Hard cube model

Approximating the real potential by a square well and infinitely hard repulsive wall, as shown in figure A3.9.2 we obtain the hard cube model. For a well depth of W, conservation of energy and momentum lead [H, 12] to the very usefiil Baule fomuila for the translational energy loss, 5 , to the substrate... 

There is a very simple model for estimating the trapping probability in atomic adsorption due to a phonon-excitation mechanism. In the hard-cube model (HCM) [6, 7], the impact of the atom on the surface is treated as a binary elastic collision between a gas phase atom (mass m) and a substrate atom (mass Mc) which is moving freely with a velocity distribution Pc(uc). This model is schematically illustrated in Fig. 1. If the depth of the adsorption well is denoted by Ead, the adsorbate will impinge... 

Figure 1 Schematic illustration of the hard cube model. An atom or molecule with mass m is impinging in an attractive potential with well depth Fad on a surface modeled by a cube of effective mass Mc. The surface cube is moving with a velocity uc given by a Maxwellian distribution.

Assuming a weighted Maxwellian velocity distribution for uc, the trapping probability in the hard-cube model can be analytically expressed as [7]... 

Figure 8 Trapping probability of 02/Pt(l 11) as a function of the kinetic energy for normal incidence. Results of molecular beam experiments for surface temperatures of 90 and 200 K (Luntz et al. [81]) and 77 K (Nolan et al. [87]) are compared to simulations in the hard-cube model (HCM).

Figure 5 Angular width measured for various systems at incidence angles of 38-45° and systems as indicated in the figure. The dotted, dashed and dash-dotted lines are results from calculations with the hard cube model. The dotted line represents calculations with a mass ratio of 32/195 and Ts = 400 K (02/Pt), the dashed line with a mass ratio of 32/150 and Ts = 600 K (C>2-Ag), and the dash-dotted line represents calculations with a mass ratio of 40/195 and Ts = 500 K (Ar-Pt). Details about the sources of the various datasets can be found in the paper by Wiskerke and Kleyn, from which the figure is taken [54].

Fig. 23. The distribution of the (scalar) velocity of atoms at different times in a molecular dynamics simulation of the impact of a 125 atom Ar cluster at a surface where the surface is simulated by the hard cube model at the temperature of 30 K. The Impact velocity is 20 km s or 1 A per 5 fs where the range parameter of the Ar-Ar potential is 3.41 A. The mean free path is very roughly of the same magnitude. Thermalization is essentially complete by 80 fs or, after roughly four collisions.

System Collision Energy (eV) Oi Percent of Particle Momentum TVansferred Momentum TVansfer Angle, 0 Hard Cube Model (Mass = 1.5 X surface atom) Binary Collision Model... 

E.K. Grimmelmann, J.C. Tully, and M.J. Cardillo. Hard-Cube Model Analysis of Gas-Surface Energy Accommodation. J. Chem. Phys. 72 1039 (1980). 

E. The hard-cube model. Adapted from E. K. Grimmelman, J. C. Tully, and M. J. Cardilo, J Chem. Phys. 72,1039 (1980). See also Harris (1987). An incident atom of mass m imdergoes a binary elastic collision with a hard cube that is viewed as a surface atom with an effective mass M. The velocity of the incident atom, V, is changed only in the direction normal to the surface, (a) Using conservation of momentum show that the outgoing velocity of the atom in the direction normal to the surface is given by = ((/r - )/ jx + l))vi -I- (2/(/x - - ))u where... 

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