Stability of phase coexistence in atomic clusters

Microcanonical critical droplet theory and molecular dynamics simulations are used to examine static coexistence between solid and liquid phases in nanoscale lead clusters. It is shown that the theory predicts the existence of a metastable coexisting state above a critical cluster radius $R_1$, with this state becoming stable for clusters of radius $R>R_2$. Molecular dynamics simulations of lead clusters confirm the existence of stable coexisting states in 1427-atom and 2057-atom clusters but find no stable coexisting state in a 931-atom cluster.

Figure 1

Caloric curves for (a) a 1427-atom Pb cluster and (b) a 2073-atom cluster. The 1427 and 2073-atom clusters exhibit coexistence for a range of energies.

Figure 2

Caloric curves for a 1427-atom cluster produced first by heating (solid line) then by cooling (dashed line).

Figure 3

A sequence of snapshots showing the coexisting solid-liquid state as the energy is increased from $E=-1.712\mathrm{eV}∕\text{atom}$ (top left) to $E=-1.706\mathrm{eV}∕\text{atom}$ (bottom right). Atoms are classified by their mobilities: the dark gray atoms are liquid (high mobility) while the light gray atoms are solid (low mobility).

Figure 4

Caloric curves for a 931-atom Pb cluster. The 931-atom cluster does not exhibit a stable coexisting phase. The large fluctuations near the melting point signal the appearance of precritical liquid nuclei. The true melting point energy probably lies closer to the dotted line.

Figure 5

Time evolution of the kinetic temperature in a 931-atom cluster at an energy $E=-1.688\mathrm{eV}∕\text{atom}$. The white line shows a time averaged trace of the temperature. The cluster starts as solid $(0–5\mathrm{ns})$, becomes coexisting $(5–8\mathrm{ns})$, and finally melts fully (after $8\mathrm{ns}$).