Surface and bulk

Surface and Bulk

Dr Ts’enolo J. Lerotholi

Room 203 (Humphrey Raikes Building)

Email: [email protected]

Course Structure

1. preamble - why surfaces and how can we study them?

2. surface composition - surface analysis v. surface science

3. surface structure - phenomenology and determination

4. surface electronic structure - surface states, surface bands

5. adsorption at surfaces - chemisorption, physisorption,vibrational, electronic and geometric structure

Why surfaces?Fundamental: A surface is a special kind of defect in a perfect 3-D

periodic solid with different geometrical (atomic) and electronic

structure

Practical:

all gas-solid and liquid-solid interactions occur at the surface. e.g.

corrosion, heterogeneous catalysis (surface reactions, chemistry)

the chemistry (compound formation) and electronic structure of solid-

solid interfaces can dominate the performance of electronic devices

surfaces and interfaces can also be modified by ‘adsorption’

(segregation) from the bulk - e.g. grain boundary segregation and

intergranular brittle fracture

Surface Reaction (CO oxidation)

“God has created crystals,

surfaces are the work of the devil.”

Wolfgang Pauli

What is difficult about studying surfaces?

Theory:

surfaces break the 3-D periodicity commonly exploited in describing many properties of solids.

Experiment:

1. Surface Sensitivity

need to detect very small amounts of material (very few atoms)

e.g 1 ML (monolayer) ≈ 1019 atoms m-2

say surface probe is 1 mm2, so in 1% of 1 ML have 1011 atoms

for carbon (m=2x10-23 g) this is equivalent to 2X10-12 g

(cf ‘wet chemistry’ – detect ≈ 10-4 g)

What is difficult about studying surfaces?

Experiment:

2. Surface Specificity

need to detect these small amounts of material (very few atoms) in the presence of the underlying bulk solid.

e.g. 1 mm thin sample has ≈ 5X106 atomic layers

so 1% of a monolayer is 1 part in 5x108 of the total no. of atoms

What is difficult about studying surfaces?Experiment:

3. Need of ultra-high vacuum (UHV)

consider the rate of arrival of molecules at a surface from the surrounding gas

kinetic theory of gases; rate of arrival of molecules, r, is

For N2 and CO at 300 K,r = 2.87 x 1024 p molecules m -2

1 ML ≈ 1019 molecules m -2

for sticking probability of 1

Then monolayer time is 3.48 x 10 -6/ p s

What this means is that if

p = 1 mbar, τ = 3.5 μs

p = 3.5 x 1 0-6 mbar, τ = 1 s

p = 3.5 x 10-10 mbar, τ = 104 s or ≈ 3 hrs

MORAL – need UHV for realistic experimental timescales on clean surfaces

The usual units for the pressure in vacuum technology are torr or mbar(1 torr = 1.3332 mbar = 133.32 Pascal)

Also…

We can also calculate the mean free path of the molecules at a given pressure, i.e. the mean distance before hitting another molecule

where ξ is the molecular diameter

What does this mean for UHV pressures and is it important….?

How to achieve UHV?

1. Use ‘clean’(oil-free) pumps

e.g.

titanium sublimation pumps (molecule trapping on walls)

ion pumps (Ti+ ions spiral in magnetic field & capture molecules)

turbo molecular pumps (high speed ‘fans’)

2. ‘Bake’ chamber: remove weakly-adsorbed gas molecules from walls of chambers which act as ‘virtual leaks’

A typical UHV chamber

Typical mass spectrum using a quadrupole mass spectrometer

How to produce a ‘clean’ surface in UHV?

1. cleavage - need brittle crystal, only one cleavage

plane, cannot re-clean surface

2. heating to high temperature - desorb adsorbed species

3. ‘chemical’ cleaning - heat the sample in a partial pressure of gas

Cads + O2 → CO/ CO2 ↑

Oads + H2 → H2O ↑

4. Ion bombardment - Ar+, Ne+ ~500-5000 eV to remove surface atoms

+ annealing - to heal damage (BUT note problem of surface segregation of bulk impurities on annealing)

Description of Solid Surfaces

Description of Solid Surfaces

• Most solids have a well-defined crystalline structure

– single crystals

– grains with identical crystalline bulk structures

• The orientation of each crystallite surface can be characterized by its Miller indices:

– the parallel crystallographic plane (hkl) (specific)

– the corresponding family of equivalent crystallographic planes {hkl} (general).

