Processes at Solid Surfaces

Question 1

What is the Bragg equation for constructive interference?

Answer 1

2dsin(θ) = nλ

Question 2

Why is x-ray diffraction not a suitable surface experiment?

Answer 2

X-rays penetrate the bulk of the crystal so the technique is not sensitive to the relatively few surface atom layers (there are many more bulk atoms). However, using a shallow angle enhances the surface sensitivity because it allows many more surface atoms to be sampled before entering the bulk.

Question 3

Describe low energy electron diffraction (LEED).

Answer 3

Low energy electrons give surface selectivity because electrons with kinetic energy of ~100 eV have an escape depth of ~0.7 nm. They only travel 0.7 nm (i.e. a few atomic radii) before colliding and losing energy. This is universal, so it is roughly true for all solids.

Thekey features of the technique are:

1. A monochromatic electron beam is used.
2. Electric back-scattered electrons are detected.
3. It only works for conducting surfaces.

Question 4

What are the requirements for a good surface experiment?

Answer 4

1. Surface selective
2. Sensitive
3. Avoids contamination

Question 5

Describe a 2D LEED pattern.

Answer 5

The pattern spacing decreases as the interatomic separation increases.

Constructive interference requires that:

2asin(θ) = nλ and 2bsin(θ) = nλ

Therefore, you get a 2D spot pattern of the 2D surface.

Question 6

How many near neighbours does a bulk atom have in a FCC crystal? What about when the crystal is cleaved along the (111), (100) or (110) planes? How does this affect the surface energy?

Answer 6

In the bulk each atom is surrounded by 12 nearest neighbours, which is a stable arrangement. If there are fewer neighbours, the atoms are more exposed and reactive so they have a high a high surface energy.

Surface energy: (110) > (100) > (111) > Bulk

Question 7

What is surface reconstruction and which experiment provides evidence for it?

Answer 7

Surface reconstruction is the rearrangement of atoms to lower the surface energy. It is most likely for high surface energy planes: (110) > (100) > (111). There is evidence of reconstruction from LEED (e.g. in this example the 2D pattern of spots gets closer together).

Question 8

How can you avoid contamination in surface experiments?

Answer 8

To avoid contamination use an ultra high vacuum (UHV) at < 10^-7 Pa. It avoids contamination and the probe beam is unperturbed by gases.

Question 9

What is surface relaxation and what experiment provides evidence of it?

Answer 9

A 3D LEED pattern shows a relaxed surface layer closer to the neighbour layers, which reduces the surface energy. It is greatest for high energy surfaces.

Realistically, the maximum relaxation is around 10 % for open surfaces (e.g. FCC (110)). Relaxation perturbs the first few layers, not just the surface layer.

Question 10

Describe the thermodynamics of adsorption.

Answer 10

Adsorption: A gas phase molecule (adsorbate) binds to a surface (adsorbent).

ΔG = ΔH - TΔS

There is an increase in order so ΔS is negative. For ΔG to be less than zero, ΔH must be negative. Therefore, adsorption is always an exothermic process.

Question 11

Describe how adsorption can affect crystal growth.

Answer 11

This is a special case of adsorption where the adsorbate and the adsorbent are chemically identical. High energy surfaces grow faster (e.g. for FCC: (110) > (100) > (111)). The slowest growing faces dominate the crystal appearance, and you get a low surface energy crystal.

Question 12

Describe the thermodynamics of desorption.

Answer 12

There is an increase in disorder so ΔS is positive. To desorb, the molecule must overcome attractive forces. ΔH is positive so it is an endothermic process.

Question 13

Describe how a temperature programmed desorption (TPD) experiment works.

Answer 13

1. Adsorb the molecules of interest onto the surface.
2. Increase the temperature (controlled, linear ramp).
3. Monitor the gas evolved (i.e. the desorption).

The peak position gives an insight into the activation energy.

Peak area is proportional to the molecules of gas desorbed.

Question 14

Describe physisorption and its thermodynamics.

Answer 14

Physisorption is physical adsorption. It involves van der Waals interactions between the adsorbate and the surface. There is no barrier to physisorption. ΔH_ads is always small for physisorption as the attraction is very weak. All gases physisorb below their condensation temperature. It is a reversible process and can form multi-layers.

Question 15

Describe chemisorption and its thermodynamics.

Answer 15

Chemisorption is chemical adsorption. A true chemical bond forms between the adsorbate and the surface so it involves electron transfer. Bonds within the adsorbate molecule are weakened.

ΔH varies but it is always larger than for physisorption.

Question 16

What is surface coverage?

Answer 16

Surface coverage depends on:

1. The characteristics of the gas-phase molecule and the surface.
2. The concentration/partial pressure of the gas-phase molecule.
3. Temperature.

Question 17

What are the assumptions of the Langmuir isotherm?

Answer 17

1. The surface has a fixed number of identical sites (i.e. monolayer only).
2. ΔH_ads is independent of coverage.
3. The adsorbates do not interact.

Question 18

What is the equation for the Langmuir isotherm?

Answer 18

Where θ is the surface coverage, b is the equilibrium constant and P is the partial pressure of the gas-phase molecule.

Question 19

Table 1 shows data for a gas (A) adsorbed on a surface.

Using the Langmuir isotherm, calculate the amount of A needed for monolayer coverage, A_max.

Answer 19

A_max = 110 nmol

Check the notes for full working.

Question 20

Table 2 shows data for adsorption of CO onto a Rh catalyst at 298 K.

