Probability of discharge

Because of the non-probabilistic sampling approach, this step is not applicable. Several measures are proposed as a means to reduce the probability of discharging water with the VOC concentrations exceeding the discharge permit limitations, such as the following ... 

As a next step Xd, the electron yield or the probability of discharge per unit time and surface A of the active electrode is introduced. Assuming that the probability that a discharge occurs in the time interval dt is independent of the time t, it follows ... 

By repeating this experiment for different conditions, it is possible to determine Xd as a function of the terminal voltage U. At each value of U, the number of pulses in a fixed time interval (40 ms) are counted several times (500 times), and the probability of discharge Xd is evaluated by fitting the corresponding Poisson distribution (4.37). Figure 4.15 shows the experimental results for a 0.4 mm active cathode. 

Two qualitatively different behaviours are observed. For terminal voltages from the critical voltage Ucnt to about 32 V, the probability of discharge decreases with the voltage as a power law such as ... 

Above 32 V, the probability of discharge follows a law similar to field emission ... 

Not only is the probability of discharge d of interest, but also the current evolution with time. From the description of the current evolution with time one can deduce the mean current, which is easily accessible experimentally and is important to evaluate the quantity of heat generated by the process. From the description of the stochastic process of the discharge activity given previously, the current can be computed. In order to obtain the current evolution equation, an auxiliary random variable n(t) defined by the time derivation of the random variable N(t) is introduced ... 

The plasma-wall interaction of the neutral particles is described by a so-called sticking model [136, 137]. In this model only the radicals react with the surface, while nonradical neutrals (H2, SiHa, and Si H2 +2) are reflected into the discharge. The surface reaction and sticking probability of each radical must be specified. The nature (material, roughness) and the temperature of the surface will influence the surface reaction probabilities. Perrin et al. [136] and Matsuda et al. [137] have shown that the surface reaction coefficient of SiH3 is temperature-independent at a value of = 0.26 0.05 at a growing a-Si H surface in a... 

Information about the surface reaction coefficients of radicals Si H2 +i where n > 1 is scarce. Because the structure of these radicals is similar to that of SiH3, the same surface reaction coefficients are used. It is assumed that if Si H2 i+1 radicals recombine at the surface with a hydrogen atom, a Si H2,+2 neutral is formed and is reflected into the discharge. Another possibility is the surface recombination of Si,H2 +i radicals with physisorbed Si ,H2m + i radicals at the surface. Matsuda et al. [137] have shown that the probability of surface recombination of SiHs with physisorbed SiH3 decreases with increasing substrate temperature. Doyle et al. [204] concluded that at a typical substrate temperature of 550 K, SiH3 radicals mainly recombine with physisorbed H atoms. 

Similar effect of relatively stable cycling on the level of discharge capacity of 500 mA-h/g can be achieved, for example, using tin-based alloys with different metals (please, see the detailed investigation of such alloys in this book [5]). These metals perform probably the functions of elastic matrix in such alloys and gave possibility to compensate for the volumetric changes of Sn. 

The reason of slow charge/discharge capacity reduction is probably gradual loss of contact between the active particles and current collector. Nevertheless, in the case of copper current collector usage we observed even smaller increase of discharge capacity after 400th cycle (Figure 1). 

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