3. Development of the methodology applied at CDTN

control (QA/QC), training of technical group, good laboratory practice and others. All of these requirements are needed to meet the demand for analytical values that are even increasing in all fields, contributing to environmental monitoring, individual and population health and economical decisions. According to the development of human knowledge, the requirements for quality have been diversified and increasing in several fields. Therefore, the demand for analytical data with smaller uncertainties and lower detection limits is expanding and more

The nuclear analytical technique, NAA [1, 2], fulfils several requirements. It is well-known that NAA requires a non-chemical preparation—a non-destructive technique—and analyses a large number of elements simultaneously. Besides, it is a traceable technique [3, 4]. It presents sensitivity, multi-element ability, selectivity and versatility and determines chemical elements

The technique is well established at the Laboratory for Neutron Activation Analysis, LNAA, located at the Nuclear Technology Development Centre (CDTN) sponsored by the Brazilian Commission for Nuclear Energy (CNEN), in Belo Horizonte, capital of the Brazilian state of Minas Gerais. The nuclear research reactor, the 100 kW TRIGA MARK I IPR-R1, has enabled the NAA to be applied determining the elemental concentration of different samples, such as soil, sediment, plants, food, medicines and biological tissues of humans and animals, among others [7–20]. The NAA has been applied through relative and parametric methods and has been applied meeting requests of customers both of CDTN and at industries, universities and other institutions. The technique has also been applied in researches of the LNAA. The standardised k0-method [21] was established in 1995, being the most efficient form of application of this nuclear analytical technique [8, 9]. The k0-method has been continuously improving along its nuclear data [22, 23], which can be found in the form of an Excel file, the k0-database

The usual procedure in NAA is to analyse a sample whose mass is lower than 500 mg, considering it as a geometrical point source. This entails a number of simplifications during irradiation and gamma spectrometry [25, 26]. This way, several simplifications can be made such as disregarding the neutron self-shielding, neutron-flux gradients over the sample and self-

On the other hand, there is a growing demand for the NAA established at CDTN to explore its potential in order to overcome the main limitations when analysing point samples, which are: to reach lower detection limits than those currently in use (for instance in food samples, plants, medicines and lichens) and to carry on analysis at lower cost, that is, to analyse a smaller number of samples and shorter time of analysis. For example, instead of analysing 20 small samples, a single about 4 g composite sample could be analysed; to provide greater representativeness of samples of non-homogeneous materials, for instance, industrial waste materials; to enable the analysis of whole parts in which it is not possible or permitted to remove an

attenuation of gamma rays. The impact to the accuracy of the results is negligible.

requirements are necessary to meet the quality required by the clients.

90 Advanced Technologies and Applications of Neutron Activation Analysis

with precision and accuracy [5, 6]. That is why it is a powerful technique.

2015 [24].

2. Small samples versus large samples

The LNAA determines chemical elemental concentrations following the usual procedure small cylindrical samples. The irradiations are carried out in the carousel facility of the TRIGA MARK I IPR-R1 reactor that operates at 100 kW with an average thermal neutron flux of 6.3<sup>10</sup><sup>11</sup> cm<sup>2</sup> <sup>s</sup> 1 . The laboratory has a high demand of analysis, answering the clients' request, analysing several kinds of samples. It is often necessary to overcome the difficulties due to low neutron fluency, inhomogeneity of unknown sample and time consumption of analysis. For that reason, to analyse larger samples would be an attractive possibility. However, it is not allowed to change the infrastructure of irradiation; therefore, a study was developed to verify the possibility to analyse 5 g-samples, maximum mass content in the irradiation vial, 25 times larger than usual samples analysed. The k0-method of neutron activation analysis [21] would be applied and the current infrastructure for irradiation and gamma spectrometry facilities would be used. To develop this study, the mass of the small sample analysed was around 200 mg and the larger cylindrical sample, around 5 g.

Aiming at solving the main limitations when dealing with small samples and exploring a new possibility of analysis, a methodology of analysing larger samples or cylindrical samples was established in LNAA at CDTN [16, 36, 37]. All experiments were developed in geological matrix. The reason was that matrix is the one most used in routine elemental analysis at CDTN. All irradiations were performed in the carousel facility of the 100 kW TRIGA MARK I IPR-R1 reactor under an average thermal neutron flux of 6.3 <sup>10</sup><sup>11</sup> cm<sup>2</sup> <sup>s</sup> <sup>1</sup> and average spectral parameters f (thermal to epithermal ratio neutron fluxes) and α (the epithermal flux distribution parameter), 22.67 and 0.0026, respectively. The induced activities were measured on absolutely calibrated HPGe detectors [9]. The vials were inserted in a polystyrene container for irradiation during 8 hours.

