Thermoelastic properties of ferropericlase R. Wentzcovitch Dept. of Chemical Engineering and Materials Science, Minnesota Supercomputing Institute J. F.

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Presentation transcript:

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

Outline Ab initio calculations of Fe in (Mg 1-x Fe x )O Thermodynamics of the spin transition Thermoelastic properties of (Mg 1-x Fe x )O Geophysical implications

Motivation: Earth’s Minerals (Mg 1-y Fe y )SiO 3 perovskite (Mg 1-x Fe x )O ferropericlase + Lower Mantle: Ferrosilicate Perovskite + ferropericlase Low iron concentration (< 0.20) High-temperatures and high pressures Elasticity

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)

Optimized Hubbard U HS LS

P T = 32±3 GPa No systematic dependence on X Fe (Tsuchiya et al., PRL, 2006) First Principles Calculations: HS-LS transition

Experimental: + (J.F.Lin et al., Nature, 2005) 17% Fe and room temperature Equation of State (Mg 0.81 Fe 0.19 )O (Tsuchiya et al., PRL, 2006) ∆V ~- 4%

Temperature Effects: n(P,T) 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: (Tsuchiya et al., PRL, 2006)

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

Elasticity of Ferropericlase Elasticity of Ferropericlase

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 x Fe =18.75%

High temperature elasticity  Compressibility:  Compliances:

IMPORTANT: crystal structure and phonon frequencies depend on volume alone!! Static +vibrational free energy  VDoS and F(T,V) within the quasiharmonic approximation

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

“Approximate” Virtual Crystal model MgO (Mg Fe )O Replace Mg mass by the average cation mass of the alloy ω(V) = ω LS (V) = ω HS (V)

 Compute C ij LS (P,T) and C ij HS (P,T)  S LS (P,T) = [C LS (P,T)] -1 and S HS (P,T) =[C HS (P,T)] -1  Calculate  Compute V(P,T,n) and S ij (P,T,n)  C(P,T,n) = [S(P,T,n)] -1  Compute K(P,T,n) and G(P,T,n) Procedure to obtain C ij (P,T,n):

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

Elastic Constants (x Fe = 18.75%)

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

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

Geophysical Implications Geophysical Implications

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

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

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

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

Summary  HS-LS transition in (Mg 1-x Fe x )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 GPa, i.e., 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

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