Structural and thermal behavior of compact core-shell nanoparticles: Core instabilities and dynamic contributions to surface thermal stability

An orbital-free density-functional-theory molecular dynamics technique is applied to investigate the minimum-energy structure and meltinglike transition of ${\mathrm{Cs}}_{55}$, ${\mathrm{Li}}_{13}{\mathrm{Na}}_{32}{\mathrm{Cs}}_{42}$, and ${\mathrm{Li}}_{55}{\mathrm{Cs}}_{42}$ nanoparticles. Icosahedral packing is found to be optimal for homogeneous ${\mathrm{Cs}}_{55}$, as expected. Heterogeneous particles show a complete segregation of Cs atoms to the cluster surface, and form perfect core-shell structures, that is, structures where each atomic species occupies and completes a different concentric atomic shell. For ${\mathrm{Li}}_{13}{\mathrm{Na}}_{32}{\mathrm{Cs}}_{42}$, the size mismatch between atomic species forming different shells leads to polyicosahedral packing. For ${\mathrm{Li}}_{55}{\mathrm{Cs}}_{42}$, however, the size mismatch is huge and perfect polyicosahedral ordering is frustrated, resulting in more complex structural behavior. The three clusters investigated share the same surface shell, formed by 42 Cs atoms, and comparison of their melting behaviors helps to rationalize the increased thermal stability of the cluster surface upon alloying. ${\mathrm{Cs}}_{55}$ melts homogeneously at approximately $85\mathrm{K}$. Both ${\mathrm{Li}}_{13}{\mathrm{Na}}_{32}{\mathrm{Cs}}_{42}$ and ${\mathrm{Li}}_{55}{\mathrm{Cs}}_{42}$ show a substantial thermal stability, compared to ${\mathrm{Cs}}_{55}$ and other alloy compositions where a perfect core-shell structure does not appear. We demonstrate that an important contribution to this increased thermal stability in the nanoalloys comes from the large difference in the atomic masses of the constituent particles, which results in a poor coupling of atomic vibrations along the radial direction. We also give arguments to show that the meltinglike transition in these clusters is triggered by the thermal instability of interior rather than surface atoms. Segregation of Cs atoms to the cluster surface is fully maintained in the liquid state, so that core and surface shells form two inmiscible liquid layers.

Figure 1

(Color online) Comparison of Mackay (left) and anti-Mackay (right) growing on top of a 13-atom icosahedron. Surface and core atoms are given different shades of gray (colors) to help visualization. The 55-atom Mackay icosahedron is the ground state structure for ${\mathrm{Cs}}_{55}$. Anti-Mackay growing leads to the 45-atom polyicosahedral shell closing, which is favored for binary metallic systems with a large size mismatch and surface tension difference between the two components.

Figure 2

Caloric curve (left) and rms bond-length-fluctuation parameter (right) of ${\mathrm{Cs}}_{55}$ as a function of the cluster internal temperature.

Figure 3

(Color online) Comparison between SIESTA (full symbols) and present (continuous line) OFAIMD results for the interatomic forces of the ${\mathrm{Cs}}_{55}$ icosahedral atomic configuration which is optimal (zero atomic forces) for the previous OFAIMD realization (Ref. 43). Both SIESTA and present OFAIMD results produce interatomic forces significantly deviating from zero.

Figure 4

(Color online) Lowest energy structure of ${\mathrm{Li}}_{13}{\mathrm{Na}}_{32}{\mathrm{Cs}}_{42}$ (left side). The core shell $\left({\mathrm{Li}}_{13}{\mathrm{Na}}_{32}\right)$ is a perfect anti-Mackay icosahedron as shown in Fig. 1. On the right side, we show the different local coordination environments of the Na atoms occupying vertex (upper plot) and edge (lower plot) positions of ${\mathrm{Li}}_{13}{\mathrm{Na}}_{32}$. All Na atoms are placed at the center of a (slightly distorted) 13-atom icosahedron, which shows that the ground state structure of ${\mathrm{Li}}_{13}{\mathrm{Na}}_{32}{\mathrm{Cs}}_{42}$ presents polyicosahedral packing. The surface shell, formed by 42 Cs atoms, is exactly the same as that of ${\mathrm{Cs}}_{55}$.

Figure 5

(Color online) Caloric curve (left) and rms bond-length-fluctuation parameter (right) of ${\mathrm{Li}}_{13}{\mathrm{Na}}_{32}{\mathrm{Cs}}_{42}$ as a function of the cluster internal temperature. The caloric curve of the same cluster, assuming the masses of all atomic species are equal to the Cs atomic mass, is also shown on the left side (square symbols). This curve is displaced along the vertical axes to help visualization.

Figure 6

(Color online) Species-resolved power spectra of ${\mathrm{Li}}_{13}{\mathrm{Na}}_{32}{\mathrm{Cs}}_{42}$ for solid (left side) and liquid (right side) phases. The upper part shows the power spectra obtained when all atomic masses are equal to the Cs atomic mass, while the lower graphs show the real power spectra. Note the different frequency scales in the two cases.

Figure 7

(Color online) Time averaged radial atomic density distributions of ${\mathrm{Li}}_{13}{\mathrm{Na}}_{32}{\mathrm{Cs}}_{42}$, at some representative temperatures. A deep minimun in $g\left(r\right)$ persists in the liquid state, indicating the strong surface seggregation of Cs atoms. Mixing of Li and Na species at the core shell is observed in the liquid phase.

Figure 8

(Color online) Low-lying isomers of ${\mathrm{Li}}_{55}$, together with energy differences, in meV/atom, with respect to the ground state structure (a Mackay icosahedron as shown in Fig. 1). The first (second) row shows OFDFT (SIESTA) results. The first two isomers present a decahedral 13-atom core shell, while core and surface shells are twisted relative to each other so that (100) facets are avoided. These two isomers differ only in the relative orientations of core and surface shells. The isomer on the right side is a fragment of the bcc crystalline lattice. Different colors (shades of gray) are employed for core and surface Li atoms to help visualization.

Figure 9

(Color online) Ground state structure of ${\mathrm{Li}}_{55}{\mathrm{Cs}}_{42}$ (upper left), based on a twisted decahedral core as shown in the middle part of Fig. 8. Atoms in different radial shells are given different colors to help visualization. The surface shell, formed by 42 Cs atoms, is close to icosahedral but has some neighboring pentagons due to the twisting distortion. On the right side, we show the different atomic environments of the Li atoms occupying the outermost radial core shell. Some of them can be viewed as frustrated icosahedra, due to the very large size mismatch in the Li-Cs system. The lower left plot is a low-lying local minimum, based on an icosahedral ${\mathrm{Li}}_{55}$ core. The orientation of this figure is chosen to easily appreciate the icosahedral symmetry of the core shell. Transformations between these isomers are observed at finite temperatures lower than the melting point (see text).

Figure 10

Caloric curve (left) and rms bond-length-fluctuation parameter (right) of ${\mathrm{Li}}_{55}{\mathrm{Cs}}_{42}$, as a function of the cluster internal temperature.

Figure 11

(Color online) Time evolution of atomic equivalence indexes of ${\mathrm{Li}}_{55}{\mathrm{Cs}}_{42}$, averaged over 3000 time steps $\left(9\mathrm{ps}\right)$, showing the back and forth solid-solid transformations prior to the melting transition. Portions from three different MD runs in the temperature range $110–130\mathrm{K}$ are shown together. The legends “ICO” and “DEC” help to differenciate between the sets of $\sigma$ lines corresponding to icosahedral and ground state isomer, respectively.