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

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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

Surfaces

Slab + Vacuum

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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

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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.

Key considerations of surface structures

1.  Which termination?

2.  Is the termination polar?

3.  Does surface reconstruction occur?

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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

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.

Reconstruction of Surfaces

Tasker 3 -> Tasker 2b

Structural distortions

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Move half of M+ to bottom layer.

Si(111)-(7x7) – 25 years of science!

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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!

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γ =12A

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

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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.

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.

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.

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.

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.

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.

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.

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.