fall mrs 2013 - mgo grain boundaries structure and transport

Structure and transport of vacancies in MgO grain boundaries with misfit dislocationsKedarnath 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

Solid Interfaces can enhance mass transport

trolyte material. So far, yttria-stabilized zirconia(Y2O3)x(ZrO2)1–x (YSZ) is the material mostlyused in SOFCs because of its mechanical sta-bility, chemical compatibility with electrodes, andhigh oxygen ionic conductivity. It is well knownthat doping ZrO2 with Y2O3 stabilizes the cubicfluorite structure of ZrO2 at room temperature andsupplies the oxygen vacancies responsible forthe ionic conduction, resulting in high valuesof the oxygen conductivity at high temperatures(5–7). Amaximumvalue of 0.1 S/cm (where 1 S =1 A/V) at 1000°C is observed for the 8 to 9 molepercent (mol %) yttria content (2–4). A severedrawback toward the final implementation ofSOFCs is the relatively low room temperatureionic conductivity of this material, which imposesrather high operational temperatures around 800°C(1–4). The search for alternative electrolytes hasnot yet been successful in reaching the conduc-tivity value of 0.01 S/cm desired for room tem-perature operation (1–4).

Only modest reductions in the operationtemperature of SOFCs (500° to 700°C) can beanticipated with the recently proposed optimizedelectrolytes such as gadolinia-doped ceria andlanthanum gallates (8–11). On the other hand, theone to two orders of magnitude increase of theelectrical conductivity reported (12–14) in nano-crystalline samples as compared with single crys-tals outlines the importance of processing as analternative route to increasing conductivity valuestoward the desired levels. Because modern thinfilm growth techniques allow a precise control oflayer thickness and morphology, they provide apathway for the production of solid electrolyteswith optimized properties. Maier et al. found asubstantial increase of the dc ionic conductivityof superlattices of CaF2 and BaF2 when thethickness of the individual layers was decreaseddown to 16 nm, assigned to a size effect due tothe space charge regions being smaller than thelayer thickness (15, 16). Kosacki et al. havereported enhanced conductivity in highly tex-tured thin films of YSZwith thicknesses between60 and 15 nm, reaching 0.6 S/cm at 800°C (17).Because reducing film thickness (and thereforeincreasing the fraction of material near the in-terface) produces such a noticeable conductivityenhancement, the interfaces themselves wouldseem to play a determining role in the outstand-ing conductivity properties observed.

To search for interface effects, we fabricatedheterostructures where YSZ layers (with 8 mol %nominal yttria content) in the thickness range from62 nm down to 1 nm were sandwiched betweentwo 10-nm-thick layers of insulating SrTiO3 (STO).Also, superlattices were grown, alternating 10-nm-

thick STO films with YSZ layers with thicknessbetween 62 and 1 nm (18). Figure 1A displays alow-magnification (inset) and a high-resolutionannular dark field (or Z-contrast) image of a[YSZ1nm/STO10nm]9 superlattice (with ninerepeats), showing the excellent crystalline qualityof the sample. The layers appear continuous andflat over long lateral distances (a few microns).The interfaces between the STO and the YSZare seen to be atomically flat. From the high-magnification image it is possible to count thenumber of unit cells of STO and YSZ, nomi-nally 25 of STO and 2 of YSZ. Most impor-tantly, the YSZ is perfectly coherent with theSTO, in agreement with x-ray diffraction (XRD)results (fig. S1), meaning that the ultrathin layerof YSZ grows rotated by 45° around the c axisand strains to match the STO lattice. Because thebulk lattice constants of STO and YSZ are

0.3905 (19) and 0.514 nm (20), respectively, theepitaxial growth of the YSZ on top of the STOensures a large, expansive strain in the thin YSZlayers of 7% in the ab plane. Increasing the thick-ness of YSZ (for constant STO thickness) resultsin a loss of structural coherence, as reflected by areduction of superlattice satellites in XRD. Elec-tron microscopy observations confirm that therelease of strain results in a granular morphology,although the growth remains textured.

