Lecture 4: Ab-initio atomistic thermodynamics and computational catalysis and electrochemistry. Flashcards
1
Q
- Name four properties that can be calculated with DFT
A
- Lattice constant
- Adsorption energy
- Work function
- Ground state structure
2
Q
(IMP) What is the problem with how we have been calculating properties thus far?
A
- All the properties are ground-state properties at 0K in idealised conditions
- Macroscopic observables are measured at finite temperature.
3
Q
- What are some examples of macroscopic observables?
A
- Dynamically averaged structures
- Phase diagrams of surface stability as function of temperature and pressure conditions.
4
Q
- 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
A
- 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
5
Q
- Briefly outline 2 multiscale modelling techniques for DFT data
A
- 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.
6
Q
- What is the motivation behind Ab-initio thermodynamics?
A
- To extend the time/length scale of DFT by considering the effect of finite temperature effects.
7
Q
- What is the general process of Ab-initio thermodynamics?
A
- Separate system into sub-systems
- Calculate properties of sub-system
- Connect by assuming equilibrium between sub-systems
8
Q
- Give an example of a system being separated in to sub-systems
A
- 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
9
Q
What are the drawbacks of Ab-initio atomistic thermodynamics?
A
- No temporal information included
- No kinetic effects described
- Equilibrium assumed.
10
Q
Describe the result of the sign of a surface tension, γ, between two phases
A
- Positive: surface needs more energy to form/higher T
- Negative: surface formation occurs freely at given T/p
11
Q
- Define the free energy of a system of surface interacting with two reservoirs
A
- G1+2 = G1 + G2 + ΔGsurf
- 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)
12
Q
- Why are Fvib and Fconf ignored in the following equation associated with Gsurf
A
- 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
13
Q
- What do different signs of Gibbs free energy of adsorption indicate?
A
- Positive: oxygen adsorption more stable on surface than clean
- Negative: oxygen adsorption less stable on surface than clean
14
Q
Describe the terms of the following equation ΔGad(T, P)
A
- . Total DFT energy of forming an oxide on surface
- Energy of clean surface
- Difference in metal atoms on surface
- # oxygen atoms on surface (only quantity dependent on T/P as opposed to values generated from DFT)
15
Q
- Why are we interested in surface tension?
A
- Want to know as value as a function of many T/P’s to find ideal conditions for metal surface oxide.
16
Q
- Give the overall equation for the surface free energy of adsorption at a given T,P
A
- Energy costs to form oxide covered surface
- Energy to add/remove particles from bulk on to surface
- Energy cost to change number of oxygen atoms by exchanging them from bath/gas phase on to the surface.
17
Q
- Will an increase in temperature make it easier or harder to deposit a molecule on to a surface?
A
- Harder, as increase entropic freedom disfavours being restrained to surface, resulting in decreasing chemical potential.
18
Q
- How can surface free energy of adsorption be represented graphically?
A
- Straight line as a function of chemical potential
19
Q
(IMP) Describe and explain the features of following plot
A
- 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
20
Q
(IMP) Describe the lowest µ0 region of the phase diagram and the overall trend following it
A
- 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
21
Q
(IMP) Explain the formation of a bulk oxide displayed in the phase diagram
A
- At this high µ0, 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.
22
Q
- How can the phase diagram as a function of chemical potential be adapted
A
- can rescale in terms of temperature varied with pressure