used to validate the full-energy peak efficiency, εp, calculated by KayWin. Both software need information on the detector characteristics, container and geometry dimensions, composition of the sample and reference efficiency curve. The full-energy peak efficiency, εp, and the effective solid angle will be calculated. It is important to mention that ANGLE software makes

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In this step, the neutron self-shielding and the spatial neutron flux distribution factors [36, 40, 42–44] during irradiation in geological matrix were determined. The objective was to evaluate how significant were their contributions to the final elemental concentration results and which correction factor may be determined to correct the neutron flux gradient

Several programmes calculate the thermal neutron self-shielding factor (Gth). To calculate this factor, it is necessary to know the sample composition and geometry. In this methodology

It is relevant to verify the axial and radial distributions of neutron fluxes in the vial. They can be evaluated experimentally during irradiation [40] and after by measuring the Fc,Au-factor, called the comparator factor, calculated based on neutron monitors irradiated together with the sample in sandwich form. This factor provides the trend of the axial neutron flux gradient, while radial gradient is negligible due to similar diameter of the sample and standard (Al-0.1%

Simplified equation of the k0-method [21] for elemental concentration calculation for an analyte

<sup>k</sup>0,Auð Þ<sup>a</sup> � <sup>1</sup>

<sup>k</sup>0,Auð Þ <sup>m</sup> � <sup>1</sup>

where Asp,m and Asp,a are the specific activities of monitor (m) and analyte (a); k0,Au(m) and k0,Au(a) are k0-factors of monitor Au (by definition � 1) and analyte; εp,m and εp,a are the fullenergy peak detection efficiency of the monitor (Al-0.1%Au alloy in disc form) and radionuclide of analyte; f is thermal to epithermal neutron flux ratio; Gth,m and Gth,a are the correction factors for thermal neutron self-shielding; Ge,m and Ge,a are the correction factors for epithermal

Gth, <sup>a</sup>:<sup>f</sup> <sup>þ</sup> Ge, <sup>a</sup>:Qo, <sup>a</sup>ð Þ <sup>α</sup> � <sup>1</sup>

Gth,m:<sup>f</sup> <sup>þ</sup> Ge,m:Qo,mð Þ <sup>α</sup> � <sup>1</sup>

εp, <sup>a</sup>

εp,m

(1)

(2)

efficiency calculations only for coincidence-free gamma lines.

and self-shielding effects.

3.2.1. Neutron self-shielding

Au alloy).

(a), is below, Eq. (1):

3.2.2. Spatial neutron flux distribution factors

<sup>r</sup><sup>a</sup> <sup>¼</sup> Asp, <sup>a</sup> Fc,Au

where the Fc,Au-factor, the comparator factor, Eq. (2), is:

Fc,Au <sup>¼</sup> Asp,m:10�<sup>6</sup>

� <sup>1</sup>

3.2. Neutron self-shielding and the spatial neutron flux distribution factors

development, the KayWin [39] and MATSSF software [45] were applied.

Gamma spectroscopy was carried out after suitable decay on an absolute calibrated HPGe detector named D4, GC 5019, CANBERRA, with 50% relative efficiency. The absolute calibration was done following a recommended procedure in the k0-standardisation method [6, 9, 21].

The HyperLab programme [38] was used for peak area deconvolution and the software package Kayzero for Windows® [39], also called KayWin, was applied. It is a specific programme to calculate the elemental concentration for the so-called small samples—routine procedure—including the efficiency and coincidence correction calculations. It also calculates the values of efficiency for each energy based on the experimental full-energy peak efficiency determined previously for point-source geometry aiming at point sample analysis. This software determines the reference full-energy peak efficiency, εp, of the detector [9].

The main experimental steps carried out to establish the methodology based on Menezes and Jaćimović [16] and Menezes et al. [36, 37] will be described. Some tables and figures related to the development have already been published and are shown here with permission. However, other tables are original.

To establish the methodology to analyse a large sample, it was necessary to check three parameters: (i) detector efficiency over the volume source, (ii) neutron self-shielding during neutron irradiation and (iii) gamma-ray attenuation within the sample during counting [26, 35, 40].

#### 3.1. Detector efficiency over the volume source

To evaluate the detector efficiency over the volume of the sample applying the k0-method, using the KayWin software, it is necessary to determine the reference full-energy peak efficiency, εp. This programme calculates the elemental concentration for small samples routine procedure—while calculating the efficiency and coincidence correction. The values of efficiency for each energy are also calculated based on the experimental full-energy peak efficiency. This efficiency was determined previously for point-source geometry aiming at point sample analysis. It is necessary to provide the detector characteristics, container and geometry dimensions, composition of the sample and reference efficiency curve to determine its efficiency. The final calculations will give the full-energy peak efficiency, εp, and the effective solid angle (Ωeff ).

