Role and Applications of Boron and Its Compounds in Industrial and Nanotechnology Fields

#### **Chapter 4**

## Boron and Boron Compounds in Radiation Shielding Materials

*Ahmet Hakan Yilmaz, Bülend Ortaç and Sevil Savaskan Yilmaz*

#### **Abstract**

A risk to the nuclear industry is radiation, specifically neutron radiation. In order to maintain a safe workspace for workers, better shielding is being developed. Current shielding methods are examined and boron is considered a potential material for shielding. All living beings and non-living things on earth are exposed to the daily radiation of natural radiation sources in the air, water, soil, and even in their bodies, as well as artificial radiation sources produced by humans. To be safeguarded from the detrimental influences of radiation, it is important to be careful about three basic issues: time, distance, and shielding. The longer the exposure time to radiation from the radioactive source or the closer one is to the radioactive source, the higher the radiation dose to be received. The radiation emitted by some radionuclides is so intense that you can be exposed to it even though you cannot see it from miles away. It can only be protected from the effects of such intense radioactive materials with strong shielding. Boron, having a large cross-section, is combined with other materials in order to obtain the desired material properties to have shielding that can be applied in different situations.

**Keywords:** boron, boron compounds, shielding materials, radiation, gamma ray, neutron, polymers, glasses

#### **1. Introduction**

Radiation is the emission or transmission of energy in the form of waves, particles, or electromagnetic radiation through space or matter. It can be produced by the sun, radioactive elements, X-ray machines, and nuclear reactions, among other things [1–3]. There are two types of radiation: ionizing and non-ionizing radiation. Ionizing radiation is powerful enough to knock electrons off atoms, causing damage to living tissue and DNA. Non-ionizing radiation, such as visible light and radio waves, lacks the energy to cause this type of harm. Radiation is used in various fields, including medicine, industry, and research, but excessive exposure can harm human health.

In daily life, we can encounter high-energy radiation such as alpha, beta particle emissions, X-ray or gamma-ray, or neutron particle emissions in any form, for

example, in many various industrial products, including nuclear power plants, in the health sector, both in diagnosis and treatment and in the aviation field [4]. Any of these radiations that we are unintentionally exposed to can be life threatening for us. However, the consequences of such exposures depend on various factors, such as the type of radiation and the energy associated with it, the amount of absorbed dose, exposure time, and so on.

The radiation energies of galactic cosmic rays, solar particle events, medical X-rays, gamma rays, electrons, and neutrons can vary dramatically depending on the source and particle energy. Here are some rough energy ranges for each type of radiation: High-energy particles that originate outside of our solar system are known as galactic cosmic rays. They can range in energy from a few MeV to several hundred TeV, with some rare events exceeding 1020 eV. Solar particle events are bursts of high-energy particles that originate from the sun. These particles have energies ranging from a few MeV to several GeV, with the most energetic events reaching tens of GeV. Medical X-rays are a type of electromagnetic radiation that is used in medical imaging. X-rays used in medical imaging can have energies ranging from a few keV (thousand electron volts) to several MeV. Gamma rays are a type of electromagnetic radiation with extremely high energies. They can be generated by a variety of processes, including nuclear reactions and astronomical phenomena. Gamma-ray energies can range from a few keV to several TeV. Electrons are subatomic particles that have a negative charge. Depending on the source, their energies can range from a few keV to several GeV. Neutrons are subatomic particles that have no charge. Their energies can also vary greatly depending on the source and method of production, ranging from a few MeV to several GeV.

Radiation therapy is a common cancer treatment method. Cancer cells are stopped or killed using high-energy radiation. Radiation therapy can also be used to treat some benign tumors as well as certain blood diseases (e.g., Hodgkin lymphoma). Radiation therapy, also known as radiotherapy, is a type of targeted therapy. While radiation only affects cancer cells, it has little effect on normal cells. As a result, radiation therapy is frequently combined with other cancer treatment modalities (e.g., chemotherapy). Bone diseases can be treated with radiation therapy. Bone cancer (such as osteosarcoma), lymphoma, or multiple myeloma may have spread to the bones or formed tumors in the bones. Radiation therapy is used to shrink or destroy bone tumor formations to treat these types of cancer. Regional pain and bone fractures can also be treated with radiation therapy. Bone metastases (spreading cancer from another site to the bones) frequently cause pain and fractures.

