Abstract
We have performed a genetic algorithm search on the tight-binding interatomic potential energy surface (PES) for small TiN (N = 2-32) clusters. The low energy candidate clusters were further refined using density functional theory (DFT) calculations with the PBEsol exchange-correlation functional and evaluated with the PBEsol0 hybrid functional. The resulting clusters were analysed in terms of their structural features, growth mechanism and surface area. The results suggest a growth mechanism that is based on forming coordination centres by interpenetrating icosahedra, icositetrahedra and Frank-Kasper polyhedra. We identify centres of coordination, which act as centres of bulk nucleation in medium sized clusters and determine the morphological features of the cluster.
Highlights
We have performed a genetic algorithm search on the tight-binding interatomic potential energy surface (PES) for small TiN (N = 2–32) clusters
To help understand the structural stability of GM and lower energy metastable LM, in this study we investigate the surface area of each cluster by employing the Delaunay’s triangulation (DT) method[62,63] from the Python Visualisation ToolKit library in the following manner: (i) atoms of the cluster are treated as points and triangulated, (ii) triangles from the surface triangulation are extracted, (iii) the sum of the extracted triangles is defined as the surface area of the cluster – cf. some alternative approaches to the definition and the calculation of the surface area.[64,65,66,67]
The results clearly indicate the tendency for the small (N o 19) TiN clusters to stabilize in a magnetic state, whereas bigger (N Z 19) TiN clusters prove to be non magnetic in the ground state with the exceptions described above
Summary
Simulations in this work were carried out using the Knowledge-Led Master Code (KLMC) software suite[37,38] and its recently improved genetic algorithm (GA) module,[39] which has proved to locate efficiently local (LM) and global (GM) minima[39,40,41,42] on PES. After completing the search on the IP PES, we have selected for refinement a subset of the lowest energy LM within approximately 1.0 eV energy range above the corresponding tentative GM Using this criterion, for example, Ti32 subset included 250 LM. The tentative GM structures were evaluated using the hybrid functional PBEsol[0,59,60] which includes 25% Hartree–Fock-like electron exchange, by performing single point energy calculations with the tight basis sets. To help understand the structural stability of GM and lower energy metastable LM, in this study we investigate the surface area of each cluster by employing the Delaunay’s triangulation (DT) method[62,63] from the Python Visualisation ToolKit library in the following manner: (i) atoms of the cluster are treated as points and triangulated, (ii) triangles from the surface triangulation are extracted, (iii) the sum of the extracted triangles is defined as the surface area of the cluster – cf. some alternative approaches to the definition and the calculation of the surface area.[64,65,66,67]
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