Mean free path, for collisions

The different regions are delineated by the Debye length (d), the mean-free path (X), and the Larmor radius rL). In a plasma, there can be many mean-free paths, since there are many different types of particles (different neutral species, electrons and ions). Of primary interest are the mean-free paths for collisions between electrons and heavy particles (Xe) and ions and heavy particles (Xd). 

Despite being a relatively simple reactor, there are many variables in the deposition process which must be controlled to give good material. The gas pressure determines the mean free path for collisions of the gas molecules and influences whether the reactions are at the growing surface or in the gas. The gas flow rate determines the residence time of the gas species in the reactor. The rf power controls the rate of dissociation of the gas and therefore also the film growth rate, and the temperature of the substrate controls the chemical reactions on the growing surface. 

Figure 4. A log-log plot of some of the important reaction product external variables calculated using a modeling program to represent the free expansion of those products from a pellet 3mm diameter and 3 mm high. The products have been given an equation of state somewhat characteristic of PETN. The particular mathematical cell considered here is at the cylinder end opposite to the detonation point. In the legend d stands for density, p for pressure, T for gas temperature, MFP for the mean free path for collisions in the gas, TBIM is the inverse of the rate for bimolecular exchange reactions, TUNI is the inverse of the rate for unimolecular decomposition. For the TBIM curve an activation...

Vacuum deposition is the deposition of a film or coating in a low pressure plasma environment. The deposition process requires increasing the mean free path for collisions of atoms and ions. In physical vapor deposition processing (PVD), for example, this ionic activity is leveraged to sputter a surface as a source of deposition material and/or bombard a polymer film to modify the film properties. Vacuum plasmas are also used to activate reactive species in deposition processes and fragment chemical precursors in plasma-enhanced chemical vapor deposition (PECVD) processes. 

When the mean free path for collision is long, the molecules move independently of each other and the flow is called molecular flow. In molecular flow conditions, backstreaming may be appreciable. All oil-sealed and oil vapor vacuum pumps show some degree of backstreaming that contributes to surface contamination in the deposition system. Knudsen flow is the transition region between viscous flow and molecular flow regimes. 

Some PVD processes take place in a good (10 -10 Torr) vacuum where the mean free path for collision is long, but many PVD processes are done where the mean free path is short. Examples of this are the plasma-hased processes and reactive PVD processes where typical pressures are in the range of Torr. In these processes the total pressure... 

At 1 mTorr the mean free path for collision in a gas is about 5 centimeters. If the holes in the manifold face outward, the gas density can be non-uniform in regions between the holes. 

Flow, molecular (vacuum technology) Gas flow conditions where there are few collisions between molecules because of the long mean free path for collision (low pressure). 

Viscous flow (vacuum technology) Gas flow where the mean free path for collision is very small compared to the dimensions of the system. Viscous flow may be laminar or turbulent. 

We assumed that diffusion in the gap between the two particles is the same as in the bulk. This assumption is valid as long as the gap is much larger than the mean free path for collision between gas molecules. At room temperature and normal pressure, typical free path lengths are of the order of 100 nm. In some cases, the gap width can be significantly below 100 nm. Then collisions with the walls become more likely than collision with other gas molecules. This is called Knudsen flow. It can significantly slow down the process [571, 572]. 

For hard sphere collisions, v(v) would be proportional to v9 and the mean free path independent of v A(v) is an equivalent mean free path for a- general force law. Cf. S. Chapman and T. G. Cowling, The Mathematical Theory of Non- Uniform Oases, pp. 91 and 348, Cambridge University Press, 1958. 

In situations where the surrounding fluid behaves as a non-continuum fluid, for example at very high temperatures and/or at low pressures, it is possible for Nu to be less than 2. A gas begins to exhibit non-continuum behaviour when the mean free path between collisions of gas molecules or atoms with each other is greater than about 1/100 of the characteristic size of the surface considered. The molecules or atoms are then sufficiently far apart on average for the gas to begin to lose the character of a homogeneous or continuum fluid which is normally assumed in the majority of heat transfer or fluid... 

Liquefied rare gases(LRGs) are very important both from the fundamental point of view and in application to ionization chambers. In these media, epithermal electrons are characterized by a very large mean free path for momentum transfer -10-15 nm, whereas the mean free path for energy loss by elastic collision is only -0.5 nm. This is caused by coherence in momentum transfer scattering exhibited by a small value of the structure factor at low momentum transfers... 

Improved vacuum conditions effect an elongated mean free path for the ions and thus a lower risk of collision on their transit through the TOF analyzer. The background pressure in the analyzer is directly reflected by the resolution. [40] Despite improvements of resolving power in the order of a factor of two can be realized (Fig. 4.9), enhanced pumping systems alone are not able to effect a breakthrough in resolving power. 

The total cross sections shown in Fig. 3 can be used to provide information on the relative distances between collisions, i.e., the mean free path of an electron moving in the target medium. The mean free path between collisions is simply obtained from the reciprocal of the cross section 1/oy, where/designates the interaction channel of interest. For... 

The change from a viscous to a molecular flow regime occurs when the mean free path L of the gas molecules in the system exceeds the minimum physical dimensions of the system. The mean free path is a measure of the average distance a molecule travels between collisions. The derivation of L involves a number of assumptions about the ideality of the gas and the nature of the collisions and by definition some 63.2% of the molecules in a particular gas collide with other molecules within the distance L. The mean free path for any gas can be calculated from Equation (1.1)... 

For the effects of thermal transpiration to be observed it is necessary that the mean free molecular path be greater than the tube diameter. At higher pressures and smaller mean free paths, molecular collisions destroy the effect. 

The Auger and photoemitted electrons of interest have relatively low KE (50 to 2000 eV) and have a high probability of undergoing inelastic collision with an atom in the matrix. Thus, only those photoelectrons generated near the sample surface (< 10 nm) will contribute to XPS signals. Detailed experimental values of the inelastic mean free path for electrons having the energies important in XPS have been reported [7]. Furthermore, detailed descriptions of the hardware and instrumentation involved in the XPS technique are also available [8]. 

Assuming that the molecules are rigid elastic spheres a typical value for the mean free path for a gas, say oxygen, can be calculated from (2.516). Consider a typical room temperature at 300 (K) and a pressure of 101325 (Pa). The collision diameter of molecular oxygen can be set to 3.57 x 10 ° (m) in accordance with the data given by [51], example 1.4. We can then calculate the mean free path / for oxygen ... 

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