Range distributions

For normal-incidence projectiles, the range spreading is equal to the transverse projected range. 

The depth distribution, Y(x). of implanted ions, normalized for an ion implantation dose / is given by the expression 

The expression for peak atomic density in the ion implantation distribution is obtained by setting x = Rp in (6.5) 

To obtain the atomic concentration resulting from this peak number of implanted ions requires knowing N, the atomic density of the substrate. The general relation for the concentration of the implanted species at the peak of the distribution is given by 

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Fig. 7. A shows range distributions for channeled ions implanted along the <100> axis of Si. B shows the Gaussian distribution for incident ions aligned...

Kalbitzer and his colleagues used the Si (p, y) resonant nuclear reaction to profile the range distribution of 10-MeV Si implanted into Ge. Figure 8 shows their experimental results (data points), along with theoretical predictions (curves) of what is expected. 

Baker (1978b) analyzed 25 accidental vessel explosions for mass and range distribution and fragment shape. This statistical analysis is considered the most complete in the open literature. Because data on most of the 25 events considered in the analysis were limited, it was necessary to group like events into six groups in order to yield an adequate base for useful statistical analysis. 

Statistical analyses were performed on each of the groups to yield, as data availability permitted, estimates of fragment-range distributions and fragment-mass distributions. The next sections are dedicated to the statistical analysis according to the Baker et al. (1978b) method. 

TABLE 6.15. Estimated Means and Standard Deviations for Log-Normal Range Distributions (base e) for Six Event Groups... 

Here, the statistical approach will be used to predict the range distribution of the fragments. 

The polyoxyethylene group is obtained by addition of ethylene oxide to fatty alcohols, mostly with an alkalic catalyst such as NaOH or NaOCH3, giving a broad polyoxyethylene oxide distribution. For special applications the ethoxyl-ation can be catalyzed by Lewis acids [11] to achieve a narrow range distribution. Other narrow range catalysts can also be used to improve certain properties. 

For cosmetic compositions an ether carboxylate is used, derived from a fatty acid monoethanolamide [35]. It is known that the ethoxylation takes place on the OH and not on the NH of the ethanolamide group. Due to the acid H atom a narrow range distribution is obtained. The carboxymethylation is carried out with NaOH and SMCA, followed by a washing step with an aqueous solution of a strong acid at high temperatures. The ether carboxylates have the structure... 

The majority of crystallites observed were 3 or 4 nm In size. In Figure 3, a bar graph Illustrates the size range distribution and a comparison of mass variation for the 3 and 4 nm crystallite sizes. Although only thirty analyses were oiade, overall visual analysis confirmed the presence of hundreds of 3 to 4 nm platinum crystals with negligible numbers less or greater than these dimensions. It appears that slight variations In crystallite diameter and thickness have resulted In a fairly uniform number of platinum atoms per crystallite for the majority of the crystallites analyzed. In order to normalize count rates, the decrease In the field emission Intensity was taken Into account. 

FIGURE 2.4 Range distribution of 200-eV electrons in N2. See text for details. Reproduced from Mozumder and LaVeme (1985), with permission from Am. Chem. Soc. ... 

FIGURE 2.8 Range distribution of 100-eV electrons in the vapor and liquid phases of water. Reproduced from La Verne and Mozumder (1986), with permission of Am. Chem. Soc. ... 

Material comprising more than one phase where at least one of the phases consists of finely divided phase domains, often in the colloidal size range, distributed throughout a continuous phase domain. 

Figure 5 Range distribution in nitrogen for 200-eV electrons obtained via the convolution method at 110 eV [38]. The final energy is about twice the ionization potential. See text for details.

Suppose that an atom starts it motion with an energy E in an arbitrary direction from a plane x = 0 in an infinite lattice composed of atoms placed at random locations (see Fig. 13). The probability that an atom will come to rest at a distance x from the starting point is given by the range distribution, Fn(x, E,t ), where T = cos P and p is the initial angle between the beam and the x-direction. Then the trapping coefficient is given by... 

The results given in the last column of Table 4.3 are well represented by the analytical form, Eq. 4.30, with B °) = 0.0386 a = 1.371, Rq = 4.5, b = 0.04832, and B(7 = -290, in atomic units. We note that the B 7 coefficient was determined from a fit of the long-range distributions, ptot — pmlrd, for separations from 6.5 to 7.5 bohr. It must not be identified with a Dj dispersion coefficient because, at such separations, contributions from higher-order dispersion terms are not negligible, albeit non-discernible in the data given in the table. 

Many related measurements have been made of the range distribution of electrons emitted in (3 decay. These studies were particularly important before... 

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