Surfaces binary collision model

In ISS, ions such as H, He and Ar are scattered off a surface and their energy distribution is observed. During the scattering process, the ions lose energy to the surface atoms. The collision process is usually so rapid (with kinetic energies of the order of 1 keV to 1 MeV) that a binary collision model is a good description of the situation. 

Figure 4 Results from classical trajectory calculations for in-plane scattering of Ar from Ag(l 11) with an incidence angle of 40° measured with respect to the surface normal. In the panels a and c results for the relative final energy Ef/Ei are shown, where E is the initial energy. Lines indicate the energy transfer computed with the cube model (parallel momentum conservation) and a binary collision model. In panels b and d angular distributions are shown. Calculations for 0.1, 1,10 and lOOeV are shown. The panels a and b are calculated for a zero temperature, static lattice panels c and d for Ts = 600 K. From Lahaye et al. [43].

The binary collision model has been successfully applied to a variety of systems from the scattering of noble gases off liquid surfaces to the scattering of polyatomic molecules off thin polymer films. 

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... 

The dynamics of ion surface scattering at energies exceeding several hundred electronvolts can be described by a series of binary collision approximations (BCAs) in which only the interaction of one energetic particle with a solid atom is considered at a time [25]. This model is reasonable because the interaction time for the collision is short compared witii the period of phonon frequencies in solids, and the interaction distance is shorter tlian the interatomic distances in solids. The BCA simplifies the many-body interactions between a projectile and solid atoms to a series of two-body collisions of the projectile and individual solid atoms. This can be described with results from the well known two-body central force problem [26]. 

The reflection of carbon atoms and ions at the limiter or divertor surfaces in the ERO modeling is determined by TRIM [29], However, the binary collision approximation used in the TRIM code is no longer valid at small energies of the incoming particles where chemical effects start to influence the interaction of the particles with the solid. To take this into account reflection coefficients calculated with a molecular dynamic code MolDyn [55] were implemented. 

The results of detailed gas/surface scattering experiments reveal the precise momentum transferred to a surface by an incident gas particle. Relatively simple models, such as the binary collision approximation, provide... 

The basic theoretical concepts describing the interaction of a sufficiently massive and energetic particle with a surface are the binary collision (BC) model and the molecular or classical dynamics (MD) model. 

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... 

The theoretical studies of rapid granular flows are generally based on the assumption that the energy dissipation in a binary particle collision is determined by a constant coefficient of restitution e, the ratio of the relative approach to recoil velocities normal to the point of impact on the particle. However, measurements show that the coefficient of restitution is a strong function of the relative impact velocity [10]. Physically, the energy dissipation relates to the plastic deformation of the particle s surface. Thus, a realistic microscopic model should include the deformation history of the particle s surface. However, such a model might become computationally demanding and thus not feasible. 

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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