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Fall MRS 2013 - MgO grain boundaries structure and transport
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Fall MRS 2013 - MgO grain boundaries structure and transport

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  • 1. Structure and transport of vacancies in MgO grain boundaries with misfit dislocations Kedarnath Kolluri and Blas Uberuaga MST-8, Los Alamos National Lab, NM 87545 Acknowledgments: Louis Vernon, Satyesh Yadav, Michael Demkowicz, John Hirth, Richard Hoagland, Amit Misra, and Gopinath Subramanian
  • 2. the yers The nm. ystal hick minal ance as a ni. ductrs at are con- abrupt conductivity decrease when the thickness ionic conductivity of this material, which imposes results (fig. S1), meaning that the ultrathin layer range or sd changes from 30 to 62 nm is most likely due to rather high operational temperatures around 800°C a of YSZ grows rotated by 45° around the c axis obtained fr degraded search for alternative electrolytes has (1–4). Theinterface structure when the YSZ layers and strains to match the STO lattice. Because the frequency p exceed the critical thickness. not yet been successful in reaching the conduc- bulk lattice constants of STO and YSZ are due to grai tivity value of 0.01 S/cm desired for room temperature operation (1–4). Only modest reductions in the operation temperature of SOFCs (500° to 700°C) can be anticipated with the recently proposed optimized electrolytes such as gadolinia-doped ceria and lanthanum gallates (8–11). On the other hand, the one to two orders of magnitude increase of the electrical conductivity reported (12–14) in nanocrystalline samples as compared with single crystals outlines the importance of processing as an alternative route to increasing conductivity values toward the desired levels. Because modern thin film growth techniques allow a precise control of layer thickness and morphology, they provide a pathway for the production of solid electrolytes with optimized properties. Maier et al. found a substantial increase of the dc ionic conductivity of superlattices of CaF2 and BaF2 when the Fig. 1. (A) Z-contrast scanning transmission electron microscopy (S thickness of the individual layers was decreased the [YSZ1nm/STO10nm]9 superlattice (with nine repeats), obtain J. assigned to a size effect due to microscope. 676 (2008) down to 16 nm, Garcia-Barriocanal et. al., Science, 321,A yellow arrow marks the position of the YSZ layer. (In the space charge regions being smaller than the in the VG Microscopes HB501UX column. In both cases a white arrow layer thickness (15, 16). Kosacki et al. have spectra showing the O K edge obtained from the STO unit cell at the reported enhanced conductivity in highly tex- into the STO layer (black squares). (Inset) Ti L2,3 edges for the same tured thin films of YSZ with thicknesses between are the result of averaging four individual spectra at these position 60 and 15 nm, reaching 0.6 S/cm at 800°C (17). Because reducing film thickness (and therefore Fig. 2. Real part of the lateral increasing the fraction of material near the in- electrical conductivity versus fre- Solid Interfaces can enhance mass transport www.sciencemag.org on September 17, 2011 scaling, ductance the large res orig-
  • 3. ffusion cell. The growth rates of the films were monid by quartz crystal oscillators ͑QCOs͒. Al2O3͑0001͒ e crystal substrates were ultrasonically cleaned in acIonic conduction is sensitive to interface 131906-3 Azad et al. structure FIG. 4. Conductivities of Inverse ofYSZ ͑Ref. 14͒, two-, four-, eight-, single crystal layer thickness ten-, and sixteen-layer films at 650 K. Azad et. al., Appl. Phys. Lett., 86, 131906 (2008) reference missing! 1. TEM micrograph showing a cross sectional view of an eight-layer was measured as a function of temperature using a four3-doped CeO2 and ZrO2 film grown on Al2O3͑0001͒. probe van der Pauw technique.12 Since the electronic conductivity of Physics © 2005 American Institute in these oxides is significantly less compared to ionic conductivity, especially at low temperatures, ionic concopyright; see http://apl.aip.org/about/rights_and_permissions ductivity dominates in these materials.13 As such, the total conductivity will be identified as oxygen ionic conductivity
  • 4. Goal: Relate interface structure to mass transport
