Collision model binary

Robinson and Torrens have discussed the limitation of the binary-collision approximation. They concluded, for example, that it was likely to fail at energies below 9 eV for collisions between copper atoms in a copper lattice and below 33 eV for gold atoms in a gold lattice. Therefore, phenomena which depend sensitively upon motions of particles with very low energy are likely to be described only qualitatively by the binary collision model. 

Even though the binary collision model is very useful, it is still an approximation to the real situation and a more detailed understanding probably requires computer simulation studies such as those pioneered by Harrison . 

A binary collision model has been developed for particles migrating over planar supports. The rate-controlling steps in these mechanisms are either particle... 

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. 

This behavior can be attributed to the local CC>2-density around the solute and can be rationalized within the framework of the isolated binary collision model. The deactivation rate of the excited molecule in this case is proportional to the collision frequency Zip, T) which is correlated with the local density [23]. 

Simulations. In addition to analytical approaches to describe ion—solid interactions two different types of computer simulations are used Monte Carlo (MC) and molecular dynamics (MD). The Monte Carlo method relies on a binary collision model and molecular dynamics solves the many-body problem of Newtonian mechanics for many interacting particles. As the name Monte Carlo suggests, the results require averaging over many simulated particle trajectories. A review of the computer simulation of ion—solid interactions has been provided (43). 

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 lifetime (Ti) of a vibrational mode in a polyatomic molecule dissolved in a polyatomic solvent is, at least in part, determined by the interactions of the internal degrees of freedom of the solute with the solvent. Therefore, the physical state of the solvent plays a large role in the mechanism and rate of VER. Relaxation in the gas phase, which tends to be slow and dominated by isolated binary collisions, has been studied extensively (11). More recently, with the advent of ultrafast lasers, vibrational lifetimes have been measured for liquid systems (1,4). In liquids, a solute molecule is constantly interacting with a large number of solvent molecules. Nonetheless, some systems have been adequately described by isolated binary collision models (5,12,13), while others deviate strongly from this type of behavior (14-18). The temperature dependence of VER of polyatomic molecules in liquid solvents can show complex behavior (16-18). It has been pointed out that a change in temperature of a liquid solute-solvent system also results in a change in the solvent s density. Therefore, it is difficult to separate the influences of density and temperature from an observed temperature dependence. 

Fig. 6. The relative final energy versus scattering angle of Ne" " incident on Si(lOO) at 45°. The solid line represents the binary collision model. (Data from Ref. 15).

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... 

A qualitative, if not quantitative, measure of Ef /Ei at hyperthermal energies is given by the binary collision model. Inserting Eq. (5) into Eq. (7), yields ... 

Several experimentally observed dephasing results were found to agree qualitatively with these types of theoretical prediction. Binary collision models have also been proposed. Fischer and Laubereau calculated dephasing times using... 

Since the introduction of the isolated binary collision model there has been considerable controversy over its applicability. A number of theoretical papers have challenged its basic assumptions and proposed corrections due to collective effects (usually within the weak coupling approximation of Section II.B), while others have supported and extended the model. In this section, we outline the development of the controversy over the binary collision approximation, which is not resolved even today. 

The first pubUshed criticism of the binary collision model was due to Fixman he retained the approximation that the relaxation rate is the product of a collision rate and a transition probabihty, but argued that the transition probability should be density dependent due to the interactions of the colliding pair with surrounding molecules. He took the force on the relaxing molecule to be the sum of the force from the neighbor with which it is undergoing a hard binary collision, and a random force mA t). This latter force was taken to be the random force of Brownian motion theory, with a delta-function time correlation ... 

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