SURFACE STRUCTUREleung.uwaterloo.ca/CHEM/750/Lectures 2007/SSNT-3 Surface Struct… · SURFACE STRUCTURE A surface is often described as a “selvedge”, i.e. a region with finite

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SURFACE STRUCTURE A surface is often described as a “selvedge”, i.e. aregion with finite thickness but no periodicity in thedirection normal to the surface. This region derivesfrom the “bulk” (sometimes referred to as the“substrate”). We will start by reviewing what wealready know about the basic lattice structure of the“bulk” (the subject of Solid State Chemistry or SolidState Physics). In particular, we will first discuss someof the fundamental concepts including the basicdescriptions of the crystal structure, Xray diffraction,reciprocal lattices and Brillouin zones. We will thenproceed to discuss the structure of the “selvedge”,which in some ways is simpler (because of thereduction from 3D to 2D) but in other ways morecomplex (because of the loss of continuity in the thirddimension). Finally, we will describe electrondiffraction as a means to determine the surfacestructure. 1. Review of “bulk” crystallography, and crystalstructure



We define earlier that a surface has twodimensionalproperties and it usually consists of not just the toplayer but lower layers whose properties deviate fromthose of the bulk (i.e. properties change with the“depth” dimension). When we reach a layer whoseproperties are identical to those of its lower layers, thenwe say that we have reached the “bulk” (or substrate)region. This part of the solid is the region of interest inSolid State Chemistry and Physics and is what we willdiscuss here. Ref: Structure & Bonding or Introductory InorganicChemistry Crystal structure A crystal is defined as a

periodic 3D array of atoms. This 3D array is calledthe lattice and it can be generated from its unit cell.

Symmetry elements and operations (5) There

are many symmetry operations corresponding tosymmetry elements (line or plane). For pointgroups, there are five such general types ofoperations:

Identity (E)



Rotation (Cn) Reflections () Inversion (i) Improper rotation (Sn) Point groups (32+9 = 41) A group can be defined

as a set of elements, each represents a symmetryoperation and all of which obey a set ofmathematical relationships (e.g. identity, products,squares and reciprocals of elements, associativelaw of multiplication, commutative property).

A point group contains symmetry elements andoperations which leave at least one point of the object(e.g. a single atom in a molecule) unchanged. There are32 threedimensional point groups that are common toboth crystals and free molecules (see table below) andthe remaining 9 groups occur only in free molecules.



Class Group



Triclinic C1 CiMonoclinic C2 Cs C2hOrthorhombic D2 C2v D2hTetragonal C4 S4 C4h D4 C4v D2d D4hTrigonal C3 S6 D3 C3v D3dHexagonal C6 C3h C6h D6 C6v D3h D6hCubic T Th O Td Oh7 32 A class consists of a complete set of elements that areconjugate with each other (i.e. If A, B and X are groupelements, then A and B are conjugates if A = X1BXand B = XAX1).



Bravais lattices (14) Hard to give a precisedefinition. A Bravais lattice is usually used toindicate a distinct lattice type, which is defined by aset of restrictions on the lattice parameters: a, b, cand .

There are 14 (each is described by its own latticeparameters) Bravais lattices, which can be separatedinto the seven systems or classes as discussed above. We can think of Bravais lattices as “skeleton” 3Dmeshes or grids when we combine the “translation”operation with the point groups. See below.



Space groups (230) There are tons... 230 in total(for crystals). When symmetry elements andoperations are considered for an extensive array ofmolecules, we must include additional symmetryelements which lead to translation of an object inspace. These additional (translationrelated)elements combined with point groups give rise tothe formation of space groups. Note that certainsymmetry point groups are forbidden in crystalsbecause they cannot be combined with translationrelated elements to give repetitive structures. Forinstance, groups with 5fold and ∞fold axes arenot allowed. In essence, the Bravais lattices definesuch restrictions and when combined with the pointgroups give the space groups.



Notation of a plane A plane can in general be

defined by three noncollinear points, each with its(x,y,z) coordinates, but it is easier to identify a planeby Miller indices (h, k, l). The “normal” of theplane is written as [h, k, l].

Recipe to label a plane: (a) Find the intercepts of theplane on axes a, b and c in terms of lattice constants(of the unit cell ). (b) Take the reciprocals of thesenumbers and then reduce to three integers h, k, l withthe same constant. The plane is defined by theseintegers (h, k, l).



EXAMPLE A plane intercepts the axes at 3a, 2b and 2c and hasreciprocals of 1/3, 1/2, and 1/2. Convert all of these tothe smallest integers (i.e. multiple by 6) to give 2,3,3. The plane is given by (2,3,3).



EXAMPLES OF COMMON CRYSTALSTRUCTURES

F, (Cl, Br, I), O, (S), Ga, CsCl cubic



Ni, (Pd, Pt), Cu, (Ag, Au), Ne, (Ar, Kr, Xe), NaCl fcc



Li, (Na, K, Rb, Cs, Fr), Ti, V, (Nb, Ta), Cr, (Mo, W),

Mn, Fe bcc



H, He, Mg, Ti, (Zr, Hf), Zn, (Cd), Co hcp



C, Si, Ge diamond



GaAs

EXERCISE Find out the crystal structures for ZnS(Wurtzite or Zinc Blend) and ZnSe. Exception: Glass Ref: Crystal Lattice Structures [ http://www.tf.unikiel.de/matwis/amat/def_en/kap_1/basics/b1_3_1.html ]

Chemical Elements [http://www.chemicalelements.com/show/crystalstructure.html ]

http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_1/basics/b1_3_1.htmlhttp://www.chemicalelements.com/show/crystalstructure.html

SURFACE STRUCTUREleung.uwaterloo.ca/CHEM/750/Lectures 2007/SSNT-3 Surface Struct… · SURFACE STRUCTURE A surface is often described as a “selvedge”, i.e. a region with finite

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