Author Archives: Hepeng Ye

Possible transition processes of Pt adatom on Pt(100) surface

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by Hepeng Ye

Introduction:

Surface diffusion is a common process for solid materials, and in our case, the Pt adatom could diffuse along the surface of Pt(100). Diffusion is governed by the thermal energy from the environment and the property of such behavior is important for understanding surface phase formation, heterogeneous catalysis and other aspects.

In our case, Pt adatom is hypothesized to undergo a hopping between two adjacent four-fold sites or undergoes concerted substitution. To study the process, a model needs to be built and in our case the model is fairly simple since neither diffusion process has linear interpolation issue, and as consequence, one just need an initial and final two-state model for the transition state study. By connecting the initial and final state of the system, one could locate the TS (transition state) of that process and use the energy barrier from the transition search to further study the kinetic of process.

Experimental:

First cleave the Pt(100) lattice, and create the slab and a five-layer slab of 2X2 super-cell with 5Å vacuum space was set as the starting point. As mentioned the goal of the experiment is to identify the more likely transition process from the two, and in order to get reasonable comparison between the two processes, one need to first optimized the system(slab) to make sure that the super-cell is large enough for boundary conditions and enough vacuum space to prevent interaction from the next periodic slab along the Z-axis. Layers of the slab will not be optimized due to time limit, and based upon experience, five layers should be enough.

For vacuum space optimization, build three slabs with 5Å, 10Å and 15Å vacuum space, and calculate energy with CASTEP, functional used is GGA PBE, pseudo-potential is OTFG-ultrasoft, and all other parameters are set to default (272.1eV energy cutoff, 6x6x1 K-points, core radii is 1.27A with electron configuration to be 5s2 5p6 5d9 and 6s1).

Figure 1. Example of the slab used for vacuum space optimization. (5layer, with 10A vacuum)

Use the lowest energy vacuum space to continue slab size optimization.

To do this, one will first identify the most stable height of the Pt adatom on the surface. Sitting on top of the fourfold site, it is obvious that the adatom cannot be either too close or too far from the surface where too close to each other there will be repulsion and too far to each other will make Pt adatom isolated from the surface and could interact with the next periodic slab. Consider the short range dispersion, there should be a local energy minimum for the Pt to sit on top of the surface and bring down the system’s energy. So the height is tuned manually by putting the adatom between 1Å to 3Å above the center of the four-fold site.

When Pt adatom transit from one four-fold site to another, the energy for it being reactant should be the same as it being the product. Using this idea, I will separately calculate the energy for Pt adatom sitting at different fourfold sites, for different size of slabs.

The lowest energy height optimized previously will be used, and start with 3×3 super-cell.

Figure 2. Position of initial and final state of fourfold site.

 

 

As shown in the Figure 2, in 3×3 super-cell, the starting point of Pt, say, at the center, and could diffuse into the nearby fourfold sites. Due to symmetry, the energy barriers for all four direction should be the same, so just consider one of the pathways. In this case, energy of the system is calculated for Pt on the center site and on the edged site.

To get energies of each initial and final state, all calculations are performed with CASTEP, functional used is GGA PBE, pseudo-potential is OTFG-ultrasoft, and all other parameters are set to be the same as above when doing slab-size optimization.

After calculations are done, and comparing the two energies and check the relative difference, and based upon that difference, one will decide whether it necessary to keep using 3×3 super-cell or increase the slab size to 4×4 super-cell or even larger.

Then, in order to find out the transition state, one need to build the initial and final state or the reactant and product state respectively. There are two possible diffusion processes, one is the hopping between two fourfold sites, another is the concerted substitution of Pt adatom with Pt on the top layer. And in the calculations, two assumptions will be made to simplify the problem and reduce computational cost:

  1. In either process, Pt atom will only diffuse with the closest Pt atom or fourfold site.
  2. Due to the fact that system used has already optimized its size, and due to the symmetry, only consider Pt adatom diffuse in one direction, instead of four.

Based upon these assumptions, two sets of reactant and product slabs will be built for corresponding diffusion pathways.

 

Figure 3. Transition process scheme for hopping between fourfold states.

Figure 4. Transition process of concerted substitution of Pt adatom with Pt atom on the surface.

After determining the initial and final state of the process, DMol3 TS-search will be used to find the transition state/energy for each process while comparing transitional energy calculated with different search protocols.

Data analysis and discussion:

For the slab size optimization, calculations were performed for 3×3 super-cell where the Pt adatom sits in the fourfold site in the middle, and the fourfold site on the edge, and the energies are close enough to say they are in the same environment.

