Neutron flux characterization techniques for radiation effects studies

Transcription

1 J Radioanal Nucl Chem (212) 291:53 57 DOI 1.17/s Neutron flux characterization techniques for radiation effects studies J. Graham S. Landsberger P. J. Ferreira J. Ihlefeld G. Brennecka Received: 5 June 211 / Published online: 28 June 211 Ó Akadémiai Kiadó, Budapest, Hungary 211 Abstract In the field of radiation effects in materials, a detailed and precise description of the radiation environment used to damage samples is often required to make sense of subsequent materials analysis. The types of reactions and extent of damage that occur during irradiation strongly depend on the flux spectrum of the particular facility. Different neutron activation techniques for characterizing neutron flux spectra were performed on the University of Texas at Austin TRIGA research reactor s in-core facilities. The results were compared in terms of spectral detail and precision. Activation of Au foils with multiple correction factors, and multiple foil activation employing different deconvolution techniques comprise the methods tested. Keywords Neutron flux Radiation effects Activation Foils Introduction When characterizing radiation damage to materials it is important to know what types of particle-atom interactions take place and the energies of said interactions. The J. Graham S. Landsberger (&) Nuclear Engineering Teaching Lab, University of Texas at Austin, R-9, Austin, TX 78712, USA s.landsberger@mail.utexas.edu P. J. Ferreira Materials Science and Engineering Program, University of Texas at Austin, Austin, TX 78712, USA J. Ihlefeld G. Brennecka Sandia National Laboratories, Albuquerque, NM 87, USA dominant mechanism and degree of damage often vary dramatically with the energy of the incident particle. One category of damage effects are those due to atomic displacements as these types of crystallographic defects can permanently alter the mechanical, chemical and electrical properties of a material. Neutron collisions with matter are an important source of displacement effects because neutrons are neutral and massive enough to transfer large amounts of energy to atomic centers. At energies greater than tens of electron volts elastic and inelastic collisions can transfer enough kinetic energy to a stationary target atom to remove it from its bound state in a crystal lattice. This type of interaction is called a knock-on event. Knockon effects typically exhibit a fine energy structure which reflects the underlying resonance regions in the nuclear scattering cross sections as well as material resonances from crystallographic structure. In the context of neutron irradiation, knock-on effects are very sensitive to the energy dependent neutron flux. Below thermal neutron energies, knock-on interactions are not energetic enough to result in atomic displacements. Radiative capture cross sections, however, are large at low energies making activation damage possible. If sufficient recoil is imparted to the daughter nucleus during decay, the daughter atom may be displaced. Such events are called recoil events. For thermal reactors the vast majority of neutrons are at energies below 1 ev thus recoil events are the dominant mechanism for displacement damage. In contrast to knock-on cross sections, recoil displacement cross sections exhibit little fine structure. Mostly they vary as the radiative capture cross section, i.e. an inverse velocity dependence with few if any resonances. Thus for characterizing a thermal neutron reactor for materials testing, a low energy resolution is acceptable in the thermal portion of the spectrum. At epithermal and greater neutron

2 54 J. Graham et al. energies a high degree of resolution is desirable but the small contribution to the total neutron flux at those energies is small enough that the gains from higher resolution are small. A widely used method for determining neutron flux spectra for thermal reactors is by NAA of metal foils and wires. Two common techniques are explored in this paper. The first uses a pair of dilute Au foils and a Cd cover to separate thermal and epithermal flux contributions. The second technique uses activation of multiple foils without Cd shielding. The 2nd technique has the advantage that spectral resolution may be increased by increasing the number of foil/wire monitors. Theory The principle behind the Au foil activation technique is based on spectral filtering. An ideal flux spectrum for a thermal reactor has a Maxwellian distribution at energies less than a thermal cutoff, E TC &.2 ev, and a slowing down behavior above E TC which goes as 1/E [1]. Natural Cd has a high absorption cross section at thermal energies but quickly drops off around.4 ev. This energy is referred to as the cadmium cutoff energy, E cc. The proximity of E cc and E TC allows one to construct a Cd shield as a high pass energy filter which absorbs nearly all thermal neutrons while passing through epithermal neutrons. Armed with analytical expressions for the thermal and epithermal parts of the flux, it is possible to reconstruct the magnitudes of both distributions by comparing the activation rates of a Au foil irradiated with a Cd cover to a Au foil irradiated without one. Assuming a flux spectrum of the form ( E E \ E TC /ðeþ ¼ / t e E=kT ðktþ 2 1 / E E [ E TC ð1þ it is possible to determine the parameters from activation rates measured for the bare Au foil, R b, and for the Cd covered foil, R Cd. They are given by 1 / t ¼ R b R Cd 1 þ gr c f 1 þ r cw NG th gr c G res I G res I R b R Cd ð2þ Nr c / ¼ R Cd ð3þ NI where N is the number of Au atoms in the foils, r c is the Maxwellian averaged radiative capture cross section and I is the resonance integral of the capture cross section. The terms G th, G res, g, w and f 1 are correction factors which account for the effects of foil self-shielding and deviations from ideal 1/v absorption at thermal energies [2]. As previously mentioned the Au foil activation method may be described as a spectral filtering technique. Another foil activation technique, which utilizes multiple foils, attempts to solve the inverse problem of determining the flux from the Fredholm equation R i ¼ Z 1 r i ðeþ/ðeþde ð4þ where R i is a reaction rate for a given reaction for a given nuclide, i. The flux may be expanded as a linear combination of orthogonal functions, w j. Assuming the expansion is well approximated by a truncation of N terms of the linear combination, the Fredholm equation can be expressed as R i ¼ XN j¼1 a j W ij ; W ij ¼ Z 1 r i ðeþw j ðeþde ð5þ If one obtains reaction rates for M [ N foils and knows the cross sections for the measured interaction, it is possible to use the method of least squares to determine the coefficients a j and hence the approximate flux a j ¼ðW T jk W klþ 1 W T lm R m /ðeþ XN i¼1 a i w i ðeþ ð6þ ð7þ Various options exist for the choice of the orthogonal functions such as Chebyshev and Laguerre polynomials [3, 4], orthogonal combinations of the monitor cross sections [5], and energy group flux. The technique used in this characterization first uses least squares to make a two parameter fit to the ideal flux spectrum (as in Eq. 1) to the measured reaction rates for a set of activation foils. Then the part of the reaction rates due to the ideal flux is subtracted from the measured reaction rates and a remnant flux is fit to minimize the remnant reaction rates. Using conventional matrix notation the N measured reaction rates are R 1 r~ 1 R ¼ r~ ½ MðE; TÞdE de=e Š / t ð8þ / R N r~ N fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} X where M(E,T) is the normalized Maxwellian. The vector arrows above the cross sections indicate row vectors and contraction of the matrix X is equivalent to integrating the