The KayWin software calculates, for each gamma energy in a spectrum, the efficiency, when the elemental concentration of a real sample is determined. The detector efficiency can also be determined by ANGLE V3.0 software [41] that was successfully installed at CDTN. This software is specific to calculate the full-energy peak efficiency of the semiconductor detector to several source geometries as point and cylindrical shapes, Marinelli, etc. In this study, it was used to validate the full-energy peak efficiency, εp, calculated by KayWin. Both software need information on the detector characteristics, container and geometry dimensions, composition of the sample and reference efficiency curve. The full-energy peak efficiency, εp, and the effective solid angle will be calculated. It is important to mention that ANGLE software makes efficiency calculations only for coincidence-free gamma lines.

#### 3.2. Neutron self-shielding and the spatial neutron flux distribution factors

In this step, the neutron self-shielding and the spatial neutron flux distribution factors [36, 40, 42–44] during irradiation in geological matrix were determined. The objective was to evaluate how significant were their contributions to the final elemental concentration results and which correction factor may be determined to correct the neutron flux gradient and self-shielding effects.

#### 3.2.1. Neutron self-shielding

spectral parameters f (thermal to epithermal ratio neutron fluxes) and α (the epithermal flux distribution parameter), 22.67 and 0.0026, respectively. The induced activities were measured on absolutely calibrated HPGe detectors [9]. The vials were inserted in a polystyrene container

Gamma spectroscopy was carried out after suitable decay on an absolute calibrated HPGe detector named D4, GC 5019, CANBERRA, with 50% relative efficiency. The absolute calibration was done following a recommended procedure in the k0-standardisation

The HyperLab programme [38] was used for peak area deconvolution and the software package Kayzero for Windows® [39], also called KayWin, was applied. It is a specific programme to calculate the elemental concentration for the so-called small samples—routine procedure—including the efficiency and coincidence correction calculations. It also calculates the values of efficiency for each energy based on the experimental full-energy peak efficiency determined previously for point-source geometry aiming at point sample analysis. This soft-

The main experimental steps carried out to establish the methodology based on Menezes and Jaćimović [16] and Menezes et al. [36, 37] will be described. Some tables and figures related to the development have already been published and are shown here with permission. However,

To establish the methodology to analyse a large sample, it was necessary to check three parameters: (i) detector efficiency over the volume source, (ii) neutron self-shielding during neutron irradiation and (iii) gamma-ray attenuation within the sample during

To evaluate the detector efficiency over the volume of the sample applying the k0-method, using the KayWin software, it is necessary to determine the reference full-energy peak efficiency, εp. This programme calculates the elemental concentration for small samples routine procedure—while calculating the efficiency and coincidence correction. The values of efficiency for each energy are also calculated based on the experimental full-energy peak efficiency. This efficiency was determined previously for point-source geometry aiming at point sample analysis. It is necessary to provide the detector characteristics, container and geometry dimensions, composition of the sample and reference efficiency curve to determine its efficiency. The final calculations will give the full-energy peak efficiency, εp, and the

The KayWin software calculates, for each gamma energy in a spectrum, the efficiency, when the elemental concentration of a real sample is determined. The detector efficiency can also be determined by ANGLE V3.0 software [41] that was successfully installed at CDTN. This software is specific to calculate the full-energy peak efficiency of the semiconductor detector to several source geometries as point and cylindrical shapes, Marinelli, etc. In this study, it was

ware determines the reference full-energy peak efficiency, εp, of the detector [9].

for irradiation during 8 hours.

92 Advanced Technologies and Applications of Neutron Activation Analysis

method [6, 9, 21].

other tables are original.

counting [26, 35, 40].

effective solid angle (Ωeff ).

3.1. Detector efficiency over the volume source

Several programmes calculate the thermal neutron self-shielding factor (Gth). To calculate this factor, it is necessary to know the sample composition and geometry. In this methodology development, the KayWin [39] and MATSSF software [45] were applied.

#### 3.2.2. Spatial neutron flux distribution factors

It is relevant to verify the axial and radial distributions of neutron fluxes in the vial. They can be evaluated experimentally during irradiation [40] and after by measuring the Fc,Au-factor, called the comparator factor, calculated based on neutron monitors irradiated together with the sample in sandwich form. This factor provides the trend of the axial neutron flux gradient, while radial gradient is negligible due to similar diameter of the sample and standard (Al-0.1% Au alloy).