For the manually adjusted Pt adatom positions, three-point-adjust method is used to iteratively adjust and narrow down the height range and get to the lowest energy and its corresponding height/distance. One could see from the plot that at 1.8Å above the surface, the energy is the lowest.

Figure 5. Energy diagram of Pt adatom with relative heights to the slab surface.

After that, a 5 layer, 3×3 super slab is applied for the Transition-State study.

In Castep transition state search, there are some different synchronous transit methods[3], and here, some of these methods were used and were compared their differences. For the fourfold to fourfold hopping, the transition energies for different TS-search protocols are shown in the Table 1 below:

Table 1. Transition energy of hopping between fourfold sites calculated from different TS-search protocol.

For concerted substitution, the transition energy for each TS-search protocol is also listed in the table2.

Table 2. Transition energy of concerted substitution calculated from different TS-search protocol.

Different transition searching protocols have different calculation process, but for each process, they are all in agreement with the transition energies are on the same magnitude. While for Pt substitution process, the transition energy barrier is ten times larger than that of hopping process, which makes sense that such process requires breaking Pt metallic bonds with the surrounding Pt atoms and then another Pt atom comes in and forms new bonds, there should be a lot more energy required for such reaction.

Conclusion:

Based upon the energy barrier calculated from the Transition-Search, it is obvious that the concerted substitution has way larger energy barrier than the fourfold sites hopping, which means at same conditions(say same temperature) it will be much less likely for Pt adatom diffuse into the Pt(100) surface and undergoes the concerted substitution process.

There are some experimental setups that could be improved, say the slab I used has 5 layers, which I did not optimize. Also, I stopped at 3×3 supercell size and did not look at 4×4 supercell simply because the energy between two fourfold sites are very close to each other(~0.005 hartree for the total system) for 3×3 supercell, but maybe 4×4 will give even more identical energy, I do not know and maybe someone could try 4×4 disregarding the computational cost.

 

Reference:

  1. J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett., 77 (1996)

2. J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C. Fiolhais,      Atoms, Molecules, Solids, And Surfaces – Applications of the Generalized Gradient  Approximation for Exchange and Correlation, Phys. Rev. B, 46 (1992)

3. CASTEP GUIDE, Transition state search task. Date of access: April. 27. 2019

https://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/content/modules/castep/tskcasteptss.htm

Binding site preference of atomic oxygen on Pt(111)

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Made by Hepeng Ye

Introduction:

On crystal surface, the property of adsorption is an interesting study case, and in my work, I will present you the adsorption of atomic oxygen atom on the surface of Pt(111) crystal, specifically the energy of adsorption at different binding sites for mono-layer coverage(1ML)[3].

Platinum crystal is rigid, however, microscopic world reveals to us that there are vast amount of empty space that other smaller molecules could ‘sneak’ in or adsorb on the surface layers. Platinum has a FCC crystal structure based on previous DFT calculations which is proved to be true referring to literature data[1][2]. (See Figure 1)

Figure 1. Platinum crystal structure with two layers shown, where the yellow atoms are the second layer atoms.

FCC is not comparably a close packing of atoms, and in our case, oxygen will get adsorbed on the surface. To systematically study the binding site of oxygen, I will assume four positions that oxygen atom are presumed to be stable staying at, and energy of adsorption will be calculated to check which position is the most favored.

Geometry optimizations are performed using CASTEP in Material Studio, and four corresponding binding sites are called: FCC hollow, HCP hollow, atop and bridge.

(See Figure 2-5)

Figure 2. Atomic oxygen binding at FCC site.

Figure 3. Atomic oxygen binding at bridge site.

Figure 4. Atomic oxygen binding at HCP site.

Figure 5. Atomic oxygen binding at Atop site.

Data analysis:

\begin{equation}E_{ads}=E_{surf+ads}-\frac{E_{ads(g)}}{2}-E_{surf}\end{equation}     Eq(1)

Equation shown above is what I used for adsorption energy calculation. Terms on the right hand side are for the energy of binding system, where 1/2EO2 stands for the energy of atomic oxygen in gas phase and Esurface for the energy of bare slab surface respectively. The equation tells us that the adsorption energy is the amount of energy required to pull an O atom off the surface into the gas phase.

To get adsorption energy, I will do the geometry optimization of Pt(111) slab, and separately for oxygen, and then for four different binding cases.

