ChE 553 Lecture 2

1. ChE 553 Lecture 2 Surface Notation

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

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. Haüy’s [1801] illustration of how molecules can be arranged to form a dodecahedron

4. Different Features In Crystals: Terraces Steps Kinks Terrace Step Kink

5. Images Of Surfaces 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

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

8. Illustration Of Basic Repeat Unit

9. Repeat Unit Not Unique: ay  ax

10. Conventional Axes of Conventional Lattice Axes of Primitive Cell Cell Cell Oblique ax ≠ ay, γ ≠ 90˚ or 120˚ Parallelogram ax ≠ ay, γ ≠ 90˚ or 120˚ Centered rectangle ax = ay, γ ≠ 90˚ or 120˚ Rectangle ax′ ≠ ay′, γ′ = 90˚ Primitive rectangle ax ≠ ay, γ = 90˚ Rectangle ax ≠ ay, γ = 90˚ Hexagonal ax = ay, γ = 120˚ with a sixfold axis Hexagonal ax = ay, γ = 120˚ Oblique ax ≠ ay, γ = 120˚ Parallelogram ax ≠ ay, γ = 120˚ 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

11. Square Rectangle Hexagon Centered Rectangle Oblique

12. Special Issue With Centered Rectangle 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.

14. Notation For Rotation Axis

15. Notation For Mirror Planes

16. Total Of 17 Combinations

17. Similar Discussion Applies To 3 Dimensional Space Groups

18. Pictures Of Lattice Groups

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

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

21. Variation In Crystal Structure Over Periodic Table

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

23. Miller Indices Continued

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

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

26. General Overview Of Structure: FCC

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

28. BCC Looks Similar But Indicies Different

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

30. HCP Different

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

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

33. More Complex Reconstructions

34. Silicon (111) Reconstructions

35. Si(100) Reconstruction

36. Si(111) Reconstruction

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

38. Example: Calculate the Phase BehaviorFor Adsorption On A Square Lattice 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.