first-principles study of fe spin crossover in the lower mantle
Post on 11-Jan-2016
38 Views
Preview:
DESCRIPTION
TRANSCRIPT
First-Principles Study of Fe Spin Crossover in the Lower Mantle
Dane Morgan, Amelia BengtsonMaterials Science and EngineeringUniversity of Wisconsin – Madison
Second VLab WorkshopUniversity of Minnesota
August 5-10, 2007
Computational Materials GroupUniversity of Wisconsin - Madison
Faculty− Dane Morgan− Izabela Szlufarska
Graduate Students− Amelia (Amy) Bengtson− Edward (Ted) Holby− Trenton Kirchdoefer− Yueh-Lin Lee− Yun Liu− Yifei Mo− Julie Tucker− Marcin Wojdyr− Benjamin (Ben) Swoboda
Undergraduates− Paul Kamenski
http://matmodel.engr.wisc.edu/
Please stop by Amy’s poster!!
Outline
Fe and Spin Crossover in the Lower Mantle
First-Principles Modeling: Opportunities and Challenges
First-Principles study of Fe Spin Crossover
− Composition effects
− Volumes effects
− Structural effect: Ferropericlase vs. perovskite
Fe and Spin Crossover in the Lower Mantle
The Lower Mantle
Largest continuous region of Earth (~50% mass/volume)
Depth ≈ 660 – 2690 km T ≈ 2000-4000 K P ≈ 25-135 GPa Made of
− (Mg,Fe,Al)(Si,Al)O3 perovskite (62%)
− (Mg,Fe)O ferropericlase (rocksalt) (33%)− (Mg,Fe)(Si,?)O3 post-perovskite (>125
Gpa) Murakami, et al., Science ‘04
− cFe/(cMg+cFe) ~ 0.2
− CaSiO3 (5%)
− Impurities (~0%) Jackson and Ridgden '98 Duffy, Nature ‘04
Octahedral Fe2+ Spin State
Intermediate spinM = 2B
Low spinM = 0B
eg
t2g
High spinM = 4B
Majority
Minority
Exf
EHund
Spin State of Fe in the Lower Mantle: Ferropericlase
X-ray emission spectra, Mg0.83Fe0.17O
P = 0 GPa high spin
P = 75 GPa low spin
Badro, et al., Science ‘03
Spin State of Fe in the Lower Mantle: Perovskite
X-ray emission spectra, perovskite
(Mg0.87Fe0.09)(Si0.94Al0.10)O3(Mg0.92Fe0.09)Si1.00O3
P = 2 GPa high spin
P = 100 GPa intermediate spin
Li, et al., PNAS ‘04
Spin State vs. Temperature: (Mg0.75,Fe0.25)O
Lin, et al., Science TBP
High vs. Low Spin - Does it Matter? YES!
Density: RHS = 0.78Å, RLS = 0.61Å (~25% change!) (Shannon, Acta Cryst. A ’76)
Composition: changes in spin could dramatically change Fe partitioning
Phase stability: spin transitions could couple to phase stability
Thermal transport: Optical absorption change change in radiative heat transfer properties
Thermoelasticity: Elastic constants could be very different – unknown at present
Kinetics, …
Fe spin in the Lower Mantle: Questions
How does spin state depend on− Pressure− Temperature− Composition− Local chemical order (Mg vs. Fe, Al neighbors)− Structure (rocksalt, iB8, perovskite, post-perovskite)− Fe valence (2+ vs. 3+)− Fe site occupancy (A, B site in perovskite)
How does the spin state impact− Fe partitioning− Lower mantle phase stability− Thermophysical properties (density, mechanical properties, heat
transport, etc.)
First-Principles Modeling: Opportunities and Challenges
Composition and Structure(e.g., Mg0.75Fe0.25O)
• Energies: Stability, Atomic Positions, …• Electronic Structure: Spin state, Bands, …• Additional modeling for T>0, optical properties, …
Quantum mechanics
(+ approximations)
First-Principles Calculations
First-Principles Approach
Broad technique: Density Functional Theory Exchange correlation: LDA, GGA, LDA+U, GGA+U
approaches Pseudopotentials: Ultrasoft pseudopotentials, Projector
Augmented Wave Method Relaxation: Full relaxation with symmetry perturbed
structures Numerics: meV/atom accuracy convergence of relative
energies with respect to kpoints and energy cutoff Disorder: Special Quasirandom Structures for
configurationally and magneticaly disordered cells (Wei, et al.,
PRB ‚90)
VASP code
Opportunities for First Principles and Spin Effects
How does spin state depend on− Pressure− Temperature− Fe composition− Structure (rocksalt, iB8, perovskite, post-
perovskite)− Fe valence (2+ vs. 3+)− Fe site occupancy (A, B site in perovskite)− Local chemical order (Mg vs. Fe, Al
neighbors) How does the spin state impact
− Fe partitioning− Lower mantle phase stability− Thermophysical properties (density,
mechanical properties, heat transport, etc.)