Crystallite

Surface planes

• Crystallites have well-defined surface planes, descibed by Miller-indices {hkl}.

• Normally only the planes with low surface (free) energy are exposed.

• Prepare and study each surface plane separately.

• Single crystals.

Typical catalyst metal particle

Description of Solid SurfacesMiller Indices

• The integer numbers (h, k, l), defining a crystallographic plane, are called ’Miller indices’.They are determined in the following way:

1. Find the intercepts of the plane with the 3 crystal directions or axes in terms of primitive vectors a, b, c.

2. Take the reciprocals (0 if no intercept).

3. Multiply the resulting 3 numbers by the smallest number that makes the result equal to 3 integers.

• These are the Miller indices h, k, l.

• A negative index is indicated by a bar: h

Miller Indices

Miller Indices

(634) crystal plane

Crystallographic planes

(100) (110) (111)

Description of Solid SurfacesMiller Indices

• Cubic symmetry: the choice of which of the three axes to label the ’x’, ’y’ and ’z’ is entirely arbitrary.

• The (100) plane is physically equivalent to the mathematically distinct (010) and (001) planes.

• Grouping of various numbers of planes into sets, or families, denoted {h, k, l}:

• Note: for a cubic crystal lattice the [hkl] direction is always perpendicular to the (hkl) plane.

This course: high symmetry (low Miller index) surfaces of metals with fccor bcc crystal lattices which are assumed by most transition metals.

fcc, bcc or hcp

fcc and bcc surfaces

{100} {110} {111}

{100} {110}

fcc

bcc

Description of Solid SurfacesSurface lattice

• Crystal surfaces are periodic in two dimensions (x and yparallel to the surface).

• Described by a two–dimensional unit mesh defined through lattice vectors a1 and a2:

• The vector R between any two points of the lattice is the sum of integer multiples of a1 and a2:

Surface Lattice

a1

a2

R

R = 3 a1 + 5 a2

Description of Solid SurfacesSurface Lattice

Only 5 possible di-periodic types of (Bravais) lattices:


Square: fcc{100} Rect. primitive: fcc{110} Rect. centred: bcc{110}

Hexagonal: fcc{111} Oblique: fcc{531}


Conventions:

Description of Solid SurfacesSurface Energy

• The creation of a surface or interface requires energy: the surface free energy

• An atom (or molecule) in the bulk of a solid experiences cohesive interaction with its neighbours.

• A surface atom has fewer neighbouring molecules

• In order to create a surface, energy must be supplied to reduce the average number of cohesive interactions

• εAA(r) = cohesive potential (negative) between two atoms of type A at a distance r.

• Nearest-neighbour interactions are dominant (condensed phase).

• Cohesive potentials are pair-wise additive.

• Energy per atom is:

NA = Avogadro’s numberΔHsub = sublimation energyzbulk, surf = number of nearest neighbours

• Different for compound solids.


εAA


• Energy difference between bulk and surface atoms (per atom):

• Total work required to create a surface is proportional to area δA:

• is called surface energy or surface tension:

Ns = surface atom density

• Strictly should be “free energy” which also includes entropy. Ignored here for simplicity.


• For solid, estimate ε from sublimation energy ΔHsub :

Example: fcc{111}

• zbulk = 12

• zsurf = 9

• Area per unit cell = a a sin(120 )

• Ns = 1 / Area = [a a sin(120 )]-1

Example: fcc{111}

• zbulk = 12

• zsurf = 9

• Area per unit cell = a a sin(120 )

• Ns = 1 / Area = [a a sin(120 )]-1


• We get the following 111 for:– Pb: 0.77 J/m2 H = 196 kJ/mol; a = 0.350 nm

– Cu: 2.5 J/m2 H = 336 kJ/mol; a = 0.255 nm

– Pt: 3.5 J/m2 H = 564 kJ/mol; a = 0.277 nm

• Relative surface energies of different surfaces of the same crystal (fcc):γ111 : γ100 : γ110 = 1.00 : 1.15 : 1.22

• Experimental values (polycrystalline samples):– Cu 1.9 J/m2

– Pt 2.5 J/m2

Surface characterisation/ analysis….

Science

Surface and bulk