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Surfaces and Interfaces
Shyue Ping Ong
Imperfections
Real-world materials are not perfect infinite
crystals
•  Defects (substitutional, interstitial, anti-site, etc.)
•  Surfaces
•  Interfaces, e.g., grain boundaries
NANO266
2
The Supercell Method
Create larger cell from unit cell
Limitations
•  Computational cost limits cell sizes and hence concentrations
•  Charged defects require complicated correction procedures
•  As always, test for convergence!
NANO266
3
Change to Al
Al in Cu example
Surfaces
Slab + Vacuum
NANO266
4
With PBC
Lattice Planes
A lattice plane of a given Bravais lattice is a plane (or
family of parallel planes) whose intersections with the
lattice are periodic (i.e., are described by 2D Bravais nets)
and intersect the Bravais lattice; equivalently, a lattice
plane is any plane containing at least three noncollinear
Bravais lattice points.
NANO 106 - Crystallography of Materials by
Shyue Ping Ong - Lecture 2
Miller indices
Lattice planes are represented by Miller indices, denoted
as , where h, k and l are integers.
NANO 106 - Crystallography of Materials by
Shyue Ping Ong - Lecture 2
hkl( )
Surface construction
NANO266
7
Sun, W.; Ceder, G. Efficient creation and convergence of surface slabs, Surf. Sci., 2013, 617, 53–59, doi:10.1016/j.susc.2013.05.016.
Key considerations of surface structures
1.  Which termination?
2.  Is the termination polar?
3.  Does surface reconstruction occur?
NANO266
8
Surface terminations
Symmetrically unique
Most terminations break bonds – how many and which
ones?
NANO266
9
(010) surface in LiFePO4
PO4 group
FeO6 octahedral
Tasker Classification
NANO266
10
Tasker, P. W. The stability of ionic crystal surfaces, J. Phys. C Solid State Phys., 1979, 12, 4977–4984, doi:10.1088/0022-3719/12/22/036.
Reconstruction of Surfaces
Tasker 3 -> Tasker 2b
Structural distortions
NANO266
11
Move half of M+ to bottom layer.
Si(111)-(7x7) – 25 years of science!
NANO266
12
https://vimeo.com/1086112
Convergence of Surface energies
Typically, most people remember
convergence wrt vacuum and slab
size, but convergence wrt surface
area can be important, particularly if
there are relaxations that can break
symmetry!
NANO266
13
γ =
1
2A
E(Slab)− NE(bulk)[ ]
Convergence wrt
vacuum size
Convergence wrt
slab size – how
many layers?
Convergence wrt
surface area
Sholl, D.; Steckel, J. A. Density Functional Theory: A Practical
Introduction; 1st ed.; Wiley-Interscience, 2009.
Practical aspects of surface calculations – k points
NANO266
14
Note: Data shown is
for unreconstructed
Si(111)
Key takeaway:
Maintaining equivalent
k-point grids is
essential to efficient
convergence!
Sun, W.; Ceder, G. Efficient creation and convergence of surface slabs, Surf. Sci., 2013, 617, 53–59, doi:10.1016/j.susc.2013.05.016.
Practical aspects of surface calculations –
functionals
NANO266
15
Singh-Miller, N. E.; Marzari, N. Surface energies, work functions, and surface relaxations of low-index
metallic surfaces from first principles, Phys. Rev. B - Condens. Matter Mater. Phys., 2009, 80, 1–9, doi:
10.1103/PhysRevB.80.235407.
Absorbates on Surfaces
NANO266
16
Sha, Y.; Yu, T. H.; Merinov, B. V; Shirvanian, P.; Goddard, W. A. Mechanism for Oxygen Reduction Reaction on Pt 3 Ni Alloy Fuel Cell Cathode,
J. Phys. Chem. C, 2012, 116, 21334–21342, doi:10.1021/jp303966u.
Applications - Catalysis
NANO266
17
Nørskov, J. K.; Abild-Pedersen, F.; Studt, F.; Bligaard, T. Surface chemistry special feature: Density functional theory in surface chemistry and
catalysis., Proc. Natl. Acad. Sci. U. S. A., 2011, 108, 937–943, doi:10.1073/pnas.1006652108.
