Introduction

The safe management and disposal of radioactive waste with negligible heat generation (low and intermediate level radioactive waste) requires knowledge of its inventory with regards to chemically toxic and nontoxic substances [1]. For the disposal of such radioactive waste in the repository Konrad (Germany) a description and declaration thresholds for nonradioactive substances were defined, usually as 1 and 5 % of the total waste package weight for new and old waste, respectively [2]. The terminology new waste refers to radioactive waste which has been conditioned according a qualified process after the entry into force of the Konrad plan approval decision [3]. To comply with these requirements and the waste acceptance criteria every waste package has to be characterized in its radiological and chemical composition. The waste producers have to indicate the substance and its mass in the material description of the waste packages if the mass fraction of the substance exceeds the description threshold. Substances which exceeds their declaration threshold are identified as hazardous and are taking into account for balancing the waste inventory. The amount of chemically toxic elements in the waste is limited in order to avoid pollution of underground water reserves.

This material characterization can be performed on the basis of existing documentation or, if the documentation is insufficient, on further analytical analysis. In a previous paper [4] related through the development of the analytical facility MEDINA (Multi Element Determination based on Instrumental Neutron Activation) we have shown that prompt gamma neutron activation analysis (PGNAA) using a pulsed 14 MeV neutron source is suitable to identify nondestructively toxic elements in 200 L radioactive waste drums.

In this work we report on the PGNAA of a 200 L steel drum filled with concrete, which often is employed as embedding material in waste conditioning. The method to assess the elemental composition of concrete including the determination of relevant parameters such as the gamma-ray detection efficiency, the thermal neutron flux and the epithermal to thermal neutron flux ratio is presented. The concentrations of the detected elements hydrogen, boron, aluminum, silicon, potassium calcium and titan are compared with the values obtained from the PGNAA of small samples (3–5 g) of the same concrete at the cold neutron beam of the Budapest Research Reactor [5]. As an example, detection limits for the toxic elements cadmium and mercury are also evaluated.

Basic considerations

The net peak area \( P_{{{\text{E}}\gamma }} \) of a prompt gamma ray with the isotope specific energy Eγ induced by thermal and epithermal neutron capture may be expressed by the following equation:

$$ P_{E\gamma } = \frac{m}{M} \cdot N_{A} \cdot \sigma_{E\gamma } \cdot \varPhi_{th} \left[ {1 + \left( {0.44 + \frac{1}{\sigma }} \right) \cdot R} \right] \cdot \varepsilon_{E\gamma } \cdot t $$
(1)

where m (g) is the mass of the element, M (g mol−1) the molar mass of the element, NA the Avogadro number, σEγ (cm2) the partial gamma-ray production cross section [6, 7], σ (cm2) the isotopic thermal neutron capture cross section [8], I (cm2) the isotopic resonance integral [8], Φth (cm−2 s−1) the average thermal neutron flux within the sample, R the epithermal to thermal neutron flux ratio, εEγ the gamma-ray detection efficiency and t (s) the counting time. The product \( \sigma_{{{\text{E}}\gamma }} \times \varPhi_{\text{th}} \times 0.44 \times {\text{R}} \) in (1) takes into account the 1/v characteristic of the absorption cross section in the epithermal region [9].

Measurements

The measurement was done with a 200 L steel drum filled with 76 cylindrical concrete bodies (4 layers with 19 bodies each) as shown in Fig. 1. The steel drum has a filling height of 83 cm, an internal diameter of 56 cm and a total weight of 53.2 kg. The iron content of the steel drum is 98.38 wt%. The total amount of concrete is 199.5 kg and due to the empty space between the bodies the apparent density of the concrete matrix is 1.02 g cm−3. The concrete drum is irradiated in the MEDINA facility with 14 MeV neutrons produced by a deuterium–tritium (D-T) neutron generator (GENIE16GT, EADS SODERN). The distance between the tritium-target of the neutron generator and the center of the drum is 55 cm. The neutron generator is operated in pulse mode with an acceleration voltage of 85 kV and an ion current of 40 μA leading to a neutron emission of about 8 × 107 n s−1. The length of the 14 MeV neutron pulses is set to 50 μs and the repetition period of the neutron pulses to 1 ms. As the repetition period of the neutron pulses is lower than the die-away time of thermal neutrons in concrete which is 2.23 ms [10] a constant average thermal and epithermal neutron flux is reached after few neutron pulses.

