Probing of nuclear radiation attenuation and mechanical features for lithium bismuth borate glasses with improving Bi 2 O 3 content for B 2 O 3 + Li 2 O amounts

Results in Physics 25 (2021) 104246

Available online 30 April 2021

2211-3797/© 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Probing of nuclear radiation attenuation and mechanical features for lithium bismuth borate glasses with improving Bi ₂ O ₃ content for B ₂ O ₃ + Li ₂ O amounts

G. Lakshminarayana

^a,*

, Ashok Kumar

^b

, H.O. Tekin

^c,d

, Shams A.M. Issa

^e,f

, M.S. Al-Buriahi

^g

, M.

G. Dong

^h

, Dong-Eun Lee

^i,*,2

, Jonghun Yoon

^j,*

, Taejoon Park

^k,*,1

aIntelligent Construction Automation Center, Kyungpook National University, 80, Daehak-ro, Buk-gu, Daegu 41566, Republic of Korea

bDepartment of Physics, University College, Benra - Dhuri, Punjab, India

cMedical Diagnostic Imaging Department, College of Health Sciences, University of Sharjah, Sharjah 27272, United Arab Emirates

dUskudar University, Medical Radiation Research Center (USMERA), 34672 Istanbul, Turkey

eDepartment of Physics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia

fPhysics Department, Faculty of Science, Al-Azhar University, Assiut, 71452, Egypt

gDepartment of Physics, Sakarya University, Sakarya, Turkey

hDepartment of Resource and Environment, Northeastern University, Shenyang 110819, China

iSchool of Architecture, Civil, Environment and Energy, Kyungpook National University, 1370, Sangyeok-dong, Buk-gu, DaeGu 702-701, Republic of Korea

jDepartment of Mechanical Engineering, Hanyang University, 55 Hanyangdaehak-ro, Ansan, Gyeonggi-do 15588, Republic of Korea

kDepartment of Robotics Engineering, Hanyang University, 55 Hanyangdaehak-ro, Ansan, Gyeonggi-do 15588, Republic of Korea

A R T I C L E I N F O Keywords:

B2O3-Bi2O3-Li2O glass system FLUKA code

Theoretical approaches Charged particles projected range Thermal neutrons total cross-section Mechanical features

A B S T R A C T

Against photon energies extending from 0.015 to 15 MeV, MCNPX, FLUKA and PHITS codes are operated to simulate mass attenuation coefficients (μ/ρ) for a total of ten B2O3-Bi2O3-Li2O glass compositions with added Bi2O3 amount from 10 to 55 mol% (5 mol% growth gradually) as a substitute for total (B2O3 +Li2O) mol% content. All the computed μ/ρ values correctness is examined by Py-MLBUF and WinXCOM programs’ μ/ρ outcomes and we found a good agreement among them. 55Bi2O3-35B2O3-10Li2O (mol%) glass half-value layer (HVL) and mean free path (MFP) quantities are compared with distinct commercial γ-ray attenuating glasses, alloys, polymers, concretes and lead and ceramics corresponding values. Next, equivalent atomic numbers (Zeq) and by employing geometric pro- gression (G–P) fitting method at 1–40 mfp PDs (penetration depths), at 0.015–15 MeV energy range ‘buildup factors’

were calculated. At all chosen twenty-five energies derived radiation protection efficiency (RPE) results assured investigated samples exemplary competence for low energy photons absorption. Applying SRIM codes Ψ_P and Φ_P and Ψ_A and ΦA (mass stopping powers (MSPs) and projected ranges (PRs) for protons and α-particles), and making use of ESTAR database Ψ_E (electron MSP) and continuous slowing-down approximation (CSDA) range for electrons are determined at KE (kinetic energy) range of 0.015–15 MeV. Moreover, fast neutron removal cross-sections (Σ_R), for 0.0253 eV energy neutrons absorption cross-sections have been estimated. Deduced Σ_R was altered at 0.1105–0.1205 cm⁻¹ range with Bi2O3 inclusion in studied samples. 10Bi2O3-70B2O3-20Li2O (mol%) glass has greater total cross-section (=23.251 cm⁻¹) for thermal neutrons absorption while 55Bi2O3-35B2O3-10Li2O (mol%) sample exhibits quality shielding factors for photons and fast neutrons confirming the included Bi2O3 positive impact.

Along with nuclear attenuation features various physical and mechanical aspects are also inspected. Derived Vm (molar volume), OPD (oxygen packing density), Vo (oxygen molar volume), Vt (packing density) and Gt (dissociation energy per unit volume) values indicated glasses rigidity. Following Makishima–Mackenzie’s theoretical model primary mechanical features like Y, K, S and L (Young’s, bulk, shear and longitudinal modulus) and σ _(Poisson’s ratio) are evaluated where 10Bi2O3-70B2O3-20Li2O (mol%) glass shows better elastic moduli in all samples.

* Corresponding authors.

E-mail addresses: gandham@knu.ac.kr (G. Lakshminarayana), dolee@knu.ac.kr (D.-E. Lee), yooncsmd@gmail.com (J. Yoon), taejoon@hanyang.ac.kr (T. Park).

1 orcid.org/0000-0002-7924-1776.

2 orcid.org/0000-0001-9205-3836.

Contents lists available at ScienceDirect

Results in Physics

journal homepage: www.elsevier.com/locate/rinp

https://doi.org/10.1016/j.rinp.2021.104246

Received 6 March 2021; Received in revised form 20 April 2021; Accepted 23 April 2021

Introduction

In contrast to other distinctive oxide glass network formers such as SiO2, P2O5, GeO2 and TeO2, B2O3 (B, Z =5) is regarded as a premier glass former as B2O3 glasses exhibit captivating features like wide glass- forming ability relatively at lesser melting points than silicate and phosphate glasses, lower fabrication cost than germanate and tellurite glasses, admirable optical transparency, better thermal stability or minimal thermal expansion coefficient, fine mechanical strength, larger bond strengths and considerable rare-earth (RE) ion solubility [1,2].

