Surface Nucleation in the Freezing of Gold Nanoparticles

We use molecular simulation to calculate the nucleation free energy barrier for the freezing of a 456 atom gold cluster over a range of temperatures. The results show that the embryo of the solid cluster grows at the vapor-surface interface for all temperatures studied and that the usual classical nucleation model, with the embryo growing in the core of the cluster, is unable to predict the shape of the free energy barrier. We use a simple partial wetting model that treats the crystal as a lens-shaped nucleus at the liquid-vapor interface and find that the line tension plays an important role in the freezing of gold nanoparticles.

Figure 1

Free energy of formation $W(n)/kT$ of an $n$-sized embryo for temperatures $T=730$, 710, 690, and 680 K.

Figure 2

The average number of surface atoms $n_{\max ,\mathrm{surf}}$ found in the largest embryo $n_{\max }$. The dark circles represent the values averaged over all temperatures. The lines are linear best fits for the larger (red) and smaller (blue) embryos. The cross symbols represent the averages for each temperature studied and give an indication of the scatter of the data. The inset is a magnification of the small embryo region.

Figure 3

Left: An isolated 71 atom embryo. Right: The same solid embryo (dark atoms) embedded in the liquid (light atoms) cluster.

Figure 4

Schematic cross section of a solid (phase 1) lens nucleus forming at the liquid (phase 2)-vapor (phase 3) interface. $A_{12}$ and $A_{13}$ are the solid-liquid and solid-vapor interfacial surface areas, respectively, and $R$ is the radius of the lens. The four arrows originating from the 3-phase contact are the force vectors of the surface tensions ${\sigma }_{ij}$ and the line tension $\tau /R$.

Figure 5

Phenomenological model data fits to the calculated free energy barrier at $T=710\mathrm{K}$. The lens model with line tension included (solid line) and CNT, assuming core nucleation (dotted line).