Simplified equation of the k0-method [21] for elemental concentration calculation for an analyte (a), is below, Eq. (1):

$$\rho\_a = \frac{A\_{sp,a}}{F\_{c,Au}} \cdot \frac{1}{k\_{0,Au}(a)} \cdot \frac{1}{G\_{th,a}f + G\_{e,a} \cdot Q\_{o,a}(a)} \cdot \frac{1}{\varepsilon\_{p,a}} \tag{1}$$

where the Fc,Au-factor, the comparator factor, Eq. (2), is:

$$F\_{c,Au} = \frac{A\_{sp,m} \cdot 10^{-6}}{k\_{0,Au}(m)} \cdot \frac{1}{G\_{th,m}f + G\_{e,m} \cdot Q\_{o,m}(\alpha)} \cdot \frac{1}{\varepsilon\_{p,m}} \tag{2}$$

where Asp,m and Asp,a are the specific activities of monitor (m) and analyte (a); k0,Au(m) and k0,Au(a) are k0-factors of monitor Au (by definition � 1) and analyte; εp,m and εp,a are the fullenergy peak detection efficiency of the monitor (Al-0.1%Au alloy in disc form) and radionuclide of analyte; f is thermal to epithermal neutron flux ratio; Gth,m and Gth,a are the correction factors for thermal neutron self-shielding; Ge,m and Ge,a are the correction factors for epithermal neutron self-shielding; Q0,m(α) and Q0,a(α) are resonance integral (1/E1 + <sup>α</sup> ) to 2200 m s�<sup>1</sup> crosssection ratio; α is the epithermal flux distribution parameter.

Note that the Fc,Au-factor, as defined in Eq. (2), is proportional to the epithermal neutron flux density and directly indicates a gradient in epithermal flux density. In this study, the Fc,Aufactor was calculated by KayWin software based on several Al-0.1%Au monitors irradiated together with the samples in sandwich form.

#### 3.3. Gamma-ray attenuation within the sample during counting

The k0-method of NAA requires a precise technique to calculate full-energy peak detection efficiency (εp) of an HPGe detector for diversified samples and various counting geometries. The procedure provided by Moens et al. [46] presented a semi-empirical approach that has been introduced in KayWin software via option SOLCOI.

The basic principles are:


$$
\varepsilon\_{p, \text{geom}} = \varepsilon\_{p, ref} \cdot \frac{\overline{\Omega}\_{\text{geom}}}{\overline{\Omega}\_{\text{ref}}} \tag{3}
$$

to 3.6 cm high. The first neutron flux monitor was placed below ampoule, the second inside the ampoule on the top of the sample, and the third outside the vial. Air space between the sample and top of vial was filled with cellulose paper; (ii) Vial 2: six polyethylene vials (9 mm in diameter and 5 mm high) filled with reference material IAEA-SOIL-7 were stacked with neutron flux monitors in sandwich form and inserted into a 5 cm high polyethylene vial; (iii) Vial 3, the small sample (SS): an aliquot of about 200 mg of reference material was sealed in a polyethylene vial (diameter of 9 mm and 5 mm high), stacked together with neutron flux monitors and inserted in a 5-cm-high vial. Air space between the sample and top of ampoule was filled with cellulose paper; (iv) Vial 4: the large sample (LS) was filled in with a soil aliquot, 3.6 cm high and 1.3 cm in diameter. After being prepared, each vial was inserted in the "rabbit". Figure 1 shows a scheme of

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In this step, the influence of distance sample-detector for small and large cylindrical samples based on gamma efficiency was verified. The LS, Vial 1, was measured at 2, 5, 10 and 20 cm sample-detector distances. The gamma efficiency values, ɛp, at sample-detector distances related to several gamma lines (non-coincidence gamma lines) and respective nuclides were given by KayWin software, [39] when calculating the elemental concentration of the large cylindrical sample. The efficiency values were also obtained by ANGLE software [41]. Table 1 displays examples of the non-coincidence gamma energies for each nuclide determined and the respective ratio of each ɛ<sup>p</sup> to ɛ<sup>p</sup> of the reference distance sample-detector,

Figure 1. Vials prepared to carry out the experiments: Vial 1, large sample with reference material; Vial 2, with six small samples with reference material; Vial 3, with one small sample filled with reference material and Vial 4, with large sample

the prepared vials.

4.1. Detector efficiency over the volume source

20 cm, for KayWin and ANGLE.

filled with soil.

It is important to mention that by the definition of the effective solid angle, two factors are included: (i) the attenuation effects which gamma rays undergo outside an HPGe detector active zone, Fatt-factor and (ii) the probability for an energy degradable gammaray interaction with the detector material, Feff-factor. Both factors can be calculated analytically.

