Thermoelastic properties of ferropericlase

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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
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Outline

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

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Motivation Earths Minerals

• Lower Mantle Ferrosilicate Perovskite
  ferropericlase
• Low iron concentration (lt 0.20)
• High-temperatures and high pressures
• Elasticity

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First Principles Calculations

• Density Functional Theory (LDAU)
• (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)

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Optimized Hubbard U
HS
LS
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First Principles Calculations HS-LS transition
(Tsuchiya et al., PRL, 2006)
PT 323 GPa No systematic dependence on XFe
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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
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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
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LS fraction n(P,T)
(Tsuchiya et al., PRL, 2006)
XFe18.75
Exp
Geotherm (Boehler, RG, 2000)
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(No Transcript)
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Volume of the mixed spin state V(P,T,n)

• Mixed spin configuration was described by the
  Vegards rule
• where n low spin fraction
• Iron-iron interaction is not significant for
  xFe18.75

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High temperature elasticity

• Compressibility

• Compliances

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Static vibrational free energy

• VDoS and F(T,V) within the quasiharmonic
  approximation

IMPORTANT crystal structure and phonon
frequencies depend on
volume alone!!
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Thermoelastic Constant Tensor Cijpure(P,T)
(Wentzcovitch et al., PRL, 2004)
Eulerian Strain
?kl
equilibrium structure
re-optimize
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Approximate Virtual Crystal model
Replace Mg mass by the average cation mass of the
alloy
?(V) ?LS(V) ?HS(V)
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Procedure to obtain Cij(P,T,n)

• Compute CijLS(P,T) and CijHS(P,T)
• SLS(P,T) CLS(P,T)-1 and 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)

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Volume V(P,T,n(P,T)) for xFe 18.75
xFe 18.75
300K (exp.)
Experiments (Lin et al., Nature, 2005)
(xFe17, RT)
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Elastic Constants (xFe 18.75)
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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)
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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)
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Geophysical Implications
Geophysical Implications
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Elasticity Along Mantle Geotherm
1150 km
1580 km
Geotherm (Boehler, Rev. Geophys. 2000)
-15
6
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Wave Velocities Along Mantle Geotherm
1580 km
1150 km
-9
-15
6
3
Geotherm (Boehler, GRL,2000)
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Seismic Parameters (Mantle Geotherm)
Geotherm (Boehler, RG, 2000)
(Kara
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Wave Velocities Along Mantle Geotherm
1580 km
1150 km
-9
-15
6
3
Geotherm (Boehler, GRL,2000)
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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/(MgFe) ratio in the lower mantle should
  increase from pyrolitic values because of the
  spin transtions in ferropericlase and
  ferrosilicate perovskite

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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