Figure 1

(Color online) Potential energy per atom with respect to equilibration time steps for CUB 309-atom cluster at $1100\mathrm{K}$. Label A shows the structural transition from CUB to ICO cluster, label B is the time range for reliable statistics, and label C stands for the surface deformation of transmitted ICO cluster. All four 3D pictures exhibit the same averaged configurations, from left to right, respectively, in the perspective, the top view, the truncated top view, and the top view without bonds.Reuse & Permissions

Figure 2

(Color online) Radial optimization of ICO and CUB shell-closed nickel clusters by minimizing their energy. From the energetic point of view, ICO clusters are more stable than CUB clusters when the clusters are small at $0\mathrm{K}$. The crossover occurs between 923- and 1415-atom clusters.Reuse & Permissions

Figure 3

(Color online) Total energy per atom as a function of cluster temperature and symmetrically truncated visualizations for ICO Ni clusters with 309 atoms. The thickness of the truncated clusters is $d=5.14\mathrm{\AA }$. Corresponding to each temperature as temperature increases before totally melting, surface premeltage is clearly visualized. The upper visualizations are symmetrically truncated by parallel planes with the $z$ (fivefold) axis as their normal direction and the lower visualizations are symmetrically truncated by parallel planes with the $x$ (threefold) axis as their direction. The bonds among atoms are only to guide the eye and the coordinate frames are for special reference.Reuse & Permissions

Figure 4

(Color online) The analogy to Fig. 2 but for CUB Ni clusters with 561 atoms and only one-directional visualizations.Reuse & Permissions

Figure 5

Contour plot of radial number distribution against temperature. Subplot (a) stands for CUB ${\mathrm{Ni}}_{309}$ and (b) for ICO ${\mathrm{Ni}}_{309}$. Gray-scale legends represent the relative number of atoms along radial direction from mass center of clusters. Label A (dash lines) stands for ICO character, label B (dash-dot lines) for CUB, and label C (dot lines) for the melting range. At the lower temperature range, clusters remain in their geometric structures, which are of parallel horizontal lines in the plots. As temperature rises, atoms in the outer shells start to displace and surface premelting occurs or the contour lines with larger radius are no longer parallel. To melting temperature, structural destruction in the core with small radius occurs at which all parallel lines disappear. In subplot (a), some of the contour structure between premelting and melting shows the identity compared with the ICO structure at the lower temperature range in subplot (b), which poses the implication of structural transition between CUB and ICO clusters.Reuse & Permissions

Figure 6

The analogy to Fig. 5 but (a) for CUB ${\mathrm{Ni}}_{561}$, (b) for ICO ${\mathrm{Ni}}_{561}$, (c) for CUB ${\mathrm{Ni}}_{923}$, and (d) for ICO ${\mathrm{Ni}}_{923}$. As clusters grow larger, the structural transition no longer exists.Reuse & Permissions

Figure 7

(Color online) Total energy per atom as a function of cluster temperature and symmetrically truncated structural visualizations of melting evolution of four-shell CUB clusters with 309 atoms. The thickness of the truncated clusters is $d=4.000\mathrm{\AA }$. The dot line as a reference is for ICO cluster with 309 atoms as plotted in Fig. 3. Below $1000\mathrm{K}$, the clusters maintain their starting CUB configuration. Through $1000\mathrm{K}$ below the melting point, CUB clusters are likely to take ICO configuration.Reuse & Permissions

Figure 8

Dependence of total energy per atom and cluster size with different atoms on temperature. (a) Stands for shell-closed CUB Ni clusters and (b) for ICO ones. These plots are analogous to caloric curves of corresponding clusters. The sharp increases of the curves indicate that cluster melting takes place in the $10\mathrm{K}$ range, as in our computations.Reuse & Permissions

Figure 9

(Color online) Plot of melting temperatures of shell-closed Ni clusters against the inverse cluster size and their linear fit lines for both CUB (dash line) and ICO (dot line) clusters, respectively. Owning to structural transition, CUB ${\mathrm{Ni}}_{309}$ has no melting point. For clusters larger than 309 atoms, the melting points do exist for both CUB and ICO clusters without structural transitions. As clusters of higher melting temperature are thermodynamically preferable, small clusters of fewer 923 atoms prefer ICO configuration while larger clusters of more than 923 atoms prefer CUB configuration, a fcc fragmentation. The crossover is near the 923-atom cluster at about $1380\mathrm{K}$. The dash-dot lines are only a guide for the eye.Reuse & Permissions