  • 5. Model systems and methods • Structure of low-angle GBs very well defined 1 nm • MgO grain boundaries using the simplest of ionic potentials available • Fixed charge on each atom (this potential has full charge) • Molecular statics and dynamics (at 2000K) 2 different MgO slabs (colors for clarity only) One twisted wrt to other by ø Mg O <100> <100> +ø/2 potential describing interatomic interactions Eij = Ae rij ⇢ C 6 rij + Cqi qj 1 ✏rij
  • 6. Outline 1 nm 1. Grain boundary (GB) models 2. Ground-state structures of GBs 3. Structure and energetics of a vacancy at (and near) GBs • compact and delocalized vacancies 4. Migrations of vacancies • observations and postulated mechanisms
  • 7. Low angle MgO grain boundaries • Contain misfit dislocations 1 nm • Misfit dislocation spacing decreases with increasing twist angle misfit dislocation intersections (MDI) ø = 3.476º {110}<110> d = 50 Å atoms colored by number of neighbors <100> +ø/2 Lateral view of the interface plane <100> +ø/2
  • 8. Misfit dislocation model valid for a certain twist range d = 50 Å 3.5º 15º d = 34 Å d = 15 Å 5º 10º 25º 37º Misfit dislocation model valid Misfit dislocation model not valid
  • 9. Outline 1 nm 1. Grain boundary (GB) models, potentials, and methods 2. Ground-state structures of GBs 3. Structure and energetics of a vacancy at (and near) GBs • compact and delocalized vacancies 4. Transport of vacancies • observations and postulated mechanisms
  • 10. Ground-state structure of MgO grain boundaries 0.5 atoms colored by type small is Oxygen, large is Mg Δ E (eV) 0 -0.5 -1 -1.5 -2 Reference state: energy of an MgO unit in bulk MgO 0 0.5 1 1.5 Number of MgO units removed 2 • Two MgO units less at an MDI • FCC-BCC semicoherent interfaces also have low densities at MDI
  • 11. Typical interface for low-angle MgO twist boundaries atoms colored by type small is oxygen, large is Mg 7.5º twist boundary Low-density plane will called the “interface plane”
  • 12. Outline 1 nm 1. Grain boundary (GB) models, potentials, and methods 2. Ground-state structures of GBs 3. Structure and energetics of a vacancy at GBs • compact and delocalized vacancies 4. Transport of vacancies • observations and postulated mechanisms
  • 13. GBs are traps to oxygen vacancies (5º twist) 3.3 Ef (eV) 3.25 3.2 3.15 3.1 3.05 3 2.95 2.9 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 z axis (scaled) interface plane Bulk Ef = 4.52 eV Atoms colored by excess energy Segregation energies of “compact” vacancies: 1.2-1.6 eV
  • 14. Structure of a compact vacancy - an Example small is Oxygen, large is Mg Atoms colored differently from blue are around a defect (vacancy) Segregation energies of “compact” vacancies: 1.2-1.6 eV
  • 15. GBs are traps to oxygen vacancies (10º twist) 3.3 ’atoms1.oxy_int’ using 3:16 Ef (eV) 3.25 3.2 3.15 top view 3.1 3.05 3 2.95 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 z axis (scaled) interface plane 0.56 coloring: vac formation energy side view Segregation energies of compact vacancies: 1.2-1.6 eV But, these energies only after conjugate gradient minimization!
  • 16. Structure of a delocalized Oxygen vacancy 0.15 0.1 Δ E (eV) 0.05 MDI 0 -0.05 Adjacent planes -0.1 -0.15 -0.2 -0.25 -0.3 7 8 1 localized at MD atoms colored differently from blue spacing between the fragments are around a defect (vacancy) (in nearest neighbor units, each of which is ~3 Å) 0 8 1 7 2 6 3 5 4 4 5 3 6 2 • Farther, the fragments of a delocalized vacancy, the lower is the energy • But, not farthest!
  • 17. Structure of a delocalized Oxygen vacancy 0.15 0.1 Δ E (eV) 0.05 MDI 0 -0.05 Adjacent planes -0.1 -0.15 -0.2 -0.25 -0.3 7 8 1 localized at MD atoms colored differently from blue spacing between the fragments are around a defect (vacancy) (in nearest neighbor units, each of which is ~3 Å) 0 8 1 7 2 6 3 5 4 4 5 3 6 2 • Farther, the fragments of a delocalized vacancy, the lower is the energy • But, not farthest!
  • 18. Structure of a delocalized Oxygen vacancy 0.15 0.1 Δ E (eV) 0.05 MDI 0 -0.05 Adjacent planes -0.1 -0.15 -0.2 -0.25 -0.3 7 8 1 localized at MD atoms colored differently from blue spacing between the fragments are around a defect (vacancy) (in nearest neighbor units, each of which is ~3 Å) 0 8 1 7 2 6 3 5 4 4 5 3 6 2 • Farther, the fragments of a delocalized vacancy, the lower is the energy • But, not farthest!
