Trapping-desorption and direct-scattering

Under particular conditions (for instance 0.14 eV incidence energy, grazing incidence angle, and a surface temperature of 185 K) a bimodal velocity distribution is observed in the scattering of Xe from Pt(111).[62]The peak at earlier arrival times (faster scattered velocity) occurs at the specular angle. This early component exhibits a narrow angular distribution. In contrast, the late component exhibits a broad angular distribution, which can be described as a cos(θ)-function peaking at the surface normal. These observations are interpreted in terms of two competing mechanisms: the early component of the velocity distribution is attributed to direct-scattering and the late component to

trapping-2. Scientific context

Figure 2.7.: The photoelectron spectra are shown for Au and Ag. Energies are given relative to the Fermi energyE_F. Figure reproduced with permission from reference [60].

©IOP Publishing. All rights reserved.

Figure 2.8.:The density of states in the valence band and conduction band of germanium.

Reprinted figure with permission from reference [61]. Copyright (1975) by the American Physical Society.

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2.5. Nonreactive dynamics at surfaces desorption. These two mechanisms have been found to be appropriate for the description of the scattering process in many projectile-surface systems. Both channels could be identified in atom-surface scattering as in the example discussed above, molecule-surface scattering for example in CO and NO[63,64] scattering from Au(111), and even in the scattering of large water clusters[65]from a graphite surface.

Trapping-desorption is thought to proceed as follows: The projectile approaches the surface and during the collision enough translational energy is transferred to surface degrees of freedom or to internal degrees of freedom of the projectile, such that it stays

“trapped” long enough to be equilibrated with the surface. A rough estimate of the residence time is given by (10¹³ s⁻¹exp(−E_b/k_BT))⁻¹.[64] For a weakly bound molecule with the binding energy E_b = 0.3 eV at a 300 K surface, this yields a residence time of 10 ns. After this timespan, the projectile desorbs and its translational energy as well as the internal state distribution is determined by the surface temperature. This does not necessarily mean that for example the velocity distribution of the molecule can be described by a Maxwell-Boltzmann distribution at the surface temperature. The effective desorption temperature can be affected by the desorption well depth, which can be understood as a consequence of detailed balance.[66] Moreover, in certain cases it can be shown that the residence time of the molecule at the surface is not long enough to equilibrate all the molecular degrees of freedom. This is the case for the high energy vibration of HCl(v= 2), which has been shown to trap and desorb with a thermal velocity distribution while the vibrational quantum number is conserved.[67]

Nevertheless, the classification trapping-desorption is helpful to differentiate against direct-scattering. In this process, the interaction time of the projectile with the surface is short and typically on the order of femto- to picoseconds.[63]Direct-scattering is charac-terized by strong departures in the scattered energy distributions from thermal expectation as well as a “memory effect”, meaning that the scattered projectile’s distribution of the excitation of different degrees of freedom can be directly influenced by incidence para-meters. Both characteristics can be identified in the direct-scattering of nitric oxide from Ag(111).[68]For this system, it has been shown that the rotational state distributions do not follow a Boltzmann distribution. Instead, the distributions are characterized by strong rotational rainbow features (as discussed in detail in Section 2.5.2), which depart strongly from the thermal expectation. In addition, both the final translational and rotational energy of the molecule scale with the incidence translational energy of the molecule, which is a classic example for the “memory effect” in direct-scattering.

A simple model that describes the trapping probability and thus also the branching ratio

2. Scientific context

between direct-scattering and trapping-desorption is known as the hard cube model.[69]In this model the collision is treated as a collision of two hard cubes with the surface atom massmand the mass of the projectileM. It is assumed that the projectile is accelerated by a structureless potential well with the depth before a purely impulsive collision occurs.

The surface atom motion can be described by a 1D-Maxwell-Boltzmann distribution at the surface temperatureT. In this case, the trapping probability P can be described by Equations 2.41-2.44.[70]

Here, E_idenotes the normal incidence translational energy of the projectile. This model predicts a trapping probability of 50 % at a critical incidence translational energy of E_i=

m+M m−M

2

−1

. Moreover, an increase of the surface temperature reduces the slope of the decline of the trapping probability from unity at low incidence translational ener-gies to zero at high incidence translational enerener-gies. The hard cube model has been used to describe the trapping probability for many different systems. See for instance refer-ences [70, 71]. However, by a comparison between different projectile-surface systems Rettneret al. found that a molecular projectile with more internal degrees of freedom is more easily trapped than an atom with comparable mass and binding energy.[72]The more internal degrees of freedom are available in the projectile the larger is the underestimation of the trapping probability by the hard cube model. This can be taken as a strong indication that this simple model fails for molecular projectiles, and excitation of internal degrees of freedom in the collision might have a strong impact on the probability for trapping. For some diatomic molecule-surface systems rotational excitation has been shown to promote trapping.[73,74] The trapping probability in NO/Ag(111) surface scattering is enhanced if the incoming molecule points with the O-atom towards the surface, though this config-uration is energetically less favorable than the opposite orientation. This observation is explained in terms of a more efficient translational energy transfer to rotational excitation for orientations in which the O-atom points towards the surface.

24

2.5. Nonreactive dynamics at surfaces

(a) (b)

Figure 2.9.: a) Potential energy surface for the NO/Ag(111) surface interaction[77] as a function of the molecule-surface distancezand the orientation angleθ. For each contour the potential energy is given in eV. b) Correlation between rotational excitation in the collision and the orientation angle θ based on classical trajectory calculations. Adapted from reference [77].