Surface Structure II crystal structure of elements Bravais lattices, Miller indices, Weber symbols close-packing, fcc, hcp, bcc, stacking faults low-index surfaces, reconstructions: fcc metals, silicon

14 Bravais lattices: supplemental reading: Ch.3, Desjonqueres

Miller indices (hkl): directions: [hkl] family of directions: planes: (hkl) family of planes: {hkl} [001] [010] [001] a b c to identify planes: Step 1 : Identify the intercepts on the x-, y- and z- axes. Step 2 : Specify the intercepts in fractional coordinates Step 3 : Take the reciprocals of the fractional intercepts

Miller indices (hkl): e.g.: cubic system: to identify planes: Step 1 : Identify the intercepts on the x-, y- and z- axes (a/2, ∞, ∞) Step 2 : Specify the intercepts in fractional co-ordinates (a/2a, ∞, ∞) = (1/2,0,0) Step 3 : Take the reciprocals of the fractional intercepts (2, 0, 0) careful: Only for cubic systems! surface normal has the same Miller indices as the plane (e.g. [111] perp. to (111)) (210) (110) (111) (100)

hexagonal systems label ‘low-index’ planes parallel to c axis: 4 indices (Weber symbols), one is redundant: (a b t c) a + b + t = 0 t a = b, c  = 120°

periodic table: Hexagonal closed packed (hcp) face-centered cubic (fcc) body-centered cubic (bcc)

close packing! face-centered cubic (fcc) or cubic close packing (ccp) hexagonally closed packed (hcp) A BC ABCABC... A B ABAB...

Shockley notation: A B C A B C A B C... ccp C B A C B A C B A... ccp A B C A B C B C A B C... ccp with dislocation A B C A B C B A C B A... twinned crystal e.g., Co: ccp - > 25° A B A A B A B A B... hcp B A B A B A B A B... hcp

fcc(100)

Pt fcc(100) - ‘hex reconstruction’ G. Ritz, M. Schmid, P. Varga, A. Borg, and M. Rønning The Pt(100) quasihexagonal reconstruction: A comparison between STM data and EMT simulation calculations Phys. Rev. B 56 (1997)

fcc(110)

STM of fcc(110) - ‘missing-row reconstruction’ F. Besenbacher, U. Aarhus

fcc(111)

fcc(111) - ‘Herringbone reconstruction’ Stroscio et al Au(111) ML Fe

herringbone reconstruction - surface stress O. Schaff, A.K. Schmid, N.C. Bartelt, J. de la Figuera and R.Q. Hwang, Sandia The characteristic dislocation networks present on the surfaces of Au thin films can be changed by bending the substrates to which the films are attached. Monitoring such changes as a function of strain in thin films offers a precise experimental probe of the balance between the various forces that are responsible for the complicated dislocation networks that often occur on metal surfaces.

-> the tendency to pack surfaces even more closely drives many reconstructions on fcc materials!

Silicon: tetrahedrally coordinated, two fcc lattices, shifted by 1/4 of the body diagonal “dangling bonds” - reconstructions minimize the ‘dangling bonds’

Silicon (001)-(1x2) ‘buckled dimer rows’ NonTech.html

Silicon (001)-(1x2) M. Lagally, Wisconsin Growth of Si/Si(001) - anisotropic diffusion! A-step B-step

one of the most inert surfaces available. H can be ‘stimulated’ off the surface with e-beam bombardment (e.g., with the STM tip) -- template for growth - ‘nanolithography’

Silicon (111)

Si(111)-(7x7)

Si(111)-7x7 surface Takayanagi et al. 1985

Surface Structure II - summary Bravais lattices, Miller indices, Weber symbols - need to know! low-index metal surfaces: fcc metals: (100), (110), (111) - reconstructions: close packing rules! silicon (100), (111): minimize ‘dangling bonds’

HW3 due Feb 1, 2005 Consider tungsten. a) Find its crystal structure (type ?, lattice constant a = ?Å). Make a drawing of the atoms within the unit cell. b) The W (110) surface is quite popular in surface science. Why? Give your own arguments (based on what you’ve learned in the lecture) and see what you can find in the literature about this material. c) Make a drawing of the W(111) surface. What do expect to happen with this surface? Can you assert your assumption by reading up on the current literature?