We plotted the lateral electrical conductivity(real part s!) of the thinnest YSZ trilayer versusfrequency in a double logarithmic plot (Fig. 2).The characteristic electrical response of ionic con-ductors (21–23) is observed in the figure. The longrange or sdc ionic conductivity of the material isobtained from the plateau found in s! versusfrequency plots. In the presence of blocking effectsdue to grain boundaries or electrodes, a further

1Grupo de Física de Materiales Complejos, UniversidadComplutense de Madrid, Madrid 28040, Spain. 2MaterialsScience and Technology Division, Oak Ridge NationalLaboratory, Oak Ridge, TN 37831, USA. 3Escuela TécnicaSuperior de Ingenieros de Telecomunicaciones, Universi-dad Politécnica de Madrid, Madrid 28040, Spain.

*To whom correspondence should be addressed. E-mail:[email protected]

Fig. 1. (A) Z-contrast scanning transmission electron microscopy (STEM) image of the STO/YSZ interface ofthe [YSZ1nm/STO10nm]9 superlattice (with nine repeats), obtained in the VG Microscopes HB603Umicroscope. A yellow arrow marks the position of the YSZ layer. (Inset) Low-magnification image obtainedin the VGMicroscopes HB501UX column. In both cases a white arrow indicates the growth direction. (B) EELspectra showing the O K edge obtained from the STO unit cell at the interface plane (red circles) and 4.5 nminto the STO layer (black squares). (Inset) Ti L2,3 edges for the same positions, same color code. All spectraare the result of averaging four individual spectra at these positions, with an acquisition time of 3 s each.

Fig. 2. Real part of the lateralelectrical conductivity versus fre-quency of the trilayer with 1-nm-thick YSZ in a double log plot.Isotherms were measured in therange of 357 to 531 K. The solidline represents a NCL contribution(s! ~ Aw, where A is a temperature-dependent proportionality factorand w is the angular frequency),as explained in the text. Stars iden-tify the value of sdc. The uncertain-ty of conductance measurements is1 nS (10!2 S/cm in conductivity forthe sample shown, see error bar).(Inset) Imaginary versus real partof the impedance (Nyquist) plots at492, 511, and 531 K. Whereas thehigh-frequency contribution is a Debye-like process characterized by a conductivity exponent n = 0, the“grain boundary” term observed in the Nyquist plots shows a clear deviation from a Debye behavior, asreflected by the distorted impedance arcs.

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decrease of s! (below bulk sdc values) may occurtoward lower frequencies. For clarity, the value ofsdc has been identified by using stars. The sdcvalue is found to be thermally activated, so whenthe temperature is reduced the conductivity curvesshift downwards in Fig. 2. The inset in Fig. 2displays Nyquist plots for the same sample. Todetermine the nature of the charge carriers, wemeasured the conductance of the samples bymeans of dc measurements. As can be observed infig. S2, the dc conductance (open circles) is threeto four orders of magnitude lower than the valuesobtained from ac measurements (solid squares) inthe entire temperature measurement range. Thisresult indicates that the electronic contribution tothe ac measurements can be considered negligi-ble, and thus, the measured ac transport isattributable to an ionic diffusion process.

In Fig. 3, the temperature dependence of thesdc of [STO10nm/YSZXnm/STO10nm] trilayers isshown together with data corresponding to a singlecrystal and the 700-nm thin film from (7). Whereasthe “bulklike” samples (the thin film and the singlecrystal) show the well-known Arrhenius behaviorwith an activation energy of ~1.1 eV, the trilayersshow much larger conductivity values and smallervalues of the activation energy. The thickest trilayer(62-nm YSZ) already shows an increase of abouttwo orders of magnitude in the high-temperature dcconductivity, and the dc activation energy decreasesto 0.72 eV. When decreasing the thickness of theYSZ layer to 30 nm, the dc conductivity increasesanother three orders of magnitude, and the activa-tion energy decreases to 0.6 eV. The high values ofthe pre-exponential factor of ~107 (ohm·cm)!1 arecomparable to those found in other ion conductors(24) [see supporting onlinematerial (SOM) text]. Ifthe thickness is further reduced all the way downto 1 nm (two unit cells of YSZ), the conductivityis observed to increase as the inverse of the YSZlayer thickness, but the conductance is essentiallythickness-independent (bottom inset in Fig. 3).We can think of three parallel conduction pathsdue to the interfaces and the bulk YSZ and STOlayers. The bulk conductivity of YSZ is 10!7 S/cmat 500 K, which would yield a conductance valueof ~10!14 S for 1-nm-thick layers. This value ismuch lower than the 10!6 S value measured withthe ac technique. If we instead assume that the highconductance (G = 10!6 S) is due to electronicconduction in the STO, both ac and dc techniqueswould provide this same value, contrary to what isobserved (fig. S2).Moreover, reported conductivityvalues in STO thin films (25) are also much lowerthan those necessary to explain the high conduct-ance observed. Because bulk YSZ or STO contri-butions can be ruled out, an interface conductionmechanism is inferred.

