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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 http://matmodel.engr.wisc.edu/ 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 ≈ 2000-4000 K P ≈ 25-135 GPa Made of −(Mg,Fe,Al)(Si,Al)O 3 perovskite (62%) −(Mg,Fe)O ferropericlase (rocksalt) (33%) −(Mg,Fe)(Si,?)O 3 post-perovskite (>125 Gpa) Murakami, et al., Science ‘04 −c Fe /(c Mg +c Fe ) ~ 0.2 −CaSiO 3 (5%) −Impurities (~0%) Jackson and Ridgden '98 Duffy, Nature ‘04

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Octahedral Fe 2+ Spin State Intermediate spin M = 2 B Low spin M = 0 B egeg t 2g High spin M = 4 B Majority Minority E xf E Hund

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Spin State of Fe in the Lower Mantle: Ferropericlase X-ray emission spectra, Mg 0.83 Fe 0.17 O 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 (Mg 0.87 Fe 0.09 )(Si 0.94 Al 0.10 )O 3 (Mg 0.92 Fe 0.09 )Si 1.00 O 3 P = 2 GPa high spin P = 100 GPa intermediate spin Li, et al., PNAS ‘04

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Spin State vs. Temperature: (Mg 0.75,Fe 0.25 )O Lin, et al., Science TBP

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High vs. Low Spin - Does it Matter? YES! Density: R HS = 0.78Å, R LS = 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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Composition and Structure (e.g., Mg 0.75 Fe 0.25 O) Energies: Stability, Atomic Positions, … Electronic Structure: Spin state, Bands, … Additional modeling for T>0, optical properties, … Quantum mechanics (+ approximations) First-Principles Calculations

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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 V HS V LS P H=H HS –H LS HS LS PTPT

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First-Principles Prediction – (Mg,Fe)O Lin, et al., Science TBP Tsuchiya, et al., Phys. Rev. Lett. ‘06 C Fe = 19%, Theory, 2006 C Fe = 25%, Expt, 2007

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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)SiO 3 (Bengtson, et al., Submitted) −Increasing crossover pressure for Fe 3+ vs. Fe 2+ (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!)

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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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Spin Transition Calculations Sensitivity: Calculation Parameters - (Mg 0.75 Fe 0.25 )SiO 3 PTPT 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?

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Spin Transition Calculations Sensitivity: Materials Parameters - (Mg 0.75 Fe 0.25 )SiO 3 PTPT 200 GPa 170 GPa 140 GPa d Fe-Fe = 4.98 Ǻ d Fe-Fe = 3.38 Ǻ Fe 2+ GGA-PBE (Perdew, et al. PRL ’97) Fe local order Valence effect Al local order Fe 3+ + Al Sensitivity to valence/configurations – need to compare like configurations

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Spin Transition Calculations Sensitivity: Materials Parameters - FeSiO 3 PTPT 900 GPa 240 GPa 77 GPa Cubic symmetry (Cohen, et al. Science ’92) MgSiO 3 symmetry (Stackhouse, et al. EPSL ’07) No symmetry (Bengtson, et al. Submitted) Structural relaxations 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 (Fe 2+ vs. Fe 3+ ) ~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 What drives the crossover? What drives composition effect? Persson, et al., GRL ‘06

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Ferropericlase: What Drives the Crossover? E does not go to zero! P V term is the most important driver of the transition! Both E, P V terms drive up crossover pressure with Fe content Effect of chemical pressure? P∆V ∆E Spin crossover (T=0) when H = E HS -E LS + P(V HS -V LS ) = 0

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Understanding P T vs. C Fe Trend Chemical Pressure P T ▲Volume (P=100GPa) HS LS Mg compresses Fe-HS HS less stable P T ↓ Mg does not expand Fe-LS LS unaffected P T ↔ Increasing Mg pushes P T ↓ P=0: R(Fe-HS)>R(Mg)≈R(Fe-LS)

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Perovskite (Mg,Fe)(Si)O 3 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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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? P∆V ∆E P V 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!)

