what is meant by: (i) ferromagnetism spin up only (ii) ferrimagnetism spin up/down unequally (iii) antiferromagnetism spin up/down (iv) paramagnetism non-aligned spin (v) diamagnetism magnetic in presence of external field (vi) Curie temperature T at which ferromagnetic goes paramagnetic (vii) Neel temperature T at which antiferromagnet goes paramagnetic (viii) magnetic susceptibility. Degree of magnetisation in response to a magnetic field 3. What happens to magnetism as pressure is increased? Band gap increases such that too high for unpaired electrons so jump down a level and pair making magnetism reduce until eventually at high P is zero. What magnetic state would you expect Fe3C to have at core conditions and why? Very high P so non-magnetic 4. The table below shows equation of state parameters for Fe3C: NSR = non-spinrestricted calculations (allowed to be magnetic); SR = spin-restricted calculations (forced to be non-magnetic); the bottom three rows are experimentally determined values. NSR: 6.25≤V≤10.31 NSR: 9≤V≤10.31 Å3 SR: 5≤V≤9.69 Å3 Li et al. Å3 V0 Å3/atom 9.578(37) 8.968(7) 9.705 Lidunka Vočadlo UCL Earth Sciences University College London Gower Street London WC1E 6BT Tel: +44 (0)20 7679 7919 Fax: +44 (0)20 7679 2685 [email protected] bowfell.ucl.ac.uk/~lidunka K0 GPa 173.02(8) 228.55(1) 316.62(2) 174(6) K’ 5.79(41) 5.36(64) 4.30(2) 4.8(0.8) Scott et al. Jephcoat 9.704(9) 175.4(35) 162 5.1(3) 6.4 The Birch Murnaghan 3rd order EOS is given by: 7 5 2 3 V V 3 3( K '4) V 3 3K 0 P 1 1 4 V0 2 V0 V0 Use this equation and the EOS parameters in the table above to plot a PV-curve (6Ǻ3<V<10Ǻ3) for the calculations (both SR and NSR) and the experimental data of Scott et al.. What do you notice about the three lines you have drawn. 5. The isothermal incompressibility is then given by: 3K KT 0 2 7 5 3 V V 3 K ' 16 7 5 0 3 3K 0 0 4 3 V 2 3 V 7 3 V V 3 ( K ' 4 ) 7 0 3 0 3 4 3 V V The adiabatic incompressibility is given by: K S K T (1 T ) where α~1x10-5 K-1 and γ~1.5. Use this relation to plot KS as a function of density at 5500 K for non-magnetic Fe3C. Include on your plot the seismic observations from PREM for the inner core. What does your plot tell you about the likelihood of carbon in the Earth’s inner core? For a definitive answer, what other factors have to be taken onto account. Please hand in your answers to David Dobson at noon, Friday March 3rd. Lidunka Vočadlo