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ChE 553 Lecture 2 Surface Notation 1

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Objectives Learn Notation To Describe the Structure Of Surfaces –Bravis Lattices: BCC, FCC, HCP –Miller Indicies: (111), (100), (110) –Woods Notation: (2x2), (7x7) 2

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Introduction to Surface Structure Key idea: metals are crystals with known crystal patterns. When you make/cut a surface the surface structure often looks like a termination of bulk. 3 Ha ü y ’ s [1801] illustration of how molecules can be arranged to form a dodecahedron

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Different Features In Crystals: Terraces Steps Kinks 4 Terrace StepKink

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Images Of Surfaces 5 Picture of the Surface Of A Tungsten Needle Moh'd Rezeq, Avadh Bhatia Jason Pitters, Robert Wolkow J. Chem. Phys. 124, (2006)

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Can Be Crystalline (Periodic) Or Non-Crystalline (Non-Periodic) But Crystalline Dominates 6

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Next Changing Topics: Notations For Crystal Structure, Surface Structure General idea: Figure out the basic repeat unit of the surface Develop notation to describe the repeat unit Notation: Unit cell- Basic repeat unit Primitive unit cell - unit cell with smallest repeat unit 7

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Illustration Of Basic Repeat Unit 8

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Repeat Unit Not Unique: 9 axax ayay

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Next Bravis Lattices: Idea – classify unit cells in terms of their symmetry properties, space groups There are only 6 primitive Bravis lattices in two dimensions two of which (obliques) are equivalent 10 ConventionalAxes of Conventional LatticeAxes of Primitive CellCell Obliquea x ≠ a y, γ ≠ 90˚ or 120˚Parallelograma x ≠ a y, γ ≠ 90˚ or 120˚ Centered rectanglea x = a y, γ ≠ 90˚ or 120˚Rectanglea x ′ ≠ a y ′, γ′ = 90˚ Primitive rectanglea x ≠ a y, γ = 90˚Rectanglea x ≠ a y, γ = 90˚ Hexagonal a x = a y, γ = 120˚ with a sixfold axis Hexagonala x = a y, γ = 120˚ Obliquea x ≠ a y, γ = 120˚Parallelograma x ≠ a y, γ = 120˚ Square a x =a x square a x =a y x=90 0

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11 Hexagon Square Rectangle Centered RectangleOblique

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Special Issue With Centered Rectangle 12 Primitive Unit Cell Conventional Unit Cell

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One Needs To Also Know The Space Group To Define The Atomic Arrangement There can be more than one atom per unit cell. 13

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Notation For Rotation Axis 14

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Notation For Mirror Planes 15

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Total Of 17 Combinations 16

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Similar Discussion Applies To 3 Dimensional Space Groups 17

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Pictures Of Lattice Groups 18

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Much Less Difference Between Lattices Than It Would Appear From Diagrams On The Previous Chart 19

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FCC, BCC, HCP All have stacked nearly hexagonal planes 20 BCC (110)FCC (111)HCP (001)

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Variation In Crystal Structure Over Periodic Table 21

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Next Miller Indices Designate a plane by where it intersects the axes 22

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Miller Indices Continued 23

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Next The Structure Of Solid Surface Idea: cut surfaces and see what atoms left 24

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(111), (100), (110) Of FCC 25 Figure 2.29 The (111), (110), and (100) faces of a perfect FCC crystal. (111) (100) (110)

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General Overview Of Structure: FCC 26

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Trick To Quickly Work Our Surface Structure 27 (331)=2(110)+(111) (110)(111)(311)

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BCC Looks Similar But Indicies Different 28

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General View: BCC 29 BCC (LMN) FCC(L, M+N, M-N)

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HCP Different 30

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Relaxations: Distances Between Planes Shrink 31 Reconstructions: Atoms rearrange to relieve dangling bonds

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Next Surface Reconstructions 32 These ideal structures only an approximation: real structures change when atoms removed: Two kinds of changes: relaxations and reconstructions

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More Complex Reconstructions 33

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Silicon (111) Reconstructions 34

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Si(100) Reconstruction 35

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Si(111) Reconstruction 36

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Woods Notation For Overlayers 37 Pt(110)(1x2)

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Example: Calculate the Phase Behavior For Adsorption On A Square Lattice 38 Figure 4.22 The absorption of molecules in a P(2x2), C(2x2), (2x1) overlayer. The dark circles represent sites, the red circles represent adsorption on the sites.

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Summary Surfaces are often periodic - if metal is periodic, surface will be periodic with defects. Designate symmetry by space & point group For metals FCC, BCC, HCP most important. Need miller indices to define plane Surface structures often relax or reconstruct. 39

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