Can be obtained from first-principles or first-principles + modeling
Calculating Spin-Transitions
HSLS
V
E
VHS VLS
P
H=HHS–HLS
HS
LS
PT
First-Principles Prediction – (Mg,Fe)O
Lin, et al., Science TBPTsuchiya, et al., Phys. Rev. Lett. ‘06
CFe = 19%, Theory, 2006 CFe = 25%, Expt, 2007
First-Principles Fe-Spin Results
Spin state− HS state for iB8 in lower mantle (Persson, et al., Geo. Res. Lett. ‘06)− HS state for post-perovskite in lower mantle (Zang and Oganov, EPSL ’06,
Stackhouse, et al., Geo. Res. Lett. ‘06) − LS state for B-site Fe in perovskite in lower mantle (Cohen, et al., Science ‘97)
Crossover trends with composition, local order, valence, temperature− Increasing crossover pressure with increasing Fe content for (Mg,Fe)O (Persson,
et al., Geo. Res. Lett. ‘06)− Decreasing crossover pressure with increasing Fe content for (Mg,Fe)SiO3
(Bengtson, et al., Submitted)− Increasing crossover pressure for Fe3+ vs. Fe2+ (Li, et al., Geo. Res. Lett. ’05)− Increasing crossover pressure with increasing temperature (Tsuchiya, et al.,
Phys. Rev. Lett. ‘06)− Decreasing crossover pressure from local Fe neighbors in perovskite
(Stackhouse, et al., Geo. Res. Lett. ‘06)− Decreasing of crossover pressure with local Al neighbors in perovskite (Li, et al.,
Geo. Res. Lett. ’05) Spin effects
− Changes in optical properties (Tsuchiya, et al., Phys. Rev. Lett. ‘06)− Changes in volume, elastic constants (Persson, et al., Geo. Res. Lett. ‘06)
(apologies to those I missed!)
Challenges for First-Principles and Spin Effects
Why so much spread in
calculation?
Challenges for First-Principles and Spin Effects
Accuracy of calculation parameters− Exchange-correlation type: LDA/GGA− Exchange-correlation parametrization: PW, PBE, …− Correlated electron corrections: LDA/GGA+U− Pseudopotentials: All electron, Ultrasoft, PAW, …
Correct materials system parameters− Composition: global and local chemical order− Valence− Site occupancy− Temperature− Structural relaxation− Magnetism
Spin Transition Calculations Sensitivity: Calculation Parameters - (Mg0.75Fe0.25)SiO3
PT
200 GPa
150 GPa
100 GPa
GGA
GGA-PW (Perdew, et al. PRB ’92)
GGA-PBE (Perdew, et al. PRL ’97)
Exchange-correlation effects
LDA
Sensitivity to calculation method - which is best?
Spin Transition Calculations Sensitivity: Materials Parameters - (Mg0.75Fe0.25)SiO3
PT
200 GPa
170 GPa
140 GPa
dFe-Fe = 4.98 Ǻ
dFe-Fe = 3.38 Ǻ
Fe2+
GGA-PBE (Perdew, et al. PRL ’97)
Fe local order Valence effectAl local order
Fe3+ + Al
Sensitivity to valence/configurations – need to compare like configurations
Spin Transition Calculations Sensitivity: Materials Parameters - FeSiO3
PT
900 GPa
240 GPa
77 GPa
Cubic symmetry(Cohen, et al. Science ’92)
MgSiO3 symmetry(Stackhouse, et al. EPSL ’07)
No symmetry(Bengtson, et al. Submitted)
Structural relaxations
Sensitivity to structural relaxations – need to compare identical structures
Scale of Different Sensitivities
Calculation parameters− Exchange correlation type (LDA/GGA) ~100 GPa
− Exchange correlation parametrization ~30 GPa
− Pseudopotential choice ~30 GPa
− Correlation corrections (LDA+U) ~50 GPa
Materials system parameters− Structural relaxation ~1000 GPa
− Compositions ~100 GPa
− Local chemical ordering ~30 GPa
− Valence (Fe2+ vs. Fe3+) ~30 GPa
− Magnetic ordering ~30 GPa
Sensitivities ≠ Errors!Need good choices!
