Figure 1

(Color online) The average potential energy $U$ as a function of temperature $T$ for the nanoparticles consisting of 56 545 (lower curve) and 2091 (upper curve) atoms. Melting points $T_m$ are indicated by vertical dotted lines. The linear extrapolations of data for the solid and liquid phases are also shown in the case of the system containing 2091 atoms in order to identify the latent heat of fusion $\Delta H_m$.Reuse & Permissions

Figure 2

The melting points $T_m$ of the nanoparticles considered as a function of the particle radius $R_p$ at 300 K. Data arrange according to a smooth trend, the lowest melting points pertaining to the smallest systems.Reuse & Permissions

Figure 3

The latent heats of fusion $\Delta H_m$ of the nanoparticles considered as a function of the particle radius $R_p$ at 300 K. As in the case of the melting point $T_m,\Delta H_m$ values decrease as the system size decrease.Reuse & Permissions

Figure 4

The average potential energies $U_b\left(r\right)$ and $U_s\left(r\right)$ of the core region of radius $r$ and of the external region of thickness $\Delta =R_p-r$, respectively, as a function of the radial distance $r$. The average potential energy $U_{\text{bulk}}$ of the bulk solid at 300 K is indicated by the horizontal dotted line. It appears that the average potential energy $U_b\left(r\right)$ of the core region roughly coincides with the one of the bulk solid $U_{\text{bulk}}$ up to a radius $r_b$ of about 3.1 nm, indicated by the vertical dotted line. Marked deviations of $U_b\left(r\right)$ from $U_{\text{bulk}}$ are instead observed at radial distances $r$ larger than $r_b$. The average potential energy $U_s\left(r\right)$ of the external shell undergoes a smooth increase up to the radius $r_b$, keeping an approximately constant value at larger $r$. These features permit us to distinguish between a bulklike core region and a surface layer with different properties. The radial distance $r_b$ can be then regarded as the boundary between bulklike and surface behavior. Data refer to the system of 22 303 atoms.Reuse & Permissions

Figure 5

(Color online) The change of the particle radius $R_p$ as a function of temperature $T$ from 300 K to the melting point $T_m$. The latter is indicated by the vertical dotted line. The particle radius undergoes a smooth, approximately linear increase as the temperature increases. Data refer to the system of 22 303 atoms.Reuse & Permissions

Figure 6

(Color online) The dependence of the surface layer thickness $\Delta$ on the temperature $T$ in the range between 300 K and the melting point $T_m$, indicated by the vertical dotted line. The surface layer thickness increases regularly as the temperature increases. Data refer to the system of 261 790 atoms.Reuse & Permissions

Figure 7

The dependence of the surface layer thickness $\Delta$ on the particle radius $R_p$ at 300 K. A monotonic decrease of the surface layer thickness is observed as the system size increases.Reuse & Permissions

Figure 8

The thickness $\Delta$ of the surface layer at the melting point $T_m$ as a function of the particle radius $R_p$ at the same temperature. A monotonic decrease is observed as in the case of data referred to 300 K.Reuse & Permissions

Figure 9

The thickness $\Delta$ of the surface layer at the melting point $T_m$ as a function of the melting point $T_m$. The thickness $\Delta$ of the surface layer undergoes a monotonic decrease.Reuse & Permissions

Figure 10

(Color online) The average potential energies $U_b\left(r_b\right)$ and $U_s\left(r_b\right)$ of the bulklike core region of radius $r_b$ and of the surface layer of thickness $\Delta$ as a function of the temperature $T$. It can be seen that the two quantities change at different rates, the highest one pertaining to $U_b\left(r_b\right)$. While $U_s\left(r_b\right)$ displays an approximate linearity over the whole temperature range explored, at temperatures close to $T_m{U}_b\left(r_b\right)$ shows a nonlinear behavior. At melting, $U_b\left(r_b\right)$ undergoes a sudden upward jump the amplitude of which is larger than the one undergone by the potential energy of surface atoms. The average potential energy $U_s\left(r_b\right)$ is indeed remarkably close to the one of the liquid. Data refer to the system of 261 790 atoms.Reuse & Permissions

Figure 11

(Color online) The average potential energy $U_s\left(r_b\right)$ of surface atoms at 300 K as a function of the particle radius $R_p$ for the systems investigated. The almost constant value observed points out that the quantity $U_s\left(r_b\right)$ is independent of the system size.Reuse & Permissions

Figure 12

(Color online) The rms atomic displacements ${\delta }_{r,b}$ and ${\delta }_{r,s}$ of bulklike and surface atoms, respectively, as a function of temperature $T$. The quantity ${\delta }_{r,s}$ is always larger than ${\delta }_{r,s}$, indicating that the structure of the surface layer is more disordered than the one of the bulklike core region. As usual, the rms atomic displacement increases as temperature increases. ${\delta }_{r,b}$ increases at rates higher than ${\delta }_{r,s}$. The horizontal line in the figure indicates the Lindemann threshold ${\delta }_{r,\mathrm{crit}}$. The vertical lines indicate, instead, the temperatures $T_{\mathrm{PM}}$ and $T_m$ at which surface and bulklike atoms attain such value. Data refer to the system of 12 213 atoms.Reuse & Permissions

Figure 13

The ratio between premelting temperature $T_{\mathrm{PM}}$ and melting point $T_m$ as a function of the particle radius $R_p$ at $T_m$ for the systems investigated. The premelting ratio decreases regularly as the system size decreases. Premelting phenomena are then more pronounced in small particles than in large ones.Reuse & Permissions

Figure 14

(Color online) The rms atomic displacement ${\delta }_{r,s}$ of surface atoms as a function of the particle radius $R_p$ at 300 K. An approximately constant value of about 0.024 nm is observed irrespective of the system size.Reuse & Permissions