To further test this scenario, we grew super-lattices repeating the [YSZ1nm/STO10nm] growthunit. We found (top inset in Fig. 3) that con-ductance scales nowwith the number of interfacesup to a number of eight (four bilayer repetitions).There is a scaling breakdown in the figure, ob-served for a larger number of bilayer repetitions,

most likely resulting from disorder building up inthis highly strained structure. The experimentaldata indicates that the first STO/YSZ interfacedoes not contribute to the large ionic conductivityobserved in the samples, probably because the firstSTO layer is somehow different from the others asit is grown directly on the substrate. This scaling,together with the invariance of the conductancewith the thickness of the YSZ, shows that the largeconductivity values in these heterostructures orig-

inate truly at the interfaces between YSZ and STO.Our results indicate a superposition of two parallelcontributions—one due to the bulk and one at-tributable to the interface—and the colossal ionicconductivity is observed as long as the interfaceconductance is larger than that of the bulk. Theabrupt conductivity decrease when the thicknesschanges from 30 to 62 nm is most likely due to adegraded interface structure when the YSZ layersexceed the critical thickness.

Fig. 3. Dependence of the logarithm of thelong-range ionic conductivity of the trilayersSTO/YSZ/STO versus inverse temperature. Thethickness range of the YSZ layer is 1 to 62 nm.Also included are the data of a single crystal(sc) of YSZ and a thin film (tf) 700 nm thick[taken from (7)] with the same nominalcomposition. (Top inset) 400 K conductanceof [YSZ1nm/STO10nm](ni/2) superlattices as afunction of the number of interfaces, ni.(Bottom inset) Dependence of the conduct-ance of [STO10nm/YSZXnm/STO10nm] trilayers at500 K on YSZ layer thickness. Error bars areaccording to a 1 nS uncertainty of the con-ductance measurement.

Fig. 4. (A) EELS chemical maps. The ADF image in the upper panel shows the area used for EELSmapping(spectrum image, marked with a green rectangle) in the [YSZ1nm/STO10nm]9 superlattice. The middle panelshows the averaged ADF signal acquired simultaneously with the EEL spectrum image, showing the STO(low-intensity regions) and YSZ (higher-intensity) layers. The lower panel shows the Ti (red) and Sr (darkyellow) EELS line traces across several consecutive interfaces. These line traces are averaged from theelemental 2D images shown in the insets, each framed with the same color code (red for Ti, dark yellow forSr). Data was obtained in the VG Microscopes HB501UX. Because the STEM specimen was relatively thick(several tens of nanometers), the wide chemical interface profiles are most likely attributable to beambroadening. (B) Solid spheres model of the YSZ/STO interface showing: (1) The compatibility of theperovskite and fluorite (rotated) structures. (2) A side view of the interface between STO (at the bottom)and YSZ (on top) with realistic ionic radius. The shaded oxygen positions in the interface plane arepresumed absent or displaced because of volume constraints, enabling the high ionic conductivity. (3) A3D view of the interface, with the ionic radius reduced by half to better visualize the plane of oxygenvacancies introduced in the interface. The square symbol in the legend indicates the empty positionsavailable for oxygen ions at the interface.

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J. Garcia-Barriocanal et. al., Science, 321, 676 (2008)

Nanoscale effects on ion conductance of layer-by-layer structuresof gadolinia-doped ceria and zirconia

S. Azad,a! O. A. Marina,b! C. M. Wang, L. Saraf, V. Shutthanandan, D. E. McCready,A. El-Azab, J. E. Jaffe, M. H. Engelhard, C. H. F. Peden, and S. Thevuthasanc!Pacific Northwest National Laboratory, Richland, Washington 99352

!Received 13 September 2004; accepted 9 February 2005; published online 21 March 2005"

