Design of defected TaN supercells dataset
Five kinds of supercells which contain point-defects (metal and nitrogen vacancies) are designed to simulate by DFT calculations the configurationnel effects of defects distribution (perfectly ordered, symmetric, clusters and random vacancies) within the lattice, on the structural and elastic properties of defected cubic and non-cubic TaxN y. Same number of metal and nitrogen randomly distributed mimic the random distribution of Schottky defects. The POSCAR files are provided for different defects concentration (removing 1, 2, 3 ..., 12 atoms). "Random" distribution of defects on the metal and nitrogen sites has been obtained by ATAT Monte Carlo calculations within teh Special quasi-random structure method (SQS), while for “Perfectly ordered” structures were found by Cluster Expansion method to have the lowest energies within the interested concentration range. Although they have higher symmetry compared to SQS, it is better to name them specifically as "CE ground state (ordered) structures" to distinguish them from the symmetric ones that were generated manually as for the clusters ones. For the "symmetric case", we considered ordered distribution of vacancies (denoted as “symmetric” configuration) by removing atoms with certain site symmetries from the 2×2×2 supercell. Hence, in the symmetric configurations, all the defected structures remain cubic. The vacancies in “symmetric” configurations are not randomly distributed as in SQS. They are created in a symmetric manner referring to the 4-fold rotational symmetry in cubic lattice . The configurations are generated progressively by removing an atom from the 2×2×2 supercell by one of the following manners, (i) 1 cubic center atom (1 V), (ii) i+ 1 vertex of the cubic (2 V), (iii) 3 face centers (3 V), (iv) i+iii (4 V), (v) i+ii+iii (5 V), (vi) iii+ 3 edge centers (6 V), (vii) vi+i (7 V), (vii) vi+ii (8 V). Note that the structure has still cubic symmetry (equal in 3 directions) after vacancies creation for each step. In the case of "clusters" configurations, the vacancies are manually created by removing adjacent Ta or N atoms, respectively for clustered Ta or N vacancies. For example, a N(0) atom has 12 neighboring N(1-12) atoms, we first remove one N(0), then a neighboring N(1) of this first N(0), then a second neighboring N(2), ... The vacancies form a cluster in such a way. It is the same methodology for Ta atoms.