Investigation of Gamma Radiation Shielding Properties of Some Zinc Tellurite Glasses

The mass attenuation coefficient (m), half-value layer (HVL) and mean free path for xZnO-(100-x) TeO2, where x = 10, 20, 30, and 40 mol.%, have been measured with 0.662, 1.173 and 1.33 MeV photons emitted from Cs and Co using a 3  3 inch NaI(Tl) detector. Some relevant parameters, such as the effective atomic numbers (Zeff) and electron densities (Nel), of the glass samples have also been calculated in the photon energy range of 0.015–15 MeV. Moreover, exposure buildup factors (EBF) were estimated using the five-parameter Geometric Progression (G-P) fitting approximation for penetration depths up to 40 times the mean free path and within the same energy range of 0.015–15 MeV. The measured mass attenuation coefficients were found to agree satisfactorily with the theoretical values obtained using WinXCom. The effective atomic numbers (Zeff) and electron densities (Nel) were found to be the highest for a 40ZnO-60TeO2 glass in the energy range of 0.04–0.2 MeV. The 10ZnO-90TeO2 glass sample had lower values of gamma ray exposure buildup factors in the intermediate energy region. These data on the radiation shielding characteristics of zinc tellurite glasses may be useful for the design of gamma radiation shields.


1.
High-en radioiso kilometr extensiv importan against constitu their st preparat develop range of not pho and ther The additi y. 10,11 on shielding p such as mas omic number efers to the g material.S ld before an often of more the absorbe us codes, suc invariant em onal Standar -up factor d ndard energi p to a penetra es have been rent glass sa c tellurite gla ry out this w easured for t effective ato were calculat re buildup fa pths up to a type of el on sources, amma ray h as industry mixtures o on. 1-3Mate = 52), are w X-rays, gam of transpar ion shield.T ay good mec ion of ZnO properties of ss attenuatio r (Z eff ), elect exposure in Since a prima nd after the e general use ed dose. 13Th ch as the Ge mbedding met rds ANSI/AN data for 23 ies in the en ation depth o n performed amples, [20][21][22][23][24][25]   Where M ∑ A n is the molecular weight of the sample, A i is the atomic weight of the i-th element, n i is the number of formula units of the molecule and N A is Avogadro's number.
The effective atomic cross section  a is calculated using the following equation: The total electronic cross section  e is calculated by:   where f i denotes the fractional abundance of element I, and Z i is the atomic number of the constituent element.
The effective atomic number (Z eff ) is related to  a and  e by the following equation: The electron density (number of electrons per unit mass, [N el ]) of the sample can be calculated by the following equation:

Buildup Factors
The logarithmic interpolation method for the equivalent atomic number (Z eq ) was used to calculate the exposure buildup factor values and the G-P fitting parameters of the tellurite glass samples.The computation method is illustrated step-by-step as follows: 1. Calculation of equivalent atomic number (Z eq ); 2.
Calculation of the G-P fitting parameters; and 3.

Calculation of the exposure buildup factors
Since any single element has a fixed atomic number Z, a mixture, such as the zinc tellurite glasses studied here, will have an equivalent atomic number (Z eq ), which describes the properties the of glass systems.Because the partial interaction of a gamma ray with a material depends on the energy, Z eq is an energy dependent parameter.Using the winXCom program, 29,30 the total mass attenuation coefficient of selected ZnO-TeO 2 glasses and Compton partial mass attenuation coefficient for elements from Z = 4 to Z = 50 were obtained in the energy range of 0.015-15 MeV.The equivalent atomic number was calculated by matching the ratio of the Compton partial mass attenuation coefficient to the total mass attenuation coefficient of the selected glass systems with an identical ratio of a single element of the same energy.The following formula was used to interpolate the Zeq: 31 where Z 1 and Z 2 are the atomic numbers of the elements corresponding to the ratios R 1 and R 2, respectively, and R is the ratio of the glass sample at a specific energy.For example, the ratio Compton total = 0.645 of Z = 47.Using Equation 7, Z eq = 46.42 is calculated.The G-P fitting parameters are calculated using a similar logarithmic interpolation method to that used for Z eq .The G-P fitting parameters for the elements were taken from a report by the American Nuclear Society. 19The G-P fitting parameters for the glass samples were logarithmically interpolated using the same formula as follows: 31 where C 1 and C 2 are the values of the G-P fitting parameters corresponding to the atomic numbers of Z 1 and Z 2 , respectively, at a given energy.The G-P fitting parameters were used to calculate the exposure buildup factors of the glasses as follows: 32 where,

