Neutron source

In the neutron energy range from 13.5 to 15.0 MeV, irradiations were performed at the K-400 neutron generator of the China Academy of Engineering Physics (CAEP). The neutron yield of the K-400 neutron generator is approximately (3–5)× 10¹⁰ n/s. The neutrons were produced by a T(d,n)⁴He reaction with a D⁺ beam current of 250 μA. The thickness of the solid tritium-titanium (T-Ti) target used in the generator was 2.5 mg/cm², and the energy of the incident D⁺ beam was 300 keV. An Au-Si surface barrier detector was installed at 135 with respect to the D⁺ beam and at a distance of 100 cm from the T-Ti target for the detection of accompanying particles. The neutron flux was recorded and kept every ten seconds to obtain the neutron flux fluctuation over the entire irradiation period.

Samples irradiation and neutron energy

High purity aluminum (0.5 mm, 99.999% purity) foil was sandwiched between natural zirconium (0.1 mm, 99.5% purity) and niobium (0.1 mm, 99.95% purity) foils. The first set of foils was tailored to form a round disk with a diameter of 20 mm. Four sandwich samples were placed approximately 5.0 cm away from the T-Ti target relative to the deuteron beam’s incident angles of 0, 30, 60 and 100. The dimensions of the second set of foils were 0.5 cm in width and about 4 cm in length, which were in arc shape and placed about 3.0 cm away from the T-Ti target and about 60 to 135 relative to the deuterium ion incident direction. The schematic diagram of experimental geometry is shown in Fig. 2. The second set of foils was cut into 8 squares with a side length of 0.5 cm after the irradiation. The precise weight of each foil was determined with an analytic balance (±0.01 mg) after irradiation.

Fig. 2Full-screen View

(Color online) Schematic diagram of experimental geometry

Two sets of aluminum samples placed at different locations from the tritium titanium target were irradiated for 20 h. It is essential to accurately determine the neutron energy for cross-sectional measurements, particularly those near the threshold. The neutron energies were measured using the Zr-Nb method [19, 20]. As a cross-check, the neutron energies of the first set of foils were calculated using an improved theoretical method, which was used to determine the mean D-T neutron energies in a large solid angle sample [21, 22]. There are two sets of parameters for the Zb-Nb method, and the neutron energies were calculated using these two sets of parameters. The mean value of the two results was used to determine the final neutron energy, as described in Sect. 5. The uncertainties in the incident neutron energies given above are the quadratic roots of the summed square of the uncertainties caused by the results of the activity measurements for Zr and Nb foils [23]. The entire available energy range starts from the threshold of the (n,2n) reaction to approximately 14.90 MeV. It is reasonable to suppose that the scattered neutrons from the target construction and the surrounding environment are insignificant because of the high threshold of the ²⁷Al(n,2n)²⁶Al reaction. In addition, the cross-section of ⁹³Nb(n,2n)^{92 m}Nb was used as a standard to monitor the integral neutron flux for all samples. The relevant nuclear parameters for ⁹³Nb(n,2n)^{92 m}Nb and ⁹⁰Zr(n,2n)^{89 m+g}Zr are listed in Table 1.

Measurement of ^{92 m}Nb and ^{89 m+g}Zr activity

After irradiation, there was a cooling period. Then, the activities of those Nb and Zr samples were determined using an HPGe γ-ray detector(as shown in Fig. 3). Before Nb and Zr samples were measured, a series of standard point sources (²²Na, ⁶⁰Co,¹³³Ba, ¹³⁷Cs, and ¹⁵²Eu) of known activity were used to determine the absolute full-energy peak efficiency of a lead-shielded high-purity germanium detector (ORTEC, USA). The radioactivity of the reaction product was determined via the well-calibrated HPGe detector with a relative efficiency of 68% and an energy resolution of 1.82 keV FWHM at 1.33 MeV. The distance between the sample and the detector was 5.0 cm. Efficiency calibration was determined using point-like standard gamma-ray sources. The detection efficiencies for the point source placed at a distance of 5.0 cm from the detector were determined using Eq. (1) $\begin{array}{l}{ϵ}_{\text{p}}=\frac{C^{\prime }}{A_0{{\displaystyle \exp }}^{-\lambda t}\text{Δ}t{I}_{\gamma }}\hfill \end{array}$ (1) where $C^{\prime }$ is the count number of the point source during the counting time ($\text{Δ}t$), A₀ is the source activity at the time of manufacturing, t is the time elapsed from the date of manufacturing to the start time of counting, γ is the decay constant, and $I_{\gamma }$ is the decay γ intensity.