Layer-by-layer structures of gadolinia-doped ceria and zirconia have been synthesized onAl2O3!0001" using oxygen plasma-assisted molecular beam epitaxy. Oxygen ion conductivitygreatly increased with an increasing number of layers compared to bulk polycrystallineyttria-stabilized zirconia and gadolinia-doped ceria electrolytes. The conductivity enhancement inthis layered electrolyte is interesting, yet the exact cause for the enhancement remains unknown. Forexample, the space charge effects that are responsible for analogous conductivity increases inundoped layered halides are suppressed by the much shorter Debye screening length in layeredoxides. Therefore, it appears that a combination of lattice strain and extended defects due to latticemismatch between the heterogeneous structures may contribute to the enhancement of oxygen ionicconductivity in this layered oxide system. © 2005 American Institute of Physics.#DOI: 10.1063/1.1894615$

Development of electrolyte materials that possess highoxygen ion conductance at relatively low temperatures is es-sential to increase the efficiency and lifetime of electro-chemical devices such as solid oxide fuel cells !SOFC". Themost advanced SOFCs employ oxide ion conducting zirconiabased electrolytes, specifically, yttria stabilized zirconia!YSZ". The conductivity of the electrolyte determines theoperating temperature of this device, which is currentlyaround 1000 °C.1 Lower operating temperatures of%500 °C would make SOFCs much more cost efficient and,most importantly, facilitate the practical use of SOFCs inelectric vehicles. It is well established that ceria !CeO2",doped with a divalent or trivalent cation, exhibits higher ionconductance at intermediate temperatures compared withYSZ, making ceria a promising candidate material for SOFCapplications.2 The addition of an insoluble second phase, isknown to dramatically increase the ion conductance of elec-trolytic crystalline materials where the major effect of theaddition of the second phase particles is to create highlyconductive paths along the interfaces as a result of redistri-bution of ions in the space charge regions.3,4 In a recentstudy, Sata and co-workers5 found that an increase in theinterface density in a two-phase multilayered calcium andbarium fluoride !CaF2 and BaF2" structure drastically en-hances the fluorine ion conductance of the material, particu-larly at film thicknesses in the range of 20–100 nm. Specifi-cally, it was observed that this nanoscale lamellar structureexhibits higher ion conductance compared to either bulk cal-cium fluoride or barium fluoride along the interfacial direc-tions at moderate temperatures when the number of hetero-junctions is increased. The authors attributed theenhancement of fluorine ionic conductivity in this layered-

halide system to the influence of space charge regions at theinterfaces.

Previous work by Yahiro et al.6 and Steele7 showed thatGd2O3 or Sm2O3-doped ceria !CeO2" have the highest con-ductivity among a series of solid solutions made of ceria andalkaline earth and rare earth oxides. As such, a layered nano-structure of Gd2O3-doped ceria and zirconia !ZrO2" can beused as a test system to search for interface effects similar tothose observed in the fluoride multilayered system. In thisstudy, layer-by-layer structures of gadolinia !Gd2O3" dopedceria and zirconia have been synthesized on Al2O3!0001".The number of interfaces was varied by increasing the num-bers of discrete layers, while the total film thickness was keptconstant at %155 nm.

The films were grown in a dual-chamber ultrahighvacuum !UHV" system8 equipped with an electron cyclotronresonance !ECR" oxygen plasma source. Ce and Zr sources!both 99.98% purity" were evaporated from separate electronbeam sources and Gd !99.98% purity" was evaporated froman effusion cell. The growth rates of the films were moni-tored by quartz crystal oscillators !QCOs". Al2O3!0001"single crystal substrates were ultrasonically cleaned in ac-

a"Present address: Chemistry Department, Rice University, Houston, Texas77251-1892.

b"Present address: Mechanical Engineering Department, Florida State Uni-versity, Tallahasse, Florida 32306.

c"Electronic mail: [email protected]. 1. TEM micrograph showing a cross sectional view of an eight-layerGd2O3-doped CeO2 and ZrO2 film grown on Al2O3!0001".

APPLIED PHYSICS LETTERS 86, 131906 !2005"

0003-6951/2005/86"13!/131906/3/$22.50 © 2005 American Institute of Physics86, 131906-1Downloaded 31 Oct 2012 to 18.7.29.240. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions

