Generating special quasirandom structures (SQS) for surface calculations?

Question

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?

Answer 1

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.

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Answer 2

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.

Answer 3

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!