1. ChE 553 Lecture 2 Surface Notation 1

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

3. 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

4. Different Features In Crystals: Terraces Steps Kinks 4 Terrace StepKink

5. 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, 204716 (2006)

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

7. 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

8. Illustration Of Basic Repeat Unit 8

9. Repeat Unit Not Unique: 9 axax ayay 

10. 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 2 90 0 square a x =a y x=90 0

11. 11 Hexagon Square Rectangle Centered RectangleOblique

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

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

14. Notation For Rotation Axis 14

15. Notation For Mirror Planes 15

16. Total Of 17 Combinations 16

17. Similar Discussion Applies To 3 Dimensional Space Groups 17

18. Pictures Of Lattice Groups 18

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

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

21. Variation In Crystal Structure Over Periodic Table 21

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

23. Miller Indices Continued 23

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

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

26. General Overview Of Structure: FCC 26

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

28. BCC Looks Similar But Indicies Different 28

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

30. HCP Different 30

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

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

33. More Complex Reconstructions 33

34. Silicon (111) Reconstructions 34

35. Si(100) Reconstruction 35

36. Si(111) Reconstruction 36

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

38. 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.

39. 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