Introduction

Nuclear technology is one of the generic technologies and it becomes a part of our life as it started to be used in a variety of fields. Therefore, radiation protection physics developed and become popular subject for researcher. In the radiation protection development of shielding material is important and rocks are widely used especially as building and architectural covering stones in many engineering structures and also as aggregate to produce concrete and some other construction material. Thus, it is important to investigate radiation shielding properties of rocks.

The radiation property of a material is expressed in terms of the linear attenuation coefficient μ (cm-1) and it is defined as the probability of a radiation interacting with a material per unit path length depending on the intensity of the incident gamma rays, atomic number and density of shielding material (Woods 1982; Akkurt et al. 2005). Although lead and lead based materials are conventional materials to be used in radiation shielding, due to its hazardous effect some other materials needed to be developed. Being as the conventional building materials, the concrete is one of the important construction materials and it is made up mainly rock based material. Thus, there are a number of previous works done to investigate radiation shielding properties of concretes and rocks but they were mostly as calculation works as the experiment is more difficult (Shamsan et al. 2018; Singh et al. 2020; Hossain et al. 2020; Mahmoud et al. 2019; Rammah et al. n.d.; Al-Obaidi et al. 2020; Shah and Ravindra 2020; Sarıyer 2020; Çelen and Evcin 2020; Sarıyer and Kucer 2020; Akkurt et al. 2010; Gong et al. 2020; Kurtulus et al. 2020; Malidarrea et al. 2020; El-Agawany et al. 2020; Luo et al. 2019; Sayyed et al. 2020; Akkurt et al. 2012; Masoud et al. 2020; Akkurt et al. 2005b; Kaçal et al. 2019; Kaur et al. 2012; Akkurt et al. 2007; Jawad et al. 2019; Parlar et al. 2019; Akkurt et al. 2006; Akkurt et al. 2021; Kulali 2020; Tekin et al. 2020; Çelen 2021; Çelen et al. 2019).

In this work, in order to test radiation shielding properties of rock samples, those of detailed parameters have been measured and also simulated:

  • The linear attenuation coefficients (LAC, μ, cm-1) have been measured at 0.511, 0.835, and 1.275 MeV gamma ray energies.

  • The results were compared with the calculation obtained by using photon shielding and dosimetry (PSD) software.

  • The mass attenuation coefficients (MAC, μ/ρ, cm-1) have been simulated.

  • The mean free path (mfp), the half value length (HVL), and the tenth value length (TVL) have been obtained using Phy-X/PSD software.

  • The effective atomic number (Zeff), electron density (Ne), and equivalent atomic number (Zeq) have been calculated.

  • The exposure buildup factors (EBF) have been obtained.

  • The fast neutron effective removal cross section (ΣR cm-1) have been obtained.

Materials and method

Four different types of igneous class rock namely granite, granodiorite, black andesite, and normal andesite samples have been collected from various places in Turkey. The rocks were cutted in a spesific dimention in order to fit geometry of the spectrometer. The chemical compositions and densities of the selected rocks are given in Table 1. The linear attenuation coefficients of rocks have been measured at 0.511, 0.835, and 1.275 MeV gamma ray energies using the gamma spectrometer which contains a 3”×3” NaI(Tl) detector (Akkurt et al. 2020; Akkurt et al. 2014).

Table 1 Chemical contents of the igneous rocks (Çelen et al. 2019)
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The shematic view of the spectrometer is shown in Fig. 1. As it can be seen in this figure that the amplified signal from the detector is analysed by a 16 k channel Multi-Channel-Analyser (MCA) which communicates with computer. The MCA can analyse energy spectrum and conversion of channel to energy scale on the spectrum. Those of gamma rays have been obtained by 22Na and 54Mn radioactive sources. The gamma ray energy spectrum from 22Na source is given in Fig. 2 where 0.511 and 1.275 MeV peaks are clearly seen.

