# A detailed investigation on highly dense CuZr bulk metallic glasses for shielding purposes

• Huseyin Ozan Tekin , Ghada ALMisned , Gulfem Susoy , Hesham M. H. Zakaly , Shams A. M. Issa , Gokhan Kilic , Yasser Saad Rammah , Gandham Lakshminarayana and Antoaneta Ene
From the journal Open Chemistry

## Abstract

Gamma-ray shielding properties of eight different metallic glasses based on CuxZr100-x: x = 35 (Cu35Zr65) − 70 (Cu70Zr30) were determined using Monte Carlo simulations and Phy-X/PSD software. A typical gamma-ray transmission setup has been modeled in MCNPX Monte Carlo code. The general trend of the linear attenuation coefficients (μ) was reported as (μ)Cu35Zr65 < (μ)Cu40Zr60 < (μ)Cu45Zr55 < (μ)Cu50Zr50 < (μ)Cu55Zr45 < (μ)Cu60Zr40 < (μ)Cu65Zr35 < (μ)Cu70Zr30. In terms of half value layer (HVL) values, the Cu35Zr65 sample has the highest value (2.984 cm) and the Cu70Zr30 sample has the lowest value (2.769 cm) at 8 MeV photon energy. The mean free path (MFP) values were 4.305 and 3.995 cm for Cu35Zr65 and Cu70Zr30 samples, respectively. Generally, MFP and HVL values of the studied glasses were reported as (MFP,HVL)Cu35Zr65 > (MFP,HVL)Cu40Zr60 > (MFP,HVL)Cu45Zr55 > (MFP,HVL)Cu50Zr50 > (MFP,HVL)Cu55Zr45 > (MFP,HVL)Cu60Zr40 > (MFP,HVL)Cu65Zr35 > (MFP,HVL)Cu70Zr30 for all photon energy range. The Cu70Zr30 sample showed maximum values of both the effective conductivity (C eff) and effective electron density (N eff). In addition, the Cu70Zr30 sample has minimum exposure and energy absorption buildup factor (EBF and EABF) values at all studied gamma-ray energies. The results revealed that the Cu70Zr30 sample has superior attenuation properties among all studied samples.

## 2 Materials and methods

Eight distinct CuxZr100-x metallic glass systems [2] were comprehensively investigated in this work in terms of their gamma-ray shielding capabilities, effective conductivity, and buildup factors (BUFs). In the reference study, material densities of glass samples were reported as 7.01, 7.17, 7.26, 7.33, 7.47, 7.53, 7.75, and 7.86 g/cm3 for sample codes Cu35Zr65, Cu40Zr60, Cu45Zr55, Cu50Zr50, Cu55Zr45, Cu60Zr40, Cu65Zr35, and Cu70Zr35, respectively (see Table 1). The calculated nuclear radiation shielding parameters will be discussed in this section, along with technical information.

Table 1

Sample codes, composition, elemental weight fractions, and density

Code Composition wt% Density (g/cm3)
Cu Zr
Cu35Zr65 34.77 65.23 7.01
Cu40Zr60 39.88 60.12 7.17
Cu45Zr55 44.94 55.06 7.26
Cu50Zr50 49.86 50.14 7.33
Cu55Zr45 55.14 44.86 7.47
Cu60Zr40 59.92 40.08 7.53
Cu65Zr35 64.92 35.08 7.75
Cu70Zr30 69.93 30.07 7.86

### 2.1 Nuclear radiation shielding properties

To simplify the mass attenuation coefficient, it is essential to understand the Lambert–Beer law [11,12], which is shown in equation (1):

(1) I = I o e μ t ,

where I 0 is the original energy of the beam, μ is the linear attenuation coefficient, t is the absorber thickness, and I is the gamma-ray intensity after transit through the absorber.

The mass attenuation coefficient (μ m) is the ratio of the linear attenuation coefficient to the density. It is generally represented in cm2/g [13,14,15,16,17,18] and is computed using the following equation:

(2) μ m = μ ρ ,

where μ is the linear attenuation coefficient and ρ is the density of the sample.

Equation (3) was used to calculate the values of μ m using the Py-MLBUF platform:

(3) μ m = i w i μ ρ i ,

where w i is the weight fraction of the ith constituent of the element and ρ is the density of the sample.

