CHEN4235 - Lecture - Surface Structure

Structures of Solid Surfaces & Adsorbates
Useful reading materials: Textbook: 2.1-2.9
Learning objectives:
1. Most common Bravais lattices and low-index planes
2. Relaxation and reconstruction of solid surfaces
3. Adsorbate/surface structures: real and reciprocal spaces
4. Experimental technique to measure surface structure: Low

Energy Electron Diffraction (LEED)
Well-defined Surfaces as Model Catalysts
1. Transition from “trial-and-error” to rational design of

catalysts requires atomic-level understanding:
- Single crystal surfaces with well-characterized arrangement of
atoms and adsorbates
- Theoretical methods, such as density functional theory (DFT),
use single crystal surfaces as model catalysts
2. Modern synthesis techniques produce catalyst particles

with well-defined structures:
- Cube: surfaces are (100) planes
- Octahedron and pyramid: surfaces are (111) planes
3. For thermodynamic reasons, low-index surfaces, such as

(100), (110) and (111), are dominant planes in catalyst
particles.
Nomenclature of Solid Structures and Surfaces
1. There are 7 crystal structures:
- Structures with 90o angles: Cubic, Tetragonal, Monoclinic,
Orthorhombic
- Structures without 90o angles: Hexagonal, Triclinic,
Rhombohedral
2. There are 14 Bravais lattices:

- primitive (atoms at corners of crystal structures)
- face-centered (additional atoms on all planes of crystal
structures)
- Side-centered (additional atoms at sides of crystal structures)
- body-centered (additional atoms inside crystal structures)
3. There are 3 most common Bravais lattices for catalysts:

- face-centered cubic (FCC or fcc)
- body-centered cubic (BCC or bcc)
- hexagonal closed packed (HCP or hcp)
Common Bravais Lattices for Metal Catalysts
There are 3 most common Bravais lattices for catalysts:

- face-centered cubic (FCC or fcc)
- body-centered cubic (BCC or bcc)
- hexagonal closed packed (HCP or hcp)
Most Metal Catalysts are Transition Metals
Bravais Lattices: FCC, BCC, HCP
Question: why are transition metals good catalysts

Nomenclature of Surface Planes
The atomic arrangement of a single crystal surface is

described using Miller index:
- For cubic structures (FCC and BCC), a three-integer system is

used inside a parenthesis: (hkl)
e.g. Pt(100), Pt(111), Pt(211), Pt(547), etc.
- For hexagonal structure (HCP), a four-integer system is used

inside a parenthesis: (hkil)
e.g. Co(0001), Co(1011), etc.
Examples of Low Miller-Index Planes
- The “-” above a number means negative with respect to origin

- Low Miller-index: typically the h, k and l values are 1 or 2
Procedures for Identifying Planes for FCC and BCC
1. Draw plane away from coordinate (x=0,y=0,z=0)

2. Determine the intercepts of plane on each axis, x, y, and z
3. Take reciprocals of intercepts
4. If necessary, normalize the 3 numbers to smallest integers
by multiplying or dividing by a common factor
5. Use the three numbers to describe the plane (hkl)
Example: FCC(110)
Nomenclature of Surface Directions
The direction on a single crystal surface is described using

numbers inside a bracket:
- For cubic structures (FCC and BCC), a three-integer system is
used inside a bracket: [uvw]
e.g. [100], [111], [211], etc.
- For hexagonal structure (HCP), a four-integer system is used

inside a bracket: [uvtw]
e.g. [0001], [1011], etc.
Procedures for Identifying Directions for FCC and BCC
1. Draw vector starting from coordinate (x=0,y=0,z=0)

2. Determine the projection of the vector on each axis, x, y,
and z
3. If necessary, normalize the 3 numbers to smallest integers
by multiplying or dividing by a common factor
4. Use the three numbers to describe the direction [uvw]
Example: [120]
Procedures for Converting Cubic[uvw] to Hexagonal[uvtw]
Not required for this class
Comparison of Surface Structures of FCC
Comparison of Surface Structures of BCC
Comparison of Surface Properties
Different surfaces have different coordination number (CN),

which is the number of atoms that are bonded to a surface atom.
Different CN leads to different electronic properties, which play a
role in controlling catalytic performance.
CN Bulk (100) (110) (111)

