1 Introduction

Both X- and gamma ray photons are of ionizing electromagnetic radiation (IEMR) types and since it is mass-less and uncharged, their energies are sufficient to ionize the atoms of any material they interact with. Moreover, penetrating capabilities of X- and gamma-ray photons in material is quite high compared to other radiations [1]. It is quite possible for us or any electronic equipment to be exposed to this kind of radiation in our daily life. The most practical way to well control radiation dose to a level that cannot be harmed is to use an effective shielding material. Although lead (Pb) is superior over other metal based materials because of its high density, high atomic number and low cost, there are some important drawbacks which limit its usages and application fields [2].

Except many other absorbers such as alloy [3, 4], ceramics [5], green product [6], granite [7, 8], rocks [9] etc., composite materials which can be produced by reinforced various matrix and inorganic fillers exhibit great potential as novel shielding materials. Especially, the most preferred matrix materials as traditional shielding composites because of their efficient shielding ability, easy prepared, light weight, and multifunctional design are polymers [10]. In view of this, there are various investigations on the radiation shielding features of different polymer doped composites [11,12,13,14,15]. Moreover, the exposure buildup factors (EBF) are the important quantities utilized in determining the distribution of photon flux in irradiation environment. These coefficients correspond to the ratio of the total detector response to that of un-collided photon and are used to assess the corrected response to the un-collided photons by including the contribution of the scattered photons. Among the EBF estimations, it has been found that geometric–progression (G–P) fitting technique is the most suitable to reproduce coefficients with better precision.

In this study, transition metal (namely Zn) as filling content enhances the chemical stability of material. This paper contains the detailed shielding and EBF coefficients to reveal an alternative material which consisted of light weight polymer composites for attenuation of high energetic X- and gamma-rays, as well as mechanical features of the investigated Zn-doped composites.

2 Materials and methods

2.1 Sample preparation

The unsaturated polyester (UP) and zinc (Zn) contents were used as resin and functional fillers in the synthesized polymer composites, respectively. To start and accelerate the formation process, cobalt octoate (CO) and methyl ethyl ketone peroxide (MEKP) were included as initiator and accelerator materials, respectively. At first, the essential contents were weighed in appropriate proportions with the help of the precision balance. Thereafter, the Zn filler was added to the UP resin in 2, 4, 6, 8, and 10% (Fig. 1a) by weight which was chosen based on its weight. The mixing process kept for 5 min to wet completely all the fillers. MEKP and CO were contained to the present mixture, respectively, and mixed for 3 min. It is poured into various molds that will take shape and was left to harden. Then, the composites with 2 cm diameter and 0.5, 1.0, 2.0 and 3.0 cm thicknesses (Fig. 1b) were prepared and cured in convenient conditions for 28 days. The elemental compositions and densities of the prepared Zn-doped composites are listed in Table 1.

Fig. 1
figure 1

Images of a the prepared composites and b Zn (10%) samples at different thicknesses

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Table 1 The elemental compositions and densities of the prepared Zn-doped composites
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2.2 Theoretical calculation

A photon beam with the initial intensity (I0) after passing across the material reduces to the attenuated intensity (I). The relation of this reduction is defined by Lambert–Beer rule [16]:

$$\mu = - \frac{{\ln \frac{I}{{I_{0} }}}}{x},$$
(1)

where μ represents the linear attenuation coefficient (cm−1) of the material and x is thickness of the sample.

After calculating μ values, mass attenuation coefficients (µ/ρ) of the studied polyester-based composites can be estimated dividing the μ with the density (ρ) of the samples [17]:

$$\mu_{{\text{m}}} = \frac{\mu }{\rho } = \sum w_{i} \left( {\frac{\mu }{\rho }} \right)_{i} ,$$
(2)

where wi and (µ/ρ)i shows the weight fraction and mass attenuation coefficients for the individual element in any compound or mixture.

Some useful quantities e.g. total atomic and electronic cross sections, the effective atomic number and electron density, etc. can be derived with help of this parameter. The total atomic cross section (\(\sigma_{{\text{a}}}\)) can be determined using the following relation [18]:

$$\sigma_{{\text{a}}} = \frac{{\left( {\mu_{{\text{m}}} } \right)}}{{N_{{\text{A}}} \mathop \sum \nolimits_{i} \frac{{w_{i} }}{{A_{i} }}}} .$$
(3)

It is expressed in cm2/atom.

The total electronic cross section (\(\sigma_{{\text{e}}}\)) can be written as [19]:

$$\sigma_{{\text{e}}} = \frac{1}{N}\mathop \sum \limits_{i} \mu_{{{\text{m}}i}} \frac{{f_{i} A_{i} }}{{Z_{i} }},$$
(4)

where \(Z_{i}\) and \(f_{i}\) are the atomic number and the fractional abundance of the ith element. It is expressed in cm2/electron.