The mean free path (MFP) is defined as the average distance a photon can travel between two successive interactions within a material [19], and can be calculated using equation (4):

(4) MFP = 1 μ .

After traveling 1 MFP through a shielding material in perfect narrow-beam geometry, the power of monoenergetic gamma rays is reduced by about 37%. The optical thickness (OT), a dimensionless quantity, is calculated by multiplying the linear attenuation coefficient by the distance in cm between the point source and the detector. The OT depicts the number of MFP lengths covered by gamma photons as they travel through the shield. The half value layer (HVL) is the thickness of material with a transmitted radiation intensity equal to half that of the incoming radiation, while the tenth value layer (TVL) is the thickness of material with a beam intensity equal to one-tenth of its original value [20]. HVL and TVL may be determined using equations (5) and (6):

(5) HVL = ln ( 2 ) μ ,

(6) TVL = ln ( 10 ) μ .

Equation (7) relates the effective conductivity C eff (s/m) of a shielding material for attenuation at room temperature (300 K) to the effective number of electrons N eff:

(7) C eff = N eff ρ τ e 2 m e × 10 3 ,

where ρ, e, and m e are the density of shielding materials (g/cm3), the charge on an electron (C), and the electron’s rest mass (kg), respectively. τ depicts the electron’s relaxation time and is calculated using equation (8):

(8) τ = h 600 π k ,

where h is the Planck constant and k is the Boltzmann constant.

The effective atomic number (Z eff) is a critical parameter in radiation sciences. It can be utilized to describe how complex shielding materials strengthen their shielding capabilities. The direct method was used in this study to calculate the effective atomic number by comparing the atomic and electronic cross sections:

(9) Z eff = Σ i f i A i μ ρ i Σ j f j A j Z j μ ρ j ,

where f i , A i , and Z j are the fractions by mole, atomic weight, and the atomic number of the ith constituent element, respectively.

Incoherent scattering is the only way to determine the equivalent atomic number (Z eq) of the shielding material. Z eq values are used to calculate BUFs.

The Z eq values in this work were obtained using the interpolation method, as displayed in equation (10):

(10) Z eq = Z 1 ( log R 2 log R ) + Z 2 ( log R log R 1 ) log R 2 log R 1 ,

where the ratio R is the determining factor for the equivalent atomic number, for particular photon energy,

(11) R = μ m compton μ m total .

The atomic numbers Z 1 and Z 2 of the elements correspond to their respective R 1 and R 2 ratios.

The BUF is a multiplier that takes into account the contributions of scattered photons to the corrected response to uncollided photons. In other words, it is the number of incoming photons divided by the total number of photons. The ANS standard was developed for the purpose of calculating gamma-ray BUFs for a point isotropic source operating at energies ranging from 0.015 to 15 MeV. In the energy absorption buildup factor (EABF), the quantity of interest is the amount of energy absorbed or contained in the interacting substance. Geometric progression (G–P) fitting is often used to record EABFs. After determining the Z eq values, the five G–P fitting parameters for the elements (b, a, c, and d Xk) are retrieved from the ANS-standard database, which contains a variety of elements with energies ranging from 0.015 to 15 MeV and OT of 40 MFP. The G–P fitting parameters for the glass materials were calculated using the interpolation approach. The exposure accumulation factor refers to the amount of radiation in the air after it passes through the shielding material (EBF). EABF and EBF are calculated using equations (12–14) for single-layered gamma-ray shielding enclosures (GSEs) with OT up to 100 MFP and energy between 0.015 and 15 MeV.

(12) B ( E , X ) = 1 + b 1 K 1 ( K x 1 ) for K     1 ,

(13) B ( E , X ) = 1 + ( b 1 ) x for K = 1 ,

(14) K ( E , x ) = c x a + d tanh x X k 2 tanh ( 2 ) 1 tanh ( 2 ) 1 tanh ( 2 ) for x 40 MFP,

where E, x, and B denote incoming photon energy, penetration depth in MFP, and accumulation factor at 1 MFP, respectively, and K denotes the photon-dose multiplication factor.