Fig. 1
figure 1

Experimental setup of gamma ray spectrometer

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Fig. 2
figure 2

Energy spectrum of attenuated and un-attenuated gamma rays for 22Na source

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In experimental study with the gamma spectrometer, it is a well-known rule and equation (so-called Lambert’s law) that the linear attenuation coefficient (LAC) can be obtained. This is described in Fig. 3 as schematically and is extracted using Eq. 1:

$$N={N}_0{e}^{-\mu x}$$
(1)
Fig. 3
figure 3

Description of gamma ray attenuation processes for a material

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where No is the initial number of gamma ray counts, N is the attenuated number of counts for gamma ray, μ is the linear attenuation coefficient of the shielding material in cm-1 and x is the thickness of shielding material in cm.

The number of counts for gamma rays of (No) and (N) are obtained from the counts under peaks of the energy spectrum in Fig. 2 where it is clearly seen that the No (dotted line) and N (full line) without and with rock samples between 22Na source and NaI(Tl) detector.

The measured linear attenuation coefficients (μ) were compared with the calculation obtained by using Phy-X/PSD software and some other parameters were also obtained using this software. The Phy-X/PSD is an open source code developed by Sakar et al. (Şakar et al. 2020) and it can be used as online [https://phy-x.net/PSD]. The code can simulate several parameters for shielding material for desired energy range of gamma rays.

Results and discussions

The linear attenuation coefficients (LAC) is a main parameters to test radiation shielding properties of any materials and the other parameters may be extracted using LAC. Thus the measurement have been performed at 0.511, 0.835, and 1.275 MeV gamma rays to obtain the LAC of four different rocks (as listed in Table 1) in this study. The obtained LAC results were compared with the online calculation obtained using Phy-X/PSD software. On the based of LAC results some other parameters such as, the mass attenuation coefficients (MAC), mean free path (mfp), half value length (HVL), tenth value length (TVL), effective atomic number (Zeff), effective electron density (Neff), effective conductivity (Ceff), equivalent atomic number (Zeq), and neutron removal cross section have also been calculated using Phy-X/PSD software.

The obtained LAC results both experimentally (for 0.511, 0.835, and 1.275 MeV gamma rays) and also simulated (for 10-3 to 105 MeV) have been displayed in Fig. 4. It can be seen from this figure that the agreement between simulation and experiment is good. It is also seen from this figüre that the LAC depends on incoming gamma ray energies and it varried with the varrying gamma ray energies. This is due to the well known reality of gamma ray interaction processes with the materials (Akkurt et al. 2005). The interaction of gamma rays with the matter is in three way depending on its energy.

  • Gamma rays can be absorbed by the material at low energy so-called photoelectric proceses (PE).

  • For the case of middle energy range some of gamma energy absorbed by material and some of gamma scattered. This is called Compton scattering processes (CS).

  • After 1.022 MeV energy pair production proceses (PP) is also possible. In this processes when gamma rays interact with the electric field of an atom a pair of electron-positron is created and thus konwn as pair production.

Fig. 4
figure 4

Measured and calculated LAC as a function of gamma ray energies for rocks

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The agreement between experiment and simulation can also be seen in Fig. 5 where the linear attenuation coefficients displayed as a function of gamma energy of 0.511, 0.835, and 1.275 MeV. It can also clearly be seen from this figure that the linear attenuation coefficients decreased with increasing gamma ray energy linearly (R2 is over 97% for all type rocks for both experiment and calculation).

Fig. 5
figure 5

Measured and simulated LAC results as a function of gamma rays of 0.511, 0.835, and 1.275 MeV

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When density of the material taken into account the parameters is called mass attenuation coefficient (MAC). It can be obtained by dividing LAC to density and the results obtained by Phy-X software were displayed in Fig. 6 for gamma ray energies of 10-3 to 105 MeV.

Fig. 6
figure 6

The calculated (Phy-X) MAC as a function of gamma ray energies for all types rocks

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It can be seen from this figure that similar distribution has been seen for MAC with the LAC. In Fig. 7, the LAC values have been displayed as a function of rock density and it is clearly seen the effect of density on the radiation shilding properties of rock.

Fig. 7
figure 7

The measured LACand comparison with Phy-X calculation as a function of density of rocks

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With the LAC value, the mean free path (mfp) of rock can be obtained. It is defined as identification of the average penetration length where a radiation can go in the shielding material before being interacting, have been obtained using Eq. 2:

$$mfp=\frac{1}{\mu }$$
(2)

The simulated mfp as a function of gamma ray energies were displayed in Fig. 8. It can be seen from this figure that the mfp increased upto 0.1 MeV sharply while slight increases observed upto 10 MeV after peaking at about 10 MeV then decreased. As the mfp directly related to LAC and thus the mfp depends on energy of the gamma rays.