Though pure B2O3 can form glass with BO3 units, with an inclusion of other glass formers (e.g. SiO2) and modifiers (e.g. alkali/alkaline oxides) or intermediates (e.g. Al₂O₃) along with RE ions (e.g. Dy³⁺, Nd³⁺and Sm³⁺), B2O3-based glasses, possessing especially secluded (BO3)³⁻ units as well as (B3O6)³⁻, (B3O7)⁵⁻, (B3O9)⁹⁻, (B4O9)⁶⁻ and (BO4)⁵⁻ units are useful in numerous optoelectronic and photonic applications like solid- state lighting, optical fibers, sensors and optical data storage [3-6].

Regardless, heavy metal oxides like Bi2O3, WO3, BaO or PbO and/or different metal fluorides are commonly added in suitable amounts to B2O3-rich glass compositions to decrease phonon energy (B2O3 ~ 1300- 1500 cm⁻¹) and to enhance chemical stability for desired practical ap- plications [1,3–8]. For instance, Bi2O3 inclusion into borate glass network reduces melting points, improves glass moisture resistance, imparts large density (ρ), extends infrared transmission and enhances linear and nonlinear optical characteristics owing to Bi³⁺cation high polarizability [1,8,9]. Further owing to Bi³⁺low field strength and high polarizability (Bi³⁺ ionic radius = 1.03 Å), Bi2O3could form either BiO3or BiO6units in a glass matrix as a network former or modifier counting on its added content to the glass composition [10,11]. When added to the B2O3 glass matrix, Li2O as a modifier, causes structural changes (BO3 → BO4 units conversion), decreases glass melting point and enhances nonhygroscopicìty and chemical durability along with ionic conductivity [4,6,7,12].

After the world’s 1st nuclear power station (Obninsk Nuclear Power Plant, Soviet Union) was built in 1954 to produce electricity through

uranium-235 (²³⁵U) isotope fission reactions, nuclear energy being a clean energy source with no greenhouse-gas CO₂ emissions has become a vital alternative for customary nonrenewable energy origins (gas, oil, coal) for power generation worldwide. Also nowadays the usage of distinctive radioisotopes (created in nuclear reactors) is swiftly increasing in various fields like nuclear medicine (imaging and irradi- ation therapy) [13,14], agriculture [15], food sterilization [16], and industry [17], etc. Nevertheless, the utilization of radioactive sources and nuclear energy is associated with extremely energetic and pene- trating X-rays, γ-rays and neutron emissions. Prolonged unwanted or accidental exposure to these ionizing radiations can cause adverse health problems such as DNA mutations leading to cancer and death to humans where neutrons (charge =0) can directly interact with living cells’ atomic nucleus. So for minimizing the risk of getting excessive doses of ionizing radiations (radiation safety and protection) a precise shielding medium is surely required to absorb or attenuate the radiation for workers at nuclear power stations vicinity and medical personnel and patients along with the general public at radiotherapy facilities, which is one of the three crucial components in ALARA (As Low As Reasonably Achievable) [18]. Here shielding substance must have to reduce the scattered radiations to an agreeable and safer level for humans. Further radiation shields are mandatory for the spent nuclear fuel wastes stor- age, radioisotopes handling and transportation, and astronauts and spacecraft protection from the ion radiations (protons and heavy ions) during deep space missions [19,20]. Radiation attenuation by any appropriate medium depends on incident photon or neutron energy and Z, ρ and t (=thickness) of the medium. So media utilized for attenuation must hold low-cost, large ρ, good structural stability and mechanical strength after prolonged irradiation, and high σ_A. Commonly γ-ray and neutron shields are fabricated individually and later mixed for the desired application. Moreover, for free neutrons attenuation a material containing an element (e.g. H atom) with an equal atomic mass of the neutron is obligatory as it competently thermalizes them by elastic scattering.

Habitually, because of its low-cost, ease of access and promising shielding qualities for photons and neutrons as it can be made with both heavy and light nuclei in it, concrete is utilized as a radiation attenuator at particle accelerators, nuclear facilities and radiotherapy centers including to stop the radiation leakage from radioactive substances [21].

Despite that, concrete is non-transparent, immovable, and with an extended time of utilization microcracks appear in it as its H2O content reduces (free, bound and adsorbed) by radiation heat and at elevated temperatures which is unfavorable for neutrons’ scattering [22]. Further metallic Pb or Pb-based compounds in diverse shapes are also being used as radiation shields to attenuate γ-rays and X-rays at nuclear reactors and as protective wear in nuclear medicine facilities following Pb’s large ρ ₍=11.34 g/cm³), high-Z (=82) and higher σ_A. But, Pb has demerits like low melting point, light impermeability, poor corrosion resistance, low tensile strength and because of its high toxicity it causes environmental pollution and shows dangerous effects on human health [23]. So currently Pb is seldom utilized in nuclear diagnostic centers. As a replacement to Pb and concrete, more recently for radiation attenuation motives various Pb-free glasses [24–28], alloys [29], polymer compos- ites [30], glass-ceramics [31], steels [32] and ceramics [33] have been studied by researchers. Of them, particularly glasses possess favorable physical and chemical features like the ease in manufacturing in large- scale, nontoxicity and good transparency whereas their thermal, me- chanical and physical characteristics could be effectively changed just by altering the initial chemical mixtures and production methods. Here large-Z elements like W, Bi, Ba and La (all nontoxic) can be used as glass components instead of Pb to acquire high ρ glasses for photons shielding [24–28]. Moreover, nuclear wastes vitrification can be done in a glass as an adopted technique for wastes removal [34,35].