## 4. Experimental steps and results

In this study, the reference material IAEA-SOIL-7 (International Atomic Energy Agency (2000) [47] was analysed as a small cylindrical sample (SS), �200 mg, and as a large cylindrical sample (LS), �5 g. Neutron flux monitors and Al-0.1% Au disc, IRMM-530R (6 mm diameterdisc and 0.1 mm high) were used.

To carry out these experiments, according to Menezes and Jaćimović [16], the vials were prepared this way: (i) Vial 1, the large sample (LS): an aliquot of about 5 g of reference material IAEA-SOIL-7 was sealed in a polyethylene vial of 1.3 cm diameter and filled up to 3.6 cm high. The first neutron flux monitor was placed below ampoule, the second inside the ampoule on the top of the sample, and the third outside the vial. Air space between the sample and top of vial was filled with cellulose paper; (ii) Vial 2: six polyethylene vials (9 mm in diameter and 5 mm high) filled with reference material IAEA-SOIL-7 were stacked with neutron flux monitors in sandwich form and inserted into a 5 cm high polyethylene vial; (iii) Vial 3, the small sample (SS): an aliquot of about 200 mg of reference material was sealed in a polyethylene vial (diameter of 9 mm and 5 mm high), stacked together with neutron flux monitors and inserted in a 5-cm-high vial. Air space between the sample and top of ampoule was filled with cellulose paper; (iv) Vial 4: the large sample (LS) was filled in with a soil aliquot, 3.6 cm high and 1.3 cm in diameter. After being prepared, each vial was inserted in the "rabbit". Figure 1 shows a scheme of the prepared vials.

#### 4.1. Detector efficiency over the volume source

neutron self-shielding; Q0,m(α) and Q0,a(α) are resonance integral (1/E1 + <sup>α</sup>

Note that the Fc,Au-factor, as defined in Eq. (2), is proportional to the epithermal neutron flux density and directly indicates a gradient in epithermal flux density. In this study, the Fc,Aufactor was calculated by KayWin software based on several Al-0.1%Au monitors irradiated

The k0-method of NAA requires a precise technique to calculate full-energy peak detection efficiency (εp) of an HPGe detector for diversified samples and various counting geometries. The procedure provided by Moens et al. [46] presented a semi-empirical approach that has

a. A "reference" counting geometry is chosen to measure a set of calibrated point sources at a

b. For a sample, the εp,geom for particular gamma energy is expressed by employing the concept of the effective solid angle (Ωeff ), with "ref" denoting the reference geometry and

It is important to mention that by the definition of the effective solid angle, two factors are included: (i) the attenuation effects which gamma rays undergo outside an HPGe detector active zone, Fatt-factor and (ii) the probability for an energy degradable gammaray interaction with the detector material, Feff-factor. Both factors can be calculated ana-

In this study, the reference material IAEA-SOIL-7 (International Atomic Energy Agency (2000) [47] was analysed as a small cylindrical sample (SS), �200 mg, and as a large cylindrical sample (LS), �5 g. Neutron flux monitors and Al-0.1% Au disc, IRMM-530R (6 mm diameter-

To carry out these experiments, according to Menezes and Jaćimović [16], the vials were prepared this way: (i) Vial 1, the large sample (LS): an aliquot of about 5 g of reference material IAEA-SOIL-7 was sealed in a polyethylene vial of 1.3 cm diameter and filled up

Ωgeom Ωref

εp,geom ¼ εp,ref �

section ratio; α is the epithermal flux distribution parameter.

94 Advanced Technologies and Applications of Neutron Activation Analysis

3.3. Gamma-ray attenuation within the sample during counting

been introduced in KayWin software via option SOLCOI.

together with the samples in sandwich form.

The basic principles are:

lytically.

large distance, e.g., 15–20 cm;

"geom" the actual one, Eq. (3):

4. Experimental steps and results

disc and 0.1 mm high) were used.

) to 2200 m s�<sup>1</sup> cross-

(3)

In this step, the influence of distance sample-detector for small and large cylindrical samples based on gamma efficiency was verified. The LS, Vial 1, was measured at 2, 5, 10 and 20 cm sample-detector distances. The gamma efficiency values, ɛp, at sample-detector distances related to several gamma lines (non-coincidence gamma lines) and respective nuclides were given by KayWin software, [39] when calculating the elemental concentration of the large cylindrical sample. The efficiency values were also obtained by ANGLE software [41]. Table 1 displays examples of the non-coincidence gamma energies for each nuclide determined and the respective ratio of each ɛ<sup>p</sup> to ɛ<sup>p</sup> of the reference distance sample-detector, 20 cm, for KayWin and ANGLE.

