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**First-Principles Study of Fe Spin Crossover in the Lower Mantle**

Dane Morgan, Amelia Bengtson Materials Science and Engineering University of Wisconsin – Madison Second VLab Workshop University of Minnesota August 5-10, 2007

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**Computational Materials Group University 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 Please stop by Amy’s poster!!

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**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

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**Fe and Spin Crossover in the Lower Mantle**

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**The Lower Mantle Largest continuous region of Earth (~50% mass/volume)**

Depth ≈ 660 – 2690 km T ≈ K P ≈ 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

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**Octahedral Fe2+ Spin State**

eg t2g High spin M = 4mB Majority Minority Exf EHund Intermediate spin M = 2mB Low spin M = 0mB

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**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

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**Spin State of Fe in the Lower Mantle: Perovskite**

X-ray emission spectra, perovskite (Mg0.92Fe0.09)Si1.00O3 (Mg0.87Fe0.09)(Si0.94Al0.10)O3 P = 2 GPa high spin P = 100 GPa intermediate spin Li, et al., PNAS ‘04

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**Spin State vs. Temperature: (Mg0.75,Fe0.25)O**

Lin, et al., Science TBP

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**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, …

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**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.)

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**First-Principles Modeling: Opportunities and Challenges**

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**First-Principles Calculations**

Composition and Structure (e.g., Mg0.75Fe0.25O) Quantum mechanics (+ approximations) Energies: Stability, Atomic Positions, … Electronic Structure: Spin state, Bands, … Additional modeling for T>0, optical properties, …

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**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

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**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

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**Calculating Spin-Transitions**

HS LS V E VHS VLS P DH=HHS–HLS PT

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**First-Principles Prediction – (Mg,Fe)O**

CFe = 19%, Theory, 2006 CFe = 25%, Expt, 2007 Tsuchiya, et al., Phys. Rev. Lett. ‘06 Lin, et al., Science TBP

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**First-Principles Fe-Spin Results**

(apologies to those I missed!) 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)

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**Challenges for First-Principles and Spin Effects**

Why so much spread in calculation?

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**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

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**Exchange-correlation effects**

Spin Transition Calculations Sensitivity: Calculation Parameters - (Mg0.75Fe0.25)SiO3 PT 200 GPa GGA GGA-PW (Perdew, et al. PRB ’92) 150 GPa GGA-PBE (Perdew, et al. PRL ’97) Exchange-correlation effects 100 GPa LDA Sensitivity to calculation method - which is best?

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**Spin Transition Calculations Sensitivity: Materials Parameters - (Mg0**

Spin Transition Calculations Sensitivity: Materials Parameters - (Mg0.75Fe0.25)SiO3 PT 200 GPa dFe-Fe = 4.98 Ǻ Fe2+ 170 GPa dFe-Fe = 3.38 Ǻ GGA-PBE (Perdew, et al. PRL ’97) Fe local order Valence effect Al local order 140 GPa Fe3+ + Al Sensitivity to valence/configurations – need to compare like configurations

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**Structural relaxations**

Spin Transition Calculations Sensitivity: Materials Parameters - FeSiO3 PT 900 GPa Cubic symmetry (Cohen, et al. Science ’92) 240 GPa MgSiO3 symmetry (Stackhouse, et al. EPSL ’07) Structural relaxations 77 GPa No symmetry (Bengtson, et al. Submitted) Sensitivity to structural relaxations – need to compare identical structures

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**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!

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**Summary of First-Principles Challenges**

Comparing calculations: Equivalent materials systems and calculation parameters Comparing experiments: Equivalent materials systems and best calculation parameters Still learning!

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**First-Principles study of Fe Spin Crossover**

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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?

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**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

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**Ferropericlase Strong composition -spin crossover coupling**

Persson, et al., GRL ‘06 Strong composition -spin crossover coupling What drives the crossover? What drives composition effect?

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**Ferropericlase: What Drives the Crossover?**

Spin crossover (T=0) when DH = EHS-ELS + P(VHS-VLS) = 0 P∆V ∆E DE does not go to zero! PDV term is the most important driver of the transition! Both DE, PDV terms drive up crossover pressure with Fe content Effect of chemical pressure?

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**Understanding PT vs. CFe Trend Chemical Pressure**

▲Volume (P=100GPa) HS LS P=0: R(Fe-HS)>R(Mg)≈R(Fe-LS) Mg compresses Fe-HS HS less stable PT↓ Mg does not expand Fe-LS LS unaffected PT↔ Increasing Mg pushes PT↓

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**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

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**Bengtson, et al., EPSL, submitted ‘07**

Perovskite Bengtson, et al., EPSL, submitted ‘07 Strong composition -spin crossover coupling, opposite ferropericlase! What drives the crossover? What drives composition effect?