Applications
NANO266
18
Wang, L.; Zhou, F.; Meng, Y.; Ceder, G. First-principles study of
surface properties of LiFePO4: Surface energy, structure, Wulff
shape, and surface redox potential, Phys. Rev. B, 2007, 76, 1–11,
doi:10.1103/PhysRevB.76.165435.
Sun, W.; Jayaraman, S.; Sun, W.; Jayaraman, S.; Chen, W.; Persson, K.
A.; Ceder, G. Nucleation of metastable aragonite CaCO 3 in seawater,
Proc. Natl. Acad. Sci., 2015, 201506100, doi:10.1073/pnas.1506100112.
Interfaces
NANO266
19
Grain boundaries
Chen, Y. Z.; Bovet, N.; Trier, F.; Christensen, D. V.; Qu, F. M.;
Andersen, N. H.; Kasama, T.; Zhang, W.; Giraud, R.; Dufouleur, J.;
Jespersen, T. S.; Sun, J. R.; Smith, a.; Nygård, J.; Lu, L.; Büchner,
B.; Shen, B. G.; Linderoth, S.; Pryds, N. A high-mobility two-
dimensional electron gas at the spinel/perovskite interface of γ-
Al2O3/SrTiO3, Nat. Commun., 2013, 4, 1371, doi:10.1038/
ncomms2394.
Liquid metal embrittlement
in Ni
NANO266
20
Kang, J.; Glatzmaier, G. C.; Wei, S. H. Origin of the bismuth-
induced decohesion of nickel and copper grain boundaries,
Phys. Rev. Lett., 2013, 111, 1–5, doi:10.1103/PhysRevLett.
111.055502.
Luo, J.; Cheng, H.; Asl, K. M.; Kiely, C. J.; Harmer, M. P. The Role of a Bilayer
Interfacial Phase on Liquid Metal Embrittlement, Science (80-. )., 2011, 333, 1730–
1733, doi:10.1126/science.1208774.
Solutes at Fe grain boundaries
NANO266
21
Jin, H.; Elfimov, I.; Militzer, M. Study of the interaction of solutes with ??5 (013) tilt grain boundaries in iron using density-functional theory, J.
Appl. Phys., 2014, 115, doi:10.1063/1.4867400.

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NANO266 - Lecture 11 - Surfaces and Interfaces

  • 2. Imperfections Real-world materials are not perfect infinite crystals •  Defects (substitutional, interstitial, anti-site, etc.) •  Surfaces •  Interfaces, e.g., grain boundaries NANO266 2
  • 3. The Supercell Method Create larger cell from unit cell Limitations •  Computational cost limits cell sizes and hence concentrations •  Charged defects require complicated correction procedures •  As always, test for convergence! NANO266 3 Change to Al Al in Cu example
  • 5. Lattice Planes A lattice plane of a given Bravais lattice is a plane (or family of parallel planes) whose intersections with the lattice are periodic (i.e., are described by 2D Bravais nets) and intersect the Bravais lattice; equivalently, a lattice plane is any plane containing at least three noncollinear Bravais lattice points. NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 2
  • 6. Miller indices Lattice planes are represented by Miller indices, denoted as , where h, k and l are integers. NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 2 hkl( )
  • 7. Surface construction NANO266 7 Sun, W.; Ceder, G. Efficient creation and convergence of surface slabs, Surf. Sci., 2013, 617, 53–59, doi:10.1016/j.susc.2013.05.016.
  • 8. Key considerations of surface structures 1.  Which termination? 2.  Is the termination polar? 3.  Does surface reconstruction occur? NANO266 8
  • 9. Surface terminations Symmetrically unique Most terminations break bonds – how many and which ones? NANO266 9 (010) surface in LiFePO4 PO4 group FeO6 octahedral
  • 10. Tasker Classification NANO266 10 Tasker, P. W. The stability of ionic crystal surfaces, J. Phys. C Solid State Phys., 1979, 12, 4977–4984, doi:10.1088/0022-3719/12/22/036.
  • 11. Reconstruction of Surfaces Tasker 3 -> Tasker 2b Structural distortions NANO266 11 Move half of M+ to bottom layer.