Fig. 3Full-screen View

(Color online) Typical γ-ray spectrum in zirconium and niobium sample

The efficiency values obtained for the characteristic γ-ray energies of the point source are described using an exponential function [24] expressed in Eq. (2). The detector efficiency for the characteristic γ-ray energies of ^{92 m}Nb and ^89m+gZr was then obtained using Eq. (2). The detector efficiency uncertainties of ^92mNb and ^89m+gZr were obtained by evaluating the uncertainties of the standard sources. $ϵ(E)={ϵ}_0\exp \left(-E/E_0\right)+{ϵ}_c$ (2) The fitting parameter values are 2.53 (ϵ₀), 264.14 (E₀), and 0.33 (${ϵ}_{\text{c}}$), respectively. The value of R² is 0.992.

²⁶Al measurement at GYIG 1 MV AMS

Because ²⁶Al has a half-life of millions of years, it is difficult to measure ²⁶Al with high-purity germanium; therefore, an ultrasensitive AMS was needed to measure ²⁶Al in the present work. As a dedicated accelerator mass spectrometer, the GYIG 1 MV AMS instrument has been installed at the Institute of Geochemistry, Chinese Academy of Sciences since 2022 and was designed for multinuclide measurements such as ¹⁰Be, ¹⁴C, ²⁶Al, and ⁴¹Ca. After the installation was completed, the relevant acceptance and commissioning works were also completed. The present study was performed using a 1 MV AMS. A schematic of the GYIG AMS facility (model 3SDH-1 Pelletron) is shown in Fig. 4 [25], which mainly includes a cesium sputter negative ion source, a low-energy injection system (electrostatic analyzer and LE magnet), a tandem accelerator, a high-energy analysis system (HE analyzing magnet and electrostatic analyzer), and an energy-sensitive detector [26, 27].

Fig. 4Full-screen View

(Color online) Schematic of the GYIG 1 MV AMS, Model 3SDH-1. I: Ion source II: Sequencer and LE mass analyzer. III: 1 MV Pelletron accelerator and gas stripper. IV: HE analyzing magnet, off-axis Faraday cups. V: The rare isotope beamline (containing the retractable stopper foil, the electrostatic spherical analyzer, the 45 analyzing magnet). VI: Gas ionization detector [25]

Al₂O₃ was chosen as the proper sputter material. After neutron activation, approximately 0.08 g of aluminum foil was weighed and dissolved in 5 ml of hydrochloric acid (4.5 M) to ensure a uniform mixture of the irradiated sample material. The solutions were diluted with deionized water to 20 mL, respectively. The pH of the solution was adjusted by ammonium hydroxide to 9. A saturated ammonium oxalate solution was added to precipitate aluminum as aluminum hydroxide (Al(OH)₃). The Al(OH)₃ precipitate was separated by centrifugation at 10000 rpm for 5 min, washed once with saturated ammonium oxalate solution, and rinsed twice with deionized water. The aluminum hydroxide precipitate was transferred to a ceramic crucible. The sample was dried at 60 °C and then heated to 900 °C in a muffle furnace to obtain aluminum oxide powder. After mixing with Ag powder (Mass: Mass=1:1), the prepared samples were pressed into a copper holder, which acted as the cathode in the cesium sputtering negative-ion source, capable of holding 40 cathodes of solid samples [28, 29].

Before the measurement of ²⁶Al, the pilot ²⁷Al^- beam was injected into the accelerator after being selected by the injection magnet, and the current of ²⁷Al^- was 0.1–1 μA. Because the electron affinity of aluminum is relatively low, the intensity of the ²⁷Al^- current from the cesium sputtering negative ion source is insufficient compared to C^- and BeO^- in this machine. Fortunately, Mg^- ions are unstable; thus, isobaric interference is insignificant in the ²⁶Al measurement. The accelerator terminal voltage was set to 0.41 MV, and negative ions were accelerated in the first part of the accelerator. After passing through argon gas at a pressure of 27 Torr, the negative ions were stripped into positive ions with different charge states via collisions and Coulomb breakups and then accelerated in the second part of the accelerator. ²⁷Al¹⁺ particles were chosen by high-energy analysis system. The beam transmission was approximately 30%, which is the ratio of the ²⁷Al current measured in the Faraday cups before and after passing through the high-energy magnet. After the ²⁷Al¹⁺ ions reached the Faraday cup before reaching the detector, all parameters were adjusted to fit the ²⁶Al beam transport. Then, the sequential injection of ²⁷Al and ²⁶Al is achieved with a magnet bias supply coupled to the ‘bouncer magnet.’ The current of the ²⁷Al¹⁺ ion was integrated at the offline Faraday cup, whereas the radioisotope ²⁶Al was measured using an ionization chamber, which provides high resolution in the energy measurement [30]. Under the influence of the sample preparation level, mixing uniformity with the conductive medium, and sample bombardment degree in the ion source, the multiple measurement current value of ²⁷Al¹⁺ in a high-energy Faraday cup can fluctuate between tens and hundreds of nA, and the ²⁶Al count follows the same proportion. Consequently, the ²⁶Al/²⁷Al ratio measured between different rounds exhibited little deviation(as shown in Fig. 5). Because AMS is a relative measurement, the standard sample, processing the blank sample, and unknown sample should be measured sequentially. Meanwhile, the raw ratio results were subtracted from the processing blank value and normalized to the standard sample nominal value.

