The results of the experiment are discussed in the context of the random collision cascade model of sputtering. Here i, an index, denotes the particular sputtered object of interest, E the energy of the sputtered object, and e the direction of ejection with respect to the target normal. We will be concerned here with the measurement of the energy spectrum, S(E), of 235u atoms produced from enriched uranium metal and.
As McCracken (1975) has pointed out, the overall sputtering yield has been shown to be quite insensitive to the details of particular models of the sputtering process. The first was to provide additional data for testing theoretical models of the sputtering process. The amount of energy spectrum data is relatively small compared to the total amount of data on other aspects of the sputtering process.
In the language of the first paragraph, the molecular state is a discrete variable over which the summation is performed. Furthermore, no proven means is available to predict the energy distributions of the various component atoms sputtered from a heterogeneous target.
THEORY
This will lead to the establishment (after an initial transient period) of a steady state p{E,t) which will be denoted by p(E). Robinson (1965) discussed this assumption in the context of collision densities and found that the final result is surprisingly insensitive to the exact cross section used. Note that the variable E in the integral in equation (13) only appears as a parameter in the term H(E'-E).
Because of the Diraco function in the integrand, the integral is trivial, and after some rearrangement it is. Integrating the right side into parts and dividing the equation by E5/2 finally yields. In the case of argon atoms bombarding a uranium target, as in this experiment, the function ¢(E) increases monotonically in range.
However, the cross section given by equation (28) would predict that the stopping force was proportional to E1-2m (Sigmund 1972). Since the energy spectrum he derived included the stopping force as a factor in the denominator, he obtained E-2 instead of E-2+2m.) The choice of a value of my equation (28) is ultimately a choice of the shape of the interatomic potential , to be used. More will be said about this choice in the discussion of the results of the experiment.
EXPERIMENTAL APPARATUS
In the time, 2/v, that a particle sprayed with velocity v takes to reach the collector, the edge of the collector has rotated a linear distance of. This equation defines the dispersion constant, k, the value of which is a function only of the apparatus design. Like Thompson et, we also assume that the beam pulse is a fraction, f, of the collector rotation period.
A final factor to consider in the apparatus design is the constancy of the motor speed. In order not to waste the inherently high spatial resolution of the atomic tracking technique, it is necessary to set an upper limit, ~T, on the allowed fluctuation in the revolution period, T, of the motor. For this reason, it was necessary to have the capability to independently measure the pick-up disc rotation speed.
This arrangement resulted in the shortening of the iron plates (and the passage of the beam) during the short time it was fixed and moving. The integration error of less than 1% mentioned above referred to the instrumental error rather than the absolute error in determining the ion beam current.
EXPERIMENTAL PROCEDURE
The target chamber pressure during Ar+ bombardment was about 4 x l0-8torr; however, most of this was contributed by Ar introduced by the beam. The first step in actually producing a power spectrum was to obtain an analyzed and focused beam of the desired ion in the target chamber. It is likely that some beam will hit the 235u holder. the metal target, as it was rectangular.
As mentioned earlier in this section, it was important that the pressure in the target region was low enough to keep the target surface clean. Since the completion of the work described in the thesis, additional pumping has been added near the spectrometer chamber. The maximum diameter of the package that could be irradiated there was a little less than five centimeters.
After cutting, the segments of the edge of the collector containing 235u (Figure 3) were placed in contact with mica sheets. In this way, the precise location and orientation of the segment could later be reconstructed. The range where the tracks were counted for a given setting of the scene controls was.
The first step in the counting process was to determine the location of the area covered by the track. This procedure produced the coordinates of the center of the circle that best matched the curved scratch in m~ca. The radius of the circle was also obtained. This radius can be compared to the known radius of the collector disk as a consistency check.
The second step in calculating the coordinates of the microscope fields to be counted was to establish the orientation of the. The choice is largely a matter of taste on the part of the individual doing the counting.). Occasionally, a field was counted twice to test the reproducibility of the counting process itself.
DATA AND DISCUSSION
We have seen how the deviation of the spectrometer from ideal behavior changes the arrival time distribution. Throughout the region shown, s•(E) differs from S(E) by less than the line width. For this reason, a priority effort should be made to measure the sticking probability as a function of energy for uranium striking aluminum.
The large error in this number arises from uncertainties in the absolute magnitude of the neutron flux and the integration of the argon beam charge. Perhaps the single most important consideration in any spraying experiment is the condition of the surface being sprayed. In addition, there is no evidence for a bending of the data that would be characteristic of the maximum focusing energy.
Another possible explanation for the deviation in the asymptotic slope of the data in Figure 6 from the prediction of equation (27) was suggested by Sigmund (l972b). As discussed in the theory section, he assumed diameters for interaction between target atoms of the form given by equation (28), and showed that the energy spectrum of. A final possible mechanism to account for the deviation from the asymptotic slope of the random collision cascade prediction was proposed by Thompson (1968) and investigated quantitatively by Williams (1976).
Another notable feature of the oxide target spectrum is that it peaks at a lower energy than its metal target counterpart. This apparent discrepancy may be due to a lack of experimental data or to a failure of the theory when used for compound targets. A careful measurement of the 235h sputtering yield of the target used for the energy spectrum measurement would be important in this regard.
In the language of the first paragraph of this thesis, one of the discrete variables before the semicolon in. As previously discussed, it would be of interest to have a measurement of the yield of 235u from a 235uo2 sputtered target. Furthermore, the composition of the 235uo2 surface as a function of the 40Ar+ flow should be studied using an appropriate surface analysis technique.
A fairly high priority should be given to the problem of determining the energy dependence of the sticking fraction. The only other adjustments needed are to cancel the lag voltages of the VFC and amplifiers. Estimated maximum instrument error is 0.5% for currents in the range 1 nA to 1.2 rnA.
Ep(E,T)dE is the fraction of the original energy carried by atoms whose energy is between E and E+dE.