The Zeff can be derived from σe and σa [20]:

$$Z_{{{\text{eff}}}} = \frac{{\sigma_{{\text{a}}} }}{{\sigma_{{\text{e}}} }}.$$
(5)

The electron density (NE) is the electron numbers per unit mass of the interacting matter and written as follows [18]:

$$N_{{\text{E}}} = \left( {n_{{{\text{tot}}}} N} \right)\frac{{Z_{{{\text{eff}}}} }}{{A_{{{\text{tot}}}} }}.$$
(6)

Half value layer (HVL) equals to the thickness of the absorber at which the intensity of the photons after travelling is minimized to 50% of the initial photon intensities. HVL (cm) can be calculated with Eq. (7) [21]:

$${\text{HVL}} = \frac{\ln 2 }{\mu }.$$
(7)

Mean free path (MFP) is a parameter that plays a significant role to calculate the exponential shielding of gamma photon. The shorter MFP for any sample means more photons interaction with this sample, hence giving shorter distance between two interactions [22]. MFP (cm) is estimated using the following relation:

$${\text{MFP}} = \frac{1 }{\mu }.$$
(8)

The radiation protection efficiency (RPE) of any material can be found by Eq. (9) [23, 24]:

$${\text{RPE}} \left( \% \right) = \left( {1 - \frac{I}{{I_{0} }}} \right) \times 100.$$
(9)

The following equation is considered to estimate the experimental uncertainties in the mass attenuation coefficient analyses [25, 26]:

$$\Delta \mu_{{\text{m}}} = \frac{1}{\rho x}\sqrt {\left( {\frac{\Delta I}{I}} \right)^{2} + \left( {\frac{{\Delta I_{0} }}{{I_{0} }}} \right)^{2} + \ln \left( {\frac{\Delta I}{I}} \right)^{2} \left( {\frac{\Delta \rho x}{{\rho x}}} \right)^{2} } ,$$
(10)

where ρ are the density of the sample, ΔI0 and ΔI are the uncertainties for original (I0) and attenuated (I) counts, respectively.

2.3 Shielding measurements

Photon shielding properties of the prepared polymer-based composites with various Zn amounts (2, 4, 6, 8 and 10%) are assessed experimentally by means of mass attenuation coefficients (µ/ρ) employing a high purity germanium (HPGe) detector in conjunction with multi-channel analyzer (MCA). The experimental setup and geometry of the testing equipment is represented in Fig. 2. The photo-peak energies and nuclear data emitted by the 241Am, 152Eu, 137Cs, 133Ba, 60Co, 57Co, 54Mn and 22Na radioactive point sources can be found from [27]. More detail information on experimental system can be taken from our previous studies [3, 4, 6]. The analysis of the observed photo-peaks in data acquisitions were done with an MAESTRO software [28, 29]. Their net areas were determined with help of the least-squares fitting method through the Origin 7.5 program (demo). On the other hand, to obtain the small differences among experimental, theoretical, and simulation results, uncertainties in thickness of the sample, original intensity (I0), and attenuated photon intensity (I) for attenuation coefficient values have considered as given in Eq. 10.

Fig. 2
figure 2

Transmission geometry

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2.4 MCNPX calculations

Monte Carlo N-Particle Transport Code System-extended (MCNPX) has been carried out to approve the experimental µ/ρ values between 59.5 and 1408 keV photon energy range. Monte Carlo N-Particle Transport Code System-extended (MCNPX) has been carried out to approve the experimental µ/ρ results. Figure 3 demonstrates the MCNPX 3-D view of photon shielding design with several simulation elements, i.e., a point radioactive source, the composite sample, Pb blocks to prevent from the scattered photons, Pb collimator for primary radiation beam and F4 tally mesh detection field. More details on simulation layout can be found from our previous studies [4, 30].

Fig. 3
figure 3

a Simulation setup of mass attenuation coefficients. b 3-D layout of modeled 3 × 3 inch NaI(Tl) detector obtained from MCNPX Visual Editor (VE X_22S)

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2.5 Exposure buildup factors (EBF)

The exposure buildup factors (EBF) are calculated using G–P fitting technique for incident photon energy of 0.015–10 MeV. The estimations on the EBF of the investigated composites are carried out in three steps; these are: the estimations of (a) equivalent atomic number (Zeq), (b) the G–P fitting parameters (b, c, d, a and Xk) and (c) the determination of EBF values. More details on EBF calculations can be found in our previous studies [31].

2.6 Compressive strength tests

The strength values were determined by compressive strength test on polymer composite samples. The compressive strength test was performed according to TS EN 12390-3 [32]. The compressive strengths of the cube samples were made in the press with an automatic loading speed control with a capacity of 30 tons.