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Crossover Pressure vs. Fe Composition Strong Structural Coupling Transitions driven significantly by P V terms Opposite trends due to structural relaxation in perovskite Ferropericlase Perovskite

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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 (P V) makes a major contribution to the spin crossover energetics. Ferropericlase Perovskite 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: −Mg 0.5 Fe 0.5 O, Mg 0.6 Fe 0.4 O, Mg 0.8 Fe 0.2 O: Phase separation (Dubrovinsky, et al., '00,'01,’05) −Mg 0.6 Fe 0.4 O: No separation (Vissiliou and Ahrens, Geophys. Res. Lett. ’82) −Mg 0.25 Fe 0.75 O, Mg 0.39 Fe 0.61 O: 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 Phase stability, Fe partitioning, Fe spin states, Densities, … CALPHAD

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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 (Fe 2+ vs. Fe 3+ ) Thermodynamic models (T>0) Phase stability studies + integration with experimental data

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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 c Fe /(c Mg +c Fe ) ~ 0.1 Possibly strong clustering short-range-order T c (100GPa)≈900KT c (100GPa)≈4500K Low SpinHigh Spin

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First-Principles study of Fe Spin Crossover T>0

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First-Principles Model for Ferropericlase Treat system as a ternary alloy – {c} = c Mg, c Fe-HS, c Fe-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

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Free Energy Model 1. S. H. Wei, et al., Phys. Rev. B, '90 2. A. van de Walle and G. Ceder, Reviews of Modern Physics, '02 3. G. R. Burns, Minerological Applications of Crystal Field Theory, '93 First-principles

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Fitting The Free Energy AnalyticFit and interpolate MgO FeO-HS FeO-LS Set grid of fitting points in V, {c} space Fit U dis (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 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

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Phase Diagram C Fe-HS /C Fe 700 4000 Depth (km) C Fe 0-MgO1-FeO 2-phase iB8 HS B1 mixed spin HS LS 1800 2900 0.25 0.75 P≈140GPa P≈30GPa

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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 III III Courtesy of Ying Yang, CompuThermhttp://www.computherm.com/pandat.html

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First Ab Initio CALPHAD Lower Mantle Result First steps completed More accurate expressions and fitting to experiment needed P=50 Gpa P=100 Gpa

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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, Fe 2+ /Fe 3+, Al) Ferropericlase Perovskite 700 4000 Depth (km) C Fe 2-phase iB8 HS B1 mixed spin HS LS 1800 2900 0.25 0.75 0-MgO1-FeO Please see Amy Bengtson’s poster!

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(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, Fe 3+ ) P,T Lin, et al., PNAS '03 B1: Cubic paramagnetic rB1: rhomb antiferromagnetic NiAs (Mg,Fe)O phase stability All couple together – “Perfect storm” alloy

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DOS from Ab Initio

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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 = F HS – F LS = – E Hund + E xf + P(V HS -V LS ) – T S conf + F mag + F vib + F elec P (GPa) 0 –E Hund P(V HS -V LS ) E xf E FF HS LS F mag F vib LS more stable HS more stable F elec –T S conf

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First-Principles Spin Transition Calculations 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 SystemAb Initio (GPa)Expt. (GPa) FeO200 (GGA) 1 >250 (GGA+U) 2,3 >143 4 90 5 MnO150 (GGA) 1 90 6 CoO90 (GGA) 1 90 7 NiO230 (GGA) 1 >400 (GGA) 8 >600 (B3LYP) 8 >141 9 FeBO 3 23 (GGA) 10 40 (GGA+U) 0 46 11 MnS 2 0 (GGA) 12 11 (GGA+U) 12 14 13 NiI 2 25 (GGA) 14 19 (GGA) 15 FeS6 (GGA+U) 12 6.5 16 LaCoO 3 140 K 17 35-100 K 18

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Understanding P T vs. C Fe Trend The Mg Compression Argument P T ▲Volume (P=0GPa) HS LS Mg compresses Fe-HS HS less stable P T ↓ Mg expands Fe-LS LS less stable P T ↑ Affect on P T unclear? P=0: R(Fe-HS)>R(Mg)>R(Fe-LS)

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Spin Transition Calculations Sensitivity: (Mg,Fe)SiO 3 PTPT 200 Gpa C Fe = 12.5%C Fe = 25% 170 Gpa 140 Gpa d Fe-Fe = 4.98 Ǻ d Fe-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

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