UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.

1. Surfaces and Interfaces
Shyue Ping Ong

2. Imperfections
Real-world materials are not perfect infinite
crystals
• Defects (substitutional, interstitial, anti-site, etc.)
• Surfaces
• Interfaces, e.g., grain boundaries
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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!
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Change to Al
Al in Cu example

4. Surfaces
Slab + Vacuum
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With PBC

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
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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?
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9. Surface terminations
Symmetrically unique
Most terminations break bonds – how many and which
ones?
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(010) surface in LiFePO4
PO4 group
FeO6 octahedral

10. Tasker Classification
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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
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Move half of M+ to bottom layer.

12. Si(111)-(7x7) – 25 years of science!
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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!
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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
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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
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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
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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
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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
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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
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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
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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
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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.