Fig. 1
figure 1

200 L steel drum filled with concrete blocks (left) and closed with the cover (right) before loading in the MEDINA facility

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The detection of the gamma rays is achieved with a 104 % n-type HPGe-detector (CANBERRA) entirely shielded against thermal neutrons with 6LiF plates. The distance between the centre of the drum and the detector window is 105 cm so that the complete volume of the concrete drum is assayed. The processing of the detector signals for spectra acquisition is described in [4]. The gamma rays are measured between the neutron pulses over a counting time of 930 μs. The measurement was started 20 μs after the end of the neutron pulses to allow the slowing down of fast neutrons. The gamma-ray spectrum is recorded during 1860s in Zero Dead Time mode with the software Gamma Vision-32 (ORTEC) and analyzed with the spectroscopy software Gamma-W (Dr. Westmeier GmbH). The origin of the prompt and delayed gamma rays identified in the spectra of the concrete drum, the empty drum and the empty chamber are discussed in [4]. The spectrum of the empty drum recorded under the same irradiation and measurement conditions as for the drum filled with concrete is used for background correction of the hydrogen, boron, aluminum and titan gamma-ray count rates. As the Gamma-W software does not contain a procedure for analysis of Doppler-broadened photopeak [11], the 477-keV peak induced though the (n,α)-reaction on 10B is simply fitted as a multiplet including also the possible interfering 472-keV peak of 24mNa. The gamma-ray count rates for the elements of interest are given in Table 2 together with the required cross section data to determine the elemental concentrations by mean of relation (1).

Gamma-ray detection efficiency

The gamma-ray detection efficiency εEγ for the steel drum including top and bottom and for the concrete matrix is calculated numerically with an own developed algorithm [12, 13] based on the following formula:

$$ \varepsilon_{{{\text{E}}\gamma }} = \frac{{\varepsilon_{{0{\text{E}}\gamma }} }}{n} \cdot \mathop \sum \limits_{i = 1}^{n} \left( {\frac{{d_{0} }}{{d_{i} }}} \right)^{2} \cdot e^{{ - \left( {\frac{\mu }{{\rho_{c} }} \cdot \rho_{c} \cdot l_{i} } \right)}} \cdot e^{{ - \left( {\frac{\mu }{{\rho_{d} }} \cdot \rho_{d} \cdot k_{i} } \right)}} $$
(2)

where ε0Eγ is the detection efficiency of the considered gamma-ray energy for a point source at the distance d 0 = 105 cm from the detector surface, n the number of point sources distributed either in the concrete matrix or in the steel drum using cylindrical coordinates, di the distance of the ith point source from the detector surface, ρc = 1.02 g cm−3 and ρd = 7.84 g cm−3 the densities of the concrete matrix and the steel drum, respectively, μ/ρc and μ/ρd (cm2 g−1) the corresponding mass attenuation coefficients [14] at the considered gamma-ray energy and l i and k i (cm) the mean distances covered by the gamma ray of the ith point source in the concrete matrix and the steel drum, respectively to reach the centre of detector surface. Numerical simulations are performed for the half-volume of the concrete matrix and of the drum cylinder due to their symmetry with respect to the HPGe-detector. Simulations for the cover and bottom of the drum are carried out apart. The detection efficiency for the steel drum is obtained by summing the efficiencies of the different parts of the drum weighted by the corresponding weight fractions. The number of point sources distributed in the concrete matrix is 21.6 × 106 and in the steel drum 3.8 × 106.

The detection efficiency ε0Eγ for gamma-ray energies lower than 2 MeV is obtained from the measurement of 241Am, 137Cs and 152Eu standard point sources. The determination of ε0Eγ for higher energies up to 10 MeV is achieved by measuring the prompt gamma rays of 56Fe and 35Cl induced by the neutron activation of the 200-L empty drum and a 900 g NaCl sample positioned in the centre of the irradiation chamber, respectively. Afterward the prompt gamma-ray count rates are normalized to the detection efficiency obtained with the radioactive point sources using the 56Fe and 35Cl prompt gamma rays with energies lower than 2 MeV for correction of the counting geometry and gamma-ray absorption [12]. The energy dependence of ε0Eγ is shown in Fig. 2 and fitted by a polynomial function as:

$$ \varepsilon_{0E\gamma } = \mathop \sum \limits_{j} a_{j} \cdot E_{\gamma }^{j} $$
(3)

with Eγ in keV and a j the fit coefficients (j ranging from −3 to +2). The calculated detection efficiencies for the steel drum and the concrete matrix are displayed as a function of the gamma-ray energy in Fig. 3. Analytical expressions of the gamma-ray detection efficiency are obtained here by fitting the data with the polynomial function (3) where the index j is ranging from −8 to +4. The detection efficiencies εEγ are evaluated with an overall uncertainty of 5 %.

