Measurements of the Effective Atomic Numbers of ... - Science Direct

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ScienceDirect Physics Procedia 90 (2017) 41 – 46

Conference on the Application of Accelerators in Research and Industry, CAARI 2016, 30 October – 4 November 2016, Ft. Worth, TX, USA

Measurements of the effective atomic numbers of alloys using thick-target bremsstrahlung intensities S. Czarnecki, A. Short, S. Williams* Department of Physics and Geosciences, Angelo State University, San Angelo, Texas, USA

Abstract We have investigated the accuracy with which the effective atomic number (Zeff) of an alloy can be measured using the intensity of the thick-target bremsstrahlung produced by low-energy electrons incident on the alloy target. The experiments involved 5 keV-electron beams incident on thick brass, Ni/Fe/Mo, C-276, and stainless steel targets. By comparing the data obtained using alloy targets to the data obtained using a high-purity aluminum target and data from a previous study performed by our group (in which the Z-dependence of thick-target bremsstrahlung was studied), the Zeff values of the alloy targets were measured and compared to theoretical values. While the experimental Zeff values of the stainless steel and Ni/Fe/Mo targets were in relatively good agreement with the theoretical values, the experimental Z eff values of the brass and C-276 targets were not.

© Published byPublished Elsevier B.V. This is B.V. an open access article under the CC BY-NC-ND license © 2017 2017 The Authors. by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of the Conference on the Application of Accelerators in Research and Industry. Peer-review under responsibility of the Scientific Committee of the Conference on the Application of Accelerators in Research and Industry Keywords: bremsstrahlung; alloys; effective atomic number; PENELOPE.

1. Introduction Bremsstrahlung emission is of interest to those studying and working in many disciplines of science, including medical physics, astrophysics, accelerator physics, and nuclear physics. Bremsstrahlung that results from the scattering of an electron in the Coulomb field of a target-atom is typically described as being either "thin-target" or "thick-target" bremsstrahlung. Thin-target bremsstrahlung is generally emitted by electrons with energies that are roughly equal to the incident electron beam energy, and, thus, approximates the situation where an electron is incident on a single, isolated target-atom. However, when a target is sufficiently thick, many of the interactions occur after the incident electron has already lost energy and been deflected due to previous interactions with target-atoms. Furthermore, in situations involving thick targets, bremsstrahlung photons are often absorbed or deflected in the target material. These processes lead to a bremsstrahlung spectrum that is a superposition of the spectra produced by multiple electrons moving in different directions with different energies, combined with the attenuating effects of the target.

* Corresponding author. Tel.: +1-325-942-2242; fax: +1-325-942-2188. E-mail address: [email protected]

1875-3892 © 2017 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of the Conference on the Application of Accelerators in Research and Industry doi:10.1016/j.phpro.2017.09.017

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S. Czarnecki et al. / Physics Procedia 90 (2017) 41 – 46

The primary goal of the experiments described herein was to determine if the effective atomic number of an alloy could be accurately measured using the intensity of the thick-target bremsstrahlung produced by low-energy electrons incident on the alloy target. These experiments are a natural extension of those previously performed by the authors using pure, elemental targets (Czarnecki et al., 2016). Similar research measuring Zeff has also been conducted by Manjunatha and Umesh (2015) using rare earth compounds. The accuracy with which Zeff could be measured using the methods described here was determined by comparing the experimental Zeff values (hereafter referred to as Zexp) to theoretical Zeff values (hereafter referred to as Zthe) obtained using the analytical methods described by Markowicz and Van Grieken (1984). The discrepancies between the experimental and theoretical values were then investigated to determine how the experimental procedure needs to be altered in order to eliminate them. 2. Experimental Set-Up A schematic of the experimental apparatus is shown in Fig. 1. The electron beams used in the experiments were produced using an ELS5000 electron source, capable of accelerating electrons to a maximum kinetic energy of 5 keV (E o). The beams were oriented at a 45° angle relative to the targets' surfaces. All data were normalized by total charge incident on the targets, which was found by dividing the total charge collected on the targets by the fractions of incident electrons collected on the target materials. The total charge collected on the targets was measured using a current integrator, and the fractions of incident electrons collected on the targets were determined using backscattering coefficients calculated using an equation taken from Tanuma (2009). The aluminum target cell which housed the target-holder and targets was kept at pressures ranging from 1.5×10-5 torr to 3.9×10-5 torr during the experiments. The thicknesses of each of the targets used in the experiments were greater than the 5 keV-electron CSDA ranges for their respective target materials (NIST, 2016). X-rays were detected at an angle of 90° relative to the electron beam through a Kapton window in the target cell using a Si(Li) detector with a measured energy resolution of approximately 200 eV at 5.89 keV (thick-target bremsstrahlung is essentially emitted isotropically [Requena et al., 2011], except for at energies near the Duane-Hunt limit [Gonzales et al., 2011; Gonzales and Williams, 2013]). The orientations of the electron beams, targets, and detector were the same in each of the experiments.