Since atomic oxygen is unstable and unlikely to exist, I will use diatomic form, which is the oxygen molecule in the gas phase to do the calculation and half of the energy will be that of single atomic oxygen. To save computational time, instead of using CASTEP, I used DMol3 to calculate the oxygen molecule. With LDA-PWC functional and DNP basis set used.

For Pt(111) slap surface relaxation, I used five layers surface cells with the top two layer flexible for relaxation and bottom three layers fixed, and vacuum space of 15A together with K-point to be 5x5x1. In the case, there was no layer number optimization nor k-points optimization, 15A space and this k-point parameters are default parameters.

For all four binding sites situations, add the atomic oxygen to the corresponding position and do the geometry optimization for the entire system and get E(O/surf).

Figure 6. Starting from putting oxygen atom on the HCP site in 1ML.

Figure 6, as one example of all four different binding sites, show that the oxygen atom is put initially at the HCP hollow position, and system energy is calculated after geometry optimization.

Then, there comes a question of where should we start with? Where “atop”, ‘bridge’ could just tell you vertically where these binding sites are, but in the space, you could put oxygen extremely far from the surface and get meaningless energy calculation. To figure out the starting point, I was performing four trials of energy calculations.

For each binding site, I put the oxygen atom certain distance above the surface, and keep certain distance with the metal atom, for cases like HCP or bridge, where there is no atom right beneath the oxygen atom, and the distance is somehow arbitrary yet should not be a problem as one keeps the relative distance consistent for each measurement. For each binding site, each time I changed the distance around 0.1A, and calculate the energy of the system.

(Castep is used for calculation and the functional is GGA PBE with OTFG pseudo-potential. Energy cutoff is default value for fine calculation)

Figure 7. The distance between atomic oxygen and metal surface at each site condition. All four potential diagrams are shifted by 156911eV for comparison.

 

 

 

 

 

 

 

 

 

From Figure7, you could see that for each binding site, there is a local minimum energy, and that corresponding distance is the one I used for adsorption energy calculations for each site.

Use the distance from above calculation and do similar calculation for oxygen, while in case the oxygen is moving so that it will stabilize at its favored low energy sites or even deviates into another even lower energy states. And each calculation energy will be plugged into equation#1, to calculate the adsorption energy.

To compare each adsorption energy simply, I will normalize the energy based on the energy of atop site, and set it to be zero eV, then the FCC site has adsorption energy to be -1.10eV, while that for Bridge and HCP are similar to be both around -0.62eV. It is clear that the FCC site gives the lowest adsorption energy.

 

Discussion and Conclusion:

From the calculation, it is clear to see that with the lowest adsorption energy at FCC site, this site will be the most favored one when oxygen atom comes into the system and attach to the metal surface. Although these calculations are performed successfully, there might still be some limitations.

 

1ML coverage study is perform for simplicity, and ideally, different coverage need to be tested since the more concentrated oxygen on the surface, there will be more repulsive potentials build between and may not give the most promising result. And to give a reasonable guess, for lower coverage, there should be lower in absorption energy due to less inter-oxygen repulsion.

If one think of things like kinetic isotopic effect on protein system in which the reaction kinetics in both light and heavy(isotopic labeled atom) cases are affected by the protein’s reaction site donar-accepter distance in a function of temperature. At lower temperature, the surroundings could not give enough thermo-energy for fluctuation and isotopic labeled protein are giving much sower kinetics.

Maybe it is also interesting to study the magnitude of flexibility for atoms in the system and correlated atomic rearrangement or de-localization.

 

 

Reference:

[1]Timo Jacob, Richard P. Muller, and William A. Goddard “Chemisorption of Atomic Oxygen on Pt(111) from DFT Studies of Pt-Clusters” J. Phys. Chem. B 2003, 107, 35, 9465-9476

[2]] A. Kokalj, A. Lesar, M. Hodoscek, and M. Causa, “Periodic DFT Study of the Pt(111): A p(1×1) Atomic Oxygen Interaction with the Surface” J. Phys. Chem. B 1999, 103, 34, 7222-7232

[3] Sholl, David S. & Steckel, Janice A. Density Functional Theory: A Practical Introduction. John Wiley & Sons, Inc. (2009).

Pt Crystal Lattice determination by Castep

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by-Hepeng Ye

Crystallography is widely applied to study inorganic molecules, proteins, metals, etc. Such process is driven by entropy and enthalpy at the same time which makes it very tricky to control the crystallization and hard to predict what lattice will a given compound form at certain condition.

Platinum (Pt) metal is studied using Castep through energy minimization. Basic idea behind is that the lowest energy stable should be the most favored state, and that corresponding lattice should be the most likely lattice that we shall expect to observe from experiment. Now, lets pretend that we do not know what is the crystal lattice for Pt, and I will show you how to find out the more likely lattice.