Fig. 8
figure 8

The calculated mfp as a function of gamma ray energies for all types rocks

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For the case of HVL and TVL which are also two other important parameters in giving the best and desired thickness to attenuate the incident gamma rays. They are defined as the thickness of materials to stop half (%50) and to stop 10% of gamma rays and given by Eqs. 3 and 4 respectively:

$$HVL=\frac{Ln(2)}{\mu }$$
(3)
$$TVL=\frac{Ln(10)}{\mu }$$
(4)

The simulated results for HVL and TVL were displayed in Figs. 9 and 10 respectively and it is seen that the HVL and TVL increased sharply until 0.1 MeV, smooth increasing obtained between 0.1 and 10 MeV and become almost constant after 10 MeV.

Fig. 9
figure 9

Calculated HVL as a function of gamma ray energies for all types rocks

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Fig. 10
figure 10

Calculated TVL as a function of gamma ray energies for all types rocks

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This is due to the fact that the HVL and TVL are inversely proportional to LAC. This is a similar observation with the HVL and TVL of previous reports (Akkurt and Tekin n.d.). It can be concluded from this result that the selected rocks have good shielding effectiveness against low energy gamma. The obtained results show that R4 type rock has the lowest HVL and TVL, while the largest are found for R1 type rock.

The effective atomic number (Zeff), effective electron density (Neff), and equivalent atomic number (Zeq) are also anther important parameters to estimate radiation shielding properties for any material. It is defined by the Eq. 5 (Akkurt 2009):

$${Z}_{eff}=\frac{\sigma_a}{\sigma_{el}}$$
(5)

here σa and σel represent the total atomic cross section and the total electric cross section respectively. The σa is obtained via the total μ/ρ (Akkurt 2009):

$${\sigma}_a=\frac{1}{N}\ \frac{{\left(\mu /\rho \right)}_{material}}{\sum \limits_i\frac{w_i}{A_i}}$$
(6)

where, N is the Avogadro’s number, μ/ρ is total mass attenuation coefficients, Ai and wi are atomic weights (in gram) and fractional weights of the constituent of rocks respectively and the total electric cross section is obtained by the formula of (Akkurt 2009):

$${\sigma}_{el}=\frac{1}{N}\sum \limits_i\frac{f_i{A}_i}{Z_i}\left(\frac{\mu }{\rho}\right)i.$$
(7)

here fi is the number of atoms of element i relative to the total number of atoms of all elements in the mixture, (μ/ρ)i is the total mass attenuation coefficients of the ith element and Zi is the atomic number of the ith elements in a mixture.

The obtained Zeff as a function of gamma-ray energy is displayed in Fig. 11 for studied rocks. The values of the Zeff reaches maximum values upto 0.1 MeV and then decreased until 10 MeV while it is constant after this energy. In the comparison of experimental results obtained at 0.511, 0.835 and 1.275 MeV a good agreement have been found for studied rocks and those are displayed in Fig. 12.

Fig. 11
figure 11

Phy-X calculated Zeff as a function of gamma ray energies for all types rocks

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Fig. 12
figure 12

Measured and calculated Zeff as a function of gamma ray energies for rocks

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Figure 11 shows the Zeff of the studied rocks in the range of 10-3 to 105 MeV. The maximum values of Zeff occur at 0.01–0.1 MeV where it is large peaked. It stay constant until 10 MeV and then with slight increasing it was again stayed at constant until 105 MeV. In the first region, the photoelectric effect is dominant and thus the maximum values of Zeff for all rocks have been obtained. For the case of middle energy range, the Compton scattering is the key mode and thus the constancy in Zeff for this energies have been observed. This was in agreement with the some previous works reported in literature (Shamsan et al. 2018; Malidarrea et al. 2020; El-Agawany et al. 2020). In the comparison of Zeff for rock types it can be seen that the R4 type rock has highest values while R1 types has the minimum values of Zeff. This could be due to their chemical properties detailed in Table 1. In the comparison of Phy-X simulation with the experiment it is displayed in Fig. 12 for the studied rocks seperately. It is clearly seen that the agreement between measurements and simulation is very good for the studied rocks.