Fig. 1. Schematic of the experimental set-up.

3. Results and Discussion Fig. 2 is a comparison of the experimental results to the results produced using the Monte Carlo code PENELOPE (Salvat et al., 2006) for Eo = 5 keV electrons incident on thick aluminum, copper, silver, tungsten, and gold targets from a previous study by the authors (Czarnecki et al., 2016). The data points in the plots are the ratios of the bremsstrahlung intensities (at photon energies k) produced by electrons incident on targets of various atomic numbers, I(Z), to the intensities produced using the aluminum target, I(13), for k/Eo = 0.85, 0.90, and 0.95.


Fig. 2. Comparison of the ratios of the bremsstrahlung intensities produced by a beam of Eo = 5 keV electrons incident on various elements, I(Z), to those produced using aluminum, I(13), as a function of atomic number (Z) as measured by experiment (black circles) and as simulated by PENELOPE (white triangles) for k/Eo = 0.85, 0.90, and 0.95. Error bars correspond to three standard deviations.

For electrons incident on targets at high energies (Eo > 10 keV), the intensity of the resultant bremsstrahlung is approximately proportional to Z2 (Hippler et al., 1981). However, at lower incident electron energies, the bremsstrahlung intensity is less dependent on the atomic number of the target (Czarnecki et al., 2016). For a given incident electron energy, the bremsstrahlung spectral photon distribution, S(k, Z, Eo), can be expressed as:

ܵሺ݇ǡ ܼǡ ‫ܧ‬଴ ሻ ൌ ‫ܭ‬ሺ݇ǡ ‫ܧ‬଴ ሻܼ ௡ where K(k, Eo) is a proportionality constant, Z is the atomic number of the target, and n is the index value of the Z-dependence. The same raw experimental data used to calculate the ratios shown in Fig. 2 were previously used to calculate index values by Czarnecki et al. (2016) using different backscattering coefficients. The experimental data ratios shown in Fig. 2 were calculated using backscattering coefficients determined using an equation taken from Tanuma (2009), which led to better agreement with the predictions of the PENELOPE code and slightly higher index values (shown in Table 1) than those measured by Czarnecki et al. (2016).

Table 1. Index values obtained using data shown in Fig. 2.

k/E0 0.85 0.90 0.95

nexperimental 1.0786 1.1146 1.1646

Uncertainty 0.0722 0.0858 0.0977

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Using the index values shown in Table 1 and data from an experiment involving a high-purity aluminum target (in order to determine the proportionality constant), Zeff values for the four alloy targets were experimentally measured. These experimental Zeff values (Zexp) were calculated using the equation: ೙

ܼ௘௫௣ ൌ ඨܵሺ݇ǡ ܼǡ ‫ܧ‬଴ ሻȀ ቈ

ܵ஺௟ ሺ݇ǡ ܼǡ ‫ܧ‬଴ ሻ ቉ ͳ͵௡

where SAl(k, Z, Eo) is the normalized bremsstrahlung spectral photon distribution obtained using the aluminium target. Theoretical Zeff values (Zthe) were calculated using the equation from Markowicz and Van Grieken (1984): ‫ݓ‬௜ ܼ௜ଶ ‫ܣ‬௜ ൌ ‫ݓ‬௜ ܼ௜ σ ‫ܣ‬௜ σ

ܼ௧௛௘

where wi, Zi, and Ai are the mass fraction, atomic number, and atomic mass of the ith element, respectively (mass fraction values are given in Table 2).