Figure 1. Vials prepared to carry out the experiments: Vial 1, large sample with reference material; Vial 2, with six small samples with reference material; Vial 3, with one small sample filled with reference material and Vial 4, with large sample filled with soil.


4.2. Neutron self-shielding and the spatial neutron flux distribution factors

In this methodology development, the KayWin [39] and MATSSF software [45] (specific to calculate the correction factor to thermal and epithermal neutron self-shieldings, Gth and Ge, respectively), were applied. A soil sample in cylindrical geometry, large sample, with diameter of 13 mm and 36 mm high was chosen to be studied. The composition, CaCO3 (80%) and SiO2 (20%), was

Figure 3. Gamma efficiency normalised to 20 cm obtained by ANGLE software for the large cylindrical sample, LS, Vial 1.

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The KayWin calculated Gth equal to 0.997, while for the same configuration, the MATSSF obtained Gth equal to 0.998. There is a small difference from 1.0 for Gth, thermal neutron selfshielding. Due to this, no correction for thermal neutron self-shielding in the geological large sample was necessary. The Ge was considered negligible because of such experimental setup, i.e., Ge = 1.0. The same approach has been taken for biological samples studied in this work

To verify the axial and radial distributions of fast and thermal neutron fluxes in the same vial, Vial 4, experiments were carried out and are described in Jaćimović [48], and Menezes and partners [37], based on the experiment performed by Jaćimović and partners [40]. For these experiments, iron wires (99.9% Fe from Mallinckrodt, USA, 0.4 mm in diameter and 5 cm in

b. 54Fe(nf,p)54Mn, 312.2 day half-life, gamma emission of 834.8 keV from 54Mn.

59Fe, 44.50 day half-life, gamma emissions of 1099.3 keV and 1291.6 keV from 59Fe;

assumed because these two components are typically major constitutions in soil matrices.

4.2.1. Neutron self-shielding

(see Section 5), where Gth = Ge = 1.0.

4.2.2.1. Axial neutron flux gradient

length) were used.

a. 58Fe(nt,γ)

4.2.2. Spatial neutron flux distribution factors

During irradiation, the reactions were the following:

Table 1. Non-coincidence gamma lines: ratio of gamma efficiency (ɛp) determined for a gamma line at a distance to gamma efficiency at reference distance sample-detector for the large sample, reference material IAEA-SOIL-7, Vial 1.

Figure 2. Gamma efficiency normalised to 20 cm obtained by KayWin software for the large cylindrical sample, LS, Vial 1 [16].

Figures 2 and 3 display the gamma efficiency, ɛp, calculated by gamma energy for distance sample-detector normalised to 20 cm for the HPGe detector D4. The figures show a good agreement—after 200 keV—between the ratio's efficiency, ɛp, obtained by KayWin and ANGLE software at 2, 5, 10 and 20 cm and normalised to efficiency calculated at 20 cm.

Figure 3. Gamma efficiency normalised to 20 cm obtained by ANGLE software for the large cylindrical sample, LS, Vial 1.

## 4.2. Neutron self-shielding and the spatial neutron flux distribution factors

#### 4.2.1. Neutron self-shielding

In this methodology development, the KayWin [39] and MATSSF software [45] (specific to calculate the correction factor to thermal and epithermal neutron self-shieldings, Gth and Ge, respectively), were applied. A soil sample in cylindrical geometry, large sample, with diameter of 13 mm and 36 mm high was chosen to be studied. The composition, CaCO3 (80%) and SiO2 (20%), was assumed because these two components are typically major constitutions in soil matrices.

The KayWin calculated Gth equal to 0.997, while for the same configuration, the MATSSF obtained Gth equal to 0.998. There is a small difference from 1.0 for Gth, thermal neutron selfshielding. Due to this, no correction for thermal neutron self-shielding in the geological large sample was necessary. The Ge was considered negligible because of such experimental setup, i.e., Ge = 1.0. The same approach has been taken for biological samples studied in this work (see Section 5), where Gth = Ge = 1.0.

## 4.2.2. Spatial neutron flux distribution factors

## 4.2.2.1. Axial neutron flux gradient

Figures 2 and 3 display the gamma efficiency, ɛp, calculated by gamma energy for distance sample-detector normalised to 20 cm for the HPGe detector D4. The figures show a good agreement—after 200 keV—between the ratio's efficiency, ɛp, obtained by KayWin and ANGLE software at 2, 5, 10 and 20 cm and normalised to efficiency calculated at 20 cm.

Figure 2. Gamma efficiency normalised to 20 cm obtained by KayWin software for the large cylindrical sample, LS, Vial 1 [16].

