Spin crossovers in iron bearing mantle minerals

Renata WentzcovitchApplied Physics and Applied Mathematics

Lamont Doherty Earth ObservatoryColumbia University

Electronic Structure 2017Princeton, NJ, USA

Spin crossovers in iron bearing mantle minerals

Earth’s lower mantle

(Mg1-yFey)(Si1-xFex)O3perovskite

(Mg1-xFex)O ferropericlase

+

Lower Mantle: Ferrosilicate perovskite + ferropericlase Low iron concentration (x~0.1) High-temperatures and high pressures

Pressure induced spin “transition” in (Mg,Fe)O and (Mg,Fe)SiO3

2003

2004

• Spin crossovers

• Thermodynamics model of a spin crossover: (Mg,Fe)O

• (Mg,Fe)SiO3 (it is not what it seems…)

• Spin crossover in (Mg,Fe)(Si,Fe)O3 and (Mg,Fe)(Si,Al)O3

• Some geophysical consequences•• The BIG PICTURE

• Acknowledgments

Outline

DFT+U with ab initio U

DFT+U (Cococcioni and de Gironcoli, 2005)

Self-consistent Usc (Kulik, Cococcioni, Sherlis, Marzari, 2006)

Density Functional Perturbation Theory + U for phonons (Floris, de Gironcoli, Gross, Cococcioni, 2011)

Quantum ESPRESSO

QHA to compute vibrational free energy

Wien2K to compute Mössbauer QS

Methods

d-electrons in crystal fieldMm+→ [core] 3dn

EC EX

S=2High Spin

(HS)

S=1Intermediate

Spin(IS)

S=0Low Spin(LS)

Fe2+ 3d6

Pressure

Spin transition (or crossover)

d-electrons in crystal fieldMm+→ [core] 3dn

EC EX

S=2High Spin

(HS)

S=1Intermediate

Spin(IS)

S=0Low Spin(LS)

Fe2+ 3d6

Pressure

Spin transition (or crossover)

Ferropericlase

Fe

Fe

FeO

O O

O

O

O

O

O O

O

O

O

O

O O

O

O

O

ρel around Fe2+ (Isosurface:ρel=0.3 e/Å3)

A. HS Maj C. LS Maj

B. HS Min+1%

+2%

-1%

-1%

-2%

-3%

∆Voct~-8%

Tsuchiya, PRL (2006)

HS-to-LS “transition”

PT = 32±3 GPa

0 50 100

-20

0

20

40

P (GPa)

∆H=H

LS-H

HS

(kJ/

mol

) 3.125% 12.5% 18.75%

Static

Tsuchiya, de Gironcoli, and Wentzcovitch, PRL (2006)

HS-to-LS “transition”

Pexp = 45-60 GPa

0 50 100

-20

0

20

40

P (GPa)

∆H=H

LS-H

HS

(kJ/

mol

) 3.125% 12.5% 18.75%

Static

Tsuchiya, de Gironcoli, and Wentzcovitch, PRL (2006)

XFe=18.75% (6 irons in supercell)Static

Pc does not depend on HS/LS fraction

0 50 100

-20

-10

0

10

20

30

P (GPa)

∆H

(kJ/

mol

)

6FeHS 0FeLS

4FeHS 2FeLS

2FeHS 4FeLS

0FeHS 6FeLS

0 50 100

-20

-10

P (GPa)

∆

B

C0 20 40 60 80 100

8

9

10

11

12V

(cm

3 /mol

)

P (GPa)

n=0 n=1/3 n=2/3 n=1

Exp. (Lin et al., 2005)

XFe=18.75%

∆V ~-4.2%

∆VHS-LS = -2.22 nXFe cm3/mol

XFe=17%

Static equation of staten=nLS/(nLS+nHS)

Tsuchiya et al., PRL (2006)

Thermodynamics

n = nLS/(nHS+nLS)

G = (1-n)GHS + nGLS + Gmix

Ideal solid solution of HS and LS ferropericlase(xFe = cte)

n = nLS/(nHS+nLS)

G = (1-n)GHS + nGLS + Gmix

GHS/LS = FHS/LS + PVHS/LS

GHS/LS = FHS/LS(stat+vib) + FHS/LS

el + PVHS/LS

FHS/LSel = - TSHS/LS

el

Gmix = - TSideal

Ideal solid solution of HS and LS ferropericlase(xFe = cte)

Free energy minimization

1( , )1 (2 1)exp

st vibHS LS

Fe B

n P TGm S

X k T

+−

= ∆

+ +

Vibrational Virtual Crystal Model

● Replace Mg mass by the average cation mass of the alloy

● Replace “some” inter-atomic force constants of MgO to reproduce the that the static elastic constants of the alloy

Wu et al, PRB (2009)

Exp

LS fraction n(P,T)

XFe=18.75%

(Wentzcovitch et al., PNAS, 2009)

x = 0.17 Lin et al., Science (2007)

Exp

LS fraction n(P,T)

XFe=18.75%

x = 0.17 Lin et al., Science (2007)

Free energy shift (EHS – ELS = - 0.06 eV/Fe):

Lin et al., Science (2007) x=0.17■ Komabayashi et al., EPSL (2010) x=0.10

HS

LS

+ Experiments (Lin et al., Nature, 2005) (xFe=17%)o and Δ (Fei et al., GRL, 2007) (xFe=20%)

Volume V(P,T,n(P,T)) for xFe= 18.75%

+ 300K (exp.)xFe= 18.75%

+ 300K (exp.)

Experiments (o xFe=0 and += 40%)

Thermodynamics properties xFe= 18.75%

300K (exp.)