Table 2. Mass fractions of the alloys used in the experiments.

Alloy Stainless Steel

C-276

Brass

Ni/Fe/Mo

Element (Z) Cr (24) Fe (26) Ni (28) Cr (24) Mn (25) Fe (26) Co (27) Ni (28) Mo (42) W (74) Fe (26) Cu (29) Zn (30) Pb (82) Fe (26) Ni (28) Mo (42)

Mass Fraction 0.190 0.700 0.110 0.155 0.005 0.060 0.015 0.575 0.155 0.035 trace 0.700 0.300 trace 0.152 0.806 0.042

As the index values calculated using the data from Czarnecki et al. (2016) were not corrected for self-absorption, self-absorption effects (which are Z-dependent) are already incorporated into the index values used to determine the Zexp values for the alloy targets. Furthermore, for k/Eo ratios that are approximately equal to unity, self-absorption does not play a significant role, as photons with energies close to Eo are typically emitted by electrons that have only interacted with a single target-atom near the surface of the target (Gonzales and Williams, 2013). Fig. 3 is a comparison of the theoretical (Zthe) and experimental (Zexp) values. While Zthe and Zexp are in agreement for stainless steel and Ni/Fe/Mo, they are not for brass and C-276. This may be due to target-oxidation, target-impurities, target-manufacturing defects, or gases present in the target cell. Other factors, not yet investigated, may have also contributed to the discrepancies.


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Fig. 3. Comparison of the theoretical (Zthe) and experimental (Zexp) values of aluminum (red), stainless steel (yellow), Ni/Fe/Mo (green), brass (blue) and C-276 (black) for k/Eo = 0.85, 0.90, and 0.95. The values have been normalized with respect to aluminum as in Fig. 1. The dashed line has a slope of one. Error bars correspond to one standard deviation.

4. Conclusions The methods used in the alloy-target experiments described here were essentially the same as those used by the authors in the experiments using the pure, elemental targets (which yielded results that were in good agreement with the predictions of the PENELOPE code). However, the discrepancies between Zthe and Zexp for brass and C-276 (shown in Fig. 3) suggest the presence of significant experimental error, while the agreement of Zthe and Zexp in the cases of stainless steel and Ni/Fe/Mo suggest that the error is not likely systematic. There are several possible sources of the error, some of which are more likely than others. For example, oxidation may have played a role, which could account for the brass target yielding Zexp values well below Zthe, as oxygen has a relatively low atomic number. Furthermore, the experiments involving the elemental targets (which were used to measure index values) were performed at lower pressures (6.3×10-7 to 1.5×10-6 torr) than the experiments involving alloy targets (1.5×10-5 to 3.9×10-5 torr), and the presence of more nitrogen and oxygen in the target chamber in the experiments involving alloys may have also contributed to the discrepancies shown in Fig. 3. Another possibility is related to alloy composition inhomogeneities. If, for example, the Z eff of an alloy target is lower near the target's surface than near its center (due, possibly, to poor mixing of elemental components), the measured Zexp would be less than the Zthe of that alloy. We plan to reevaluate the experimental procedure to eliminate these discrepancies and to improve the method’s accuracy. If we can achieve satisfactory agreement between Zthe and Zexp for alloy targets, we plan to conduct additional experiments to determine the accuracy with which the effective atomic numbers of minerals can be measured using thick-target bremsstrahlung intensities.

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