Summary of First-Principles Challenges
Comparing calculations: Equivalent materials systems and calculation parameters
Comparing experiments: Equivalent materials systems and best calculation parameters
Still learning!
First-Principles study of Fe Spin Crossover
Our Questions
What is the composition dependence of the spin crossover?
What drives the crossover – electronic vs. volume changes?
What differences might exist between ferropericlase (rocksalt) and perovskite structures?
Ferropericlase (Rocksalt)
(Mg,Fe)O Rocksalt structure
Fe octahedrally coordinated
Mg-Fe pseudobinary alloy on metal FCC sublattice
Generally assumed to be single disordered phase under lower mantle conditions
Ferropericlase
Strong composition -spin crossover coupling
What drives the crossover?
What drives composition effect?
Persson, et al., GRL ‘06
Ferropericlase: What Drives the Crossover?
E does not go to zero!
PV term is the most important driver of the transition!
Both E, PV terms drive up crossover pressure with Fe content
Effect of chemical pressure?
P∆V
∆E
Spin crossover (T=0) when H = EHS-ELS + P(VHS-VLS) = 0
Understanding PT vs. CFe TrendChemical Pressure
0
40
80
120
160
200
0 0.2 0.4 0.6 0.8 1Fe Concentration
Pressure (GPa)
6.8
7
7.2
7.4
7.6
7.8
Volume (A
3 /atom)
PT
▲Volume (P=100GPa)HS
LS
Mg compresses Fe-HS HS less stable PT↓ Mg does not expand Fe-LS LS unaffected PT↔ Increasing Mg pushes PT↓
P=0: R(Fe-HS)>R(Mg)≈R(Fe-LS)
Perovskite
(Mg,Fe)(Si)O3 perovskite structure
Fe in pseudocubic environment
Mg-Fe pseudobinary alloy on metal cubic sublattice
Generally assumed to be single disordered phase under lower mantle conditions for low Fe content, unstable for high Fe content
Perovskite
Bengtson, et al., EPSL, submitted ‘07
Strong composition -spin crossover coupling, opposite ferropericlase!
What drives the crossover?
What drives composition effect?
Perovskite: What Drives the Crossover?
P∆V
∆E
PV still very important in transition
E terms drive down crossover pressure with Fe content
Changes in E due to structural relaxations (crossover pressure = ~900 GPa w/o relaxation!)
Crossover Pressure vs. Fe Composition Strong Structural Coupling
Transitions driven significantly by PV terms Opposite trends due to structural relaxation in perovskite
Ferropericlase
Perovskite
Conclusions
Wide range of spin crossover values possible with different calculation and system choices.
Spin crossover trends with composition are opposite in ferropericlase and perovskite.
Volume contraction (PV) makes a major contribution to the spin crossover energetics.
Ferropericlase
Perovskite
P∆V
∆E
Acknowledgements
Additional collaborators: Jie Li (UIUC)
Funding: Wisconsin Alumni Research Foundation (WARF)
End
Ferropericlase (Rocksalt)
(Mg,Fe)O Rocksalt structure Fe octahedrally coordinated Mg-Fe pseudobinary alloy on metal FCC
sublattice Phase stability: High T,P experiments
ambiguous:− Mg0.5Fe0.5O, Mg0.6Fe0.4O, Mg0.8Fe0.2O:
Phase separation (Dubrovinsky, et al., '00,'01,’05)
− Mg0.6Fe0.4O: No separation (Vissiliou and Ahrens,
Geophys. Res. Lett. ’82)
− Mg0.25Fe0.75O, Mg0.39Fe0.61O: No separation (Lin, et al., PNAS '03)
− Often assumed to be single disordered phase under lower mantle conditions for most compositions
A Multiscale Alloy Theory Approach
Multiscale Alloy Theory Approach
First-Principles Energetics
( ) 0, ,{ } T conf mag vib elecF P T c U PV F F F F== + + + + +
ThermodynamicModeling
Phase stability, Fe partitioning,Fe spin states, Densities, …
CALPHAD
Multiscale Alloy Theory Approach - What is Needed?