was measured as a function of temperature using a four-probe van der Pauw technique.12 Since the electronic con-ductivity in these oxides is significantly less compared toionic conductivity, especially at low temperatures, ionic con-ductivity dominates in these materials.13 As such, the totalconductivity will be identified as oxygen ionic conductivitythroughout this letter. Oxygen ionic conductivity results fortwo-, four-, eight-, ten-, and sixteen-layered Gd2O3-dopedCeO2 and ZrO2 films on Al2O3!0001" substrates are dis-played in Fig. 3. The oxygen ionic conductivity data frompolycrystalline13 and single crystal14 YSZ are also shown forcomparison. In general, these highly oriented films showedmuch higher conductivity compared to bulk polycrystallineYSZ. It is apparent from the impedance spectra that increas-ing the number of interfaces !i.e., the number of discretelayers" in the structure facilitates ion transport and leads toan increase in the oxygen ionic conductivity at low tempera-tures. The ionic conductivities for single crystal YSZ and thetwo-, four-, eight-, ten-, and sixteen-layered films, all at650 K extracted from Fig. 3 are shown in Fig. 4. At thattemperature, increasing the number of layers resulted inhigher oxygen ionic conductivity up to a thickness of 15 nm!for individual layers", beyond which conductivity decreases.The maximum value for the conductivity appears to be atleast an order of magnitude higher than that from either poly-crystalline gadolinia-doped bulk ceria or a single crystalyttria-stabilized zirconia thin film. However, when the thick-ness of individual layers was reduced below #15 nm, theconductivity appears to decrease probably due to the straineffects associated with the thin films compared to the thickfilms. An analogous increase in conductivity, with evengreater magnitude, was observed in undoped fluoridesuperlattices,5 and was attributed to an increase in the densityof carriers !fluorine vacancies and interstitials" due to spacecharge effects near the interfaces. However, this mechanismis unlikely to play a significant role in these heavily Gd-doped oxide superlattices, since the Debye screening lengthis inversely proportional to the square root of the carrier

density and is only #0.1 nm in this system; thus, the spacecharge region is very small. Here, enhanced ion conductancemore likely results from extended defects and lattice strainnear the layer interfaces, which may increase the solubility ofGd, and hence the density of O vacancies, in the ceria layers.Defects and strain relaxation may also increase the mobilityof the vacancies. X-ray photoemission spectroscopy !XPS"depth profiles !not shown" from these layered oxide struc-tures indeed show that, although growth conditions are thesame, the concentration of Gd in the ceria layers is higherthan it is in the zirconia layers. Detailed results of theseinvestigations will be published in another letter.

In conclusion, greatly improved ionic conductivity wasobtained in gadolinia-doped ceria and zirconia layered struc-tures compared to individual bulk electrolytes. Since the De-bye screening length is small in these oxide layered struc-tures, the increase in conductivity cannot be explained byspace charge effects alone. Strain enhancement of either dop-ant solubility or oxygen vacancy mobility is more likely, butthe exact mechanism remains unknown.

This research was supported in part by the Division ofChemical Sciences, Office of Basic Energy Sciences, U.S.Department of Energy and the Laboratory Directed Researchand Development !LDRD" Program. The experiments wereperformed in the Environmental Molecular Sciences Labora-tory, a national scientific user facility located at PacificNorthwest National Laboratory !PNNL", and supported bythe U.S. Department of Energy’s Office of Biological andEnvironmental Research. PNNL is a multiprogram nationallaboratory operated for the U.S. DOE by Battelle MemorialInstitute under Contract No. DE-AC06-76RLO 1830.

1O. Yamamoto, Electrochim. Acta 45, 2423 !2000".2R. Doshi, V. L. Richards, J. D. Carter, X. Wang, and M. Krumpelt, J.Electrochem. Soc. 146, 1273 !1999".3T. Kudo and K. Fueki, Solid State Ionics, 1st ed. !VCH, Weinheim, 1990".4J. Maier, Prog. Solid State Chem. 23, 171 !1995".5N. Sata, K. Eberman, K. Ebert, and J. Maier, Nature !London" 408, 946!2000".6H. Yahiro, Y. Eguchi, K. Eguchi, and H. Arai, J. Appl. Electrochem. 18,527 !1988".7B. C. H. Steele, Solid State Ionics 129, 95 !2000".8S. A. Chambers, T. T. Tran, and T. A. Hileman, J. Mater. Res. 9, 2944!1994".9Y. Gao, G. S. Herman, S. Thevuthasan, C. H. F. Peden, and S. A. Cham-bers, J. Vac. Sci. Technol. A 17, 961 !1999".

10S. Azad, S. Thevuthasan, V. Shutthanandan, C. M. Wang, D. E. Mc-Cready, and C. H. F. Peden, Conference Proceeding, NanotechnologySymposium, 225th ACS National Meeting !2003".