Fig. 2
figure 2

Energy dependence of the gamma-ray detection efficiency for a point source positioned at a distance of 105 cm from the HPGe-detector. The coefficient of determination for the goodness of the data fit with (3) is 0.992. The solid line represents the polynomial function

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Fig. 3
figure 3

Energy dependence of the gamma-ray detection efficiency for the steel drum and the concrete matrix. The detection efficiency is calculated numerically according (2).The coefficient of determination for the goodness of the data fit with (3) is 0.999 for both cases. The solid line represents the polynomial function

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Thermal neutron flux

The epithermal to thermal neutron flux ratio R is evaluated irradiating alternatively thin gold foils (100 μm thickness) with and without cadmium covers (1 mm thickness) positioned in the centre of an empty 200 L steel drum. The foils are irradiated for 1 h operating the neutron generator in the same way as for the measurement of the concrete drum. The activity of 198Au (T ½ = 2.69 d) induced by thermal neutrons and/or epithermal neutrons is determined measuring the gamma ray at 411.8 keV with a HPGe-detector (20 % relative efficiency) operated in a lead chamber as low-level counting system. The distance between gold foils and HPGe-detector is 5 cm and the counting time is ranging between 1 and 4 days. The gamma-ray detection efficiency is deduced from the measurement of radioactive standard point sources. The 198Au activity is determined to 0.67 ± 0.06 Bq for the irradiation with cadmium and to 2.67 ± 0.11 Bq for the irradiation without cadmium. These values lead after corrections for thermal and epithermal neutron absorption in gold and epithermal neutron absorption in cadmium to a thermal and epithermal neutron flux at the centre of the empty drum of 2700 ± 200 cm−2 s−1 and 490 ± 40 cm−2 s−1, respectively and thus to R = 0.18 ± 0.02.

The average thermal neutron flux in the concrete matrix is monitored by the steel drum [12, 13, 15] and calculated from the count rates of the 54Fe, 56Fe and 57Fe prompt gamma rays by means of relation (1). Count rate interferences due to the presence of iron in concrete are neglected since its amount (5.5 kg) is lower than that of the steel drum and the gamma-ray detection efficiency of the steel drum is higher than that of the concrete matrix as shown in Fig. 3. The values of the average thermal neutron flux evaluated from the different prompt gamma rays of iron are given in Table 1. They agree well with each other taking into account their uncertainties indicating in particularly the validity of the numerical model employed to determine the gamma-ray detection efficiency of the steel drum in presence of the concrete matrix. Therefore an average thermal neutron flux of 3400 ± 300 cm−2 s−1 is used to determine the elemental composition of concrete.

Table 1 Average thermal neutron flux within concrete determined from the prompt gamma rays of iron isotopes using the steel drum as monitor
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Results and discussion

The element composition of concrete determined by PGNAA of small samples at the cold neutron beam of the Budapest Research Reactor (BRR) [5] can be found in [4]. The concentrations of the elements detected in this work (hydrogen, boron, aluminum, silicon, potassium, calcium and titan) are presented in Table 2. They agree well with the values obtained by PGNAA of small samples (Table 2) considering the respective uncertainties. This confirms the validity of the proposed model for PGNAA of massive homogenous samples based on numerical calculation of the gamma-ray detection efficiencies and the monitoring of the neutron flux with the steel drum. Building the oxide composition assuming a maximal oxidation state of the elements (H2O, B2O3, Al2O3, SiO2, K2O, CaO, TiO2) 93 ± 2 % of the concrete weight is determined, the remaining 7 % being mainly attributed to Fe2O3 (4 %), SO3 (1.7 %), Na2O (0.70 %), Mn2O3 (0.10 %). The detection limit for cadmium and mercury is calculated by means of relation (1) with a number of counts equals to three times the standard deviation of the background below the expected gamma-ray peak. By using the gamma-rays at 558.3 keV (σEγ = 1860 b) and 1693.3 keV (σEγ = 56.2 b), respectively, detection limits of 4 mg/kg and 145 mg/kg are achieved for cadmium and mercury which are largely lower than the threshold for their description in waste packages.

Table 2 Elemental composition of concrete determined in this work (PGNAA massive sample) compared to the PGNAA of small samples (3 to 5 g) performed at the cold neutron beam of the Budapest Research Reactor [4, 5]
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Conclusions

Within this work PGNAA of a 200 L steel drum filled with concrete was carried out using a 14 MeV neutron generator at the MEDINA facility. The method proposed to evaluate the element composition of concrete provides equivalent results to PGNAA of small samples within uncertainties. Thus it may be applied to other homogeneous waste matrices to assay their chemical composition including harmful substances such as cadmium and mercury which have to be declared for the safe disposal of radioactive waste in Germany.