Identifying key interactions (T=0, P>0)
− Spin state vs. structure (rocksalt vs. perovskite)
− Spin state vs. Fe composition
− Fe – Mg interaction vs. spin state
− Fe spin state vs. valence (Fe2+ vs. Fe3+)
Thermodynamic models (T>0) Phase stability studies + integration with
experimental data
Fe – Mg Interaction vs. Spin State: Perovskite
Fe(low spin)-Mg alloy could be below miscibility gap in lower mantle Possible Fe solubility constraints, even for cFe/(cMg+cFe) ~ 0.1 Possibly strong clustering short-range-order
Tc(100GPa)≈900K Tc(100GPa)≈4500K
Low SpinHigh Spin
First-Principles study of Fe Spin Crossover T>0
First-Principles Model for Ferropericlase
Treat system as a ternary alloy – {c} = cMg, cFe-HS, cFe-LS
Consider only solid solution phases on B1 (NaCl) and iB8 (inverse-NiAs) (Fang, et al., Phys Rev. Lett. ’98)
Use first-principles based model to get F(P,T,{c}) and construct a phase diagram
MgO
FeO-HS FeO-LS
Free Energy Model
( )( )
( )( )1 21 3 1 3
First-Principles energies, SQS to simulate disorder
ln ln ln ln
ln 5
3-3 4 3 log ; 0.617
4
dis
conf Mg Mg Fe Fe Fe Fe HS Fe HS Fe LS Fe LS
mag Fe HS
vib D DB
ele
U
TS kT c c c c c c c c c
F c kT
h BF kT T T T
k M
F
π
− − − −
−
=
′ ′ ′ ′⎡ ⎤− = + + +⎣ ⎦= −
⎛ ⎞Ω⎛ ⎞= + = ⎜ ⎟⎜ ⎟
⎝ ⎠ ⎝ ⎠
( ) 2gln 3 (3 degenerate t states)c Fe HSc kT−= −
1. S. H. Wei, et al., Phys. Rev. B, '902. A. van de Walle and G. Ceder, Reviews of Modern Physics, '023. G. R. Burns, Minerological Applications of Crystal Field Theory, '93
First-principles
First-principles
Fitting The Free Energy
AnalyticFit and interpolate
MgO
FeO-HS FeO-LS
Set grid of fitting points in V, {c} space
Fit Udis(V) to Birch-Murnaghan equation of state
F to polynomial in {c} at a given P, T
i i ij i j ijk i j ki i j i j k
F Fc F c c F c c c≠ ≠ ≠
= + +∑ ∑ ∑
( ), ,{ } dis vib conf mag elecF P T c U PV F TS F F= + + − + +
Fitting The Free Energy
Fitting grid for B1 (NaCl)− Mixed spin data uncertain
so assume no Fe-HS – Fe-LS interaction
Fitting grid for iB8 (i-NiAs)− Ab initio almost no LS− Ab initio almost no Mg
solubility Easy to fit!
MgO
FeO-HS FeO-LS
MgO
FeO-HS FeO-LS
Phase DiagramC
Fe-H
S /CF
e
700
4000
Dep
th (
km)
CFe0-MgO 1-FeO
2-phase
iB8 HSB1 mixed spin
HS
LS
1800
2900
0.25 0.75
P≈140GPa
P≈30GPa
Development of CALPHAD Approach
Established collaboration with CompuTherm LLC− Makers of Pandat phase diagram software− Developing module to integrate our free energy functions into their
phase diagram solvers− Will allow far more complex phase diagram calculations, automated
free energy model optimization from experimental and theory data
I II III
Courtesy of Ying Yang, CompuThermhttp://www.computherm.com/pandat.html
First Ab Initio CALPHAD Lower Mantle Result
T[K]
x(FEO)
0
950
1900
2850
3800
0.0 0.2 0.4 0.6 0.8 1.0
x(FEO)
T[K]
MGO FEO
RS
iB8
iB8
RS+iB8
0 0.2 0.4 0.6 0.8 10
950
1900
2850
3800
T[K]
x(FEO)
0
950
1900
2850
3800
0.0 0.2 0.4 0.6 0.8 1.0
x(FEO)
T[K]
MGO FEO
RS
RS+iB8iB8
RS+iB8
RS iB8
0 0.2 0.4 0.6 0.8 10
950
1900
2850
3800
First steps completed More accurate expressions and fitting to experiment needed
P=50 Gpa P=100 Gpa
Conclusions
Identified key spin dependent interactions− Crossover pressure vs.
composition, structure
− Mg-Fe interaction vs. spin state
Constructed first-principles based thermodynamic model− Prediction of phase separation in
ferropericlase
Future challenges− Approach: LDA, GGA, +U, …
− Accuracy of models
− Full lower mantle thermodynamic model (multiphase, Fe2+/Fe3+, Al)
Ferropericlase
Perovskite
700
4000D
epth
(km
)
CFe
2-phase
iB8 HS
B1 mixed spin
HS
LS
1800
2900
0.25 0.750-MgO 1-FeO
Please see Amy Bengtson’s poster!
