Surface and bulk

Surface and Bulk
Dr Ts’enolo J. Lerotholi
Room 203 (Humphrey Raikes Building)
Email: tsenolo.lerotholi@wits.ac.uk

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)

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

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’

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
• 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).

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

Miller 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
(634) crystal plane

Crystallographic planes
(100) (110) (111)

Miller 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 fcc
or 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

Surface lattice
• Crystal surfaces are periodic in two dimensions (x and y
parallel 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

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

Surface Lattice
Square: fcc{100} Rect. primitive: fcc{110} Rect. centred: bcc{110}
Hexagonal: fcc{111} Oblique: fcc{531}

Surface Lattice
Conventions:

Surface 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 number
ΔHsub = sublimation energy
zbulk, surf = number of nearest neighbours
• Different for compound solids.
Surface Energy
εAA

Surface Energy
• 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.

Surface Energy
• 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

Surface Energy
• 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….

Surface and bulk

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Surface and bulk