# Generating special quasirandom structures (SQS) for surface calculations?

Given that most of the available codes for performing DFT calculations work with periodic boundary conditions, there are tools like mcsqs as a part of the Alloy Theoretic Automated Toolkit (ATAT) that enable generation of SQS for modelling materials with configurational disorder. Inherently, these methods of generating SQS rely on the periodicity of the supercell in all directions while generating the SQS.

In simulations where we explicitly reduce the effect of the periodic images in one or more dimensions (like when modelling surfaces), what are the points to keep in mind to ensure that the SQS are generated and used correctly?

• What do you mean by > SQS generated are being used correctly ?
– Camps
Apr 30 '20 at 13:14
• @I.Camps: Thanks, I have modified the question to clarify. May 1 '20 at 11:55
• You might be interested in this! mattermodeling.stackexchange.com/q/6821/5 Sep 30 at 20:52

First of all, it's better to define the terms here because probably not all the people here are familiar with SQS right away. SQS is an abbreviation for special quasirandom structures. The illuminating reference here is the work of Zunger et. al. that basically show you that the most relevant parameter to consider when you want if SQS truly resembles a random alloy or not is radial distribution function that basically tells you how the atoms are distributed in the space.



• Thanks for the answer, I have read the work of Zunger et. al. However, when we have surfaces, how do we use tools to generate SQS? I believe the radial distribution function (RDF) is inherently used in the available tools for getting SQS with the most "random" structure. But how do we ensure that the tools are accounting for the fact that one dimension doesn't have nearby periodic images in surfaces? Please let me know if I am able to articulate my question correctly. If not, I'll try again. May 1 '20 at 12:01

There are two different perspectives here. The first one is the creation of the SQS structure itself accomplished through the ATAT package, for example. The second one is the calculation of the slab properties.

The SQS procedure returns the smaller structure that resembles the periodic structure properties. For alloys, for instance, the inputs are the concentrations, the preferred lattice symmetry, if any, and the length of the neighbors' interactions. We can also specify the desired quantity of atoms within the unit cell (not always preserved by the code). The resulting structure can be passed to the DFT (periodic) simulation.

To perform the slab simulation, we need to add the vacuum in the desired direction. We can also repeat the structure making a supercell and perform a cleave to the desired plane.

• Thanks for the answer, but I am not convinced how adding a vacuum is non-trivial for structures generated using SQS. I understand that we can always add it ourselves, but from what I understand about the algorithms that are typically used to generate SQS, periodicity in all directions is crucial for it to work like it's expected to (i.e. represent chemically "random" structures). Dec 30 '20 at 6:34

As Anibal points in his answer, generating the SQS and using it for a surface calculation are two separate things, and shouldn't affect each other. You would still take all precautions as usual while performing the DFT calculation.

That being said, there could be scenarios where you may want to restrict/prefer certain atom types amassing at edges or corners of the surface. A friend who studied cutting tools, and materials like diamond or silica used thereof, was very peculiar about atomically uniform edges. As always, it's all system dependent. Let your intuition roll!

• Thanks for the answer, but like I mentioned in the comment on Anibal's answer, I'm not convinced that the algorithm that's used to generate SQS structures can handle non-periodic boundary conditions. There could be modifications, but I believe it should be specified when getting the structure in the first place. I don't think it's correct to manually "create" surfaces like we do with non-SQS supercells. Dec 30 '20 at 6:37