# Gamma point analysis

Hi Prof Julian,

I am working on single layer graphene(SLG) with grain boundaries(GBs). The grain boundaries are created and then relaxed. And now the coordinates are introduced into the GULP script file from which I am expecting frequencies and eigenvectors while doing Gamma point analysis.

Result obtained: Some negative frequencies with some “*****” values. The higher frequencies are much higher in value compared to pristine SLG.

Questions:

1. I obviously cannot do the k-point analysis on a non-periodic strucure. Does this mean that I also will not be alble to produce eigenvalues and eigenvectors with Gamma point analysis through GULP when I have GBs in the structure?

2. Does the negative frequencies and some unknown values are coming because of unstability (although I did relax the structure)?

3. Even if I ignore say the negative frequencies and make it zero, there are frequencies which are much higher in value compared to pristine SLG frequncies. Is that a common feature during such analysis where GBs are involved ?

4. Or is there some other way(keyword) inorder to introduce Grain Boundary in the strucure with GULP?

Hi. Here are some answers to your questions, but the important thing to note is that if you are getting frequencies with ***** it means either your structure or force field is wrong such that you have nonsensical results & so the most important thing is to fix this.

1. You can get eigenvalues and eigenvectors regardless of whether the structure is periodic or not.
2. Negative (strictly imaginary) modes normally indicate instability, but when they’re **** this usually means a major problem with your structure or force field (or both)
3. Frequencies could be higher at defect structures than for the bulk, though much higher is unlikely. Again this is just because you’re run is likely to be messed up in some way.
4. GULP can handle structures in any dimensionality from 0 to 3 & so you can build any model of grain boundaries you like (2-D would be natural). It’s up to you to generate the coordinates for your grain boundary to give to GULP though - there’s no automatic way to generate grain boundaries with a keyword as no single word can convey all the possible choices of grain boundary for every system!
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Thanks for the answer Prof Julian. I have been working on your suggestions.

I have created very big Single Layer Graphene(SLG) using lattice vectors and basis atoms. Now I am doing Gamma point analysis in two ways:
(a) Carving out a rectangular supercell: Taking a rectangular cell in the already created bigger Single Layer Graphene(SLG) structure and doing Gamma point analysis ,
Result: I get some negative frequncies.

(b) Carving out a trapezoidal supercell: But when using the same SLG lattice vector directions and expanding in these direction inorder to get a carved out supercell of SLG and doing Gamma point analysis over it I get the following.

Result: I get correct frequencies. (Correct frequncies means the frequency I obtain for the same structure by doing k-point analysis)

Why is this happening?
Does this mean that Gamma point analysis needs to have a periodicity in the structure?(I guess not. because Gamma point analysis is used in order to study defects,alloys etc. where there is no periodicity)

I think the issue here is clear from the last part of your message. Gamma point is for periodic structures (as are all k points). If you just “carve” structures out then everything will be dominated by edge effects. So you need your defects to be in a periodic system to avoid these (which is called the supercell method).

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