Optimizing special quasirandom structure (SQS) models for accurate functional property prediction in disordered 2D alloys

2D materials such as MXenes have garnered attention in a wide field of applications ranging from energy to environment to medical. Properties of 2D materials can be tailored via alloying and in some cases, solid-solutions (disordered alloys) are formed. To predict the disordered alloy properties via first-principles, the model structure needs to imitate the random arrangements of alloyants and yet remains computationally tractable. Using density functional theory and the cluster expansion method, we investigate the accuracy of using of special quasirandom structures (SQSs) for predicting disordered 2D alloy properties, evaluating the effect of SQS supercell size on the prediction quality of formation energies, elastic properties, and structural parameters. We illustrate the findings with 5 different disordered binary M2(1-x)M'2xCO2 MXene alloy systems (where M = Ti and M' = Zr, Hf, V, Nb, or Ta), demonstrating that SQSs around 6-8 times the primitive cell (N = 6-8) are sufficient to attain convergence in the property predictions versus supercell size. For formation energies, SQSs with N > 4 are found to reproduce the formation energies of the fully disordered phase within similar to 2.5 meV. For the simulation of the experimentally-synthesized TiNbCO2, we find convergence in structural parameters and elastic tensors at N similar to 6. We traced the convergence of the predictions to the convergence in the band structure-related properties via analysis of the electronic densities-of-states and the projected crystal overlap Hamilton population. Our findings suggest that modest sized SQSs would reproduce the properties of disordered MXene alloys. The results should help guide the investigations of structure-property relationships in other disordered 2D materials as well.