11S. Thevuthasan, S. Azad, O. A. Marina, V. Shutthanandan, D. E. Mc-Cready, L. Saraf, C. M. Wang, I. Lyubinetsky, C. H. F. Peden, and V.Petrovsky, Proceedings of the IEEE Nano 2003 !2003".

12L. J. van der Pauw, Philips Res. Rep. 13, 1 !1958".13N. Q. Minh and T. Takahashi, Science and Technology of Ceramic FuelCells !Elsevier, Amsterdam, 1995", p. 94.

14S. Ikeda, O. Sakurai, K. Uematsu, N. Mizutani, and M. Kato, J. Mater. Sci.20, 4593 !1985".

FIG. 4. Conductivities of single crystal YSZ !Ref. 14", two-, four-, eight-,ten-, and sixteen-layer films at 650 K.

131906-3 Azad et al. Appl. Phys. Lett. 86, 131906 !2005"

Downloaded 31 Oct 2012 to 18.7.29.240. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions

Inverse of layer thickness

Azad et. al., Appl. Phys. Lett., 86, 131906 (2008)

Ionic conduction is sensitive to interface structure

reference missing!

Goal: Relate interface structure to mass transport

Model systems and methods

1 nm• Structure of low-angle GBs very well defined

• 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)

<100> <100> +ø/2

Eij = Ae�rij

⇢ � Cr6ij

+ Cqiqj✏rij1

2 different MgO slabs(colors for clarity only)One twisted wrt to other by ø

potential describing interatomic interactionsMg

O

Outline

1 nm1. 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

Low angle MgO grain boundaries

1 nm

• Contain misfit dislocations

• Misfit dislocation spacing decreases with increasing twist angle

d = 50 Å

{110}<110>

<100> +ø/2

<100> +ø/2

ø = 3.476º

misfit dislocation intersections (MDI)

atoms colored by number of neighbors

Lateral view of the interface plane

Misfit dislocation model valid for a certain twist range

3.5º 5º 10º

15º 25º 37º

Misfit dislocation model valid

Misfit dislocation model not valid

d = 50 Å d = 34 Å d = 15 Å

Outline

1 nm1. Grain boundary (GB) models, potentials, and methods


3. Structure and energetics of a vacancy at (and near) GBs


4. Transport of vacancies


• Two MgO units less at an MDI

• FCC-BCC semicoherent interfaces also have low densities at MDI

-2

-1.5

-1

-0.5

0

0.5

0 0.5 1 1.5 2

Ground-state structure of MgO grain boundaries

Reference state:energy of an MgO unit in bulk MgO

Δ E

(eV

)atoms colored by type small is Oxygen, large is Mg

Number of MgO units removed

Typical interface for low-angle MgO twist boundaries

7.5º twist boundary

Low-density plane will called the “interface plane”

atoms colored by type small is oxygen, large is Mg

Outline



3. Structure and energetics of a vacancy at GBs




GBs are traps to oxygen vacancies (5º twist)

2.9

2.95

3

3.05

3.1

3.15

3.2

3.25

3.3

0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56

Segregation energies of “compact” vacancies: 1.2-1.6 eV

Ef (

eV)

z axis (scaled)interface plane

Bulk Ef = 4.52 eV Atoms colored by excess energy

Structure of a compact vacancy - an Example

Atoms colored differently from blue are around a defect (vacancy)

Segregation energies of “compact” vacancies: 1.2-1.6 eV

small is Oxygen, large is Mg

Ef (

eV)

z axis (scaled)

top view

side view

coloring: vac formation energy

But, these energies only after conjugate gradient minimization!

2.95

3

3.05

3.1

3.15

3.2

3.25

3.3

0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56

’atoms1.oxy_int’ using 3:16

GBs are traps to oxygen vacancies (10º twist)

interface plane

Segregation energies of compact vacancies: 1.2-1.6 eV

Structure of a delocalized Oxygen vacancy

• Farther, the fragments of a delocalized vacancy, the lower is the energy

• But, not farthest!

atoms colored differently from blue are around a defect (vacancy)

Δ E

(eV

)

spacing between the fragments(in nearest neighbor units, each of which is ~3 Å)

MDI

Adjacent planes

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 1 2 3 4 5 6 7 81234567 localizedat MD

8



atoms colored differently from blue are around a defect (vacancy)

Structure of a delocalized Oxygen vacancyΔ

E (e

V)