3 Neutron flux characterization techniques for radiation effects studies 55 cross sections with the Maxwellian and 1/E vectors as weight functions. Then using the method of least squares / t ¼ X T 1X X T R~ ð9þ / the difference between the ideal flux and the true flux can then be defined by / true ¼ / ideal þ D/ ð1þ where the remnant flux, D/, can be approximated by expressing it in N energy groups, D/ g and solving R~ X / t ¼ r / ig D/ g ð11þ If the remnant flux is small, a perturbative approach is appropriate for solving Eq. 11. Experimental 1 foils were selected for measuring activation rates. Two AuAl foils of.135 at.% Au were used in the Au foil technique. The Al acts as a diluting medium to allow for reasonably long irradiation times at moderate reactor power. One of the Au foils was encased in a set of Cd covers; the other was left bare. For the multiple foil technique Fe, Mo, Zr, CuMn, Cu, Sc, W foils, and a NaCl disk, all with natural isotopic concentrations, were used. The foils were irradiated in an in-core facility called a rotary specimen rack (RSR) at the University of Texas at Austin s TRIGA reactor. During irradiation the RSR orbits the fuel assembly, removing uncertainty associated with variations in the flux along the perimeter of the fuel assembly. Irradiation times and powers were chosen to achieve measurable and safe activity levels. The AuAl foils were irradiated for 5 min at 1 kw power. The Fe, Mo, Zr foils were irradiated for 2 h at 95 kw (full power). The MnCu, Cu, NaCl, Sc and W foils were irradiated for 1 min at 1 kw. A linear relationship between power and flux was assumed for reaction rate reconstruction. Upon irradiation the foils were allowed to decay for periods of hours to days, depending on the activity of the shortest lived nuclides. A high purity germanium detector was used to accumulate gamma spectra for the various films. The counting geometry was determined by selecting the closest sample-to-detector distance which registered a dead time less that 5%. A 152 Eu source was used to calibrate the efficiency at each counting geometry. The gamma spectra were analyzed using the MCA application Maestro. Radiative capture cross sections were obtained from ENDF/B-VI neutron libraries and prepared using NJOY99 data processing system. Nine group cross sections were constructed at 293 K using a weight function consisting of a thermal Maxwellian distribution, an epithermal 1/E spectrum, and a Watt fission spectrum. The energy groups spanned nine energy decades from to ev. Results and discussion To calculate the activation rates of the two AuAl foils, the kev gamma peak was counted until at least 5, counts were accumulated in the photopeak for each foil. Values for the Maxwellian and 1/E fit parameters were determined at 95 kw power. They are / t ¼ ð2:55 :18Þ 1 12 cm 2 s 1 and / ¼ ð1:3 :5Þ 1 11 cm 2 s 1.The± prefix indicates the standard error. Table 1 displays the activation rates for the other foils and the gamma peaks used to calculate the rates. Only the rates from 58 Fe, 98 Mo, 94 Zr and 96 Zr were used to perform the fit as it was found that the residual errors in the remaining reactions were large compared to the rates themselves. Also, including the other foils resulted in an unphysically low estimate of the epithermal parameter. The values for the ideal flux parameters determined by the Table 1 Reaction rates of eight activation foils at 95 kw power Foil Reaction Gamma energy (kev) Reaction rate (s -1 ) Fe Mo Zr Cu Mn Cu NaCl Sc W 58 Fe(n,c) 59 Fe 192.3, 199.2, (3.5 ±.17) Mo(n,c) 99 Mo 14.5, 181.1, 366.4, 739.5, (1.18 ±.4) Zr(n,c) 95 Zr 724.2, (1.68 ±.3) Zr(n,c) 97 Zr (7.35 ±.7) Mn(n,c) 56 Mn 846.8, (2.9 ±.1) Cu(n,c) 64 Cu (6.1 ±.5) Na(n,c) 24 Na (1.32 ±.5) Sc(n,c) 46 Sc 889.3, (6.98 ±.3) W(n,c) 187 W 478.6, 551.5, 618.3, 625.5, 685.7, (1.23 ±.8) 9 1-1

