Molecular dynamics simulations of the meltinglike transition in ${\mathrm{Li}}_{13}{\mathrm{Na}}_{42}$ and ${\mathrm{Na}}_{13}{\mathrm{Cs}}_{42}$ clusters

Equilibrium geometries and the meltinglike transition of ${\mathrm{Na}}_{13}{\mathrm{Cs}}_{42}$ and ${\mathrm{Li}}_{13}{\mathrm{Na}}_{42}$ are studied by means of orbital-free density-functional-theory molecular dynamics simulations. A polyicosahedral structure is found to be energetically favored for ${\mathrm{Na}}_{13}{\mathrm{Cs}}_{42}$, with a core shell formed by Na atoms and complete segregation of Cs atoms to the cluster surface. ${\mathrm{Li}}_{13}{\mathrm{Na}}_{42}$ adopts an amorphouslike structure, albeit with significant local polyicosahedral order, with the Na atoms preferentially occupying surface sites but with partial mixing of Li and Na species at the cluster core. Analysis of the thermal properties reveals that premelting effects are more important for heterogeneous than for homogeneous alkali clusters. The nature of these premelting effects is discussed in detail. For ${\mathrm{Na}}_{13}{\mathrm{Cs}}_{42}$, they involve isomerizations without significant atom diffusion; for ${\mathrm{Li}}_{13}{\mathrm{Na}}_{42}$, they also include partial melting of the surface formed by Na atoms. The mixing of Li and Na species is significantly enhanced above the melting temperature, while surface segregation of Cs in ${\mathrm{Na}}_{13}{\mathrm{Cs}}_{42}$ is maintained in the liquid state. From the study of these two clusters, we attempt to extract some general trends about the structural and thermal behaviors of heterogeneous alkali clusters.

Figure 1

(Color online) Lowest energy structure and low-lying isomers of ${\mathrm{Na}}_{13}{\mathrm{Cs}}_{42}$. Side and top views are offered on left and right columns, respectively. Small light (yellow) balls represent Na atoms, and large dark (red) balls represent the 32 Cs atoms completing the 45-atom compact anti-Mackay structure, while large white balls represent the ten Cs atoms in the outermost shell. Numbers are energy differences with respect to the ground state isomer (a) in meV∕atom.

Figure 2

(Color online) Lowest energy structure and low-lying isomers of ${\mathrm{Li}}_{13}{\mathrm{Na}}_{42}$. For the ground state isomer (a), both the core and surface shells, in two different views, are offered. In the core shell, dark (red) and light (gray) balls represent Li and Na atoms, respectively. In the surface shell, dark (blue) balls represent those Na atoms capping the faces of the core shell, and light (yellow) spheres represent the rest of the surface Na atoms. For higher energy isomers, only the core shell is shown as the surface shell is unchanged except for slight distortions. Numbers are energy differences with respect to the ground state isomer (a) in meV∕atom.

Figure 3

(Color online) Caloric and specific heat curves (left side), and rms bond length fluctuation and diffusion constants (right side) of ${\mathrm{Na}}_{13}{\mathrm{Cs}}_{42}$, taking the internal cluster temperature as the independent variable.

Figure 4

(Color online) Time-averaged radial atomic density distributions (dashed lines) of ${\mathrm{Na}}_{13}{\mathrm{Cs}}_{42}$, at some representative temperatures. The full line is the contribution of Na atoms to $g\left(r\right)$. Where both lines coincide, only the full line is displayed.

Figure 5

(Color online) Time evolution of atomic equivalence indexes of ${\mathrm{Na}}_{13}{\mathrm{Cs}}_{42}$, averaged over time intervals of 1000 steps, at $T=85\mathrm{K}$. Some of the $\sigma$ curves corresponding to Cs atoms involved in isomerization transitions are represented by bold lines.

Figure 6

(Color online) Caloric and specific heat curves (left side) and rms bond length fluctuation and diffusion constants (right side) of ${\mathrm{Li}}_{13}{\mathrm{Na}}_{42}$, taking the internal cluster temperature as the independent variable.

Figure 7

(Color online) Time-averaged radial atomic density distributions (dashed lines) of ${\mathrm{Li}}_{13}{\mathrm{Na}}_{42}$, at some representative temperatures. Full lines represent the contribution of Li atoms to $g\left(r\right)$.

Figure 8

(Color online) Time evolution of atomic equivalence indexes of ${\mathrm{Li}}_{13}{\mathrm{Na}}_{54}$, averaged over 1000 time steps, at four representative temperatures. Some $\sigma$ curves are represented by bold lines in order to better appreciate signatures of isomerizations and∕or diffusive motion.

Figure 9

(Color online) Three snapshots of ${\mathrm{Li}}_{13}{\mathrm{Na}}_{42}$, extracted from a MD run at $118\mathrm{K}$, showing the surface melting mechanism at that temperature. A group of six atoms forming a pentagonal pyramid on the cluster surface is represented by light-colored (gray) balls. The white ball represents a Na atom which substitutes for one of the Na atoms initially in that pentagonal pyramid.