Lecture 4: Ab-initio atomistic thermodynamics and computational catalysis and electrochemistry.

Question 1

• Name four properties that can be calculated with DFT

Answer 1

• Lattice constant
• Adsorption energy
• Work function
• Ground state structure

Question 2

(IMP) What is the problem with how we have been calculating properties thus far?

Answer 2

• All the properties are ground-state properties at 0K in idealised conditions
• Macroscopic observables are measured at finite temperature.

Question 3

• What are some examples of macroscopic observables?

Answer 3

• Dynamically averaged structures
• Phase diagrams of surface stability as function of temperature and pressure conditions.

Question 4

• Experiments measure … … and … averaged structures over … of experiment, we need a way to account for this in DFT to connect our … regime with the … /… scopic regimes that make up real world measurements

Answer 4

• Experiments measure free energies and dynamically averaged structures over timespan of experiment, we need a way to account for this in DFT to connect our electronic regime with the meso/macroscopic regimes that make up real world measurements

Question 5

• Briefly outline 2 multiscale modelling techniques for DFT data

Answer 5

• Ab-initio atomistic thermodynamics: using energies and referencing them with chemical potentials to compare different calculated states.
• Kinetic MC: calculate barriers of all possible reactions, attain rates from these barriers via transition state theory and use those rates to define random hops in kMC.

Question 6

• What is the motivation behind Ab-initio thermodynamics?

Answer 6

• To extend the time/length scale of DFT by considering the effect of finite temperature effects.

Question 7

• What is the general process of Ab-initio thermodynamics?

Answer 7

• Separate system into sub-systems
• Calculate properties of sub-system
• Connect by assuming equilibrium between sub-systems

Question 8

• Give an example of a system being separated in to sub-systems

Answer 8

• Gas phase adsorption on to a metal surface
• Surface sight in contact with two reservoirs/ baths
  
  • Gas phase – where molecules come from
  • Metal bulk – where metal atoms come from

Question 9

What are the drawbacks of Ab-initio atomistic thermodynamics?

Answer 9

• No temporal information included
• No kinetic effects described
• Equilibrium assumed.

Question 10

Describe the result of the sign of a surface tension, γ, between two phases

Answer 10

• Positive: surface needs more energy to form/higher T
• Negative: surface formation occurs freely at given T/p

Question 11

• Define the free energy of a system of surface interacting with two reservoirs

Answer 11

• G₁₊₂ = G₁ + G₂ + ΔG_surf
• There is a free energy contribution from both bulk phases and the surface interaction between them
• G = Nµ (N – # particles in system; µ - chemical potential of each particle)

Question 12

• Why are F_vib and F_conf ignored in the following equation associated with G_surf

Answer 12

• Surface formation energy is difference between a free surface and a surface with 1 adsorbed molecule
• Change in vibrational energy and pressure as 1 molecule makes a small contribution
• pV is negligible

Question 13

• What do different signs of Gibbs free energy of adsorption indicate?

Answer 13

• Positive: oxygen adsorption more stable on surface than clean
• Negative: oxygen adsorption less stable on surface than clean

Question 14

Describe the terms of the following equation ΔG^ad(T, P)

Answer 14

• . Total DFT energy of forming an oxide on surface
• 2. Energy of clean surface
• 3. Difference in metal atoms on surface
• 4. # oxygen atoms on surface (only quantity dependent on T/P as opposed to values generated from DFT)

Question 15

• Why are we interested in surface tension?

Answer 15

• Want to know as value as a function of many T/P’s to find ideal conditions for metal surface oxide.

Question 16

• Give the overall equation for the surface free energy of adsorption at a given T,P

Answer 16

• 1. Energy costs to form oxide covered surface
• 2. Energy to add/remove particles from bulk on to surface
• 3. Energy cost to change number of oxygen atoms by exchanging them from bath/gas phase on to the surface.

Question 17

• Will an increase in temperature make it easier or harder to deposit a molecule on to a surface?

Answer 17

• Harder, as increase entropic freedom disfavours being restrained to surface, resulting in decreasing chemical potential.

Question 18

• How can surface free energy of adsorption be represented graphically?

Answer 18

• Straight line as a function of chemical potential

Question 19

(IMP) Describe and explain the features of following plot

Answer 19

• Different coverages have different gradients as more/less oxygen atoms per surface area, which changes µ₀ dependence
• Higher µ₀ à easier for gas to push on to surface
• Surfaces are stable with more oxygen per surface area.
• Scales on x axis are how phases change with temperature, which is useful for industrial application
• Note reverse scale on y axis

Question 20

(IMP) Describe the lowest µ₀ region of the phase diagram and the overall trend following it

Answer 20

• Clean surface has 0 gradient as unaffected by chemical potential of oxygen (µ₀) as no oxygen on surface
• Lone metal in most stable until p(2x2) comes in with higher µ₀, as lowest energy coverage at that µ₀.
• This trend continues in that the more oxygen is adsorbed on the surface, the more stable it will become at higher chemical potential of oxygen

Question 21

(IMP) Explain the formation of a bulk oxide displayed in the phase diagram

Answer 21

• At this high µ_0, a point is reached where pressure is so high that maximum amount of oxygen of surface is reached, forming an infinitely thick oxide
• The energy defining this is the energy is takes to from that bulk oxide
• The chemical potential of this is roughly equal to formation energy that we can derive from DFT for comparison.

Question 22

• How can the phase diagram as a function of chemical potential be adapted

Answer 22

• can rescale in terms of temperature varied with pressure