Neutrons are neutral (zero-charged) particles that are used in nuclear power plants. They can easily pass through most materials and interact with the target atom's nucleus. The majority of sources that emit X-rays and rays also emit neutrons. Because neutrons can form a much more intense ion path as they lose energy within body tissues, neutron radiation is hazardous to body tissues. Other radiations, such as rays, protons, and alpha particles, can be produced as a result of interactions with biological matter. Workers in nuclear power plants and aircraft crews are particularly vulnerable to occupational neutron exposure.

As a result, there is a high demand for effective, long-lasting radioprotective equipment in applications dealing with potential health hazards from various types of radiation. In this section, we will look at radiation and the shielding materials made with boron and boron compounds against it.

The use of special materials such as boron-doped nanoparticles, boron-based polymers, and additives in a boric-oxide matrix to protect people and equipment from *Boron and Boron Compounds in Radiation Shielding Materials DOI: http://dx.doi.org/10.5772/intechopen.111858*

**Figure 1.**

*The boron-doped nanoparticles and boron-based polymers can be effectively used as potential radiation shielding materials in daily life and work-life environments. The use of additives in the boric-oxide matrix is another promising approach for developing glass-based composites for radiation shielding materials.*

the harmful effects of ionizing radiation is known as radiation shielding (see **Figure 1**). Ionizing radiation is made up of high-energy particles or electromagnetic waves that can cause harm to biological tissues and other materials. By absorbing, scattering, or blocking radiation, shielding materials can reduce the amount of radiation that reaches a given area. The radiation shield's effectiveness is determined by several factors, including the radiation's energy and type, the thickness and composition of the shielding material, and the distance between the radiation source and the shielding material. The following equation can be used to calculate the amount of radiation passing through a material [4]:

$$I = I\_o e^{-\mu \mathbf{x}} \tag{1}$$

where *I* is the intensity of the radiation after passing through a material, 0*I* is the initial intensity of the radiation, µ is the material's linear attenuation coefficient, and x is the material's thickness. The linear attenuation coefficient, which is affected by the energy and type of radiation as well as the material's composition, represents a material's ability to attenuate radiation. The greater the linear attenuation coefficient, the better the material attenuates radiation. The amount of radiation passing through a material is also affected by its thickness; the thicker the material, the more the radiation is attenuated. The equation can be used to calculate the thickness of a shielding material required to reduce radiation to a safe level. The material thickness required to reduce the radiation intensity to the desired level can be calculated using the material's linear attenuation coefficient and the radiation's initial intensity. Radiation shields are materials that are used to protect people and equipment from ionizing radiation. The radiation shield's effectiveness is determined by several factors, including the radiation's energy and type, the thickness and composition of

the shielding material, and the distance between the radiation source and the shielding material. Eq. (1) can be used to calculate the intensity of radiation passing through a material and the thickness of shielding material required to reduce the intensity of radiation to a desired level.