As mentioned in the “Nomenclature”, assessing impeccably μ/ρ (a pivotal parameter for γ-rays or X-rays attenuation), μ, HVL, TVL, MFP, Zeff, Neff, RPE, Zeq, and EBF and EABF for photons, for protons and α- Nomenclature

μ Linear attenuation coefficient Ψ_A Alpha particle mass stopping power

ρ _Density Φ_A Alpha particle projected range

μ/ρ Mass attenuation coefficient Ψ_E Electron total mass stopping power

Zeff Effective atomic number CSDA Continuous slowing down approximation

Neff Effective electron density Σ_R Effective removal cross-section of fast neutrons

HVL Half-value layer σ_cs Coherent scattering cross-section TVL Tenth-value layer σ_ics Incoherent scattering cross-section MFP Mean free path σ_A Absorption cross-section

RPE Radiation protection efficiency σ_T Total cross-section Zeq Equivalent atomic number M.W. Molecular weight BF Buildup factor Vm Molar volume

EBF Exposure buildup factor Vo Oxygen molar volume EABF Energy absorption buildup factor OPD Oxygen packing

density

G-P Geometric progression Vt Packing density

PD Penetration depth Gt Dissociation energy per unit volume KE Kinetic energy Yth Young’s modulus (theoretical) LSP Linear stopping power Kth Bulk modulus (theoretical) MSP Mass stopping power Sth Shear modulus

Ψ_P Proton mass stopping power Lth Longitudinal modulus Φ_P Proton projected range σ Poisson’s ratio

particles Ψ_P, Φ_P and Ψ_A, Φ_A quantities, Ψ_E and CSDA range for electrons, and for neutrons Σ_R, σ_cs, σ_ics, σ_A and σ_T values by employing related theoretical (e.g. Py-MLBUF, Phy-X/PSD, MicroShield®, BXCOM, XMu- Dat, XCOM/WinXCOM, etc.) and/or simulation (e.g. MCNP5, PHITS, FLUKA, Penelope, MNCPX, Geant4, SRIM, etc.) techniques or experi- mentally and by suitable formulae are mandatory for applying any material, for instance, glasses as nuclear radiation attenuators [1,24–28,36–40]. Here photons (mass =0 and charge =0), counting on their energy and material’s ρ, Zeff and Neff interact with materials largely in three modes such as Photoelectric absorption (PEA) or photon-atom collision, Compton scattering (CS) or photon-free-electron contact and Pair production (PP) or photon-nuclear field coaction [41]. However charged particles (e.g. protons, α and β-rays) interact in a different (continual and certain) manner than γ-rays or X-rays with a substance [1].

Giving consideration to lead-free glasses a little while ago, Mahmoud et al. [42] for 80B2O3-10Na2O-(10-x)Li2O-xCdO (x =0, 2, 4, 6, 8, 10 mol

%) glasses, for xBi₂O₃-30B₂O₃-(65-x)ZnO-5BaO (5 ≤ x ≤ 25 mol%) glasses by Mostafa et al. [43], Hegazy et al. [44] for B2O3–Bi2O3–SrO- Nd2O3 glass system, for [(100-x)TeO2)-xLi2O] (x =5, 10, 15, 20, 25, 30 mol%) glasses by El-Mallawany et al. [45], Kaur et al. [46] for xBi2O3–15Li2O–5Sb2O3–(80-x)B2O3 (x =0, 5, 10, 15, 20 mol%) glasses, for xWO3-(40–x)ZnO-50B2O3-10K2O (x = 0,5,10,15, 20 wt%) glass system by Saudi and Abd-Allah [47], Boonin et al. [48] for (90-x)TeO2- 10ZnO-xBaO (25 ≤ x ≤ 35 mol%) glasses, for (1 − x)MnO–29 K2O–70B2O3–xEr2O3 (x = 0, 0.2, 0.4, 0.6, 0.8, 1 mol%) glasses by Rammah et al. [49], Issa et al. [50] for xNb2O5-(20-x)Li2O-30Bi2O3- 50B2O3 (x =0, 2.5, 5.5, 7.5, 10 mol%) glass system and for (65-x)B2O3

+20Bi2O3 +15Na2O +xMoO3 (x =0, 1.5, 3, 4.5, 6, 7.5 wt%) glasses by Tekin et al. [51] pertinent nuclear radiation attenuation competences were investigated. Recently, for selected 65B₂O₃–12.5Bi₂O₃–12.5TeO₂– (10 − y)Na2O–yNdCl3 (0 ≤y ≤10 mol%) glass system, Eshghi [52] has examined relevant radiation attenuation features employing Phy-X/

PSD, XMuDat, and XCOM programs, and identified that in all studied glasses 65B2O3-12.5Bi2O3-12.5TeO2-10NdCl3 (mol%) (Q5) sample pos- sesses the best γ-ray shielding ability.

By applying both Py-MLBUF and WinXCOM programs, in this current work for a set of cost-effective B2O3-Bi2O3-Li2O glasses with increasing Bi2O3 amount in place of (B2O3 +Li2O) content various classic photon attenuation factors within 0.015-15 MeV energy range are inspected for their possible application as ionizing radiation shields. Also MCNPX (v.2.6.0), FLUKA and PHITS codes are employed for μ/ρ quantifications.

Deduced minimal HVL and MFP are correlated with some commonly used shielding substances corresponding quantities. Further EBFs and EABFs (by G-P fitting formulae) at 0.015 -15 MeV range are estimated at 1-40 mfp PDs. Additionally, for proton (H¹) and α (He⁺²) radiations Ψ_P, Φ_P and Ψ_A, Φ_A (by SRIM code) and for electrons Ψ_E and CSDA ranges (using ESTAR database) are investigated at 15 KeV-15 MeV KE range.

For fast neutrons Σ_R (by applying WinXCOM) and for thermal neutrons σ_cs, σ_ics, σ_{A and} σ_T (by utilizing appropriate formula) are calculated for all studied samples. We have also explored theoretically distinctive mechanical features like Yth, Kth, Sth, Lth and σ for all chosen glasses following the Makishima–Mackenzie’s (M− M) model [53,54].

Materials and methods

For considered all ten B₂O₃-Bi₂O₃-Li₂O glass compositions with added Bi2O3 content from 10 to 55 mol% in steps of 5 mol% increment instead of total (B2O3 +Li2O) amount the tested ρ values have been adopted from Ref. [55]. All ten specific glass chemical compositions (in mol%) and corresponded acquired elemental compositions (in wt%) and glass’s ρ are listed in Table 1. Here probed ten lithium bismuth borate glasses, for accessibility are stated as A, B, C, D, E, F, G, H, I and J respectively following Bi2O3 content improvement (10 to 55 mol%).

