Shape dynamics during deposit of simple metal clusters on rare-gas matrices

Using a combined quantum-mechanical–classical method, we study the collisions of small Na clusters with large Ar clusters as a model for cluster deposition. We work out basic mechanisms by systematic variation of the collision energy, system sizes, and orientations. The soft Ar material is found to serve as an extremely efficient shock absorber. The collisional energy is quickly transferred at first impact, and the Na clusters are always captured by the Ar surface. The distribution of the collision energy into the Ar system proceeds very fast at the velocity of sound. The relaxation of shapes goes at a slower pace using times of several picoseconds. It produces a substantial rearrangement of the Ar system, while the Na cluster remains rather robust.

Figure 1

Initial configurations for the deposition of ${\mathrm{Na}}_6$ (white balls) on ${\mathrm{Ar}}_7$ (left), ${\mathrm{Ar}}_{43}$ (middle), and ${\mathrm{Ar}}_{87}$ (right).

Figure 2

Snapshots of the deposition of ${\mathrm{Na}}_6$ on a planar site of ${\mathrm{Ar}}_{43}$, with an initial kinetic energy of $13.6\mathrm{meV}$/ion. Time slots are indicated on each panel.

Figure 3

(Color online) Collision of ${\mathrm{Na}}_6$ (thick lines) with an initial kinetic energy of $68\mathrm{meV}$/ion, on ${\mathrm{Ar}}_N$ (thin curves) for $N=7$ (top), 43 (middle), and 87 (bottom). Left panels, $z$ coordinates; right panels, total kinetic energies, as a function of time.

Figure 4

(Color online) $z$ coordinates (left) and total kinetic energies (right), as a function of time, in the collision of ${\mathrm{Na}}_6$ (thick curves) with ${\mathrm{Ar}}_{87}$ (thin curves), for four different initial kinetic energies $E_{\mathrm{kin}0}$.

Figure 5

Deposition coordinate $d$, defined in Eq. (1), as a function of time, for ${\mathrm{Na}}_6@{\mathrm{Ar}}_{43}$ (dots and dashes) and ${\mathrm{Na}}_6@{\mathrm{Ar}}_{87}$ (full lines), with $E_{\mathrm{kin}0}=13.6$ (left panel) and $136\mathrm{meV}$/ion (right panel). Results in both systems are presented for the top (dashes and thin curve) and the reverse (dots and thick curve) configuration of the ${\mathrm{Na}}_6$.

Figure 6

Three first multipole moments $\sqrt{⟨r^2⟩}$, ${\beta }_2$, and ${\beta }_3$, as functions of time, for ${\mathrm{Na}}_6$ (thin dashes and lines) deposited on ${\mathrm{Ar}}_{43}$ (thick dots) and ${\mathrm{Ar}}_{87}$ (thick full lines) for $E_{\mathrm{kin}0}=68\mathrm{meV}$/ion.

Figure 7

Three first multipole moments, as a function of time, for ${\mathrm{Na}}_6$ (thin curves) deposited on ${\mathrm{Ar}}_{43}$ (thick curves), with $E_{\mathrm{kin}0}=136$ (left) and $680\mathrm{meV}$/ion (right). On each panel are compared the moments obtained from the top (dots and dashes) and reverse (full lines) configurations.

Figure 8

Three multipole moments, as a function of time, for ${\mathrm{Na}}_7$ (thin curves, left panels) and ${\mathrm{Na}}_8$ (thin curves, right panel) deposited on ${\mathrm{Ar}}_{43}$ (thick curves), with $E_{\mathrm{kin}0}=68\mathrm{meV}$/ion.