  • 12. Si(111)-(7x7) – 25 years of science! NANO266 12 https://vimeo.com/1086112
  • 13. Convergence of Surface energies Typically, most people remember convergence wrt vacuum and slab size, but convergence wrt surface area can be important, particularly if there are relaxations that can break symmetry! NANO266 13 γ = 1 2A E(Slab)− NE(bulk)[ ] Convergence wrt vacuum size Convergence wrt slab size – how many layers? Convergence wrt surface area Sholl, D.; Steckel, J. A. Density Functional Theory: A Practical Introduction; 1st ed.; Wiley-Interscience, 2009.
  • 14. Practical aspects of surface calculations – k points NANO266 14 Note: Data shown is for unreconstructed Si(111) Key takeaway: Maintaining equivalent k-point grids is essential to efficient convergence! Sun, W.; Ceder, G. Efficient creation and convergence of surface slabs, Surf. Sci., 2013, 617, 53–59, doi:10.1016/j.susc.2013.05.016.
  • 15. Practical aspects of surface calculations – functionals NANO266 15 Singh-Miller, N. E.; Marzari, N. Surface energies, work functions, and surface relaxations of low-index metallic surfaces from first principles, Phys. Rev. B - Condens. Matter Mater. Phys., 2009, 80, 1–9, doi: 10.1103/PhysRevB.80.235407.
  • 16. Absorbates on Surfaces NANO266 16 Sha, Y.; Yu, T. H.; Merinov, B. V; Shirvanian, P.; Goddard, W. A. Mechanism for Oxygen Reduction Reaction on Pt 3 Ni Alloy Fuel Cell Cathode, J. Phys. Chem. C, 2012, 116, 21334–21342, doi:10.1021/jp303966u.
  • 17. Applications - Catalysis NANO266 17 Nørskov, J. K.; Abild-Pedersen, F.; Studt, F.; Bligaard, T. Surface chemistry special feature: Density functional theory in surface chemistry and catalysis., Proc. Natl. Acad. Sci. U. S. A., 2011, 108, 937–943, doi:10.1073/pnas.1006652108.
  • 18. Applications NANO266 18 Wang, L.; Zhou, F.; Meng, Y.; Ceder, G. First-principles study of surface properties of LiFePO4: Surface energy, structure, Wulff shape, and surface redox potential, Phys. Rev. B, 2007, 76, 1–11, doi:10.1103/PhysRevB.76.165435. Sun, W.; Jayaraman, S.; Sun, W.; Jayaraman, S.; Chen, W.; Persson, K. A.; Ceder, G. Nucleation of metastable aragonite CaCO 3 in seawater, Proc. Natl. Acad. Sci., 2015, 201506100, doi:10.1073/pnas.1506100112.
  • 19. Interfaces NANO266 19 Grain boundaries Chen, Y. Z.; Bovet, N.; Trier, F.; Christensen, D. V.; Qu, F. M.; Andersen, N. H.; Kasama, T.; Zhang, W.; Giraud, R.; Dufouleur, J.; Jespersen, T. S.; Sun, J. R.; Smith, a.; Nygård, J.; Lu, L.; Büchner, B.; Shen, B. G.; Linderoth, S.; Pryds, N. A high-mobility two- dimensional electron gas at the spinel/perovskite interface of γ- Al2O3/SrTiO3, Nat. Commun., 2013, 4, 1371, doi:10.1038/ ncomms2394.
  • 20. Liquid metal embrittlement in Ni NANO266 20 Kang, J.; Glatzmaier, G. C.; Wei, S. H. Origin of the bismuth- induced decohesion of nickel and copper grain boundaries, Phys. Rev. Lett., 2013, 111, 1–5, doi:10.1103/PhysRevLett. 111.055502. Luo, J.; Cheng, H.; Asl, K. M.; Kiely, C. J.; Harmer, M. P. The Role of a Bilayer Interfacial Phase on Liquid Metal Embrittlement, Science (80-. )., 2011, 333, 1730– 1733, doi:10.1126/science.1208774.
  • 21. Solutes at Fe grain boundaries NANO266 21 Jin, H.; Elfimov, I.; Militzer, M. Study of the interaction of solutes with ??5 (013) tilt grain boundaries in iron using density-functional theory, J. Appl. Phys., 2014, 115, doi:10.1063/1.4867400.