From A to J sample with increasing Bi2O3 amount ρ improves inherently owing to greater molecular weight (M.W.) and ρ of included Bi2O3

(465.96 g/mol and 8.9 g/cm³) instead of lesser M.W. and ρ Li2O (29.88 g/mol and 2.013 g/cm³) and B₂O₃ (69.63 g/mol and 2.46 g/cm³) (see Table 1). For A, B, C, D, E, F, G, H, I and J samples the calculated average M.W. is 101.317 g/mol, 125.1065 g/mol, 140.95 g/mol, 164.7395 g/

mol, 180.583 g/mol, 204.3725 g/mol, 220.216 g/mol, 244.0055 g/mol, 259.849 g/mol and 283.6385 g/mol accordingly and obtained respec- tive Vm is 29.072 cm³/mol, 31.761 cm³/mol, 30.24 cm³/mol, 32.882 cm³/mol, 31.894 cm³/mol, 34.575 cm³/mol, 34.712 cm³/mol, 36.753 cm³/mol, 37.313 cm³/mol and 39.285 cm³/mol for these glasses. As Vm

relies on both M.W. and ρ, for both C and E samples the improving rate in M.W. is less compared to ρ increasing rate thus leading to smaller Vm

values than B and D glasses.

At 0.015-15 MeV energy range distinct photon attenuation qualities like μ, μ/ρ, Zeff, Neff, HVL, TVL, MFP, RPE, Zeq and EBFs and EABFs (by G- P fitting method) were determined for all A-J samples. For mentioned all these parameters earlier in Refs. [25,26,30,31,33,36–40,42–46,51] as well as for neutron shielding aspects (e.g. Σ_R) studied in this research in Refs. [26,36,38–40,42,44,46], related physical interpretations of equa- tions and formulae were given by various researchers and us, so they are not paraphrased here.

Principally, as protons and α-particles being charged particles their KE loss per unit path length LSP (S(E) =- dE/dx) can be obtained by an expression [1,56]:

− dE

dx=4πNAmec²re2Z² β² ρ^Z

Aln4πεo

γ²mev³

Ze²f (1)

where re=_4πε^e_o²_mec2 =electron radius, β=^v_c and Ne =Z^N_A^Aρ. Subsequently MSP =LSP/ρ.

From Eq. (1) Φ_P and Φ_A can be obtained by the relation [1]:

∫_R

0

dx=

∫₀

E

dx dEdE=

∫^E

0

dE

S(E) (2)

where S(E) = −^dE_dx.

Next CSDA range for electrons could be deduced by an equation [57]:

RCSDA=

∫_(E

K)₀

0

dE

Stotal(E) (3)

where RCSDA =in a compound electrons CSDA diffusion length, EK = initial KE and

Stotal(E) =total MSP in line with EK.

Utilizing SRIM (Stopping and Range of Ions in Matter) codes created by Ziegler et al. [58], Ψ_P and Φ_P and Ψ_A and Φ_A versus KE, and by using ESTAR database (https://physics.nist.gov/PhysRefData/Star/Text/EST AR.html) [59] ΨE and CSDA range against KE are assessed for all A-J samples.

Py-MLBUF (multi-layered buildup factor) (https://pymlbuf.pytho nanywhere.com) [60] and WinXCOM [61] programs and MCNPX (Monte Carlo N-Particle eXtended) [62], FLUKA (FLUktuirende KAskade) (http://www.fluka.org) [63,64] and PHITS (Particle and Heavy Ion Transport code System) codes [65] are utilized for μ/ρ computations at selected twenty-five energies. In this study, employed simulation geometrical models are depicted in Figs. 1 and 2 and related MCNPX details are the same as we stated previously in Ref. [51] and for FLUKA (conceived collaboratively by INFN and CERN) and PHITS (created by JAEA, KEK, RIST and several other institutes) codes particulars one can look into Refs. [63–65].

For all A-J samples some physical characteristics like Vm (molar volume), OPD (oxygen packing density), Vo (oxygen molar volume), Vt

(packing density) and G_t (dissociation energy per unit volume) were evaluated using below expressions [50,66]:

Vm=M.W.

ρ ⁽⁴⁾

where M.W. =Molecular weight and ρ =density of glass.

OPD= (ρ

M )

On (5)

where On =per formula unit number of oxygen atoms.

V_o =V_m (∑

V_ixi (6) where Vm =Molar volume, xi =i^th component’s molar fraction.

Vt= (1

Vm

)∑

Vixi (7)

and

Vi=NA

(4π 3

)(

xR³_A+yR³_O)

, (8)

where NA = Avogadro’s constant, RA and RO are the Pauling’s ionic radius of metal ion and oxygen accordingly.

Gt =∑

Gixi, (9) where Gi =i^th component oxide’s dissociation energy per unit volume.

HereGi= (ρ

M )

Ui, (10)

where U_i =dissociation energy per mole.

Table 1

Chemical composition (mol%) and elements (wt%) present in the selected B2O3-Bi2O3-Li2O glasses, including their density .[55]

Glass code Glass composition (mol%) Elemental composition (wt%) Density (g/cm³)

B2O3 Bi2O3 Li2O B Bi Li O

A 70 10 20 14.9404 41.2576 2.7406 41.0614 3.485

B 75 15 10 12.9632 50.1168 1.1097 35.8103 3.939

C 60 20 20 9.2048 59.3108 1.9700 29.5144 4.661

D 65 25 10 8.5317 63.4312 0.8427 27.1944 5.010

E 50 30 20 5.9871 69.4391 1.5375 23.0363 5.662

F 55 35 10 5.8191 71.5813 0.6793 21.9203 5.911

G 40 40 20 3.9276 75.9215 1.2608 18.8901 6.344

H 45 45 10 3.9877 77.0837 0.5689 18.3597 6.639

I 30 50 20 2.4964 80.4263 1.0685 16.0088 6.964

J 35 55 10 2.6682 81.0483 0.4894 15.7941 7.220

Fig. 1.(a) MCNPX simulation setup (3-D view, obtained from Visual Editor of MCNPX) for mass attenuation coefficients computation of A-J glasses (b) MCNPX simulation setup (2-D view) for μ/ρ calculations acquired from MCNPX Visual Editor (version X_22S).

Considering glass (multicomponent) chemical composition, Vt, and G_t, Makishima–Mackenzie [53,54] developed a theoretical model to compute elastic moduli as below:

Y=8.36VtGt (11)

where Vt = packing density and Gt = dissociation energy per unit volume.

