Modeling of the deposition of Na Clusters on MgO(001)

We investigate the dynamics of deposition of small Na clusters on MgO(001) surface. A hierarchical modeling is used combining quantum mechanical with molecular mechanical description. Full time-dependent density-functional theory is used for the cluster electrons while the substrate atoms are treated at a classical level. We consider ${\text{Na}}_6$ and ${\text{Na}}_8$ at various impact energies. We analyze the dependence on cluster geometry, trends with impact energy, and energy balance. We compare the results with deposit on the much softer Ar(001) surface.

Figure 1

Schematic view of the hierarchical model for ${\text{Na}}_N$ on MgO(001) surface.

Figure 2

The structures of free ${\text{Na}}_6$ (left) and ${\text{Na}}_8$ (right). The bond distance along the five-fold ring of ${\text{Na}}_6$ is $6.5a_0$ and the top ion resides $3.1a_0$ above the ring. The bond distance in the two four-fold rings of ${\text{Na}}_8$ is $6.2a_0$ and the distance between the two rings is $5.8a_0$.

Figure 3

(Color online) Time evolution of the ionic coordinates and kinetic energies $E_{\text{kin}}$ for the deposition of a Na monomer on MgO(001) with initial kinetic energy $E_{\text{kin}}^0=0.136\text{eV}$, impinging on various sites : O site (top), Mg site (center) and hollow site (bottom). Left : $z$ coordinates of Na (thick line), Mg (thin curve), and O (gray line) cores. Right : Total $E_{\text{kin}}$ of Na (thick gray or red curve), lateral $E_{\text{kin}}$ of Na (magenta dots), vertical $E_{\text{kin}}$ of Na (black dashes), and total $E_{\text{kin}}$ of Mg (thin dark or blue curve) and O (thin light or green curve) cores.

Figure 4

(Color online) Left : Time evolution of the ionic $z$-coordinates of ${\text{Na}}_8$ approaching MgO(001). Right : Projection of the Na and MgO trajectories into the $x\text{−}y$ plane; the figures are vertically sorted by increasing initial kinetic energy : Soft deposition (top), robust deposition (center), reflection (bottom).

Figure 5

(Color online) Snapshots of the time evolution for three cases of collisions of ${\text{Na}}_8$ on MgO(001) with different initial kinetic energies $E_{\text{kin}}$. Upper panel : Soft deposition with $E_{\text{kin}}^0=0.109\text{eV}$. Middle panel : Robust deposition with $E_{\text{kin}}^0=1.09\text{eV}$. Lower panel : Reflection with $E_{\text{kin}}^0=10.9\text{eV}$.

Figure 6

(Color online) Left : Time evolution of the ionic $z$-coordinates of ${\text{Na}}_6$ approaching MgO(001). Right : Projection of the Na and MgO trajectories into the $x\text{−}y$-plane; the figures are vertically sorted by increasing initial kinetic energy : Soft deposition (top), robust deposition (center), reflection (top).

Figure 7

(Color online) The trajectories of the ${\text{Na}}_6$ center of mass, projected on a plane parallel to the surface. The lateral drift sensitively depends on the site above which the cluster impinges (hollow, O or Mg site) and on its orientation (top ion above—up— and top ion below—down—the ring).

Figure 8

(Color online) Dipole polarization of the cluster electrons during collision of ${\text{Na}}_6$ on MgO(001). Upper panels: Dipole moments of the electron cloud of the ${\text{Na}}_6$ cluster in $x\text{−}y$-(horizontal) and $z$-direction as function of time. Lower panels: Time-evolution of the $z$ component of the center-of-mass of the ${\text{Na}}_6$ cluster; the line $z=0$ corresponds to the center of mass of a fully relaxed configuration of ${\text{Na}}_6$ on MgO(001). Left panels: case of soft deposition at rather low-initial kinetic energy (as indicated). Right panels: case of more energetic collision which leads to immediate reflection.

Figure 9

Time evolution of $z$ coordinates during collision of ${\text{Na}}_6$ with initial total kinetic energy $E_{\text{kin}}^0=8.16\text{eV}$ (1.36 eV per Na atom) on an Ar(001) surface. Data taken from.[47]

Figure 10

(Color online) Time evolution of various contributions to kinetic energy for the collision of ${\text{Na}}_8$ with MgO(001) at three different initial kinetic energies as indicated. Contributions are : Total kinetic energy of the cluster ions (Na, thick curves), contributions due to center of mass motion (Na transl., dashes) and relative motion or heat (Na relat., dots), and total kinetic energy of the substrate (MgO, thin curves).

Figure 11

Time evolution of the dipole polarization energy in the MgO(001) substrate for the collision for ${\text{Na}}_6$ with MgO(001) at an initial kinetic energy of 8.16 eV (reflection case).

Figure 12

Heating of the MgO or Ar substrate after impact of ${\text{Na}}_6$ and ${\text{Na}}_8$. The energy transfer to Ar is independent of the cluster structure, whereas the energy transfer to MgO is not. ${\text{Na}}_6$ transfers about twice as much energy as the compact ${\text{Na}}_8$.

Figure 13

Upper panel : The gain in kinetic energy of the cluster when approaching the MgO surface; lower panel : Instantaneous energy loss, defined as the difference between maximum kinetic energy before the impact and next maximum after impact.

Figure 14

(Color online) Distribution of impact energy amongst various components : Kinetic energy of the cluster (split into intrinsic, open squares, and translational, close squares, motion), kinetic energy of the MgO substrate (open circles), potential energy in the oxygen dipoles (triangles), and other potential energy in the substrate (close circles). Upper panel : ${\text{Na}}_8$ with MgO, lower panel : ${\text{Na}}_6$ with MgO.