Geometry, electronic properties, and thermodynamics of pure and Al-doped Li clusters

The first-principles density functional molecular dynamics simulations have been carried out to investigate the geometric, the electronic, and the finite temperature properties of pure Li clusters (${\mathrm{Li}}_{10}$, ${\mathrm{Li}}_{12}$) and Al-doped Li clusters (${\mathrm{Li}}_{10}\mathrm{Al}$, ${\mathrm{Li}}_{10}{\mathrm{Al}}_2$). We find that the addition of two Al impurities in ${\mathrm{Li}}_{10}$ results in a substantial structural change, while the addition of one Al impurity causes a rearrangement of atoms. Introduction of Al impurities in ${\mathrm{Li}}_{10}$ establishes a polar bond between Li and nearby Al atom(s), leading to a multicentered bonding, which weakens the Li-Li metallic bonds in the system. These weakened Li-Li bonds lead to a premelting feature to occur at lower temperatures in Al-doped clusters. In ${\mathrm{Li}}_{10}{\mathrm{Al}}_2$, Al atoms also form a weak covalent bond, resulting in their dimerlike behavior. This causes Al atoms not to “melt” until $800\mathrm{K}$, in contrast to the Li atoms which show a complete diffusive behavior above $400\mathrm{K}$. Thus, although one Al impurity in ${\mathrm{Li}}_{10}$ cluster does not change its melting characteristics significantly, two impurities results in “surface melting” of Li atoms whose motions are confined around an Al dimer.

Figure 1

(Color online) The ground-state geometry and some isomers of ${\mathrm{Li}}_{10}$ and ${\mathrm{Li}}_{12}$. The label (i) represents the ground-state geometry. The energy difference $\Delta E$ is given in eV with respect to the ground-state energy.

Figure 2

(Color online) The ground-state geometry and some isomers of ${\mathrm{Li}}_{10}\mathrm{Al}$ and ${\mathrm{Li}}_{10}{\mathrm{Al}}_2$. The label (i) represents the ground-state geometry. The blue circle represents the Li atoms and the yellow circle represents the Al atoms. The energy difference $\Delta E$ is given in eV with respect to the ground-state energy.

Figure 3

The properties of the ground-state geometry. (a) The deformation parameter $\left({\epsilon }_{\mathit{def}}\right)$. (b) The binding energy $E_b$ in eV/atom.

Figure 4

The isovalued surfaces of the total charge density at $1∕3$ of its maximum values, where the maximum charge density of ${\mathrm{Li}}_{10}\mathrm{Al}$ is 0.233 and that of ${\mathrm{Li}}_{10}{\mathrm{Al}}_2$ is 0.239.

Figure 5

The difference charge density between the mixed cluster and separated units of Li and Al clusters at the same positions. (a) and (c) show the region where the charge is gained and (b) and (d) show the region where the charge is lost. The figures show the isosurfaces of difference charge density at the value of charge gain of 0.017 and loss of 0.008, respectively.

Figure 6

The normalized specific heat as a function of temperature. $C_0=(3N-9∕2)k_B$ is the zero-temperature classical limit of the rotational plus vibrational canonical specific heat.

Figure 7

The root-mean-square bond length fluctuation $\left({\delta }_{\mathit{rms}}\right)$ of Li-Li, Li-Al, and Al-Al as a function of temperature.