  • 19. Structure of a delocalized Oxygen vacancy 0.15 0.1 Δ E (eV) 0.05 MDI 0 -0.05 Adjacent planes -0.1 -0.15 -0.2 -0.25 -0.3 7 8 1 localized at MD atoms colored differently from blue spacing between the fragments are around a defect (vacancy) (in nearest neighbor units, each of which is ~3 Å) 0 8 1 7 2 6 3 5 4 4 5 3 6 2 • Farther, the fragments of a delocalized vacancy, the lower is the energy • But, not farthest!
  • 20. Structure of a delocalized Oxygen vacancy 0.15 0.1 Δ E (eV) 0.05 MDI 0 -0.05 Adjacent planes -0.1 -0.15 -0.2 -0.25 -0.3 7 8 1 localized at MD atoms colored differently from blue spacing between the fragments are around a defect (vacancy) (in nearest neighbor units, each of which is ~3 Å) 0 8 1 7 2 6 3 5 4 4 5 3 6 2 • Farther, the fragments of a delocalized vacancy, the lower is the energy • But, not farthest!
  • 21. Structure of a delocalized Oxygen vacancy 0.15 0.1 Δ E (eV) 0.05 MDI 0 -0.05 Adjacent planes -0.1 -0.15 -0.2 -0.25 -0.3 7 8 1 localized at MD atoms colored differently from blue spacing between the fragments are around a defect (vacancy) (in nearest neighbor units, each of which is ~3 Å) 0 8 1 7 2 6 3 5 4 4 5 3 6 2 • Farther, the fragments of a delocalized vacancy, the lower is the energy • But, not farthest!
  • 22. Structure of a delocalized Oxygen vacancy 0.15 0.1 Δ E (eV) 0.05 MDI 0 -0.05 Adjacent planes -0.1 -0.15 -0.2 -0.25 -0.3 7 8 1 localized at MD atoms colored differently from blue spacing between the fragments are around a defect (vacancy) (in nearest neighbor units, each of which is ~3 Å) 0 8 1 7 2 6 3 5 4 4 5 3 6 2 • Farther, the fragments of a delocalized vacancy, the lower is the energy • But, not farthest!
  • 23. Structure of a delocalized Oxygen vacancy 0.15 0.1 Δ E (eV) 0.05 MDI 0 -0.05 Adjacent planes -0.1 -0.15 -0.2 -0.25 -0.3 7 8 1 localized at MD atoms colored differently from blue spacing between the fragments are around a defect (vacancy) (in nearest neighbor units, each of which is ~3 Å) 0 8 1 7 2 6 3 5 4 4 5 3 6 2 • Farther, the fragments of a delocalized vacancy, the lower is the energy • But, not farthest!
  • 24. Structure of a delocalized Oxygen vacancy 0.15 0.1 Δ E (eV) 0.05 MDI 0 -0.05 Adjacent planes -0.1 -0.15 -0.2 -0.25 -0.3 7 8 1 localized at MD atoms colored differently from blue spacing between the fragments are around a defect (vacancy) (in nearest neighbor units, each of which is ~3 Å) 0 8 1 7 2 6 3 5 4 4 5 3 6 2 • Farther, the fragments of a delocalized vacancy, the lower is the energy • But, not farthest!
  • 25. Mg vacancy at GBs behaves similar to that of oxygen 3.1 ’atoms1.mg_int’ using 3:16 3.05 Ef (eV) 3 2.95 2.9 2.85 top view 2.8 2.75 2.7 2.65 2.6 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 z axis (scaled) interface plane 0.56 coloring: vac formation energy side view Bulk Ef = 4.22 eV Segregation energies of compact vacancies: 1.2-1.6 eV
  • 26. Structure of a delocalized Mg similar to that of oxygen 0.2 0.15 0.1 Δ E (eV) 0.05 0 -0.05 -0.1 -0.15 -0.2 -0.25 -0.3 -0.35 7 0 6 1 5 2 4 3 3 4 2 5 1 6 localized 7 at MD spacing between the fragments (in nearest neighbor units, each of which is ~3 Å) • Farther, the fragments of a delocalized vacancy, the lower is the energy • But, not farthest!
