Results

During the simulations among other observables the temperature, the pressure, the kinetic and potential energy as well as the positions have been saved to disk several times. Click here for an animation of the run. These files were used to analyze the development of the system with time where the Stillinger criterion [7] was used to determine if a cluster has formed.

In fig. 5 we plotted how the number of clusters, i.e. non-monomers, changes with time. One can see that the number of clusters sharply rises immediately after the simulation has been started. After that it falls continuously until it approaches one.

Figure 5: the number of clusters as a function of time

The free energy for the formation of a cluster $f_{cluster}$ is given by

$$\Delta f_{cluster} = f_{vap} - \left(f_{sol} + f_{surf}\right)$$

where $f_{vap}$ and $f_{sol}$ stand for the free energy of the vapor phase and the solid state, respectively. The term $f_{surf}$ represents the free energy of the surface which is introduced into the system. Accordingly one can explain the behavior of the system as follows: under the conditions of this simulation the vapor is no longer the most stable phase. Instead the system evolves into the solid state by forming clusters. But because in the beginning there are many small clusters the surface energy plays governing role. As time advances the smaller clusters merge to former bigger clusters and in the end only one big cluster remains. This final cluster is shown in fig. 6 and it can be seen that it has a crystalline structure.

Figure 6: the cluster remaining at the end of the simulation run

As described in the preceding section only the Ar atoms are used to control the temperature of the system. Equivalent to the experiment they act as the cooling gas for the Cu atoms. The energy which is released during the formation of clusters raises the temperature of the Cu atoms; fig. 7 shows the temperature¹ of the Cu atoms as a function of time. It can be seen that it takes some time until the temperature is lowered due to collisions with the Ar atoms.

Figure 7: the temperature of the Cu atoms (cf. footnote 1) as a function of time

Figure 8: the potential energy per Cu atom as a function of time

A snapshot of the system after 100ps is shown in fig. 9 and fig. 10. The clustering has already begun and several bigger clusters can be identified.

Figure 9: snapshot of the system at 100ps, showing Ar (blue) as well as Cu (red) atoms

Figure 10: snapshot of the system at 100ps, showing only Cu atoms

For the same instant of time the cluster size distribution (fig. 11) and the radial distribution (fig. 12) function have been computed.

Figure 11: the cluster size distribution (left) and the radial distribution function (right) after 100ps

Figure 12: the cluster size distribution (left) and the radial distribution function (right) after 100ps