Table 1. Non-coincidence gamma lines: ratio of gamma efficiency (ɛp) determined for a gamma line at a distance to gamma efficiency at reference distance sample-detector for the large sample, reference material IAEA-SOIL-7, Vial 1.

Large sample ratio (ɛ<sup>p</sup> at specific distance (cm) to ɛ<sup>p</sup> reference distance (cm) sample-detector)

20/20 10/20 5/20 2/20 20/20 10/20 5/20 2/20

KayWin ANGLE

96 Advanced Technologies and Applications of Neutron Activation Analysis

Sm-153 103.2 1.000 2.837 6.450 12.749 1.000 2.834 6.461 12.915 Ce-141 145.4 1.000 2.785 6.210 12.079 1.000 2.778 6.214 12.224 Sc-47 159.4 1.000 2.770 6.147 11.902 1.000 2.764 6.150 12.043 Au-199 208.2 1.000 2.734 5.987 11.455 1.000 2.727 5.989 11.589 Ru-97 215.7 1.000 2.730 5.970 11.405 1.000 2.724 5.974 11.546 Pa-233 300.1 1.000 2.699 5.832 11.024 1.000 2.693 5.838 11.163 Pa-233 311.9 1.000 2.697 5.821 10.993 1.000 2.690 5.827 11.132 Cr-51 320.1 1.000 2.695 5.814 10.972 1.000 2.688 5.819 11.111 Nd-147 531 1.000 2.667 5.693 10.637 1.000 2.660 5.695 10.763 As-76 559.2 1.000 2.665 5.682 10.607 1.000 2.657 5.685 10.733 Sb-122 564.2 1.000 2.664 5.680 10.602 1.000 2.657 5.683 10.728 Zn-65 1115.5 1.000 2.635 5.555 10.258 1.000 2.629 5.560 10.386 Fe-59 1291.6 1.000 2.630 5.532 10.194 1.000 2.623 5.538 10.323 K-42 1524.7 1.000 2.624 5.508 10.130 1.000 2.618 5.514 10.258 Sb-124 1691 1.000 2.621 5.495 10.094 1.000 2.615 5.502 10.223

Nucl. Non-coinc. gamma lines (keV)

> To verify the axial and radial distributions of fast and thermal neutron fluxes in the same vial, Vial 4, experiments were carried out and are described in Jaćimović [48], and Menezes and partners [37], based on the experiment performed by Jaćimović and partners [40]. For these experiments, iron wires (99.9% Fe from Mallinckrodt, USA, 0.4 mm in diameter and 5 cm in length) were used.

During irradiation, the reactions were the following:


The characterisation of neutron flux gradients (axial and radial) in the irradiation channels in the carousel facility was calculated. The calculation was based on the specific activities of 59Fe based on the mean value of the relative specific activities obtained for both gamma lines of 59Fe (thermal neutrons) and 54Mn (fast neutrons) applying the KayWin software. After decay time, about 2 weeks, the wires were cut into five 1-cm-pieces and submitted to gamma spectrometry on an HPGe detector D4 with 50% relative efficiency. The average specific activity of 59Fe was calculated based on the activity of 1099.3 and 1291.6 keV peaks and for 54Mn, on the peak of 834.8 keV.

One experiment was developed with one big vial filled with different materials, namely density, clay and air. The iron wires were placed in the vial: one in the centre and four near the wall of the polyethylene vial (3 cm in diameter and 5 cm high filled with clay) between the vial wall and the clay. Figure 4, position from the bottom (A = 0–1 cm) to top (E = 4–5 cm), related to thermal neutrons, shows the axial distributions for clay-air. The values of 59Fe were normalised to the average value of all the 1 cm Fe pieces. It can be observed that for thermal neutrons, the axial gradient in the geological sample is about 2%/cm. Figure 5, also related to thermal neutrons, shows the normalised radial distribution for clay-air. The figure points out that radial gradient for thermal neutrons in clay is about 2%/cm.

4.3. Gamma-ray attenuation within the sample during counting

and apply correction factors.

1291.6 keV from 59Fe, Vial 4 [37].