 
, composition and, consequently, on the glass density. 32The experimental values ( m ) increased with increasing ZnO content.This behaviour may be attributed to the addition of ZnO, which increases the glass density and decreases the molar volume, indicating that the glass structure becomes more compact and dense.The experimental mass attenuation coefficient values are in good agreement with the theoretical values.

HVL and MFP
The half-value layer was calculated using the linear attenuation coefficient (in cm -1 ) as follows: Where  ( =    m ) is the linear attenuation coefficient, and the values of HVL are listed in Table 3. Figure 2 shows that the HVL values decreased with increasing values of ZnO in the glass systems at the photon energies of 0.662, 1.173 and 1.33 MeV, which is due to an increase in the mass attenuation coefficient and density by replacing TeO 2 with ZnO.As shown in Figure 2, the half-value layer of the glass samples is lower than the corresponding values for barite and ferrite concretes at 0.662 and 1.33 MeV photon energies. 22It has been observed that ZnO-TeO 2 class systems are better than concrete at absorbing gamma rays, indicating the potential for utilising the prepared glasses as radiation shields.The values of the mean free path (MFP) (cm -1 ) of the prepared glass samples were obtained using the following equation: 31 1 Table 3 shows that the values of the mean free path of the prepared glass samples decreased with increasing ZnO content.The MFP values of the ZnO-TeO 2 glasses were compared with some standard radiation shielding concretes 33 (Figure 3). Figure 3 shows that the values of the mean free path are lower than those in ilmenite, basalt-magnetite, haematite-serpentine and ordinary concretes at 0.662, 1.173, and 1.33 MeV photon energies.This result indicates that the glass samples are better radiation shielding materials compared with standard shielding concretes.A material to be used as a gamma ray radiation shielding material must have low values of HVL and MFP.Therefore, the results indicated that ZnO-TeO 2 glass systems, which show lower values of HVL and MFP at photon energy 0.662, 1.173 and 1.33 MeV, are better for gamma ray shielding.Hence, it is thought that the prepared glass samples can be promising candidates for non-conventional alternatives for gamma ray shielding applications.

Effective Atomic Number (Z eff ) and Electron Density (N el )
The effective atomic number (Z eff ) and electron density (N el ) of the glass samples in the energy range of 0.015-15 MeV are presented in Table 4. Equations 5 and 6 have been used, respectively, to calculate the effective atomic number (Z eff ) and electron density (N el ).The variation of Z eff with photon energy for all interaction processes in the glasses is shown in Figure 4.It can be observed that initially, the photoelectric interaction dominates and the effective atomic number remains almost constant in the energy range of 0.015-0.03MeV.Then, it starts increasing and reaches a maximum at 0.04 MeV.Finally, it decreases sharply with increasing energy up to 1 MeV, which indicates that the Compton scattering process begins to occur.In the intermediate energy region (0.6-2 MeV), the Z eff values have been found to be almost constant for the selected materials, which clearly indicates that the Compton scattering cross section depends only on the energy and is almost independent of the composition of the materials.Finally, the effective atomic number increased with increasing photon energy.This is due to the domination of the pair production process, whose cross section is proportional with Z 2 .Figure 4 shows that in the photon energy range 0.04-0.6MeV, the 10ZnO-90TeO 2 glass sample has the highest effective atomic number.The variation of electron density when investigating glass systems with photons in the range of 0.015-15 MeV have demonstrated the same behaviour of Z eff as shown in Figure 5.

