Figure 1

Magic core-shell pIh clusters. PIh clusters are built by packing elementary ${\mathrm{I}\mathrm{h}}_{13}$ clusters (see also Fig. S1), as shown in the top row, where three different fragments of the ${\mathrm{p}\mathrm{I}\mathrm{h}}^7$ structure are given. From left to right, the fragments comprise one, two, and four interpenetrating ${\mathrm{I}\mathrm{h}}_{13}$. Below, a selection of magic core-shell pIh is given. Each pIh is shown in four views; in two of them the Ag atoms ( gray color) are represented by small points to show the arrangement of the core (Ni or Cu, orange color) atoms. The $(27,7){\mathrm{p}\mathrm{I}\mathrm{h}}^7$ has a decahedral Ni or Cu core of 7 atoms, and the 27 Ag atoms are placed in an anti-Mackay overlayer. The $(32,6){\mathrm{p}\mathrm{I}\mathrm{h}}^6$ is a pancake structure, with the six inner atoms placed on a regular hexagonal ring. The $(30,8){\mathrm{p}\mathrm{I}\mathrm{h}}^8$ is the perfect core-shell structure including the maximum number of core atoms at size 38. The $(32,13){\mathrm{p}\mathrm{I}\mathrm{h}}^{12}$ is the complete anti-Mackay icosahedron of size 45, including a perfect ${\mathrm{I}\mathrm{h}}_{13}$ core. It is made of 12 interpenetrating ${\mathrm{I}\mathrm{h}}_{13}$ sharing the central atom as a common vertex.Reuse & Permissions

Figure 2

$\Delta$ and ${\Delta }_2$ (in eV) for clusters of fixed size vs the number of Ag atoms $N_1$. ${\Delta }_M$ is the minimum value of $\Delta$ at the given size. Circles and squares refer to Ag-Cu and Ag-Ni, respectively. Open symbols refer to the atom-atom potential results, while full symbols refer to the DFT results. Minima in $\Delta$ and maxima in ${\Delta }_2$ both concur to single out the most stable structures, which are the perfect core-shell $(30,8){\mathrm{p}\mathrm{I}\mathrm{h}}^8$ and $(27,7){\mathrm{p}\mathrm{I}\mathrm{h}}^7$ (see Fig. 1) at sizes 38 and 34, respectively.Reuse & Permissions

Figure 3

Melting of pure clusters and of core-shell pIh. The top panel shows the molecular-dynamics caloric curves $\delta E$ (in eV) vs temperature $T$ (in K), where $\delta E=E-E_{\mathrm{G}\mathrm{M}}-3(N-1)k_{B}T$, namely, $\delta E$ is the total cluster energy minus the global-minimum energy $E_{\mathrm{G}\mathrm{M}}$ and the harmonic contribution $3(N-1)k_{B}T$. The middle panel reports $p_{\mathrm{G}\mathrm{M}}$ which is the probability of finding the cluster in its global-minimum structure as a function of $T$. The bottom panel reports the vibrational specific heat $c$ per degree of freedom (in units of the Boltzmann constant $k_B$). $p_{\mathrm{G}\mathrm{M}}$ and $c$ are calculated in the harmonic superposition approximation. Stars, diamonds, and triangles refer to pure ${\mathrm{A}\mathrm{g}}_{38}$, ${\mathrm{C}\mathrm{u}}_{38}$, and ${\mathrm{N}\mathrm{i}}_{38}$ clusters; circles and squares refer to the $(27,7){\mathrm{p}\mathrm{I}\mathrm{h}}^7$ of Ag-Cu and Ag-Ni. Core-shell pIh melt considerably higher than pure clusters.Reuse & Permissions