1. The authors studied the structure and transport of oxygen vacancies in MgO grain boundaries using molecular statics and dynamics simulations with a simple ionic potential model. 2. They found that grain boundaries act as traps for oxygen vacancies, with segregation energies of compact vacancies in the range of 1.2-1.6 eV. 3. The vacancies can also exist in a delocalized state, where the vacancy fragments are separated across multiple atomic planes near the grain boundary. Delocalized configurations were found to have lower energies when the fragments were separated by an intermediate distance.

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