  • 27. Lowest-energy state of the vacancy changes with twist angle 0.15 increasing twist angle 0.1 decreasing twist angle Δ E (eV) 0.05 MDI 0 -0.05 5º twist boundary Adjacent planes -0.1 d = 34 Å -0.15 -0.2 -0.25 -0.3 0 8 1 7 d = 34 Å 8 localized spacing between the fragments at MD 2 6 3 5 4 4 5 3 6 2 7 1 • Twist angle misfit dislocation spacing • Twist angle lowest formation energy of the vacancy d = 15 Å
  • 28. Why do delocalized fragments want to stay away? • Fragments may be considered as kinks/jogs on the screw dislocation • Fragments have like charges (+1 each for O vac and -1 for Mg vac) Wint = Welastic + Welectrostatic nL 1 a 1 µb2 a2 1 Welastic ⇡ 8⇡(1 ⌫) nL q1 q 2 1 Elastic energy as fragment spacing Welectrostatic ⇡ 4⇡✏0 nL q1 q2 1 Welectrostatic = 4⇡✏0 ✏ nL Electrostatic energy as fragment spacing
  • 29. Why do delocalized fragments want to stay away? a0 = 4.212˚ A Wint = Welastic + Welectrostatic nL a 1 µb2 a2 1 Welastic ⇡ 8⇡(1 ⌫) nL q1 1 q1 q 2 q 2 1 Welectrostatic Welectrostatic ⇡ = 4⇡✏0 ✏ 4⇡✏0 nLnL Welastic = Welectrostatic 0.63 1 a0 a0 b= p a= 2 2 ⌫ = 0.32 L = b ✏0 = 8.85 ⇥ 10 0.68 n 0.606 = n 12 Ohm µ = 132 141GP a q1 , q2 = 1e 1 m 1 ✏this model = 7.92 eV n - number of nearest neighbors eV • Assumptions for elastic interactions perhaps incorrect (“a”, for example) • Analytical model may be corrected study kink/jog on a bulk dislocation
  • 30. Structure of a screw dislocation in bulk MgO atoms colored by number of neighbors
  • 31. Oxygen vacancies dissociated on a screw dislocation 0 -0.2 ∆E(eV) -0.4 -0.6 -0.8 -1 -1.2 -1.4 -1.6 0 1 2 3 4 spacing between vacancy fragments • Contribution to energy due to other factors 5 6 atoms colored by number of neighbors
  • 32. Outline 1 nm 1. Grain boundary (GB) models, potentials, and methods 2. Ground-state structures of GBs 3. Structure and energetics of a vacancy at GBs • compact and delocalized vacancies 4. Transport of vacancies • observations and postulated mechanisms
  • 33. Oxygen vacancy migrates between misfit dislocations Atoms are colored by type and the grain to which they belong initially Oxygen vacancy at 7.5º GB Mg O • Vacancy migrates from one misfit dislocation to another This is a movie
  • 34. Oxygen vacancy migrates between misfit dislocations Oxygen vacancy at 5º GB Oxygen vacancy at 5º GB Oxygen vacancy at 7.5º GB Oxygen vacancy at 10º GB
  • 35. Mg vacancy migrates between misfit dislocations Mg vacancy at 5º GB Mg vacancy at 7.5º GB Mg vacancy at 10º GB
  • 36. Oxygen vacancy localizes at MDIs defect at interface plane (a) at adjacent plane (b) t0 at interface plane (c) t0 +4 ps t0 +8 ps • Defect migrates from one misfit dislocation to another • first by localizing at the MDI (usually at adjacent planes) • then by delocalizing again at the interface plane misfit dislocation
  • 37. Migration occurs by a multi-step process 0.5-0.75 eV Schematic 0.2-0.3 eV localized at the MDI (adjacent plane) For reference: Barrier for vacancy migration in bulk1MgO is 2.1 eV • Migration occurs through a multi-step process • Transport not complete until the vacancy reaches another misfit dislocation
  • 38. Migration rates change with twist angle 0.5-0.9 eV (?) Schematic 10º Twist 7.5º Twist 7.5º Twist 0.2-0.3 eV he een t tw ce b e n es Dista creas s in ment frag localized at the MDI (adjacent plane) Dista fragm n ce b ents i 1 For reference: Barrier for vacancy migration in bulk MgO is 2.1 eV etwee n the ncrea ses 10º Twist
  • 39. Summary: Vacancy at MgO GBs with misfit dislocations • Grain boundaries are traps to vacancies of either species • Several metastable states for vacancy to reside at the grain boundary • In their lowest energy, they delocalize at misfit dislocations • They migrate from one misfit dislocation to another – In their intermediate, they localize in the vicinity of MDI