### 2.2 Monte Carlo simulations using MCNPX (version 2.7.0)

According to the literature review, the relevance of mathematical tools and simulation techniques in radiation sciences is steadily expanding [21,22,23,24,25,26]. This is due to various physical constraints and the possibility of adverse consequences in experimental radiation investigations. On the other hand, authorized institutions should accredit radiation facilities in order to comply with safety regulations. As a result, enhanced simulation methods may be a viable option for increasing the consistency of the experimental phase and lowering the total cost of research. As such, many well-known Monte Carlo simulation-based radiation transportation codes, such as MCNP, Geant4, EGSnrc, and FLUKA, provide well-structured platforms for developing various sorts of solutions for radiation transportation-related investigations. Among the abovementioned codes, MCNPX [12] is well-known for its user-friendliness and reliability, as well as its promising technological aspects. The mass attenuation coefficients of the BMGs under discussion were determined in this inquiry using version 2.7.0 of the MCNPX general-purpose Monte Carlo method. The first step included the development of a generic gamma-ray transmission system based on experimental research. The two- and three-dimensional representations of the MCNPX code’s intended gamma-ray transmission arrangement are shown in Figure 1. In a lead (Pb) block, a point isotropic gamma-ray source has been established. Following that, an attenuator between the point isotropic source and detection field has been established. It is worth noting that the attenuator material was chosen based on the elemental characteristics of the investigated glasses (see Table 1). The BMGs’ elemental characteristics have been precisely described in the material (Mn) card of the MCNPX INPUT file. Finally, simulation was initiated for a total of 108 particle histories. It should be mentioned that each glass sample was examined for gamma-ray energies ranging from 0.015 to 15 MeV. The simulation results indicated that the relative inaccuracy for each track was less than 1%.

Figure 1

3-D model of the modeled MCNPX simulation setup (obtained from VISED_X_22S).

## 3 Results and discussions

In this study, eight different BMGs were characterized in terms of their gamma-ray attenuation competencies. The densities of Cu35Zr65, Cu40Zr60, Cu45Zr55, Cu50Zr50, Cu55Zr45, Cu60Zr40, Cu65Zr35, and Cu70Zr30 samples are shown in Figure 2. As seen in the figure, the glass density is increased from 7.01 to 7.86 g/cm3. The Cu70Zr30 sample with the greatest content of Cu had the highest glass density. Given that the linear attenuation coefficient is a density-dependent characteristic, it is assumed that a direct relationship exists between the density and the linear attenuation coefficient values, and hence, the amount of Cu contribution. The variation of linear attenuation coefficients (/cm) as a function of incoming photon energy (MeV) is shown in Figure 3. As can be seen, as the photon energy increased, linear attenuation coefficients decreased. The largest linear attenuation coefficients were observed in the low-energy region, where the photoelectric effect dominates the majority of photon–matter interactions [27,28,29,30,31,32]. However, when the glass densities are changed gradually, no significant variations in the linear attenuation coefficients are seen. We noticed an interesting impact of Cu on the photon resistance of glass samples at varying energies. Our results reveal that the Cu70Zr30 sample, which has the greatest concentration of Cu, has the maximum linear attenuation coefficients for all photon energies entering. This is explained by the Cu70Zr30 sample’s glass density, which included the largest quantity of studied glasses. For example, linear attenuation coefficients were reported as 0.409, 0.419, 0.425, 0.429, 0.438, 0.442, 0.455, and 0.462/cm for Cu35Zr65, Cu40Zr60, Cu45Zr55, Cu50Zr50, Cu55Zr45, Cu60Zr40, Cu65Zr35, and Cu70Zr30 samples at 1 MeV photon energy, respectively.

Figure 2

Variation of glass densities (g/cm3).

Figure 3

Variation of linear attenuation coefficients (1/cm) of investigated glasses as a function of incident photon energy (MeV).

Figure 4

Variation of mass attenuation coefficients (cm2/g) of investigated glasses as a function of incident photon energy (MeV).

Figure 5

Variation of HVL (cm) values of investigated glasses as a function of incident photon energy (MeV).

Figure 6

Variation of TVL (cm) values of investigated glasses as a function of incident photon energy (MeV).

Figure 7

Variation of MFP (cm) values of investigated glasses as a function of incident photon energy (MeV).

Figure 8

Variation of effective atomic number (Z eff) values of investigated glasses as a function of incident photon energy (MeV).

Figure 9

Variation of effective electron number (N eff) values of investigated glasses as a function of incident photon energy (MeV).

