3 p627_s13_l01 jan 22

1

Surface Properties

• Structure

• Chemical composition

• Bonding properties

• Kinetics (adsorption, diffusion, desorption, catalysis)

• Dynamics of surface processes

• Statistical mechanics of 2-D systems

Applications of Surfaces

• Catalysis

• Corrosion

• Friction, lubrication

• Semiconductor devices

• Electrochemistry hu

(IR X-rays)

e- ions heat

E-field

atoms, molecules

hu

atoms, molecules

ions

e-

Probing Surface Properties

Surface and Interface Science

Physics 627; Chemistry 542

Usually, strongly interacting probes!!

2

The first half of this course will focus on:

• Atomistic properties of surfaces

• Electronic properties

• Chemical composition

• Adsorption properties

The second half of this course will deal with applications:

• Biomedical applications

• Surface magnetism

• Calculation procedures

• Devices

Examination:

• Homework problem set (?)

• 3 labs

• Term paper

Primary text: Zangwill “Physics at Surfaces” Also: Woodruff and Delchar: Modern Techniques of Surface Science

3

Lectures 1 and 2

Surface crystallography

References:

1) Zangwill, Chapter 1

2) A.W. Andersen, Physical Chemistry of Surfaces, Fifth Edition (J. Wiley, New

York, 1990) Chapter VII

3) J.M. Blakely and M Eizenberg in Vol. 1, Clean Solid Surfaces, “The Chemical

Physics of Solid Surfaces and Heterogeneous Catalysis,” ed. By D.A. King

and D.P. Woodruff (Elsevier, Amsterdam, 1981) p. 1

4) G. A. Somorjai, Introduction to Surface Chemistry and Catalysis, Chapter 3.

5) A. Keijna and K.F. Wojcieckowski, Metal Surface Electron Physics, Chapter 3;

Chapter 8.

4

Simple cubic (sc)

Surface structure – starting with the bulk

5

hcp vs fcc

6

Miller Indices

For simple cubic lattice,

consider plane that is shaded.

Vector from origin intercepts

that plane at x, y, z = 1, ,

The Miller indices of this plane are:

0,0,11

,1

,1

1

x

y

In two dimensions (2D crystals)

intercept (, 1) (0, 1)

intercept (1, 1) (1, 1)

7

A. Bulk truncation structures

Miller Indices (more)

• For plane with intersections bx, by, bz write:

• If all quotients intergers or 0, this is a Miller Index.

e.g., 1, 1, 0.5 (112)

For cubic 1 (100)

In general: (i j k) =

where cd = smallest common denominator

Here (i j k) =

In fcc and bcc

x, y, z, -x, -y, -z all equivalent (100), (010), , etc.

all equivalent.

NOTE: (i j k) identifies plane;

[i,jk] identifies vector ^ plane defines direction.

zyx bbb

1,

1,

1

zyx b

cd

b

cd

b

cd,,

)364(3

12,

2

12,

4

12

)001(

x

z

y

bz

bx

by

x

z

y [100]

x

z

y

3

4

2

(100)

]034[

]204[

8

Very different surfaces:

Close packed: fcc(111) bcc(110)

Very rough: fcc(210) bcc(111)


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 between two planes:

222222

cosnmlkji

lmnijk

47.1963

112cos

e.g., for [1 1 1] and [2 1 1] :

bcc: 8 n.n. fcc: 12 n.n.

[l m n]

[i j k]

9

A. Bulk truncation structures fcc(100) fcc(110) fcc(111)

bcc(100) bcc(110) bcc(111)

hcp(100) hcp(110) hcp(111)

11

But i + j = -k

So often use 3-digit notation

Basal plane (b): (0 0 0 1) = (0 0 1)

Side (c)

Side (d)

In hcp, (1 0 0) (0 0 1)

NOTE: fcc(111) and hcp (0001) have same top layer structure,

but stacking is different: hcp: ABAB…; fcc: ABCABC…


zwyx b

cd

b

cd

b

cd

b

cdijkl

01101

1

11

1

1

For HCP surfaces:

11011

1

1

1

1

11

12

Wurtzite = hcp + basis

Example: GaN

Zinkblende = two

interpenetrating fcc

lattices

Example: GaAs, ~ Si (all

atoms the same)

More than one kind of atoms

13

A B C

Side view of 4-H silicon carbide. A,

B and C are three inequivalent

rows of atoms.

Stacking: a-b-c-b-a …

Red = Si, Black = C

Note the two different

terminations

Polar surfaces

14


15

B. Relaxations and reconstructions

Relaxation: no lateral motion

Usually vertically inwards,

sometime outwards

Crystal termination often not bulk-like

Shifts in atomic positions may be perpendicular and/or parallel to surface

Selvedge region extends several atomic layers deep

Rationale for metals: Smoluchowski smoothing of surface electronic charge

dipole formation

For semiconductors: heal “dangling bonds;

often lateral motion. Relax. Often oscillatory

dbulk

d12 d34

d56

d45

d23 Surface d12(%)

Ag(110) -8

Al(110) -10

Au(100) 0

Cu(110) -10

Cu(310) -5

Mo(100) -12.5

surf

ace

bulk

16

Periodic Lattice: repeat unit is unit cell

C. Classification of 2-D periodic structures

Unit cell is not unique.

Propagate lattice: n, m integers

Primitive cell: unit cell w/smallest

area, shortest lattice vectors,

smallest number of atoms

(if possible: |a1| = |a2|; g = 60, 90, 120;

1 atom)

Symmetry: translational symmetry // surface;

rotational symmetry: 1, 2, 3, 4, 6

mirror planes; glide planes.

All 2-D structures w/1 atom/unit cell have

at least one two-fold axis.

21 amanT

17

For 1 atom/cell and 2-D periodic structure, only 5 symmetrically different lattices

Bravais Lattices

C. Classification of 2-D periodic structures

When more than 1 atom/cell, more

complicated

•5 Bravais lattices

•10 2-D point symmetry groups

•17 types of surface structure

D. Substrate and Surface Structures Suppose overlayer of substrate surface layer has lattice different from bulk:

Substrate:

Overlayer:

21 amanTa

21 bmbnTb

18

Wood’s Notation: Simplest, most descriptive notation method

(NOTE: fails if a a’ or bi/ai irrational)

Ra

b

a

b

2

2

1

1

D. Substrate and Surface Structures

a1

a2

b1

b2

ai

aj

bi

bj

a

a’

Determine relative magnitude of respective a’s and b’s.

Identify angle of rotation ( = 0˚ here).

Notation: for above overlayer, (2 x 2) [often called p(2 x 2)]

3033 R(2 x 2)

¹

Hexa

gonal

19


Classification of Lattices

20

Examples of

coincidence lattice

Note that symmetry

does not identify

adsorption sites

all (2 X 2)

= 1/4

Domain structures:

(1 X 2) = (2 X 1)


21


Another complication:

indexing of stepped surfaces

Ambiguity: fcc(110) reconstruction models for (2 X 1) periodicity

Missing Row Paired Row Saw Tooth

3 p627_s13_l01 jan 22

Documents