The electron densities (Neff) for all rocks are calculated using Eq. 8 (Akkurt 2009).

$${N}_e=\frac{{\left(\mu /\rho \right)}_{material}}{\sigma_{el}}$$
(8)

The calculated results as a function of gamma ray energy for all rocks types are displayed in Fig. 13. As seen from this figure that a similar structure with the Zeff has been obtained for all types rocks. This could be result of being inversely proportional to the average atomic weight of the material (Eq. 8).

Fig. 13
figure 13

Phy-X calculated Neff as a function of gamma ray energies for rocks

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The effective conductivity (Ceff) was obtained as a function of gamma ray energies for all types rocks and displayed in Fig. 14 where it can be seen that similar distribution with the Zeff and Neff have been obtained. On the other hand the the Ceff values of R1 and R2 types of rocks are higher than R3 and R4 types of rocks.

Fig. 14
figure 14

Calculated Ceff as a function of gamma ray energies for all types rocks

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For the case of equivalent atomic number (Zeq), it was obtained using Phy-X/PSD software for four types of rocks in the gamma energy range between 0.015 and 15 MeV. The obtained results are displayed in Fig. 15 where it can be seen that a similar structure has been observed for the studied rocks. The lowest Zeq values were obtained at low gamma ray energy region (below 0.03 MeV), it increased upto 1 MeV then decreased sharply while stay constant after this energy.

Fig. 15
figure 15

Calculated Zeq as a function of gamma ray energies for all type rocks

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Figures 16–17 are about gamma ray exposure buildup factors (EBF) for the studied rocks. In Fig. 16, the EBF are plotted as a function of gamma ray energies for various penetration depths (mfp: 1, 5, 10, 20, 30, 40 cm). It can be seen from this figure that the Gaussian distribution observed for the studied rocks and for all mfp. On the other hand, the wideness of the Gaussian peak is large for low mfp while it decreased with the increasing mfp. It is also clearly seen that EBF is low for high mfp for R3 an R4 type rocks. The relation beween rock types are shown in this figure. For the case of Fig. 17, the EBF displayed as a function of mfp for various gamma ray energies (0.015, 0.15, 1.5, and 15 MeV) and for the studied rocks. It can be seen from this figure that similar distribution has been obtained for the studied rocks. It can also be seen from those figures that a different distributions have been obtained for different energy. For the final investigation for those of rocks, the absorption ability for neutron has been obtained in terms of effective removal cross section using Phy-X/PSD software. This is displayed in Fig. 18 where it is clear that, the highest effective removal cross section achieved for the R1 type rock sample. This could be due to the density of rock as seen in Fig. 19 where the effective removal cross section displayed as a function of density of rocks. An 99% linearity has been obtained between the effective removal cross-section and density of rocks.

Fig. 16
figure 16

EBF as a function of gamma ray energies for various mfp of rocks

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Fig. 17
figure 17

EBF as a function of mfp for various gamma ray energies of rocks

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Fig. 18
figure 18

Neutron removal cross section for rock types

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Fig. 19
figure 19

Neutron removal cross section as a function of density of rocks

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Conclusions

The radiation shielding properties of rocks have been simulated and also measured at 0.511, 0.835, and 1.275 MeV using gamma spectrometer and simulated for gamma ray energies of 10-3-105 MeV using Phy-X/PSD software. It can be concluded from this work that

  • the LAC decreased when the gamma ray energy increased and this indicates that the rocks under study have high attenuating effectiveness at low energy.

  • Among the investigated rocks, R1 type rock has the highest LAC than others.

  • The R1 type rock has the highest MAC and LAC values in comparison with other rocks but it has the lowest mfp, HVL and TVL values.

  • This will concludes ones again that density of a materials is important for radiation shielding processes.

  • The values of Zeff, Neff Zeq are highest for R1type rock and lowest for R4 type rock.

  • For the case of EBF the highest value obtained for R1 type rock while the lowest value obtained for R4 type rock.

  • The neutron removal cross-section is also found that it is related to density and as gamma attenuation it is also depends on density of materials.

  • both neutron and gamma ray shielding directly related to density of a material and also energy dependent.