Figure 10

Variation of effective conductivity (C eff) values of investigated glasses as a function of incident photon energy (MeV).

Figure 11

Variation of exposure buildup factor (EBF) values of glasses at different MFP values (from 0.5 to 40 MFP) as a function of incident photon energy (MeV).

Figure 12

Variation of EABF values of glasses at different MFP values (from 0.5 to 40 MFP) as a function of incident photon energy (MeV).

## 4 Conclusion

In the present research, the nuclear shielding properties including the effective conductivity and BUFs of eight different CuxZr100-x: x = 35 (Cu35Zr65) − 70 (Cu70Zr30) in steps of 5 wt% metallic glass systems have been studied. The density of samples was varied from 7.01 g/cm3 for the Cu35Zr65 sample and 7.86 g/cm3 for the Cu70Zr30 sample. The studied nuclear radiation shielding parameters were calculated via MCNPX simulation code and the Phy-x PSD software. The results reveal that the Cu70Zr30 sample with the greatest Cu concentration and lowest Zr content has the maximum linear attenuation coefficient (μ) for all photon energies entering, while the Cu35Zr65 (low Cu and high Zr) sample has the minimum value. The general trend of the μ value was (μ)Cu35Zr65 < (μ)Cu40Zr60 < (μ)Cu45Zr55 < (μ)Cu50Zr50 < (μ)Cu55Zr45 < (μ)Cu60Zr40 < (μ)Cu65Zr35 < (μ)Cu70Zr30. As the mass attenuation coefficient (μ m) is density-independent, it has the trend (μ m)Cu35Zr65 > (μ m)Cu40Zr60 > (μ m)Cu45Zr55 > (μ m)Cu50Zr50 > (μ m)Cu55Zr45 > (μ m)Cu60Zr40 > (μ m)Cu65Zr35 > (μ m)Cu70Zr30 for the studied metallic glasses. Our results indicated that the glasses studied reported HVL (in cm) values of 2.984, 2.934, 2.914, 2.902, 2.865, 2858, 2.792, and 2.769 cm for Cu35Zr65, Cu40Zr60, Cu45Zr55, Cu50Zr50, Cu55Zr45, Cu60Zr40, Cu65Zr35, and Cu70Zr30 samples at 8 MeV photon energy, respectively. The MFP (in cm) has the same trend of HVL values of 4.305, 4.233, 4.204, 4.187, 4.133, 4.123, 4.029, and 3.995 cm for all studied samples Cu35Zr65, Cu40Zr60, Cu45Zr55, Cu50Zr50, Cu55Zr45, Cu60Zr40, Cu65Zr35, and Cu70Zr30 at 8 MeV photon energy, respectively. The Cu70Zr30 sample possessed the maximum values of both the effective conductivity (C eff) and effective electron density (N eff). The results showed that the Cu70Zr30 sample has the minimum EBF and EABF values at all gamma-ray energies studied.

## Acknowledgements

The authors thank the “Dunarea de Jos” University of Galati, Romania, for the APC support.

1. Funding information: This work was performed under Princess Nourah bint Abdulrahman University Researchers Supporting Project Number (PNURSP2022R149), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. The authors express their sincere gratitude to Princess Nourah bint Abdulrahman University.

2. Author contributions: Conceptualization: H.O.T., A.B., H.M.H.Z., and S.A.M.I.; methodology: G.K., H.O.T.; software: H.O.T., G.L., H.M.H.Z., and A.E.; validation: S.A.M.I., Y.S.R., and A.E.; formal analysis: G.K., Y.S.R., H.M.H.Z., and G.S.; investigation: G.K. and H.O.T.; resources: G.K., G.S., and A.B.; data curation: S.A.M.I. and A.E.; writing – original draft preparation: H.O.T., G.S., G.L., Y.S.R., and A.W.; writing – review and editing: H.M.H.Z., S.A.M.I., and A.E.; visualization: Y.S.R. and G.S.; supervision: H.M.H.Z. and A.B.; project administration: H.O.T. and S.A.M.I; funding acquisition: A.E. All authors have read and agreed to the published version of the manuscript.

3. Conflict of interest: The authors declare no conflict of interest.

4. Ethical approval: The conducted research is not related to either human or animal use.

5. Data availability statement: The data presented in this study are available on request from the corresponding author.

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