3 Results and discussions

3.1 Nuclear radiation shielding performance

Mass attenuation coefficients (µ/ρ) of Zn-filled polyester based composites using the experimental and theoretical (XCOM) methods are represented in Fig. 4 and listed in Table 2. It is clear that the µ/ρ values of the studied composites dramatically reduce with the increment of photon energy, which is due to several interaction processes of gamma photons with materials. Looking at Fig. 4, the variation between µ/ρ parameter and photon energy can be evaluated in two different regions while the second region (ii) lies from 400 to 1400 keV. Along first region between 50 and 400 keV, the predominant interaction mode which is related to energy (E−3.5) and atomic number (Z4−5) is defined as photoelectric effect (PE). The energy level differences of the atoms forming composite matches the low energy photons. Therefore, this mode happens easily and leads to decrease aggressively µ/ρ values at 50 keV. In the second region (E > 400 keV), the possibility of PE is gradually reduced since the energy emitted by radioactive source is higher than the energy demanded for the electron transition and Compton scattering (CS) mode whose cross section is proportional to E−1 and Z becomes dominant. Thus, the µ/ρ values of all the composites slightly decrease with the increase of photon energy and are quite close to each other as seen in Fig. 4.

Fig. 4
figure 4

Comparison of the experimental, theoretical, and simulation mass attenuation coefficients for the studied samples

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Table 2 Experimental, XCOM and MCNPX mass attenuation coefficients of Zn-based polyester composites
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Additionally, XCOM software and MCNPX code are carried out to confirm the experimental results. The theoretical and simulation µ/ρ were estimated considering the elemental compositions of the composites at the various energies of 59.5–1408 keV. The relative deviation (RD) between mass attenuation coefficients through experimental and XCOM as well as MCNPX can be calculated as below relation [19, 33]:

$${\text{RD}} \left( \% \right) = \left| {\left( {\frac{{\frac{\mu }{\rho }_{\exp - } \frac{\mu }{\rho }_{{\text{XCOM,MCNPX}}} }}{{\frac{\mu }{\rho }_{\exp } }}} \right)} \right| \times 100.$$
(11)

As plotted in Fig. 5, RD values of different composites at certain photon energies are found to be 0.02–4.92% and 0.05–6.22% for experimental-XCOM and experimental-MCNPX, respectively, and it is clear seen that they are quite compatible. The two main reasons of very minor discrepancy between two methods: (i) detecting a part of the scattered photons with low scattering angle by the detector due to the narrow beam system (ii) to the mixture rule that disregards the interactions among atoms forming material.

Fig. 5
figure 5

The relative deviations (RD) between a experimental-XCOM and b experimental-MCNPX results

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The RPE parameter corresponds to the measure on photons that can be attenuated by the polymer based composite and can be calculated with help of the intensities of initial and attenuated photons for the polymer composites at the studied energies. The obtained results are graphically demonstrated in Fig. 6. It is clear from this figure that the polymer composites possess high shielding performance at low energy. Among the synthesized composites, the highest RPE value is observed to be 72.04% for the Zn (10%) sample at 59.5 keV and 3 cm thickness. Additionally, gamma spectra measurements were obtained for Zn (10%) with different thicknesses of 0.5, 1, 2 and 3 cm and their RPEs were determined (Fig. 7). This parameter is proportional to the thickness of the material. Moreover, it can be easily said from Figs. 6 and 7 that it minimizes with the increase in energy. Therefore, we can deduce that the Zn (10%) has best attenuating performance than the rest of the other polymer composites, and all absorbers are more effective for shielding the low energy photons.

Fig. 6
figure 6

Radiation protection efficiency (RPE) for the prepared composites at 3 cm thickness

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Fig. 7
figure 7

Radiation protection efficiency (RPE) for the prepared composites at different thicknesses

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The Zeff attitudes of the Zn-based composites towards photon energies are plotted in Fig. 8. These results are varying with photon energies form 59.5 to 1408 keV. From Fig. 8, there is increasing order of Zeff: Zn (2%) > Zn (4%) > Zn (6%) > Zn (8%) > Zn (10%). The composite tagged as Zn (10%) has the highest Zeff at all the analyzed energies and may be resulting from possessing a maximum proportion of Zn. Higher Zeff values of Zn (10%) indicate that it interacts with more gamma photons. Hence, while gamma photons have the lowest penetrating value through Zn (10%), photon penetration is highest in Zn (2%) sample. Moreover, one can easily understand from this figure that the Zeff reduces with the increasing of the energy for the prepared composites. These trends in Zeff depending on the energy are in good agreement with the data reported by Akman et al. [6] and Sharma et al. [11]. Additionally, the behaviors of Neff versus energy are almost similar to those of Zeff on account of inversely proportional to the mean atomic weight of the composite as viewed in Fig. 9. Therefore, Zn (2%) and Zn (10%) composites with lower and larger atomic weights have lowest and highest Neff values.