FCC 12 8 7 top 9
layer
BCC 8 4 top 6 some 4,
layer some 7
Comparison of Surface Properties
Different surfaces have different symmetries, which would play a

role in controlling catalytic reaction pathways.
Symmetry (100) (110) (111)
FCC Square Rectangle Hexagon
BCC Square Quasi- Triangle

hexagon
Calculating Surface Packing Density
Aatom: area occupied by atoms

AUC: area of unit cell
Surface packing density: r = Aatom/AUC
Example: FCC(100)
Aatom = # of atoms x pr2 = pr2

# of atoms = conner x ¼ + edge x ½ + center x 1= 4 x ¼ =1
AUC = a x a; a = 2r; AUC = 4r2
r = pr2/4r2 = 78.5%
Packing density: FCC(111) > FCC(100) > FCC(110)

Step (or Stepped) Surfaces
When a surface is not perfectly cut along the direction of low Miller-index
surfaces, atoms can rearrange to make stepped surfaces consisting of steps
and terraces, often referred to as high Miller-index surfaces.
Surface Relaxation
Compared to atoms in the bulk, surface atoms are under-coordinated and are
relatively unstable. One way to achieve stability is by surface relaxation,
where the bond distance between the 1st and 2nd layers are shorter (stronger
bond) than in the bulk.
Surface Reconstruction
Another way to achieve stability is by surface reconstruction, where the top
layer atoms on the FCC(110) (CN=7) and FCC(100) (CN=8) surfaces are
reconstructed into FCC(111) (CN=9).
Surface Reconstruction of Semiconductors
Surface reconstruction is very common in semiconductors, such as the Si
single crystal surfaces in many electronic devices.
Wood’s Notation of Surface Structures
For reconstructed surfaces or surfaces with adsorbates, Wood’s notation is
used describe the surface structure by identifying the repeating surface unit
cell with respect to that of the bulk.
p (primitive); c (atoms in center of unit cell); R (rotating angle)

Matrix Description of Surface Structures
Low Energy Electron Diffraction (LEED)
- LEED is an experimental technique to determine the surface structures

- Similar to XRD, LEED is a diffraction technique based on patterns
generated from the constructive interference of scattered particles
- However, LEED is a two-dimension scattering technique (XRD is 3-D) and
LEED utilizes low energy electrons (XRD uses X-ray photons)
- The scattering patterns in LEED are in reciprocal space instead of real
space. Therefore, experimentally observed LEED patterns need to be
converted from reciprocal space into real space surface structures.
- One advantage of describing the real space surface structures using
Matrix (instead of Wood’s notation) is that it can be easily converted to
reciprocal space (or vice versa) using the Matrix operation.
Matrix Conversion between Real and Reciprocal Space
LEED Technique
Examples of LEED Patterns
Example: Converting Surface Structure into LEED Pattern
Example: Converting Surface Structure into LEED Pattern

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Structures of Solid Surfaces & Adsorbates

Useful reading materials: Textbook: 2.1-2.9

1. Most common Bravais lattices and low-index planes

2. Relaxation and reconstruction of solid surfaces

3. Adsorbate/surface structures: real and reciprocal spaces

4. Experimental technique to measure surface structure: Low

1. Transition from “trial-and-error” to rational design of

2. Modern synthesis techniques produce catalyst particles

3. For thermodynamic reasons, low-index surfaces, such as

2. There are 14 Bravais lattices:

3. There are 3 most common Bravais lattices for catalysts:

There are 3 most common Bravais lattices for catalysts:

Question: why are transition metals good catalysts

The atomic arrangement of a single crystal surface is

- For cubic structures (FCC and BCC), a three-integer system is

- For hexagonal structure (HCP), a four-integer system is used

- The “-” above a number means negative with respect to origin

1. Draw plane away from coordinate (x=0,y=0,z=0)

The direction on a single crystal surface is described using

- For hexagonal structure (HCP), a four-integer system is used

1. Draw vector starting from coordinate (x=0,y=0,z=0)

Different surfaces have different coordination number (CN),

CN Bulk (100) (110) (111)

Different surfaces have different symmetries, which would play a

Symmetry (100) (110) (111)

FCC Square Rectangle Hexagon

BCC Square Quasi- Triangle

Aatom: area occupied by atoms

Aatom = # of atoms x pr2 = pr2

Packing density: FCC(111) > FCC(100) > FCC(110)

p (primitive); c (atoms in center of unit cell); R (rotating angle)

- LEED is an experimental technique to determine the surface structures

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