Thermal velocities

The traditional unipolar diffusion charging model is based on the kinetic theory of gases i.e., ions are assumed to behave as an ideal gas, the properties of which can described by the kinetic gas theory. According to this theory, the particle-charging rate is a function of the square of the particle size dp, particle charge numbers and mean thermal velocity of tons c,. The relationship between particle charge and time according White s... 

This relationship makes it possible to calculate the maximum ionic conductivity of solid electrolytes. Assuming that the mobile ions are moving with thermal velocity v without resting and oscillating at any lattice site, this results in a jump frequency... 

The experimental value for Agl is 1.97 FT cirT1 [16, 3], which indicates that the silver ions in Agl are mobile with nearly a thermal velocity. Considerably higher ionic transport rates are even possible in electrodes, by chemical diffusion under the influence of internal electric fields. For Ag2S at 200 °C, a chemical diffusion coefficient of 0.4cm2s, which is as high as in gases, has been measured... 

Typical decay curves for various ionic masses are shown in Figure 3b, where the effect of differing thermal velocity is clearly evident. Neglect of such decay characteristics can lead to serious discrimination effects. Note that all the experimental curves have the sigmoid shape... 

In the absence of a potential barrier, the rate at which liquid atoms in the interface could move to lattice sites is determined by the average thermal velocity, (3A T/m). If they travel a distance X, the interface velocity is... 

Enrichment, Isotopic—An isotopic separation process by which the relative abundances of the isotopes of a given element are altered, thus producing a form of the element that has been enriched in one or more isotopes and depleted in others. In uranium enrichment, the percentage of uranium-235 in natural uranium can be increased from 0.7% to >90% in a gaseous diffusion process based on the different thermal velocities of the constituents of natural uranium (234U, 235U, 238U) in the molecular form UF6. 

It has been reported for many years that condensation nuclei can be produced by ionizing radiation. Recent studies have improved the measurement of the activity size distribution of these ultrafine particles produced by radon and its daughters (Reineking, et al., 1985 Knutson, et al., 1985). It seems that the Po-218 ion is formed by the radon decay, is neutralized within a few tens of milliseconds, and then attached to an ultrafine particle formed by the radiolysis generated by the polonium ion recoil. Although there will be radiolysis along the alpha track, those reactions will be very far away (several centimeters) from the polonium nucleus when it reaches thermal velocity. The recoil path radiolysis therefore seems to be the more likely source of the ultrafine particles near enough to the polonium atom to rapidly incorporate it. 

Here fi2 = 1/Lv(t + r), L is the mean free path of radicals at thermal velocity v, and the initial spur radius r0 and the fictitious time T are related by r2 = Lvr. On random scattering, the probability per unit time of any two radicals colliding in volume dv will be ov/dv, where <7 is the collision cross section. The probability of finding these radicals in dv at the same time t is N(N - 1 )p2 dv2, giving the rate of reaction in that volume as crvN(n - 1 )p2 dv. Thus,... 

FIGURE 8.6 Evolution of the electron diffusion coefficient in LAr starting with an initial velocity 4.8 times the thermal velocity. Reproduced from Mozumder (1982). 

Light gases with higher thermal velocity are pumped less than heavier ones. This is why turbo pumps produce an (almost) oil-free vacuum. The lubrication of turbo pumps is made with a special vacuum grease. Pumps with magnetically levitated rotor are available, but they are more expensive. 

The electron motion trajectories in this area regarding the initial velocity with constant entry point are shown in Fig. 5, and regarding the initial velocity in Fig. 6. This figures display that the thermal velocity component can considerably influence the motion trajectory and naturally the technical characteristics of device. 

Mechanical vacuum gauges measure the pressure directly by recording the force which the particles (molecules and atoms) in a gas-filled space exert on a surface by virtue of their thermal velocity. 

As discussed by Fuchs and Sutugin (1970, 1971) and Motz and Wise (1960), in this continuous regime, distortion of the Boltzmann velocity distribution in the region close to the surface occurs if there is rapid uptake. In effect, the normal thermal velocity distribution is distorted so that the effective speed toward the surface is higher. In the case of a surface where the uptake occurs on every collision, the net speed toward the surface is effectively doubled. This adds an additional term to the rate of transfer of the gas to the surface, which when normalized using Eq. (PP), gives an additional resistance term of -1 /2. The overall normalized conductance is therefore given by... 

For the other extreme of the free molecular regime where Kn - oc, the particle radius is small compared to the mean free path. In this case, the thermal velocity distribution of the gas is not distorted by uptake at the surface. In effect, the gas molecules do not see the small particles. For this case, Fuchs and Sutugin (1970, 1971) show that for diffusion to a spherical particle of radius a... 

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