exercises:2016_uzh_cmest:defects_in_graphene
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exercises:2016_uzh_cmest:defects_in_graphene [2016/11/13 19:49] – [Comparing energies] tmueller | exercises:2016_uzh_cmest:defects_in_graphene [2020/08/21 10:15] (current) – external edit 127.0.0.1 | ||
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<note tip>When comparing scaled coordinates between papers and code input scripts, always make sure that they use the same coordinate systems and definitions for a unit cell (both real and reciprocal space). For example while many sources (like the [[http:// | <note tip>When comparing scaled coordinates between papers and code input scripts, always make sure that they use the same coordinate systems and definitions for a unit cell (both real and reciprocal space). For example while many sources (like the [[http:// | ||
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+ | <note important> | ||
====== Vacancy in graphene ====== | ====== Vacancy in graphene ====== | ||
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Quick question: Does it matter which carbon atom you remove? (hint: what kind of boundary conditions do we impose?) | Quick question: Does it matter which carbon atom you remove? (hint: what kind of boundary conditions do we impose?) | ||
- | Calculate the energy of the vacancy formation, that is $E_v = E_2 (N-1)/N \cdot E_1$ where $E_1$ is the energy of the complete system, $E_2$ that of the system with a vacancy and $N$ the number of atoms. | + | Calculate the energy of the vacancy formation, that is $E_v = E_2 - \frac{N-1}{N} \cdot E_1$ where $E_1$ is the energy of the complete system, $E_2$ that of the system with a vacancy and $N$ the number of atoms. |
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+ | ===== Analyze the PDOS ===== | ||
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+ | Would you expect the vacancy to haven any influence on the projected density of states? Check whether your assumption was right by visualizing the PDOS. | ||
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+ | ===== Replacement with oxygen ===== | ||
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+ | Now, instead of removing one carbon atom from the 6x6x1 supercell, simply replace it with an oxygen atom. Perform first a single point calculation and second a geometry optimization and compare the energy of adsorption for both cases. | ||
====== Oxygen atom adsorbed on graphene ====== | ====== Oxygen atom adsorbed on graphene ====== | ||
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+ | Now we are going to investigate the effect an adsorbent has on graphene. | ||
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+ | ===== Change in energy ===== | ||
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+ | In order to adsorb an oxygen atom on top of a graphene layer, modify the coordinate section by adding one oxygen atom which has them same coordinates as a carbon (except the z-component of course). Check whether the addition of an oxygen atom has an effect on the structure of graphene by optimizing its geometry and calculate the adsorption energy. | ||
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+ | Use $E_\text{ad} = E_3 – (E_1 + \frac{1}{2}E_2)$, | ||
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+ | ; $E_\text{ad}$ : energy of adsorption | ||
+ | ; $E_1$ : energy of graphene | ||
+ | ; $E_2$ : energy of molecular oxygen (-31.929714235694995 a.u.) | ||
+ | ; $E_3$ : energy of oxygen adsorbed on graphene | ||
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+ | <note tip>The formation of oxygen is more difficult to obtain, here we use $\frac{1}{2}$ of the total energy of molecular oxygen. This approximation introduces a large uncertainty to our calculations because the calculation of dioxygen is difficult using KS-DFT. | ||
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+ | Try to explain based on the lecture what might be the problem.</ | ||
+ | ===== Displacements ===== | ||
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+ | We are furthermore interested in the change of structure this adsorbent causes. Try to visualize which atoms have to assume a new position in order to minimize the total energy. That is: plot $\sqrt{(x^i-x^i_0)^2 + (y^i-y^i_0)^2 + (z^i-z^i_0)^2}$ in a sensible manner (one which also retains the geometry of graphene). | ||
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+ | ======= Analyzing defects in hexagonal Boron-Nitride ======= | ||
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+ | Repeat the calculations of the vacancy formation, defect formation and adsorption for the h-BN-layer structure, taking into account that now both the N and the B can be replaced. | ||
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+ | Compare the energies for the two cases, where is a vacancy more likely to be and on top of which atom does an oxygen atom preferably adsorb. | ||
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+ | <note tip>Use the total energy of a B or N atom when calculating the vacancy formation energy.</ | ||
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+ | Since N and B are radicals, you have to include the following keywords/ | ||
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+ | * '' | ||
+ | * '' | ||
exercises/2016_uzh_cmest/defects_in_graphene.1479066589.txt.gz · Last modified: 2020/08/21 10:15 (external edit)