Fig. 5Full-screen View

(Color online) ²⁶Al counting, ²⁷Al¹⁺ current and ²⁶Al/²⁷Al ratio fluctuation among different rounds

To validate the performance of the newly installed instrument, a series of standard samples with different gradients and blank samples were used. The ratio of the blank samples was less than 4×10^-15. The ratios of the Al standard (5.00×10^-11) were reproduced to be better than 1% (as shown in Fig. 6). To measure the (n,2n) cross-section, the raw ratios(before normalization) of ²⁶Al/²⁷Al are between 6×10^-15 and 10^-13, which are much larger than the machine background of ²⁶Al/²⁷Al at the GYIG 1 MV AMS. To verify the measurement results of the GYIG 1 MV AMS, four samples and one blank sample were sent to the Xi’an Accelerator Mass Spectrometry Center. The measurement standard for ²⁶Al/²⁷Al is 1.065×10^-11 in Xi’an and the background is 4.71×10^-11 [30]. The values of the four irradiated samples were between 1.77×10^-11 and 2.09×10^-11, which is in good agreement with the results of GYIG 1 MV AMS.

Fig. 6Full-screen View

(Color online) Raw measured isotope ratios for various reference samples versus their nominal values

Neutron fluence

The neutron fluence of the aluminum sample during irradiation was calculated using Eq. (4) [23]. $\begin{array}{l}{\text{Φ}}_{\text{total}}=\overline{\varphi }T=\frac{FC\lambda A}{M{N}_A\eta I_{\gamma }ϵKSD{\sigma }_{\text{m}}}T\mathrm{,}\hfill \end{array}$ (4) where $\overline{\varphi }$ is the neutron flux averaged over the sample in the total irradiation time T, ${\sigma }_{\text{m}}$ is the monitor reaction cross section for ⁹³Nb(n,2n)^{92 m}Nb, $S=1-{{\displaystyle \exp }}^{-\lambda T}$ is the growth factor of the residual nuclide, λ is the decay constant of ^{92 m}Nb, ϵ is the full-energy peak efficiency of the 934.44 keV γ ray, $I_{\gamma }$ is the emission probability of the 934.44 keV γ ray in ^{92 m}Nb decay, η is the isotopic abundance of the target nuclide ⁹³Nb, M is the mass of ⁹³Nb, $D={{\displaystyle \exp }}^{-\lambda t_1}-{{\displaystyle \exp }}^{-\lambda t_2}$ is the counting collection factor, t₁ (t₂) is the time intervals between the end of irradiation and the start (stop) of counting, A is the atomic weight of ⁹³Nb, C is the measured full-energy peak area, N_A is the Avogadro constant, F is the composite correction factor of the activity expressed by Eq. (5), and K is the neutron flux fluctuation factor expressed by Eq. (6) [31-33]. $F=F_{\text{s}}{F}_{\text{g}}{F}_{\text{c}}\mathrm{,}$ (5) where F_s, F_g and F_c are the correction factors for the self-absorption of γ-rays with a given γ energy, counting geometry, and coincidence summing effect of the cascade γ-rays in the investigated nuclide, respectively. In this study, all the samples were measured 50 mm from the surface of the detector. This distance is so large that F_g and F_c are considered negligible [32]. The self-absorption of 934.44 keV γ-ray by 0.1 mm Nb was calculated to be 1.003. $\begin{array}{l}K=\frac{{\displaystyle {\sum }_i^L{\varphi }_i}\left(1-{{\displaystyle \exp }}^{-\lambda \text{Δ}{t}_i}\right){{\displaystyle \exp }}^{-\lambda T_i}}{\varphi S}\hfill \end{array}$ (6) where L is the number of time intervals, in each of which the accompanying α counts were individually recorded, ti is the duration of the i^th time interval, Ti is the time interval from the end of the i^th interval to the end of irradiation, ϕi is the relative neutron flux averaged over the sample during ti (i.e., α counts in ti), ϕ is the relative neutron flux averaged over the sample in the total irradiation time T (i.e., total α counts in T) [34].

Uncertainty analysis

The total uncertainty of the ²⁷Al(n,2n)²⁶Al reaction consists of the monitoring reaction and the AMS contributions. Individual contributions to the total uncertainty are listed in Table 2. The uncertainty in the AMS measurements includes the statistical uncertainty (4.9%-50.2%), reproducibility of the measurement (1.0% for the standard sample), and systematic contribution from the measurement relative to reference materials (1.0%). As the most commonly used standard cross-section, the uncertainty of ⁹³Nb(n,2n)^92mNb is approximately 1.5% [5]. The uncertainty (3.0%) of the HPGe efficiency calibration was derived from the accuracy of the calibration sources and calibration procedure. The total uncertainty was estimated using the square root of the quadratic sum of the above sources, and the overall uncertainties ranged from 7% to 50.2%.