Wu et al, PRB 2009

Elastic anomalies in Mg1-xFexO

Impulsive stimulated scattering: softening of C11, C12, and C44(Crowhurst et al., 2008, )

Brillouin scattering: softening of C11 and C12, but not C44(Marquardt et al., 2009, )

Inelastic X-ray scattering: softening of C44 and C12, but not C11(Antonangelli et al., 2011, )

High temperature elasticity

( , , ) ( , ) (1 ) ( , )LS HSV P T n nV P T n V P T= + −

Compressibility:

1( ) ( ) (1 ) ( )9

LS HSij ij LS ij HS ij LS HS

T

nS n V n nS V n S V V VP

α ∂= + − − −

∂

Compliances:

11 12 1α α= = 44 0α =

THSLS

HS

HS

LS

LS

PnVV

KVn

KVn

nKnV

∂∂

−−−+= )()1()()(

(Wentzcovitch et al., PNAS 2009; Wu, Justo, and Wentzcovitch, PRL 2013)

High Tempearature Elastic Tensor(2000-)

T = 300 KP = 0 GPa

KS

G

VP

VS

Vφ

34S

P

K GV

ρ

+=

SGVρ

=

SKVφ ρ=

T = 300 K

Wu, Justo, Wentzcovitch, PRL 2013

Elastic anomalies in ferropericlase - I

Spin Crossovers in bridgmanite

(Fe+2) (Fe+3)

• At 0 GPa: HS state with QS = 2.4 mm/sec

•“New” Fe2+ (QS = 3.5 mm/s) for P > 30 GPa

• Fe2+ QS = 3.5 mm/s increases at the expense of the HS Fe2+

(QS = 2.4 mm/s)

• The two sets of peaks merge at P ~ 60 GPa

McCammon et al. Nature Geoscience (2008)

“New” species of Fe2+: IS?

HS and LS configurations at 0 GPa

Hsu, Umemoto, Blaha, and Wentzcovitch, EPSL 2009

xFe = 0.25 and 0.125

Effect of EXC and Hubbard U

24 GPa 15 GPa

4 GPa7 GPa

QS = 2.4 mm/s QS = 3.5 mm/s

• (Mg0.875Fe0.125)SiO3

• QS improved by U

• No spin crossover

Hsu et al., EPSL 2009

Spin Crossover in Perovskite

(Fe+3)Hsu, Blaha, Cococcioni, and Wentzcovitch (PRL 2011)

Spin Crossover in Post-Perovskite

(Fe+2) (Fe+3)Yu, Hsu, Cococcioni, and Wentzcovitch (EPSL 2012)

Spin crossover in aluminous Pv and PPv

(Fe+2) (Fe+3)Al

Fe

Hsu, Yu, and Wentzcovitch (EPSL 2012)

Consequences for Mantle Structure

S1

S2

P

Body wave (acoustic) velocities

● Longitudinal waves (P-waves)(compressive waves)

●Transverse waves (S-waves)(shear waves)

ρ

GKVP

34

+=

VS =Gρ

K and G from Voigt-Reuss-Hill boundsρϕKV =

Making sense of mantle heterogeneities(Seismic Tomography)

δVS

+

Mineral sequence II

Lower Mantle

(Mgx,Fe(1-x))O(Mg(1-x-z),Fex, Alz)(Si(1-y),Aly)O3

+

CaSiO3

Elastic anomalies in ferropericlase - IIWu and Wentzcovitch, PNAS 2014

P = 75 GPa

Mg0.88Fe0.12OMg0.79Fe0.21O

34S

P

K GV

ρ

+= S

GVρ

=

Lower mantle aggregateWu and Wentzcovitch, PNAS 2014

P = 75 GPa

78% Mg0.91Fe0.09)SiO3 (MgPv) + 7% CaSiO3 + 15% Mg0.88Fe0.12O

78% Mg0.91Fe0.09)SiO3 (MgPv) + 7% CaSiO3 + 15% Mg0.79Fe0.21O

Predicted effectWu and Wentzcovitch, PNAS 2014

Slow (hot) anomaly (plume) with spin crossover

VS VP

1500 km

2000 km

Potential seismic signatures of spin crossover Wu and Wentzcovitch, PNAS 2014

Zhao, Gondwana Res. 2007 P-models

Potential seismic signatures of spin crossover Wu and Wentzcovitch, PNAS 2014

Zhao, Gondwana Res. 2007 P-models

Potential seismic signatures of spin crossover Wu and Wentzcovitch, PNAS 2014

Zhao, Gondwana Res. 2007 P-models

Geodynamic/seismological analysis of global models

Simultaneous analyses of 2 global P-models and 3 global S-modelsBoschi, Becker, Steinberger, G3, 2007

ρ,α,Cp,μ,κ

ρ,Vs,Vp,Rs/p,…

Consistent w/experimental data

The Big Picture

Some Challenges

• ANHARMONIC EFFECTS: temperature dependent phonon frequencies, thermal conductivity, anharmonicfree energy, pre-melting behavior, etc…

• SEARCH FOR new phases, particularly with high iron content

• MULTI-PHASE EQUILIBRIUM: address co-existing complex solid solutions (more accurate free energies).

Acknowledgments

• Koichiro Umemoto (UMN, ELSI)• Matteo Cococcioni (UMN, EPFL, Lausanne)• Stefano de Gironcoli (SISSA, Trieste)• Gaurav Shukla (UMN)• João F. Justo (USP, São Paulo, Brazil)• Zhongqing Wu (USTC, Hefei)• Taku and Jun Tsuchiya (Ehime, Japan)• Peter Blaha (Vienna, Austria)• Maribel Núnez-Valdéz (Potsdam, Germany)• Yonggang Yu (NOAA, USA)• Pedro da Silveira (UMN, Digital River, Minneapolis)