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

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. Computational Materials Group University of Wisconsin - Madison.

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

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  1. 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

  2. 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!!

  3. 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

  4. Fe and Spin Crossover in the Lower Mantle

  5. 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

  6. Octahedral Fe2+ Spin State High spin M = 4mB Intermediate spin M = 2mB Low spin M = 0mB Minority Exf eg EHund t2g Majority

  7. 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

  8. 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

  9. Spin State vs. Temperature: (Mg0.75,Fe0.25)O Lin, et al., ScienceTBP

  10. 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, …

  11. 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.)

  12. First-Principles Modeling: Opportunities and Challenges

  13. 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, …

  14. 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

  15. 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

  16. Calculating Spin-Transitions LS DH=HHS–HLS E LS HS P PT HS VHS VLS V

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

  18. 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)

  19. Challenges for First-Principles and Spin Effects Why so much spread in calculation?

  20. 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

  21. Spin Transition Calculations Sensitivity: Calculation Parameters - (Mg0.75Fe0.25)SiO3 PT GGA 200 GPa 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?

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

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

  24. 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!

  25. Summary of First-Principles Challenges • Comparing calculations: Equivalent materials systems and calculation parameters • Comparing experiments: Equivalent materials systems and best calculation parameters Still learning!

  26. First-Principles study of Fe Spin Crossover

  27. 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?

  28. 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

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

  30. Ferropericlase: What Drives the Crossover? P∆V ∆E Spin crossover (T=0) when DH = EHS-ELS + P(VHS-VLS) = 0 • 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?

  31. Understanding PT vs. CFe TrendChemical Pressure  PT ▲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↓

  32. 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

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

  34. 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

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

  36. Conclusions Perovskite Ferropericlase P∆V ∆E • 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.

  37. Acknowledgements • Additional collaborators: Jie Li (UIUC) • Funding: Wisconsin Alumni Research Foundation (WARF)

  38. End

  39. 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

  40. A Multiscale Alloy Theory Approach

  41. Multiscale Alloy Theory Approach First-Principles Energetics Thermodynamic Modeling CALPHAD Phase stability, Fe partitioning, Fe spin states, Densities, …

  42. 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

  43. Fe – Mg Interaction vs. Spin State: Perovskite High Spin Low Spin Tc(100GPa)≈900K Tc(100GPa)≈4500K • 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

  44. First-Principles study of Fe Spin Crossover T>0

  45. First-Principles Model for Ferropericlase MgO FeO-LS FeO-HS • 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

  46. Free Energy Model First-principles 1 First-principles 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

  47. Fitting The Free Energy MgO FeO-LS FeO-HS • 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 Fit and interpolate Analytic

  48. 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-LS FeO-HS MgO FeO-LS FeO-HS

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

  50. Development of CALPHAD Approach I II III • 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 http://www.computherm.com/pandat.html Courtesy of Ying Yang, CompuTherm

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