K=10V_t²Gt (12)

S= 30V_t²Gt

(10.2Vt− 1) (13)

L=K+ (4

3 )

S (14)

σ=0.5− ( 1

7.2Vt

)

(15) where Y, K, S and L are Young’s, bulk, shear and longitudinal modulus individually, and σ =Poisson’s ratio.

Here Y, K, S, L and σ values for all A-J glasses were calculated using above formulae 11-15. If the unit of Gt is kcal/cm³, Eqs. (11-14) provides the theoretical elastic moduli values in GPa.

Results and discussion

All discussed photon shielding factors are explored at 15 KeV–15 MeV energy range for all A–J samples. Corresponding obtained μ/ρ re- sults by Py-MLBUF and WinXCOM and MCNPX, FLUKA and PHITS codes for all A-J samples are listed in Table S1 (i-v) of Supplementary material and as an example Fig. 3 shows derived μ/ρ quantities analogy for glass J. Likewise Figs. S1 (a-i) (see Supplementary material) represent all A-I glasses μ/ρ comparisons respectively. Here one can clearly notice that through utilized all five explicit approaches deduced μ/ρ values are in adequate agreement within themselves. However it is worth mentioning that owing to fewer distinctnesses in preferred physical models and geometry of particular simulation codes used for μ/ρ computations, re- searchers can normally anticipate some minor variations in the outputs against calculated μ_/ρ via theoretical procedures. Accordingly, for glass J through Py-MLBUF and WinXCOM, and MCNPX, FLUKA and PHITS codes at 15 KeV energy 94.3 cm²/g, 94.29 cm²/g, 91.5406 cm²/g, 94.32 cm²/g and 94.24 cm²/g are the achieved μ/ρ values whereas 0.0498 cm²/g, 0.04977 cm²/g, 0.0501 cm²/g, 0.04909 cm²/g and 0.04918 cm²/g separately are these results at 15 MeV for the same glass with intimated same five processes. Next, with photon energy enhancement from 15 KeV to 15 MeV μ/ρ is declined for all A-J glasses (see Table S1).

As particular PEA (∝Z^4–5), CS (∝Z) and PP (∝Z²) events govern at lower, intermediate and higher energy ranges, for all A-J samples for μ/ρ, at 15 -50 KeV - a sharp reduction and >50 → 500 KeV - a minor decrement (because of PEA), at >0.5→(5-8) MeV - a negligible change or slight reduction (due to CS) and >5-8 → 15 MeV - a slight rise (as a conse- quence of PP) is identified. Observed little rise at 0.1 MeV in the vicinity of Bi: K-edge could be linked to PEA influence. Typically photons attenuation chances are minimal in CS, and greater energy photons possess larger penetration odds and they cause increased multifold scattering compared to low energy ones. Moreover, Bi2O3 inclusion instead of total (B₂O₃ +Li₂O) amount i.e. ρ upsurge from 3.485 to 7.22 g/cm³ leads to μ/ρ increment from A to J sample illustrating similar μ/ρ drift with rising energy. Sample J holds comparatively greater μ/ρ at the examined energy range in all chosen glasses disclosing it as a dominant photons attenuator. Here μ/ρ results derived by Py-MLBUF are used for some other photon shielding qualities (μ, Zeff, Neff, HVL, TVL, and MFP) assessment (see Figs. S2-S6 in Supplementary material).

MFP and HVL of glass J determined at 0.2 MeV, 0.662 MeV (¹³⁷Cs) and 1.25 MeV (⁶⁰Co) energies are contrasted with commercial SCHOTT AG: RS 253, RS 253 G18, RS 323 G19, RS 360, and RS 520 glass shields [67] particular values and are portrayed in Fig. 4 (a) and Fig. S7 (a) in Supplementary material correspondingly. As one can see here at all three energy points sample J has lesser MFP and HVL than all mentioned commercial glasses’ relevant values. For instance, at 1.25 MeV energy Fig. 2. Diagram of principle simulation geometry employed for FLUKA and PHITS codes (dimensions are in cm).

Fig. 3. Comparison of Py-MLBUF and WinXCOM programs, MCNPX, FLUKA and PHITS codes derived mass attenuation coefficients (cm²/g) versus photon energy (KeV) for glass J.

sample J possesses HVL ~ 1.63 cm whereas for RS 520 glass it is 2.31 cm at the same energy, hinting to decrease 1250 KeV photons intensity to a half, ~1.417 times less thickness glass J is sufficient than RS 520 glass.

Further, calculated glass J MFP and HVL at 15 KeV-15 MeV range are compared with distinct alloys (SS403, CN, CS516, IL600 and MN400) [68], polymers (natural rubber, polyacrylonitrile, polyethylacrylate, polyethylene tetraphthalate, polyoxymethylene and polyphenyl meth- acrylate) [69], concretes (OC, BMC, HSC, IC, ILC, SMC and SSC) [70], Pb and ceramics (calcium silicide, magnesium silicide, magnesium boride, calcium hexaboride, Al2O3 and TiO2) [71] respective quantities sepa- rately and are shown in Figs. 4 (b-e) and Figs. S7 (b-e) (see Supple- mentary material). Following these illustrations it is obvious that sample J owns fewer HVL and MFP in opposition to all polymers, concretes and ceramics related quantities. For example at 600 KeV energy 1.168 cm and 3.052 cm are computed MFP for glass J and TiO₂ individually indicating that number of photon collisions will be the same in sample J even with ~ 2.612 times lower thickness than in TiO2 at this energy.

Regarding alloys, at ~ 0.932-4.26 MeV range CN and MN400, at ~ 1- 3.5 MeV region IL600 and 1.3-2.4 MeV range CS516 holds lesser HVL

and MFP than glass J while SS403 has the same HVL and MFP as sample J at 1.45-2 MeV range. At all other energies sample J contains lower quantities than these alloys. However, Pb at examined entire photon energy region bears inferior HVL and MFP than glass J. So sample J with relatively less thickness is enough to competently deplete or scatter X- rays/γ-rays in contrary to commercial glasses, ceramics, concretes, a few alloys and polymers.

