Collision cross-section calculation

Top typical saturation curve and variation of mean electron energy with applied field. Middle fraction of the electron swarm exceeding the specific energy at each field strength. Calculated assuming constant collision cross-section and Maxwell-Boltzman distribution. Bottom variation of products typical of involvement of ionic precursors (methane) and excited intermediates (ethane) with applied field strength... 

In Equation 3, e and m are the impinging electron energy and mass, (e) is the reaction cross section, and / (e) is the electron energy distribution function. Of course, if an accurate expression for fie) and if electron collision cross sections for the various gas phase species present are known, k can be calculated. Unfortunately, such information is generally unavailable for the types of molecules used in plasma etching. 

A second type of gas phase collision is that occurring between the various (heavy) species generated by electron impact reactions, as well as between these species and the unreacted gas-phase molecules (25,2d). Again, dissociation and ionization processes occur, but in addition, recombination and molecular rearrangements are prevalent. Similar rate expressions to that of Equation 2 can be written for these collisions (27). In this case, the concentration of each chemical species, along with the collision cross section, and the species energy distribution function must be known if k is to be calculated. Clearly, much of this information is presently unknown. 

Elastic collision cross sections are important for track simulation and diiferential cross sections are needed to calculate angular deviation in the track trajectory. Pimblott et al. [9] have given an elaborate analysis for gaseous water and compared the results with the experiments of Katase et al. [12]. In brief, the total elastic cross section... 

The first of these factors reduces the complexity of the simulation, but the second has entirely the opposite effect as charge cycling events affect both the energy of the primary ion and its inelastic collision cross section. While the proximity of energy loss events does not affect the details of track structure simulation (at reasonable LET), it may cause significant complications in subsequent diffusion-kinetic calculations due to the (potentially unphysi-cally) high local concentration of radiation-induced reactants. 

The mean free path X, of a molecule in air can be calculated from the sizes of the molecules involved. The most probable collision partners for a trace molecule (such as CFC-12) in air are molecular nitrogen (N2) and oxygen (02). The trace molecule i is hit whenever its center gets closer to the center of an air molecule than the critical distance, rcrit = r, + rair (Fig. 18.8). Picturing the molecules as spheres, the molecular radius r, can be estimated from the collision cross-section A listed in chemical handbooks such as the Tables of Physical and Chemical Constants (Longman, London, 1973) ... 

If He has a collision cross-section radius of 2.18 x 10-10m, calculate the mean free path of He atoms at lO mbar and 293 K. 

The kinetic theory of gases was briefly discussed. It enables the mean or thermal velocity (c) of gas molecules at a given temperature to be obtained and gas flux to be calculated. From the latter, effusion rates, area-related condensation rates and conductances under molecular flow can be determined (see Examples 1.5 and 1.7-1.10). Calculation of collision frequency (obtained from c, n and the collision cross-section of molecules), enables the mean free path (f) of particles to be determined. The easily obtained expression for Ip is a convenient way of stating the variation of / withp (Examples 1.11-1.15). 

Utilization of both ion and neutral beams for such studies has been reported. Toennies [150] has performed measurements on the inelastic collision cross section for transitions between specified rotational states using a molecular beam apparatus. T1F molecules in the state (J, M) were separated out of a beam traversing an electrostatic four-pole field by virtue of the second-order Stark effect, and were directed into a noble-gas-filled scattering chamber. Molecules which were scattered by less than were then collected in a second four-pole field, and were analyzed for their final rotational state. The beam originated in an effusive oven source and was chopped to obtain a velocity resolution Avjv of about 7 %. The velocity change due to the inelastic encounters was about 0.3 %. Transition probabilities were calculated using time-dependent perturbation theory and the straight-line trajectory approximation. The interaction potential was taken to be purely attractive ... 

The problem of cross-section calculation for various inelastic collisions is mathematically equivalent to the solution of a set (in principle, infinite) of coupled wave equations for nuclear motion [1]. Machine calculations have been done recently to obtain information about nonadiabatic coupling in some representative processes. Although very successful, these calculations do not make it easy to interpret particular transitions in terms of a particular interaction. It is here that the relatively simple models of nonadiabatic coupling still play an important part in the detailed interpretation of a mechanism, thus contributing to our understanding of the dynamic interaction between electrons and nuclei in a collision complex. 

We have shown that combining ion mobility spectrometry (IMS) equipment with mass spectrometry (MS) provides a powerful tool to examine the three-dimensional structure of polyatomic ions by measuring collision cross sections of mass identified ions. The technique is particularly useful in conjunction with molecular modeling or electronic structure calculations. Further, we have reviewed applications where the IMS-MS equipment is used to obtain kinetic and thermo chemical data of ions. 

Ion mobility is based on the measurement of the amount of time it takes for an ion to drift through a buffer gas under the influence of a weak electric field. This drift time inherently contains information about the conformation of the ion. Differently shaped ions have various collision cross sections and hence different mobilities (and drift times) when drifting through the gas. Thus, various computational methods are then used to generate model structures of the ions and calculate their cross sections for comparison to experiment. For instance. X-ray crystallography and NMR spectroscopy are usually used to obtain structural data on POSS molecules. However, POSS-polymer systems can be difficult to examine with these methods since synthetic polymers exist as a mixture of chain lengths data can thus only be obtained for the entire polymer distribution as a collective using these methods. In this respect, detailed information about how POSS interacts with one particular... 

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