4 56 J. Graham et al. Fig. 1 Ideal neutron flux spectrum for RSR facility at 95 kw power determined by the Au foil and multi-foil activation methods multiple foil technique are / t ¼ ð2:63 :17Þ 1 12 cm 2 s 1 and / ¼ ð1:1 :2Þ1 11 cm 2 s 1. Figure 1 shows the ideal flux with the fit parameters determined from the Au foil and multi-foil activation methods. The two ideal curves are in good agreement in the thermal portion. Clearly the largest discrepancies occur in the epithermal portion of the spectrum. This is expected because the magnitude of the flux is more sensitive to systematic uncertainty at higher energies. A common convention used in radiation effects for expressing the energy integrated neutron flux uses the reaction rate for atomic displacements in Si normalized by a displacement cross section for 1 MeV neutrons. This notion is referred to as the 1 MeV equivalent flux [6]. The 1 MeV equivalent flux was determined from the ideal flux spectrum for both methods. The values were calculated using the neutron damage kerma for Si and are displayed in Table 2. A high energy cutoff of 1 MeV was imposed in each case. The substantial difference in the two values indicates that the 1 MeV equivalent flux is highly sensitive to the accuracy of the ideal fit parameters. Better spectral resolution may be required to more accurately determine the 1 MeV flux. The energy group flux based which was determined from the ideal spectrum obtained by the multi-foil technique was readjusted per Eq. 11. Values of the nine group flux were iteratively perturbed using a normally distributed remnant flux. The approximate adjusted flux was determined by selecting the perturbed flux with the least squares Fig. 2 Nine group flux spectrum for RSR facility at 95 kw power determined by method of least squares using multiple activation foils Table 3 Percent differences from experimental reaction rates Reaction error in 1, iterations. The adjusted group flux is shown in Fig. 2. The errors between the measured reaction rates to those calculated from the ideal and adjusted spectra are shown in Table 3. Errors in the ideal flux are small suggesting that the true flux does not deviate greatly from ideal. Therefore the perturbative approach used in the flux adjustment is appropriate. Additionally, the general improvement in error gained by adjusting the group flux indicates that the group flux adjustment technique is able to produce a better approximation of the true flux. Conclusions % Difference in experimental and ideal reaction rates 58 Fe(n,c) 59 Fe Mo(n,c) 99 Mo Zr(n,c) 95 Zr Zr(n,c) 97 Zr % Difference in experimental and adjusted reaction rates This experiment demonstrates the ability of the multiple foil activation technique to determine the approximate neutron flux spectrum in a thermal reactor. Fit parameters Table 2 Ideal flux parameters and corresponding 1 MeV equivalent flux Method / t (cm -2 s -1 ) / (cm -2 s -1 ) / 1 MeV (cm -2 s -1 ) Au foil (2.55 ±.18) (1.3 ±.5) (5.84 ±.23) Multi-foil (2.63 ±.17) (1.1 ±.2) (4.95 ±.9)

5 Neutron flux characterization techniques for radiation effects studies 57 for the Maxwellian and 1/E fit agree reasonably well between the multi-foil method and the Au foil activation method. Furthermore the multi-foil method is equipped with the ability to readjust energy group fluxes to better approximate the true flux. In theory, spectral resolution is proportional to the number of flux monitors used. The multi-foil technique can more accurately resolve greater spectral detail with the addition of more flux monitors. Improved spectral detail is important in correctly determining the 1 MeV equivalent flux metric used in radiation effects studies. Acknowledgments This work is supported, in part, by the National Institute of Nano Engineering and the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the U.S. Department of Energy under contract DE-AC4-94AL85. References 1. Stoughton RW, Halperin J (1959) Nucl Sci Eng 6:1 2. ASTM E262-8 (23) Standard test method for determining thermal neutron reaction rates and thermal neutron fluence rates by radioactivation techniques. doi:1.152/e Gold R (1964) Nucl Sci Eng 2: Di Cola G, Rota A (1965) Nucl Sci Eng 23: Ryufuku H (1966) Jpn J Appl Phys 5:93 6. ASTM E722-9 (29) Standard practice for characterizing neutron fluence spectra in terms of an equivalent monoenergetic neutron fluence for radiation-hardness testing of electronics. doi: 1.152/E722-9E1