Within tested energy range at ten separate (1, 2, 5, 10, 15, 20, 25, 30, 35 and 40 mfp) PDs the probed EBFs and EABFs disparities for A and J glasses are shown in Figs. 5 (a, b) and (c, d) accordingly. Also EBFs and EABFs alterations for all B-I samples are displayed in Figs. S8 (a-h) and (i-p) (see Supplementary material) correspondingly. Moreover, for all A- J glasses derived Zeq and G-P fitting coefficients (a, b, c, d and Xk) concerning EBFs and EABFs calculations are given in Tables S2-S11 of Supplementary material. For any medium, under practical exposure circumstances, after primary photons absorption for an assessment of scattered photons dealing with ‘Buildup factors’ is essential. Commonly larger EBFs and EABFs articulate lower γ-rays attenuation strength. For all selected samples EBFs and EABFs changes exhibit an akin tendency

10^-1 10⁰ 10¹

10^-2 10^-1 10⁰

10^-1 10⁰ 10¹

10^-3 10^-2 10^-1 10⁰ 10¹

0.1 1 10

0.01 0.1 1 10

0.1 1 10

10^-2 10^-1 10⁰ 10¹ 10²

0.2 MeV 0.662 MeV 1.25 MeV 0

1 2 3 4 5 6

7 ^{Glass J}

RS 253 RS 253 G18 RS 323 G19 RS 360 RS 520

(e) (c) (d)

(b)

MFP (cm)

Energy (MeV) (a)

MFP (cm)

Energy (MeV)

Glass J Ordinary concrete Basalt-magnetite concrete Hematite-serpentine concrete Ilmenite concrete Ilmenite-limonite concrete Steel-magnetite concrete Steel-scrap concrete Lead (Pb)

MFP (cm)

Energy (MeV) Glass J SS403 CN CS516 IL600 MN400

Glass J CaSi₂ Mg₂Si MgB₂ CaB₆ Al₂O₃ TiO₂

MFP (cm)

Energy (MeV)

Glass J Natural Rubber Polyacrylonitrile Polyethylacrylate Polyethylene tetraphthalate Polyoxymethylene Polyphenyl methacrylate

MFP (cm)

Energy (MeV)

Fig. 4. Comparison of MFP of the glass ‘J’ with some (a) commercial glasses, (b) alloys, (c) polymers, (d) standard shielding concretes and Lead and (e) ceramics.

with interacting photon energy as well as PD. Here close to L1 and L2 edges (Bi: L1- 16.3875 KeV and L2- 15.7111 KeV) and K-edge of Bi a sudden increase has occurred in EBF and EABF values at 20, 30, 60 and 100 KeV energies respectively. At 0.1 MeV one can clearly notice a progressive hike in photons ‘buildup’ from E to J sample with Bi improvement from 69.4391 wt% to 81.0483 wt%. Outside of these sharp rises at 0.015-0.2 MeV range EBFs and EABFs are negligible for all examined glasses as photons are completely absorbed owing to PEA eminence at lower energies. At > 0.2 → 2-3 MeV energy range on grounds of CS action dominance both EBFs and EABFs are consistently increased for all A-J samples. In this intermediate energy region glass chemical constituents’ effect on EBFs and EABFs is not so effective.

Moreover, an account of PP mechanism control over greater energy range (>2-3 → 15 MeV) and higher PDs (>10 → 40 mfp) EBFs and EABFs are enhanced swiftly. Here more secondary photons are created from electron and positron annihilation (due to PP phenomenon).

However at lower PDs (e.g.1 and 2 mfp) EBFs and EABFs variations are trifling with increasing energy though usually a constant rise in EBFs and EABFs could be expected with sample thickness or MFP improve- ment. Following calculated Z_eq values one can see that all studied glasses at medium energies where CS commands have maximal quantities. In all samples, glass J has bigger Zeq values varying at 34.35 (at 15 KeV) -

62.78 (at 15 MeV) and has lesser EBFs and EABFs. This further confirms that Bi2O3 content increment in the samples improves their γ-rays ab- sorption ability.

For all A-J glasses (thickness (t) =3 mm) within the selected energy range the quantified RPE deviations are illustrated in Fig. 6. From Fig. 6 it is obvious that RPE betters from sample A to J with Bi2O3 insertion from 10 to 55 mol% instead of total (Li₂O +B₂O₃) content as having larger ρ and Z, Bi enhances γ-ray interactions with glasses than Li and B (low-Z) elements in them (RPE improves with Zeff). Here glass J owns relatively a higher shielding ability in all chosen samples. At 15-40 MeV range all samples wholly (100%) absorb incident photons in conse- quence of PEA, after all, all E-J glasses exhibit substantial RPE up to 100 KeV energy. As one can see from Fig. 6 beyond 0.1 MeV RPE declines (in an exponential form) with increasing energy for all glasses. For instance, at 150 KeV energy 62.51%, 73.04%, 83.52%, 87.23%, 92.00%, 93.34%, 95.31%, 96.20%, 97.10% and 97.58% are the individual calculated RPE values for A, B, C, D, E, F, G, H, I and J glasses whereas for the same samples at 5 MeV 3.45%, 4.05%, 4.97%, 5.45%, 6.27%, 6.61%, 7.20%, 7.56%, 8.03% and 8.33% are the respective RPE values. This validates that greater energy photons could effortlessly go through the samples.

For example for glass J RPE at 15 MeV energy is 10.21% revealing that this sample attenuates just 10.21% of 15 MeV photons and unconsumed Fig. 5. Variations of (a, b) exposure buildup factor (EBF) and (c, d) energy absorption buildup factor (EABF) with photon energy at distinct mean free paths for A and J glasses.

89.79% could escape through it. In fact, derived RPE outcomes confirm all Li₂O-B₂O₃-Bi₂O₃ samples’ effective absorption efficacy for lower energy photons up against larger ones.