Calculate the equilibrium constant (b) for adsorption and the number of adsorption sites (n).

Answer 20

b = 0.15 kPa^-1

n = 6.6 x 10¹⁶

See the notes for the full working.

Question 21

How can you probe surface coverage?

Answer 21

1. By surface analysis using traditional methods (e.g. mass/weight or radioactivity) or modern techniques (e.g. microscopy or spectroscopy).
2. By looking at changes in gas-phase volume, pressure, radioactivity, mass spectrometry or spectroscopy.
3. By using desorption methods.

Question 22

What is the assumption for the BET isotherm?

Answer 22

The BET isotherm assumes random site distribution.

Question 23

What is the equation for the BET isotherm?

Answer 23

Question 24

Describe scanning tunnelling microscopy (STM) and how it works.

Answer 24

It allows magnification of x10⁸, which allows direct observations of surface atoms and featues. It can be used in a vacuum, in air or in liquid. It is technically demanding and can only be used for conducting surfaces. Atomic force microscopy can be used for insulators.

The tip is positioned close to the surface and a small potential is applied. This causes tunnelling (the electrons tunnel from the surface to the probe tip).

The tunnelling current (in nA) is related to the separation (d): I ∝ exp(-d) which allows atomic resolution.

Question 25

What are the two modes of STM?

Answer 25

1. Constant distance and voltage. You map the current as the surface is scanned, which is not good for rough surfaces.
2. Constant current. This is more common and safe for rough surfaces. You scan the tip over the surface and adjust the probe height to maintain a constant current. You map the voltage applied to the piezotube as the surface is scanned.

Question 26

What are the different types of surface defects and how many near neighbours do they have in simple cubic and FCC crystals?

Answer 26

Question 27

Describe how x-ray photoelectron spectroscopy (XPS) works.

Answer 27

This technique probes the core electron configuration to give elemental identification.

You can use it to find the electron binding energy (E_BE).

E_BE = hν - 1/2 mv²

Core electron binding energies are almost independent of bonding/environment and they are characteristic of each element.

XPS experiments are:

1. Conducted under UHV
2. Sensitive
3. Surface selective if you only consider LEE

You need to integrate the peaks areas to determine the % composition. The main problem is that it has poor spatial resolution. Works for conductors and insulators, but you need to avoid charge build up.

Question 28

Describe how Auger electron spectrscopy (AES) works.

Answer 28

This technique probes the core electron configuration to give elemental identification.

AES is conducted under UHV. It is sensitive and surface selective, and it has better spatial resolution than XPS.

How it works:

1. X-ray or electron beam induced ionisation.
2. The initial excited state is unstable so an electron drops down to fill the hole.
3. The relaxation energy is transferred to higher energy electrons, and this second ionisation is the Auger emission. The energy of this emission depends on three electron energy levels.

It is characteristic of the elemental composition. It is independent of excitation energy. It is only for conductors.

Question 29

How can we learn about adsorption thermodynamics?

Answer 29

We can do experiments at different temperatures. We can use the Clausius Clapeyron equation to measure the adsorption isotherm as a function of temperature.

Where ΔH_ads is the isosteric enthalpy of adsorption (same size/density/coverage).

Question 30

Find the isosteric heat of adsorption (ΔH_ads) for a fixed coverage of 2 cm³ g^-1 of CO₂ on a surface given the data in table X.

Answer 30

ΔH_ads = -48 kJ mol^-1

See the notes for the full working.

Question 31

Describe the thermodynamics of surface reconstruction and chemisorption.

Answer 31

There is a large barrier, Ea(2), for spontaneous reconstruction without adsorption. This only occurs for the highest energy surfaces.

There is a small barrier, Ea(1), for chemisorption. This is faster for high energy surfaces.

Reconstruction is catalysed by the adsorbate.

Question 32

How does the TPD spectrum change with ΔH_ads and coverage?

Answer 32

The TPD spectrum for a larger ΔH_ads is shifted to a higher temperature because you need more energy to break the stronger surface-adsorbate bonds.

TPD signal ∝ coverage

The desorption rate is higher for a larger ΔH_ads due to dissociative adsorption.

Question 33

What evidence is there for dissociative adsorption?

Answer 33

1. Thermochemistry
2. Coverage data at constant temperature
3. Desorption kinetics
4. Surface spectroscopy

Question 34

How does coverage data provide evidence for dissociative adsorption?

Answer 34

Using Langmuir-like assumptions:

Question 35

How can desorption kinetics provide evidence for dissociative adsorption?

Answer 35

Desorption is second order with respect to surface coverage (θ).

TPD experiments at different surface coverages if good evidence for dissociation.

Question 36

How can surface spectroscopy provide evidence for dissociative adsorption?

Answer 36

If an adsorbate XY dissociates on a surface, there will be a change in X-Y bonding so we can check the IR spectrum.

Question 37

What is the selection rule for reflection-absorption IR spectroscopy (RAIRS)?

Answer 37

The oscillating dipole must be perpendicular to the surface. Some modes are inactive so the absence of RAIRS is not evidence of dissociation.

Question 38

What are the strengths and limitations of reflection-absorption IR spectroscopy (RAIRS)?

Answer 38

Strengths:

1. Sensitive when using a shallow angle
2. Surface selective because the reflections are monitored

Limitations:

1. Highly reflective (metal crystal) surfaces only
2. Difference spectra are needed
3. No information < 600 cm^-1
4. Strong IR absorbers only