(Fe,Mg)O Very Complex …
Structural changes (B1, NiAs)
Jahn-Teller distortions Magnetic order Mg-Fe composition Metal-insulator
transition Spin transition Point defects
(vacancies, Fe3+) P,T
Lin, et al., PNAS '03
B1: Cubicparamagnetic
rB1: rhombantiferromagnetic
NiAs
(Mg,Fe)O phase stability
All couple together – “Perfect storm” alloy
DOS from Ab Initio
FeO AF rB1
-2
-2
-1
-1
0
1
1
2
2
-10 -5 0 5
E (eV)
States/cell
t2g spin-up
t2g spin-dn
eg spin-up
eg spin-dn
The Thermodynamic Terms
Pressure drives HS → LS (volume and crystal field effects)Temperature effects all stabilize HS or increase mixing
F to flip a spin = FHS – FLS =
– EHund + Exf + P(VHS-VLS) – TSconf+ Fmag + Fvib + Felec
P (GPa)0
–EHund
P(VHS-VLS)Exf
E F
HSLSFmag
Fvib
LS more stable
HS more stable
Felec
–TSconf
First-Principles Spin Transition Calculations
0 Persson - Private communication1 Cohen, et al. Science '972 Gramsch, et al. Am. Min. '033 Fang, et al. Phys Rev B '994 Badro, et al. Phys Rev Lett '995 Milner, et al. ‘046 Kondo, et al. J App Phys '007 Guo, et al. Phys. Cond. Matt. '028 Feng and Harrison, Phys Rev B '049 Eto, et al. Phys. Rev. B '0010 Parlinski, Eur Phys J B '0211 Sarkisyan, et al. JETP Lett. '0212 Rohrbach, et al. J Phys C '0313 Chattopadhyay, et al. J. Phys. Chem.
Solids '85; Physica '8614 Dufek, et al. Phys. Rev. Lett. '9515 Pasternak, et al. Phys. Rev. Lett. '9516 Rueff, et al. Phys. Rev. Lett. '9919 Nekrasov et al. Phys. Rev. B ’0320 Yan, et al. Phys. Rev. B ’04
System Ab Initio (GPa) Expt. (GPa)
FeO 200 (GGA)1
>250 (GGA+U)2,3
>1434
905
MnO 150 (GGA)1 906
CoO 90 (GGA)1 907
NiO 230 (GGA)1
>400 (GGA)8
>600 (B3LYP)8
>1419
FeBO3 23 (GGA)10
40 (GGA+U)0
4611
MnS2 0 (GGA)12
11 (GGA+U)12
1413
NiI2 25 (GGA) 14 19 (GGA) 15
FeS 6 (GGA+U)12 6.516
LaCoO3 140 K17 35-100 K18
0
40
80
120
160
200
0 0.2 0.4 0.6 0.8 1Fe Concentration
Pressure (GPa)
8.5
9
9.5
10
10.5
11
Volume (A
3 /atom)
Understanding PT vs. CFe TrendThe Mg Compression Argument
PT
▲Volume (P=0GPa)HS
LS
Mg compresses Fe-HS HS less stable PT ↓ Mg expands Fe-LS LS less stable PT ↑ Affect on PT unclear?
P=0: R(Fe-HS)>R(Mg)>R(Fe-LS)
Spin Transition Calculations Sensitivity: (Mg,Fe)SiO3
PT
200 Gpa
CFe = 12.5% CFe = 25%
170 Gpa
140 Gpa
dFe-Fe = 4.98 Ǻ
dFe-Fe = 3.38 Ǻ GGA-PW (Perdew, et al. PRB ’92)
GGA-PBE (Perdew, et al. PRL ’97)
Local order
Exchange-correlation parametrization
Make this cofig 210-170, Fe2+-Fe3+ 200-140, And summarize
top related