As charged particles like protons (mass =1.673 ×10⁻²⁴ g, charge = +1) , α- (mass =6.645 ×10⁻²⁴ g, charge = +2) and electrons (mass = 9.109 ×10⁻²⁸ g, charge =-1) possess lesser penetration capacity than that of photons, usually any X-ray or γ-ray attenuator is applicable for blocking them entirely. Nevertheless, it is appropriate to study shielding efficacies of all selected A-J samples concerning heavy and light charged particles. “Stopping power” commonly indicates a medium’s potential to weaken the charged particles that pass through it. For all studied glasses Figs. 7 (a) and (b) shows the computed Ψ_P and Ψ_A variations at 0.015-15 MeV KE range accordingly. Following Fig. 7 it is clear that both ΨP and Ψ_A profiles follow the same trend with a rise in KE. At the beginning with KE increment from 15 KeV both Ψ_P and Ψ_A values are enhanced. At 0.09 MeV for glasses A-C and 0.1 MeV for all D-J samples the biggest Ψ_P quantitites are found. Likewise the largest Ψ_A values are sighted at 0.7 MeV KE for all A-J glasses. Ever since, both Ψ_P and Ψ_A values reduced continually up to 15 MeV for all A-J samples with KE. Here MSP values are higher for α-particles compared to protons’ MSPs as α-particles own larger mass effectuating slower motion (greater KE in reaching bigger MSP) compared to protons. Normally for α-particles their high mass leads to a very small penetration in a medium as they lose their KE over a comparatively short distance. For α-particles ionization and excitation (electronic) is the basic KE loss mechanisms. When protons travel through a target substance they interact by nuclear or electronic pro- cesses. Here Ψ_P and Ψ_A values are the largest for sample A (ρ =3.485 g/

cm³) whereas glass J (ρ =7.22 g/cm³) has these values minimally. Also estimated relevant Φ_P and Φ_A diversifications for all A-J glasses are displayed in Figs. 8 (a) and (b) at 0.015-15 MeV KE limits while corre- sponding inset plots show the expanded KE region at − 0.02-2.1 MeV.

Before coming to rest, the distance traveled by a charged particle is termed as its “range”. “Range” is essentially an average value charac- tered for charged particle beams and not for a single particle. In any medium α-particles particularly travel in straight paths. Here both ΦP

and ΦA quantities at any specific KE declined regularly with added Bi2O3

(10 to 55 mol%) content over (Li2O +B2O3) amount from glass A to J revealing that for protons and α-particles glass J holds a superior stop- ping capacity. At examined KE range for both ΦP and ΦA values almost a linear rise can be noticed against varying movement of Ψ_P and Ψ_A values (see Fig. 7). Though Φ_P and Φ_A deviations are small at lower KE range for all A-J samples they become significant with increasing KE. Here quantitatively Φ_P >Φ_A and principally ~ 1/9 value of Φ_P is good enough to halt the incident α-particles. At 0.015-15 MeV KE range for sample J

calculated ΦP and ΦA values differed at 0.124- 893.06 μm and 0.084- 101.35 μm ranges correspondingly. For all A-J samples, for electrons the calculated corresponding Ψ_E and CSDA range changes at 0.015-15 MeV KE region are shown in Figs. 9 (a) and (b) while the inset figures illus- trates enlarged 0.9-15.5 MeV and 0.014-0.21 MeV KE ranges accord- ingly. When electrons pass through a medium they lose KE by two types of channels: (a) owing to collisions with interacting medium’s electrons and (b) bremsstrahlung (radiative emissions in the medium’s nuclei Coulomb field). But the chances of both mechanisms vary for a specific KE. Usually bremsstrahlung emerges as a prominent one at greater KE (say, >10 MeV) whereas collision energy losses (ionization and exci- tation of atoms) are high at smaller KE [72]. From Fig. 9 (a) one can observe that Ψ_E decreases with KE from glass A to J getting to the minimal values at 1 MeV for A-C glasses, 0.9 MeV for samples D-I and 0.8 MeV for glass J with improving KE.Maximum ΨE ~ 10.81 MeV cm²/ g has ensued at 0.015 MeV KE for sample A. Later Ψ_E rises slightly up to 15 MeV KE for all samples. Glass A is effective in attenuating lesser KE electrons while sample J is better in shielding larger KE ones. CSDA ranges grow with KE though initially at 15-400 KeV KE range the gains or changes are not much (Fig. 9 (b)). As glass A possesses the highest N_eff , at minimal KE it holds lower CSDA ranges. As being a major origin of indirectly ionizing radiation, started by greater energy particles in accelerator beams, neutrons can be generated in nuclear by-products.

Radioisotopes can be formed when a nucleus capture neutron, and for a larger nucleus this could lead to a fission process (fissile fuels: ²³⁵U or Fig. 6.Variation of radiation protection efficiency (RPE) with photon energy

(MeV) for all A-J samples.

Fig. 7. Variations of (a) proton mass stopping power (Ψ_P) and (b) alpha mass stopping power (Ψ_A) as a function of kinetic energy (KE) for all A-J glasses.

239Pu). Primarily neutrons are sectioned into distinct types following their KE as fast (>500 keV), intermediate (1–500 keV), slow (<1 keV), epithermal (0.1 eV–1 keV) and thermal (<0.1 eV) neutrons [73]. For all A-J glasses related Σ_R arithmetic ways and obtained Σ_R values are given in Table 2. Accordingly 0.1107 cm⁻¹, 0.1105 cm⁻¹, 0.1166 cm⁻¹, 0.1160 cm⁻¹, 0.1201 cm⁻¹, 0.1192 cm⁻¹, 0.1192 cm⁻¹, 0.1205 cm⁻¹, 0.1191 cm⁻¹ and 0.1205 cm⁻¹ are the estimated Σ_R quantities for A, B, C, D, E, F, G, H, I and J samples. Glasses F and G and samples H and J possess the same ΣR (adjusted values to four decimal points) whereas glass B shows the lowest Σ_R in all selected glasses. Predominately Σ_R rests on material’s ρ (high and low-Z elements composition), the greater the ρ, the bigger the ΣR. Here glass J holds the highest ρ (B: 2.6682 wt%, Bi: 81.0483 wt%, Li: 0.4894 wt% and O: 15.7941 wt%). Sample B contains 12.9632 wt% of B, 50.1168 wt% of Bi, 1.1097 wt% of Li and 35.8103 wt% of O in it. These results reveal that an optimum mixture of glass constituents provides superior attenuation quality for fast neu- trons. Table 3 presents sample J ‘Σ_R’ comparison with some other latterly examined distinctive radiation shields and appropriate con- ventional neutron attenuators Σ_R [24,26,42,74–83]. It is clear from Table 3 that glass J has higher Σ_R as opposed to TAW-D [24], BNLC10 [42], SBBN7 [74], S1 [75] and ‘PZCdO Pure’ [76] glasses, Ti1 alloy [79], NPW05 polymer composite [80], PbCl2(0%) polymer-based composite