Energy calculation involves GGA-PBE functional[1], and pseudo-potentials were set as default as OTFG ultrasoft[2]. And the ultrasoft pseudopotential for Pt is set to have core radii to be 2.403 Bohr radii (~1.27Å), vis using valence electrons in the 4f14 5s2 5p6 5d9 6s1 configuration.

Two lattices are studied, face center cubic(FCC) and hexagonal close packing(HCP), and the following part will present parameters optimization and energy minimization for both lattice.

For FCC, m-3m space group is used since it is the only possible space group, and by using lattice parameter (a) equals 4.0Å, energy cut-off convergence is determined.

Figure1. energy cut-off optimization for Pt FCC

As shown in the figure 1, energy difference converges as I use larger energy cut-off, and the difference between using 420ev cut-off and 480eV are very close. Base on this, I am confident to say that 480eV is a good stop point and larger cut-off may no longer be efficient for DFT calculation.

 

Then, another parameter optimized is the K-points. I used three cell sizes and all with 480eV cut-off energy. And plot below shows the energy per atom from irreducible K-points from 10 up to 120.

Figure 2. K-points optimization for Pt FCC at three different lattice parameters using optimized energy cut-off.

It is clear that as irreducible k-points used go beyond ~25, energy starts to stabilize, though still fluctuates in a tolerable range. And by considering the computation capability and energy accuracy, I use the irreducible k to be 56 (fourth point from left) as the optimized K-points for further calculation.

Energy cut-off is determined to be 480eV and K-points is 56, then the only parameter left for FCC structure is the cell length. I performed the a-optimization by randomly picking three a values, and do the calculation until energy is minimized for each, then I use these three energies in function of a-values to fit a parabola, and use that as an indication to look for another three a-values on the curve which are likely to give me the minimized energy.

Figure 3. Energy diagram verses lattice parameter using optimized K-points and energy cut-off.

Three iterations are performed and totally nine data points give a nice parabola. And the minimum energy (energy per atom) from the parameter a=3.975Å with corresponding energy to be -13051.00eV(per atom).

For platinum in HCP lattice, D3H-3 space group is used. And to make data from FCC and HCP calculation comparable with each other, energy cut-off is kept the same (480eV). But for D3H-3 space group, k-points need to be re-optimized since the real space and reciprocal space are both different from the fcc.

Figure 4. K-points optimization for Pt HCP lattice structure.

Starting with a equals 3.9Å and a/c ratio being 1.53. k-points are tested from 16 to 312.

Usually, more than 10 K-points should be enough, and it is true from the plot. There is a bump around 40 k-points and as a reason, I choose to use k equals 135 for calculation.

Since HCP has two lengths to be modified, one edge is defined as ‘a’ and another one as ‘c’. We know that in the crystal structure, size matters, and we know the density is a description of how many mass in a certain volume, so similar idea is used here that we analyze the energy of lattice at different pressure (isobaric condition), and for each pressure there should be a corresponding volume, which is a function of ‘a’ and ‘c’. By modifying the ratio of a/c, there should be an optimized (lowest) energy for that specific volume. Eventually, a plot of energy with respect to volumes will be plotted.

Figure 5. Energy diagram for Pt HCP at multiple lattice parameters’ ratios for each specific volume.

The plots above shows: at each volume(Å3), there are 10 a/c ratios evaluated from a/c equals 1.3 to 1.8 (most metal hcp fall into this range).

And by extracting the lowest energy from each volume, the minimum energy is get from the lowest point, to be -13050.24eV per atom.

FCC has minimum energy to be -13051.00 eV

HCP has minimum energy to be -13050.24 eV

So, FCC has lower energy, and should be the expected crystal structure for platinum.

As mentioned at the beginning, after showing the energy difference between these two possible lattice structures, what is the actual structure?

From Crystallography Open Database[3], I could infd the experimental result for Pt is FCC, with lattice parameter ‘a’ to be 3.944+/-0.004Å. The final lattice is fcc which is what we expect.

 

reference:

[1]:Setting up pseudopotentials- ultrasoft and norm-conserving pseudopotentials.

https://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/content/modules/castep/tskcastepsetelecpotentials.htm

[2]:J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple.
Phys. Rev. Lett. 77, 3865 (1996)

[3]: Entry 1011103, F m -3 m #225, Crystallography Open Database.

http://www.crystallography.net/cod/1011103.html