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Thermoelastic properties of ferropericlase

Thermoelastic properties of ferropericlase. Thermoelastic properties of ferropericlase. R. Wentzcovitch Dept. of Chemical Engineering and Materials Science, Minnesota Supercomputing Institute J. F. Justo , C. da Silva, Z. Wu Dept. of Chemical Engineering and Materials Science

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Thermoelastic properties of ferropericlase

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  1. Thermoelastic properties of ferropericlase Thermoelastic properties of ferropericlase R. Wentzcovitch Dept. of Chemical Engineering and Materials Science, Minnesota Supercomputing Institute J. F. Justo, C. da Silva, Z. Wu Dept. of Chemical Engineering and Materials Science T. Tsuchiya Ehime University, Japan

  2. Outline • Ab initio calculations of Fe in (Mg1-xFex)O • Thermodynamics of the spin transition • Thermoelastic properties of (Mg1-xFex)O • Geophysical implications

  3. (Mg1-xFex)O ferropericlase (Mg1-yFey)SiO3 perovskite + Motivation: Earth’s Minerals • Lower Mantle: Ferrosilicate Perovskite + ferropericlase • Low iron concentration (< 0.20) • High-temperatures and high pressures • Elasticity

  4. First Principles Calculations • Density Functional Theory (LDA+U) • (Cococcioni and de Gironcoli, PRB, 2005) • Plane waves + Pseudopotential (Troullier-Martins, PRB, 1991, Vanderbilt, PRB, 1990) • Structural relaxation in all configurations • Density Functional Perturbation Theory (Baroni et al., RMP, 2001)

  5. Optimized Hubbard U HS LS

  6. First Principles Calculations: HS-LS transition (Tsuchiya et al., PRL, 2006) PT = 32±3 GPa No systematic dependence on XFe

  7. Equation of State (Mg0.81Fe0.19)O (Tsuchiya et al., PRL, 2006) ∆V ~-4% Experimental: + (J.F.Lin et al., Nature, 2005) 17% Fe and room temperature

  8. Temperature Effects: n(P,T) (Tsuchiya et al., PRL, 2006) 1) Magnetic entropy 2) HS/LS configuration entropy 3) Fe/Mg configurational entropy is insensitive to spin state 4) Vibrational energy and entropy are insensitive to spin state 5) Minimization of G(P,T,n) with respect to n:

  9. LS fraction n(P,T) (Tsuchiya et al., PRL, 2006) XFe=18.75% Exp Geotherm (Boehler, RG, 2000)

  10. Elasticity of Ferropericlase Elasticity of Ferropericlase

  11. Volume of the mixed spin state V(P,T,n) • Mixed spin configuration was described by the Vegard’s rule: where n = low spin fraction • Iron-iron interaction is not significant for xFe=18.75%

  12. High temperature elasticity • Compressibility: • Compliances:

  13. Static +vibrational free energy • VDoS and F(T,V) within the quasiharmonic approximation IMPORTANT: crystal structure and phonon frequencies depend onvolumealone!!

  14. Thermoelastic Constant Tensor Cijpure(P,T) (Wentzcovitch et al., PRL, 2004) Eulerian Strain kl equilibrium structure re-optimize

  15. MgO (Mg0.8125Fe0.1875)O “Approximate” Virtual Crystal model Replace Mg mass by the average cation mass of the alloy ω(V) = ωLS(V) = ωHS(V)

  16. Procedure to obtain Cij(P,T,n): • Compute CijLS(P,T) and CijHS(P,T) • SLS(P,T) = [CLS(P,T)]-1and SHS(P,T) =[CHS(P,T)]-1 • Calculate • Compute V(P,T,n) and Sij(P,T,n) • C(P,T,n) = [S(P,T,n)]-1 • Compute K(P,T,n) and G(P,T,n)

  17. Volume V(P,T,n(P,T)) for xFe= 18.75% xFe= 18.75% + 300K (exp.) + Experiments (Lin et al., Nature, 2005) (xFe=17%, RT)

  18. Elastic Constants (xFe= 18.75%)

  19. Isotropic Elastic Constants Experiments: ○ (Lin et al., GRL, 2006) xFe = 25% (NRIXS, RT) ● (Lin et al., Nature, 2005) xFe= 17% (X-ray diffraction, RT) □ (Kung et al., EPSL, 2002) xFe = 17% (RUS, RT)

  20. Sound Wave Velocities xFe= 18.75% Experiments: ○(Lin et al., GRL, 2006) xFe = 25% (NRIXS, RT) □(Kung et al., EPSL, 2002) xFe = 17% (RUS, RT)

  21. Geophysical Implications Geophysical Implications

  22. Elasticity Along Mantle Geotherm 1580 km 1150 km Geotherm (Boehler, Rev. Geophys. 2000) -15% 6%

  23. Wave Velocities Along Mantle Geotherm 1580 km 1150 km -9% -15% 6% 3% Geotherm (Boehler, GRL,2000)

  24. (Karato, Karki, JGR, 2001) Seismic Parameters (Mantle Geotherm) Geotherm (Boehler, RG, 2000) (Kara

  25. Wave Velocities Along Mantle Geotherm 1580 km 1150 km -9% -15% 6% 3% Geotherm (Boehler, GRL,2000)

  26. Summary • HS-LS transition in (Mg1-xFex)O is well reproduced theoretically • There is a strong softening in the bulk modulus across the spin transition. This effect broadens and decreases with temperature • Along a lower mantle geotherm this softening is more pronounced between 45-70 GPa, i.e., 1150-1580 km • The shear modulus increases monotonically in the same region • Transition can produce negative values of R/s in the upper part of the lower mantle • The softening will likely occur also in ferrosilicate perovskite • The Si/(Mg+Fe) ratio in the lower mantle should increase from pyrolitic values because of the spin transtions in ferropericlase and ferrosilicate perovskite

  27. Acknowledgements NSF/EAR 0135533 NSF/EAR 0230319 NSF/ITR 0428774 Japan Society for the Promotion of Science (JSPS) Brazilian Agency CNPq Computations performed at the MSI-UMN

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