[81], C, H2O and Fe/NaCl [82], and OC, HSC, ILC, BMC and IC [83], and lesser ΣR than LYBB6 glass [26], Cu49Hf42Al9 (MG3) metallic glass [77], Fe80B20 alloy [78], and SSC and SMC [83] related values. Table 4 pre- sents respective σ_cs, σ_ics, σ_A and σ_T of all A-J samples for 0.0253 eV energy neutrons calculated applying the related formula supplied in our earlier work [38] whereas Table S12 (see Supplementary material) provides σ_cs, σ_ics, σ_A and σ_T values of B, Bi, Li and O elements for thermal neutrons. Following Table 4 data one can notice that σ_A serves greatly to σ_T and it is correlatively higher against σ_cs and σ_ics. Here σ_T of all samples decreases in accordance with B content reduction in them as we can clearly see from Table S12 that σ_T of B is much bigger than other ele- ments and also σ_A of B is much larger than other two interactions. In all chosen glasses, glass A (B: 14.9404 wt%, Bi: 41.2576 wt%, Li: 2.7406 wt

%, O: 41.0614 wt%) has the highest σ_T (23.251 cm⁻¹) for thermal neutrons absorption with high potency while sample I possesses the lowest σ_T (8.265 cm⁻¹). However for E and F, G and H and I and J glasses there exists only a minor change in σ_T value.

The rigidity of a glass shield could be assessed by exploring its me- chanical features. Computed distinct physical and mechanical charac- teristics like M, Vm, Vo, OPD, Vt, Gt, Yth, Kth, Sth, Lth and σ values of all A-J glasses are listed in Table 5. With increasing ρ, V_m increases from sample Fig. 8. Variations of (a) proton projected range (Φ_P) and (b) alpha projected

range (Φ_A) as a function of kinetic energy (KE) (insets, within KE regions at

− 0.02–2.1 MeV) for all A-J glasses. Fig. 9.Variations of (a) electron stopping power (Ψ_E) (inset, within the range of 0.9–15.5 MeV KE) and (b) CSDA range for electrons (inset, within the 0.014–0.21 MeV KE range) as a function of kinetic energy (KE) for all A- J samples.

Table 2

Effective removal cross-sections for fast neutrons, Σ_R(cm⁻¹), for all A-J glasses.

Glasscode Element ΣR/ρ _(cm²_/g) Fraction by weight % Partial density (g/cm³) ΣR(cm⁻¹)

A

Li 0.084 0.027406 0.09550991 0.00802283244

B 0.0575 0.149404 0.52067294 0.02993869405

O 0.0405 0.410614 1.43098979 0.0579550865

Bi 0.0103 0.412576 1.43782736 0.01480962181

ΣR =0.1107262348

Total ΣR for glass ‘A’ =0.1107 cm⁻¹ B

Li 0.084 0.011097 0.043711083 0.00367173097

B 0.0575 0.129632 0.510620448 0.02936067576

O 0.0405 0.358103 1.410567717 0.05712799254

Bi 0.0103 0.501168 1.974100752 0.02033323775

ΣR =0.110493637

Total ΣR for glass ‘B’ =0.1105 cm⁻¹ C

Li 0.084 0.0197 0.0918217 0.0077130228

B 0.0575 0.092048 0.429035728 0.02466955436

O 0.0405 0.295144 1.375666184 0.05571448045

Bi 0.0103 0.593108 2.764476388 0.0284741068

ΣR =0.1165711644

Total ΣR for glass ‘C’ =0.1166 cm⁻¹ D

Li 0.084 0.008427 0.04221927 0.00354641868

B 0.0575 0.085317 0.42743817 0.02457769478

O 0.0405 0.271944 1.36243944 0.05517879732

Bi 0.0103 0.634312 3.17790312 0.03273240214

ΣR =0.1160353129

Total Σ_R for glass ‘D’ =0.1160 cm⁻¹ E

Li 0.084 0.015375 0.08705325 0.007312473

B 0.0575 0.059871 0.338989602 0.01949190212

O 0.0405 0.230363 1.304315306 0.05282476989

Bi 0.0103 0.694391 3.931641842 0.04049591097

ΣR =0.120125056

Total Σ_R for glass ‘E’ =0.1201 cm⁻¹ F

Li 0.084 0.006793 0.040153423 0.00337288753

B 0.0575 0.058191 0.343967001 0.01977810256

O 0.0405 0.219203 1.295708933 0.05247621179

Bi 0.0103 0.715813 4.231170643 0.04358105762

ΣR =0.1192082595

Total Σ_R for glass ‘F’ =0.1192 cm⁻¹ G

Li 0.084 0.012608 0.079985152 0.00671875276

B 0.0575 0.039276 0.249166944 0.01432709928

O 0.0405 0.188901 1.198387944 0.04853471173

Bi 0.0103 0.759215 4.81645996 0.04960953759

ΣR =0.1191901014

Total Σ_R for glass ‘G’ =0.1192 cm⁻¹ H

Li 0.084 0.005689 0.037769271 0.00317261876

B 0.0575 0.039877 0.264743403 0.01522274567

O 0.0405 0.183597 1.218900483 0.04936546956

Bi 0.0103 0.770837 5.117586843 0.05271114448

ΣR =0.1204719785

Total Σ_R for glass ‘H’ =0.1205 cm⁻¹ I

Li 0.084 0.010685 0.07441034 0.00625046856

B 0.0575 0.024964 0.173849296 0.00999633452

O 0.0405 0.160088 1.114852832 0.0451515397

Bi 0.0103 0.804263 5.600887532 0.05768914158

ΣR =0.1190874844

Total ΣR for glass ‘I’ =0.1191 cm⁻¹ J

Li 0.084 0.004894 0.03533468 0.00296811312

B 0.0575 0.026682 0.19264404 0.0110770323

O 0.0405 0.157941 1.14033402 0.04618352781

Bi 0.0103 0.810483 5.85168726 0.06027237878

Σ_R =0.120501052

Total ΣR for glass ‘J’ =0.1205 cm⁻¹