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**Perovskite: What Drives the Crossover?**

PDV still very important in transition DE terms drive down crossover pressure with Fe content Changes in DE due to structural relaxations (crossover pressure = ~900 GPa w/o relaxation!) P∆V ∆E

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**Crossover Pressure vs. Fe Composition Strong Structural Coupling**

Ferropericlase Perovskite Transitions driven significantly by PDV terms Opposite trends due to structural relaxation in perovskite

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Conclusions Ferropericlase Perovskite 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 (PDV) makes a major contribution to the spin crossover energetics. P∆V ∆E

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**Acknowledgements Additional collaborators: Jie Li (UIUC)**

Funding: Wisconsin Alumni Research Foundation (WARF)

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End

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**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

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**A Multiscale Alloy Theory Approach**

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**Multiscale Alloy Theory Approach**

First-Principles Energetics Thermodynamic Modeling CALPHAD Phase stability, Fe partitioning, Fe spin states, Densities, …

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**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

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**Fe – Mg Interaction vs. Spin State: Perovskite**

Tc(100GPa)≈900K Tc(100GPa)≈4500K Low Spin High Spin 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

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**First-Principles study of Fe Spin Crossover T>0**

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**First-Principles Model for Ferropericlase**

MgO FeO-HS FeO-LS 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

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**Free Energy Model First-principles First-principles 1 2 3**

S. H. Wei, et al., Phys. Rev. B, '90 A. van de Walle and G. Ceder, Reviews of Modern Physics, '02 G. R. Burns, Minerological Applications of Crystal Field Theory, '93

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**Fitting The Free Energy**

Fit and interpolate Analytic 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

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**Fitting The Free Energy**

MgO Fitting grid for B1 (NaCl) Mixed spin data uncertain so assume no Fe-HS – Fe-LS interaction FeO-HS FeO-LS MgO Fitting grid for iB8 (i-NiAs) Ab initio almost no LS Ab initio almost no Mg solubility Easy to fit! FeO-HS FeO-LS

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**Phase Diagram HS CFe-HS/CFe Depth (km) B1 mixed spin iB8 HS 2-phase LS**

700 4000 Depth (km) CFe 0-MgO 1-FeO 2-phase iB8 HS B1 mixed spin HS LS 1800 2900 0.25 0.75 P≈140GPa P≈30GPa CFe-HS/CFe

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**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, CompuTherm

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**First Ab Initio CALPHAD Lower Mantle Result**

P=50 Gpa P=100 Gpa First steps completed More accurate expressions and fitting to experiment needed

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**Please see Amy Bengtson’s poster!**

Conclusions Ferropericlase Perovskite 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) 700 4000 Depth (km) CFe 2-phase iB8 HS B1 mixed spin HS LS 1800 2900 0.25 0.75 0-MgO 1-FeO Please see Amy Bengtson’s poster!

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**All couple together – “Perfect storm” alloy**

(Fe,Mg)O Very Complex … (Mg,Fe)O phase stability Structural changes (B1, NiAs) Jahn-Teller distortions Magnetic order Mg-Fe composition Metal-insulator transition Spin transition Point defects (vacancies, Fe3+) P,T B1: Cubic paramagnetic NiAs rB1: rhomb antiferromagnetic Lin, et al., PNAS '03 All couple together – “Perfect storm” alloy

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DOS from Ab Initio

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**The Thermodynamic Terms**

DF to flip a spin = FHS – FLS = – EHund + Exf + P(VHS-VLS) – TDSconf+ DFmag + DFvib + DFelec LS more stable Exf E P(VHS-VLS) DF –TDSconf P (GPa) DFvib HSLS DFelec DFmag HS more stable –EHund Pressure drives HS → LS (volume and crystal field effects) Temperature effects all stabilize HS or increase mixing

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**First-Principles Spin Transition Calculations**

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 K18 0 Persson - Private communication 1 Cohen, et al. Science '97 2 Gramsch, et al. Am. Min. '03 3 Fang, et al. Phys Rev B '99 4 Badro, et al. Phys Rev Lett '99 5 Milner, et al. ‘04 6 Kondo, et al. J App Phys '00 7 Guo, et al. Phys. Cond. Matt. '02 8 Feng and Harrison, Phys Rev B '04 9 Eto, et al. Phys. Rev. B '00 10 Parlinski, Eur Phys J B '02 11 Sarkisyan, et al. JETP Lett. '02 12 Rohrbach, et al. J Phys C '03 13 Chattopadhyay, et al. J. Phys. Chem. Solids '85; Physica '86 14 Dufek, et al. Phys. Rev. Lett. '95 15 Pasternak, et al. Phys. Rev. Lett. '95 16 Rueff, et al. Phys. Rev. Lett. '99 19 Nekrasov et al. Phys. Rev. B ’03 20 Yan, et al. Phys. Rev. B ’04

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**Understanding PT vs. CFe Trend The Mg Compression Argument**

▲Volume (P=0GPa) HS LS P=0: R(Fe-HS)>R(Mg)>R(Fe-LS) Mg compresses Fe-HS HS less stable PT ↓ Mg expands Fe-LS LS less stable PT ↑ Affect on PT unclear?

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**Spin Transition Calculations Sensitivity: (Mg,Fe)SiO3**

PT CFe = 12.5% CFe = 25% 200 Gpa dFe-Fe = 4.98 Ǻ Make this cofig , Fe2+-Fe , And summarize 170 Gpa dFe-Fe = 3.38 Ǻ GGA-PW (Perdew, et al. PRB ’92) Local order 140 Gpa GGA-PBE (Perdew, et al. PRL ’97) Exchange-correlation parametrization

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