# How can visualize a rectangular super cell of Graphene by VESTA

How can I build (visualize) a rectangular supercell of graphene as shown in the figure? Can I use VESTA to do that and how? Yes, you can do that in VESTA.

1. First you need a structure file. I use VASP so here's the POSCAR I used.
graphene
1.00000000000000
2.4653795071174938    0.0000000002172037    0.0000000000000000
-1.2326903951325390    2.1350817378200184    0.0000000000000000
0.0000000000000000    0.0000000000000000   24.0000000000000000
C
2
Direct
0.0000000000000000  0.0000000000000000  0.5000000000000000
0.3333329857695233  0.6666669845004449  0.5000000000000000


You can just create a POSCAR file in a directory and drag it into the VESTA window.

1. The idea is to apply a nondiagonal supercell transformation on the original hexagonal lattice. You can apply lattice transformations by doing "Edit" -> "Edit Data" -> "Unit Cell..." on the upper left hand panel, then click "Transform..." in the window that opens.

2. We need to figure out the nondiagonal supercell transformation to use. The original hexagonal lattice I started out with had the form $$\begin{equation} L = a \begin{pmatrix} 1 & -\frac{1}{2} \\ 0 & \frac{\sqrt{3}}{2} \end{pmatrix} \end{equation}$$ where the lattice vectors are the columns of $$L$$ and $$a$$ is the lattice parameter. Let the transformation matrix be $$\begin{equation} T = \begin{pmatrix} h & k \\ 0 & \ell \end{pmatrix} \end{equation}$$ The new lattice vectors after the supercell transformation would then be $$\begin{equation} LT = a\begin{pmatrix} h & k - \frac{\ell}{2} \\ 0 & \frac{\sqrt{3}\ell}{2} \end{pmatrix} \end{equation}$$ To make sure the new lattice vectors are orthogonal (i.e. the lattice is rectangular), the only restriction is hence $$2k = \ell$$.

3. Pick some explicit values for the transformation matrix. I went with a simple $$\begin{equation} T = \begin{pmatrix} 2 & 1 \\ 0 & 2 \end{pmatrix} \end{equation}$$ Input that in the "Rotation matrix P" in the window that popped up previously when you clicked "Transform...". "OK" and then "Apply". You should now have a rectangular looking cell. You can adjust the values of the supercell matrix to make a bigger supercell.

4. To make the plot in the picture, you might want to get rid of the atoms outside the supercell lattice bounds. To do this, click "Edit" -> "Bonds". Then, click the first entry and select "Do not search atoms beyond the boundary", and "Apply".

At the end, you should hopefully be left with something like this. You can then save the structure file in whatever format you desire for computation in relevant software, or export the image if you're creating this for visualization or diagram purposes. • Thank you so much, Mr. CW Tan. I really appreciate that. I got the rectangular supercell as shown below, but I did not get (L, T, and LT) what is the meaning, and how can apply them in VESTA? Jun 5 at 17:14
• You're most welcome Ahmed. The (L, T, LT) stuff is just my way of figuring out what transformation matrix to use to convert a hexagonal lattice to an orthogonal one. I think 3Blue1Brown's linear algebra series on Youtube has nice visuals that gives some intuition to what all that stuff means. Jun 5 at 17:54