MDI

Adjacent planes

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 1 2 3 4 5 6 7 81234567 localizedat MD

8

Mg vacancy at GBs behaves similar to that of oxygenE

f (eV

)

top view

side view

coloring: vac formation energy 2.6

2.65 2.7

2.75 2.8

2.85 2.9

2.95 3

3.05 3.1

0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56

’atoms1.mg_int’ using 3:16

Bulk Ef = 4.22 eV interface plane

z axis (scaled)

Segregation energies of compact vacancies: 1.2-1.6 eV

Structure of a delocalized Mg similar to that of oxygen

-0.35-0.3

-0.25-0.2

-0.15-0.1

-0.05 0

0.05 0.1

0.15 0.2

0 1 2 3 4 5 6 7



Δ E

(eV

)


123456 localizedat MD

7

Lowest-energy state of the vacancy changes with twist angle

MDI

Adjacent planes

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 1 2 3 4 5 6 7 81234567 localizedat MD

5º twist boundary

increasing twist angle

decreasing twist angle

• Twist angle misfit dislocation spacing

• Twist angle lowest formation energy of the vacancy

Δ E

(eV

)

spacing between the fragments8

d = 34 Å d = 15 Å

d = 34 Å d = 15 Å

Why do delocalized fragments want to stay away?

Wint

= Welastic

+Welectrostatic

nL

a 11

Welastic

⇡ µb2a2

8⇡(1� ⌫)

1

nL

Welectrostatic

⇡ q1q24⇡✏0

1

nLElastic energy as fragment spacing

Welectrostatic

=q1q24⇡✏0✏

1

nL

Electrostatic energy as fragment spacing

• 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

Welectrostatic

=q1q24⇡✏0✏

1

nL

Welectrostatic

=0.606

n

Welastic

⇡ µb2a2

8⇡(1� ⌫)

1

nL

Welectrostatic

⇡ q1q24⇡✏0

1

nL

eV

eV

n - number of nearest neighbors

nL

a 11

a0 = 4.212A

b =a0p2

a =a02

µ = 132� 141GPa

⌫ = 0.32 L = b q1, q2 = 1e

✏0 = 8.85⇥ 10�12Ohm�1m�1 ✏this model

= 7.92

Welastic = �0.63� 0.68

n

• Assumptions for elastic interactions perhaps incorrect (“a”, for example)

• Analytical model may be corrected study kink/jog on a bulk dislocation

Why do delocalized fragments want to stay away?

Structure of a screw dislocation in bulk MgO


Oxygen vacancies dissociated on a screw dislocation∆E

(eV

)

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 1 2 3 4 5 6spacing between vacancy fragments

• Contribution to energy due to other factors


Outline



3. Structure and energetics of a vacancy at GBs




Oxygen vacancy migrates between misfit dislocations

Oxygen vacancy at 7.5º GB

• Vacancy migrates from one misfit dislocation to another

This is a movie

Atoms are colored by type and the grain to which they belong initially

MgO

Oxygen vacancy at 5º GBOxygen vacancy at 5º GB Oxygen vacancy at 7.5º GB

Oxygen vacancy migrates between misfit dislocations

Oxygen vacancy at 10º GB

Mg vacancy at 5º GB Mg vacancy at 7.5º GB

Mg vacancy at 10º GB

Mg vacancy migrates between misfit dislocations

Oxygen vacancy localizes at MDIs

• 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

t0 t0 +4 ps t0 +8 ps

at adjacent planedefect at interface plane at interface plane(a) (b) (c)

Migration occurs by a multi-step process

1

localized at the MDI(adjacent plane)

0.2-0.3 eV

0.5-0.75 eV

• Migration occurs through a multi-step process

• Transport not complete until the vacancy reaches another misfit

dislocation

Schematic

For reference: Barrier for vacancy migration in bulk MgO is 2.1 eV

Migration rates change with twist angle

1

localized at the MDI(adjacent plane)

Distance between the

fragments increases

7.5º Twist10º Twist 7.5º Twist 10º Twist

0.2-0.3 eV

0.5-0.9 eV (?)

Distance between the fragments increases

Schematic

For reference: Barrier for vacancy migration in bulk MgO is 2.1 eV

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

fall mrs 2013 - mgo grain boundaries structure and transport

Technology

thickness ionic conductivity

electrical conductivity

oxygen ionic conductivity

conductivity values

abrupt conductivity

total conductivity

nm mgo grain boundaries

single crystal layer