Textrahex Carbon Simulation

Textrahex Carbon Simulation for 11 Angstrom

Kristian Dolghier

Professor Xihong Peng

Goal of the experiment

The goal of this overall experiment was to create an 11 angstrom ribbon for a tetrahex carbon structure with silicon edges, carbon edges, and both with carbon edges. We must find the ideal length of the Y axis as this is the axis that the ribbons are propagated on when we extend the length in Vesta. The X and the Z axis have empty space so they must not necessarily be idealized. Initially, the simulation was done with ISIF=3 so VASP can relax the axises and the directions to find the lowest energy structure. However, this changed the structure of the unit cell to something that did not represent a textrahex carbon structure. Thus, we must Change ISIF=2 and change the strain from -4 to +4 percent to get a second degree polynomial and simulate the energy of the most stable version of the structure with the ideal Y.

How did I create a 11 angstrom length POSCAR?

To create the 11A POSCAR, you must initially migrate the POSCAR file to an excel document. Then you can assign each atom the designation of whether it is a silicon, carbon, or hydrogen atom. This way, you can filter them back to how they initially started. After assigning this, you can filter the X column from least to greatest which will designate the order that the atoms are depicted from left to right. After filtering this, you can simply copy a set of the silicon and carbon atoms that you want and paste them below all of the other atoms. Following this, you can calculate the average distance between two different sets of silicon atoms, and add this distance to the last set of silicon atoms to get the proper X, and Z coordinates. Notice that the Z coordinates may need to be reversed for some of the atoms as you might need a mirror of the Z direction to get a proper extension. Following this, you can add hydrogen atoms to the edge if needed, and filter the set of atoms to the same order they were in initially. If initially, your POSCAR said Si H C, then you must make sure that the silicon atoms are first followed by hydrogen and carbon. Verify the extension of the atoms in Vesta and make sure that the extension was correct and is accurate in all 3 cardinal directions.

How did I change the strain from -4 to +4%

To change the strain, we must copy the initial 100% base POSCAR that the new 11 angstrom function is based off of. Then, we can multiply the Y part of the unit cell by various percent to get the new POSCAR. For instance, the -4% structure was multiplied by .96 and the -2% structure was multiplied by .98. Additionally, since the coordinates are set up in cartesian coordinates, we must multiply the Y coordinates of every atom by its respective percent strain. This step is only required if you are using cartesian coordinates. Now, we have 5 different POSCAR's for each ribbon simulation, and we must run them in VASP to find the pressure and the energy of each.

How did I find the ideal strain?

After finishing the simulation of each strain, we can gather the Total Energy (eV) and the respective Y lattice from the OUTCAR. With 5 data points for percent strains +4%, +2%, 0%, -2%, -4% we can plot a polynomial. You must plot the Y lattice on the X axis and the total energy on the Y axis. By plotting these data points and fitting them with a second degree polynomial, we can get a Polynomial fit equation which is 5.14696x^2-75.2373x+62.2213 for the silicon hydrogen edge. Now, we can simply find the minimum of this equation which will be the ideal Y for the respective tetrahex carbon structure. With this ideal Y, we can create a new POSCAR with the new Y lattice and do not forget to change the Y coordinate of each of the atoms as well. Finally, after simulating this, we can observe the energy and the external pressure of this structure and verify that it has the lowest energy as c compared to the rest of the simulations. Now we have an ideal Tetrahex ribbon for 11 angstrom.

The final step is to find the Cohesive Energy. We need to do 3 more calculations for a lone carbon, hydrogen, and silicon atom. This will get us the energy of each respective atom. By using the equation provided below, where x is the number of silicon atoms, and y is the number of carbon Atoms and Etot is the energy of the tetrahex ribbon, we can find the cohesive energy. Esi and Ec are the energy of a lone silicon and carbon atoms that just found.

Conclusions of stability between the different ribbons

It is intriguing that for both the silicon and carbon edged structures, we see a more negative Total energy for structures with hydrogen atoms on the edge but a less negative cohesive energy. This is interesting, as we do know that Cohesive energy is the energy gained by forming atoms in a crystalline state. Solids that are bound more strongly and with better mechanical strength have higher cohesive energies. Therefore, it would be reasonable to assume that since the non hydrogen ribbons have a more negative cohesive energy, then they have more stability.

With regards to the carbon and silicon edged structures, we see that carbon edged structures also have a more negative cohesive energy making it seem like the carbon edged structures are more stable. The external pressure seems to confirm this as we see lower overall pressures for the carbon edge simulations as opposed to the silicon edge simulations.

Lastly, this conclusion matches with the chemical structure of each of the simulations. For the silicon edge simulation we see that the silicon is the larger atom and forms bonds with the carbon that are even over the X direction. For instance, the silicon on the edge will form a double bond with the carbon, and the silicon inside the ribbon will form a single bond with that same carbon. The carbon is also bonded to another carbon with a single bond, but this inequality of bond structure may be a reason for the instability. For the carbon egged structure we see that all silicon atoms have 4 single bonds to other carbons and the carbons of the edge have a single bond to the silicon and a triple bond to another carbon. This is inherently more uniform and would locally result in a more stable structure.

Data example:

Figure 5: Silicon hydrogen edge POSCAR at 0% strain

Figure 6: Silicon hydrogen edge calculation with 2nd degree polynomial fit