Surface and Interface Science Physics 627; Chemistry 542. Lectures 3 Feb 1, Surface Structure
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1 Surface and Interface Science Physics 67; Chemistry 54 Lectures 3 Fe, 03 Surface Structure References: ) Zangwill, Pp. 8-3 ) Woodruff & Delchar, Chapter 3) Masel, Chapter 4) Ertl & Kuppers, ) Luth, ) Attard and Barnes, 7 -
2 x x [00] x [403] 4 x z z z z 3 y A. Bulk truncation structures (00) [40] y y y Miller Indices (again) For plane with intersections x, y, z write: If all quotients rational or 0, this is Miller Index. e.g.,,, 0.5 () For cuic (00) In general: (i j k) = cd cd cd,, x y z where cd = common denominator Here (i j k) = 4,, 3 (364) x, In fcc and cc x, y, z, -x, -y, -z all equivalent (00), (00), (00), etc. all equivalent. NOTE: (i j k) identifies plane; [i,jk] identifies vector ^ plane defines direction. y, z
3 A. Bulk truncation structures Very different surfaces: Close packed: fcc() cc(0) Very rough: fcc(0) cc() cc: 8 n.n. fcc: n.n. Note: Cross product of two vectors in a plane defines direction perp. to plane: [i j k] = [s t w] x [p q r] where latter vectors lie in (i j k). Angle etween two planes: ijk lmn [i j k] [l m n] cos i j k e.g., for [ ] and [ ] : l m cos n
4 A. Bulk truncation structures fcc(00) fcc(0) fcc() cc(00) cc(0) cc() hcp(00) hcp(0) hcp() 4
5 For HCP surfaces: ijkl But i + j = -l So often use 3-digit notation Basal plane (): (0 0 0 ) = (0 0 ) Side (c) cd x A. Bulk truncation structures cd y cd w cd z 00 Side (d) 0 In hcp, ( 0 0) (0 0 ) NOTE: fcc() and hcp (000) have same top layer structure, ut stacking is different: hcp: ABAB ; fcc: ABCABC 5
6 Other structures: A. Bulk truncation structures Wurtzite (hex w/tetrahedral onds), Zinclend (interpenetrating fcc lattice) NOTE: polar terminations not equivalent Diamond (or Si): Like zinclend, ut all atoms the same Stereographic projection: Surface atom density: ~ 0 5 6
7 A. Bulk truncation structures 7
8 surface B. Relaxations and reconstructions Crystal termination often not ulk-like Shifts in atomic positions may e perp and/or parallel to surface Selvedge region extends several atomic layers deep Rationale for metals: Smoluchowski smoothing of surface electronic charge dipole formation Inward relaxation; little or no lateral motion For semiconductors: heal dangling onds; often lateral motion. Relax. Often oscillatory d 3 d 45 Surface d (%) d ulk d ulk d 34 d 56 Ag(0) -8 Al(0) -0 Au(00) 0 Cu(0) -0 Cu(30) -5 Mo(00) -.5 8
9 C. Classification of -D periodic structures Periodic Lattice: repeat unit is unit cell Unit cell is not unique. Propagate lattice: n, m constants T na m a Primitive cell: unit cell w/smallest area, shortest lattice vectors, smallest numer of atoms (if possile: a = a ; g = 60, 90, 0; atom) Symmetry: translational symmetry // surface; rotational symmetry:,, 3, 4, 6 mirror planes; glide planes. All -D structures w/ atom/unit cell have at least one two-fold axis. 9
10 C. Classification of -D periodic structures For atom/cell and -D periodic structure, only 5 symmetrically different lattices Bravais Lattices When more than atom/cell, more complicated 5 Bravais lattices 0 -D point symmetry groups 7 types of surface structure D. Sustrate and Surface Structures Suppose overlayer of sustrate surface layer has lattice different from ulk: Sustrate: Overlayer: T a T na n m m a 0
11 Hexagonal D. Sustrate and Surface Structures Wood s Notation: Simplest, most descriptive notation method (NOTE: fails if a a or i /a i irrational) a i a a j a a ¹ a j Determine relative magnitude of respective a s and s. Identify angle of rotation (= 0 here). Notation: for aove overlayer, ( x ) [often called p( x )] a a R i ( x ) 3 3R30
12 D. Sustrate and Surface Structures Matrix Notation: Use mtx to transform sustrate asis vectors, a, a, into overlayer asis vectors,, G Ga Ga a Ga where: Gˆ G G G G so that: ˆ a G a For p( X ) on cuic (00) a 0 0 a Ĝ 0 0 For p( X ) on fcc() a 0 0 a Ĝ 0 0 For a a a a 3 3 R30 on fcc() Ĝ Areas: A = a X a ; B = X ; det G ˆ B / A
13 D. Sustrate and Surface Structures Comparison of Wood s and Matrix Notation Classification of Lattices (a) Simple: All G ij are integers all sites identical in overlayer (strong corrugation). Here = a () Coincidence: one or more of G ij are rational numers different types of sites 3 (c) Incoherent: one or more of G ij are irrational inf. Numer of ads sites, flat surface pot l.
14 D. Sustrate and Surface Structures Examples of coincidence lattice Note that symmetry does not identify adsorption sites, only all ( X ) how many there are = /4 Domain structures: ( X ) = ( X ) 4
15 D. Sustrate and Surface Structures Amiguity: fcc(0) reconstruction models for ( X ) periodicity Missing Row Paired Row Saw Tooth Another complication: indexing of stepped surfaces 5
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