Photon energy dependence
The calculated equivalent atomic numbers (Z eq ) and EBF G-P fitting parameters for the glass samples in the energy range of 0.015-15 MeV are shown in Tables 5-8. Figure 6 shows the variation in the exposure buildup factor with photon energy for the glass samples at different penetration depths.It is observed that the exposure (EBF) buildup factors of the glass samples are small at both low and high energies.This may be attributed to the absorption processes, photoelectric effect and pair-production dominating at the low and high energy regions, respectively, in which photons are completely absorbed or removed.A sharp peak in the EBF values was observed at 40 keV as shown in Figure 6, which may be due to the K-absorption edge of Te at approximately 31.8 keV.Around the K-edge of high-Z elements, the mass attenuation coefficients jump to very large values at the upper side of the K-edge, and the element exhibits two mass attenuation coefficients, corresponding to the lower and upper sides of the edge.This abrupt change in the mass attenuation coefficient could lead a sharp peak in the buildup factor.The EBF values increase with increasing photon energies and show a maximum at 0.8 MeV due to multiple Compton scattering at intermediate energies.In Compton scattering, photons are not completely removed, but rather they lose energy.Finally, the EBF values begin to decrease upon further increases in the photon energy up to 8 MeV due to pair production.We found that EBF values increased at a high energy (>8 MeV) for all of the glass samples and showed increasing penetration depths, which might be due to the increase in multiple scattering as the penetration depth increased.The EBF values were found to be in the range of 1.005-4180.6,1.004-2730.3,1.004-1741.2and 1.004-1073.1 for the 10ZnO, 20ZnO, 30ZnO, and 40ZnO glass samples, respectively.The dependence on the chemical composition agreed with what was observed elsewhere. 34ble 5: Equivalent atomic number (Z eq ) and G-P exposure (EBF) buildup factor coefficients for 10ZnO-90TeO 2 glass sample.

Penetration depth dependency
Figure 7 shows the variation of the EBF with penetration depth for four incident photon energies (0.015, 0.15, 1.5, and 15 MeV).It is clear that the of EBF values increased with increasing penetration depth for the glass samples.At low penetration depths, up to 3 mfp and 0.15 MeV incident photon energy, the EBF values remained constant with increasing ZnO content.At a photon energy of 1.5 MeV, the EBF values remained constant with increasing ZnO content and penetration depths up to 20 mfp.This may be due to the domination of photoelectric absorption, which depends on 4 5  eq Z at photon energies below 0.15 MeV.In the high photon energy region (2 MeV), another absorption process, pair and triplet production, overwhelms the Compton scattering.

Figure 2 :
Figure 2: Variation of half value layer as a function of ZnO at 0.662 and 1.33 MeV photon energy in the () ZnO-TeO 2 glass systems.Theoretical values at same energies for barite concrete and ferrite concrete.

Figure 3 :
Figure 3: Variation of mean free path as a function of ZnO oxide at 0.662, 1.173 and 1.33 MeV photon energy in the () ZnO-TeO 2 glass systems.Theoretical values at same energies for ordinary concrete, hematite-serpentine, basaltmagnetite and ilmentite.

Figure 4 :
Photon energy (MeV)Figure4: The variation of Z eff with photon energy of glass samples.

Figure 5 :
Photon energy (MeV)Figure5: The variation of N el with photon energy of glass samples.

Table 2 :
Theoretical (µ m ) Xcom and experimental (µ m ) exp mass attenuation coefficient of glass systems.

Table 3 :
HVL and MFP of glass systems.

Table 4 :
Effective atomic number (Z eff ) and electron density (N el )  10 23 of glass samples.