Menezes and Jaćimović [16].

results

The programme KayWin makes several corrections as already mentioned in the subsection 3.3, Gamma-ray attenuation within the sample during counting, during elemental concentration calculations. As the values obtained for IAEA-SOIL-7 for small and large samples were according to recommended values, according to next subsection 5 (Comparison between small and large samples' elemental concentration results), it was not necessary to develop more tests

Figure 5. Radial gradient for thermal neutrons in clay-air in the IC-7 irradiation channel of the TRIGA reactor. The values are normalised related to 59Fe and error bars are calculated based on the average statistics counting of 1099.3 and

An Overview of the Establishment of Methodology to Analyse up to 5g-Sample…

http://dx.doi.org/10.5772/intechopen.83812

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5. Comparison between small and large samples' elemental concentration

KayWin software calculated the efficiencies of the large sample accordingly, and the calculated Fc,Au–factors for the large sample obtained for Al-0.1% Au monitors were described by a linear equation. Then, it was decided to verify the experimental mass fractions for the small (Vial 3) and the large sample (Vial 1). The samples were measured at 2, 5, 10 and 20 cm at detector D4 (50% relative efficiency), and the elemental concentrations were calculated for each distance and for several distances, called RP, a routine procedure of analysis for customers, i.e., suitable distance sample-detector depending on the activity/dead-time. The experimental results and recommended values for reference material IAEA-SOIL-7 calculated by KayWin are shown in

Table 2 shows the normalised values of small and large samples to IAEA-SOIL-7 recommended data. It is possible to observe that majority of results are within 95% of confidence interval for assigned values. For the small sample, 88% of the results presented deviations from the recommended values lower than 10%, while for cylindrical samples, the deviations were 74%. For both samples measured at 10 cm, they presented 12% of deviations, and it was the best

#### 4.2.2.2. Fc,Au-factor

It was assumed that the Fc,Au-factor value is the correspondent to the average height of the sample. The Fc,Au-factors, calculated by KayWin based on Al-0.1%Au monitors in Vials 1 and 2, were used to verify the trend of axial gradient. Menezes and Jaćimović [16] pointed out that the Fc,Au-factors have a linear trend.

Figure 4. Axial gradient for thermal neutrons in clay-air in the IC-7 irradiation channel of the TRIGA reactor. The values are normalised related to 59Fe and error bars are calculated based on the average statistics counting of 1099.3 and 1291.6 keV from 59Fe, Vial 4 [37].

Figure 5. Radial gradient for thermal neutrons in clay-air in the IC-7 irradiation channel of the TRIGA reactor. The values are normalised related to 59Fe and error bars are calculated based on the average statistics counting of 1099.3 and 1291.6 keV from 59Fe, Vial 4 [37].

#### 4.3. Gamma-ray attenuation within the sample during counting

The characterisation of neutron flux gradients (axial and radial) in the irradiation channels in the carousel facility was calculated. The calculation was based on the specific activities of 59Fe based on the mean value of the relative specific activities obtained for both gamma lines of 59Fe (thermal neutrons) and 54Mn (fast neutrons) applying the KayWin software. After decay time, about 2 weeks, the wires were cut into five 1-cm-pieces and submitted to gamma spectrometry on an HPGe detector D4 with 50% relative efficiency. The average specific activity of 59Fe was calculated based on the activity of 1099.3 and 1291.6 keV peaks and for 54Mn, on the peak of

One experiment was developed with one big vial filled with different materials, namely density, clay and air. The iron wires were placed in the vial: one in the centre and four near the wall of the polyethylene vial (3 cm in diameter and 5 cm high filled with clay) between the vial wall and the clay. Figure 4, position from the bottom (A = 0–1 cm) to top (E = 4–5 cm), related to thermal neutrons, shows the axial distributions for clay-air. The values of 59Fe were normalised to the average value of all the 1 cm Fe pieces. It can be observed that for thermal neutrons, the axial gradient in the geological sample is about 2%/cm. Figure 5, also related to thermal neutrons, shows the normalised radial distribution for clay-air. The figure points out

It was assumed that the Fc,Au-factor value is the correspondent to the average height of the sample. The Fc,Au-factors, calculated by KayWin based on Al-0.1%Au monitors in Vials 1 and 2, were used to verify the trend of axial gradient. Menezes and Jaćimović [16] pointed out that

Figure 4. Axial gradient for thermal neutrons in clay-air in the IC-7 irradiation channel of the TRIGA reactor. The values are normalised related to 59Fe and error bars are calculated based on the average statistics counting of 1099.3 and

that radial gradient for thermal neutrons in clay is about 2%/cm.

98 Advanced Technologies and Applications of Neutron Activation Analysis

834.8 keV.

4.2.2.2. Fc,Au-factor

the Fc,Au-factors have a linear trend.

1291.6 keV from 59Fe, Vial 4 [37].

The programme KayWin makes several corrections as already mentioned in the subsection 3.3, Gamma-ray attenuation within the sample during counting, during elemental concentration calculations. As the values obtained for IAEA-SOIL-7 for small and large samples were according to recommended values, according to next subsection 5 (Comparison between small and large samples' elemental concentration results), it was not necessary to develop more tests and apply correction factors.