Fig. 8
figure 8

Comparison of effective atomic number (Zeff) for the prepared composites

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Fig. 9
figure 9

Effective electron density (NE) for the prepared composites

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MFP parameter is significant in terms of directly and shortly revealing the attenuation performance of any material investigated to minimize radiation dose to an admissible level for environment health. Lowering MFP values of any composite material, corresponds to effective shield absorber. Figure 10 displays the results for MFP for Zn doped polyester composites. It is obvious that the changes of the MFP are found to be linearly dependent upon photon energy for the synthesized composites. It is observed that the highest and lowest values of MFP are Zn (2%) and Zn (10%) with densities of 1.301 and 1.322 g/cm3 (Table 1), respectively. It can be easily deduced that the MFP parameter is related to densities of materials and thus, the shielding performance is proportional to its density.

Fig. 10
figure 10

Theoretical MFP values of different Zn-based composites

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The HVL values of the Zn reinforced composites are estimated utilizing Eq. (8). Figure 11 demonstrated the variation in HVL data towards photon energy between 59.5 and 1408 keV. Similar to Fig. 10, HVLs of these samples aggressively increase depending on energy. The HVLs of the Zn (2%) > Zn (4%) > Zn (6%) > Zn (8%) > Zn (10%) composites are found to be 6.62, 6.61, 6.59, 6.58 and 6.56 cm at 661.6 keV, respectively. Therefore, the increase in the density as a result of containing Zn content enhances more than about 10% HVL decrease.

Fig. 11
figure 11

Theoretical HVL values of different Zn-based composites

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3.2 Dependence of EBF values on incident photon energy

Tables 3, 4, 5, 6 and 7 tabulates the calculated equivalent atomic number (Zeq) and EBF G-P fitting coefficient values for Zn (2%), Zn (4%), Zn (6%), Zn (8%) and Zn (10%) composites against photon energies of 0.015–10 MeV, respectively. The variation of equivalent atomic number (Zeq) values as a function of photon energy for composite samples is presented in Fig. 12. Additionally, the changes in EBF depending on incident photon energy at penetration depths such as 1, 5, 10, 20, 30 and 40 mean free paths are graphically represented in Fig. 13. It is clear that the EBF possess low values in lower photon energy region. Similar to shielding quantities, the EBF trend demonstrated in Fig. 13 can be ascribed by partial photon interaction modes. At the low energies, as PE mode dominates, photons are removed or absorbed; thus possibility of the scattering is quite small. Subsequently, since CS mechanism is predominant at the intermediate energies, the EBF leads to a larger proportion of multiple scattering over absorption. It causes a reduction of photon energy without exact annihilation of the photon, thence the higher EBF.

Table 3 Zeq and G–P exposure buildup factor (EBF) coefficients for Zn (2%) based composites
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Table 4 Zeq and G–P exposure buildup factor (EBF) coefficients for Zn (4%) based composites
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Table 5 Zeq and G–P exposure buildup factor (EBF) coefficients for Zn (6%) based composites
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Table 6 Zeq and G–P exposure buildup factor (EBF) coefficients for Zn (8%) based composites
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Table 7 Zeq and G–P exposure buildup factor (EBF) coefficients for Zn (10%) based composites
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Fig. 12
figure 12

Variation of equivalent atomic number (Zeq) values as a function of photon energy for composite samples

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Fig. 13
figure 13

The changes in EBF with penetration depth at different photon energies

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3.3 Compressive strength analysis

When the strength values given in Fig. 14 are examined, it is seen that when zinc powder is added at 2% of polymer weight, the increased rate increases the pressure strength by 7% compared to the control. This result can be explained that zinc powder can provide a more compact structure in the composites and increase the strength. As Zn powder ratio increases, strength decreases. This reduction in the use of 8% Zn powder has reached up to 49%. When the data were examined, the best results were obtained from polymer composites produced using 2% Zn powder.

Fig. 14
figure 14

Compressive strength results

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4 Conclusions

In this study, the attenuation and compressive strength properties of Zn-based composites with the compositions (where % = 2, 4, 6, 8 and 10) have been investigated. Experimental μm values determined by gamma spectrometer in the photon energy range of 59.5–1408 keV were confirmed with MCNPX code and XCOM software. From Zeff, MFP and HVL results, the adding of Zn content to composite possesses a positive impact on photon shielding characteristics. Therefore, it has been found that Zn (10%) composite containing high amount of Zn has superior gamma radiation shielding effectiveness than the rest of the prepared samples. Moreover, G-P method in calculation of EBF at further deep penetrations for different absorbers can be employed in many works since the collected data will be helpful in the confirmation of ANSI/ANS 6.4.3-1991 standards. Consequently, this composite may be considered as an alternative protective material for photon attenuation practices due to its superior in light weight, easy manufacturing, high mechanical performance, and designability.