#### **2. Gamma, X-ray, and neutron shielding properties of boron and boron compounds**

#### **2.1 Gamma, X-ray, and neutron shielding of boron polymers**

Nagaraja et al. [5] investigated X-ray and gamma radiation shielding parameters such as mass attenuation coefficient, linear attenuation coefficient, Half Value Layer (HVL), Ten Value Layer (TVL), effective atomic number (Zeff), and electron density of various boron-based polymers [Polymer A-Polyborazilene (B3N3H4), Polymer B-4-Vinylphenyl Boronic acid (C8H9O2B), Polymer C-Borazine (B3N3H6), Polymer D-3- Acrylamidophenylboronic acid (C9H10BNO3) Polymer E-Phenylethenylboronic acid (C14H19BO2), Polymer F-4-Aminophenylboronic acid (C12H18BNO2) and Polymer G-3- Aminophenylboronic acid (C6H8BNO2)]. In addition, the neutron shielding properties of boron polymers were examined. These parameters included the coherent neutron scattering length, the incoherent neutron scattering length, the coherent neutron scattering cross section, the total neutron scattering cross section, and the neutron absorption cross section. They analyzed the different boron polymers' shielding properties and compared them to one another. Based on the findings of the in-depth study, it is clear that the boron polymer phenylethenylboronic acid is an efficient radiation absorber, particularly for X-ray, gamma, and neutron radiation. They concluded that the boron polymer phenylethenylboronic acid is an effective material for shielding X-rays, gamma rays, and neutrons from the environment. They used a NaI(Tl) crystal detector with a detection area of 2.54 × 2.54 cm2 that was put on a photomultiplier tube that was enclosed in a lead chamber. Additionally, they made use of an advanced PC-based MCA. A powdered form of the compound was placed within a circular holder made of perspex with a diameter of 1 cm and a standard thickness of 1 cm. The substance was attached straightforwardly to the opening in the lead shield that served as the location of the source. During the course of their research, they discovered that the half-value layer and the tenth-value layer of the boron polymer derived from phenylethenylboronic acid were significantly thinner than those of the other boron polymers that were studied. Boron polymer with phenylethenylboronic acid added makes it less permeable to gamma and X-rays compared to other boron polymers with the same composition. It was demonstrated that the boron polymer derived from phenylethenylboronic acid has a shorter mean free path compared to the other boron polymers that were investigated. Boron polymer with added phenylethenylboronic acid makes it less permeable to gamma and X-rays than other boron polymers with the same composition. Nagaraja et al. [5] were able to show that the boron polymer made from phenylethenylboronic acid had a greater effective atomic number compared to the other boron polymers that were investigated. In addition to this, they found that the effective electron density of the boron polymer that was generated from phenylethenylboronic acid had the greatest value of all of the values that were investigated. They studied a variety of boron polymers and compared their lengths, cross sections, total neutron scattering cross sections, and neutron absorption cross sections for coherent and incoherent neutron scattering parameters. For the phenylethenylboronic acid boron polymer, both the coherent

#### *Boron and Boron Compounds in Radiation Shielding Materials DOI: http://dx.doi.org/10.5772/intechopen.111858*

neutron scattering length and the incoherent neutron scattering length were found to be at their shortest possible lengths. Phenomenally small coherent and total neutron scattering cross sections characterize the phenylethenylboronic acid boron polymer. A boron polymer that contains phenylethenylboronic acid has been shown to have a significant neutron absorption cross section. They assessed several different metrics of coherent and incoherent neutron scattering for a variety of boron polymers. These metrics included lengths, cross sections, the total neutron scattering cross section, and the neutron absorption cross section. The researchers concluded that the coherent neutron scattering length and the incoherent neutron scattering length for the phenylethenylboronic acid boron polymer were both at their shortest conceivable lengths. This was determined by finding that both lengths were at their smallest possible lengths. Both the coherent and total neutron scattering cross sections are exceedingly low in the case of the boron polymer made from phenylethenylboronic acid. The neutron absorption cross section is relatively high in the case of the phenylethenylboronic acid boron polymer.

#### **2.2 The effectiveness of gamma irradiation of polystyrene-b-polyethyleneglycolboron nitride (PS-b-PEG-BN) nanocomposites**

Cinan et al. [1] wanted to investigate the effectiveness of gamma irradiation and the shielding characteristics of PbO-doped crosslinked PS-b-PEG block copolymers and polystyrene-b-polyethyleneglycol-boron nitride (PS-b-PEG-BN) nanocomposites materials in their work. In order to investigate the gamma-ray shielding properties, crosslinked PS-b-PEG block copolymers and PS-b-PEG-BN nanocomposites were combined with varying percentages of PbO. The production of the copolymer was carried out using various techniques, including emulsion polymerization [6, 7]. For the purpose of their research, the researchers utilized the crosslinked PS-b-PEG block copolymers as a polymeric matrix. They also utilized BN and PbO as the radiation absorption functional material in order to lessen the impact of high-energy gamma rays. The gamma-ray attenuation coefficients were compiled, and a study was conducted using the Linear Attenuation Coefficients (LACs, μL) and Mass Attenuation Coefficients (MACs, μm) of the crosslinked PS-b-PEG block copolymers-BN-PbO nanocomposites for a variety of items in the linked photon energy area. They found an admissible consistency between the experimental and theoretical μL and μm of the samples, and the measured and calculated values reflect variations with the modification of the polymer type used to improve the gamma radiation shielding materials. In addition, they found that the samples had an admissible consistency between the experimental and theoretical μms and μLs. In order to achieve the same goal, HVL, TVL, the Mean Free Path (MFP), and the Radiation Protection Efficiency (RPE) values of crosslinked PS-b-PEG block copolymers-BN-PbO nanocomposites were examined in the important critical photon energy area for the gamma-ray attenuation properties. Their findings are a very crucial indicator of the degree to which the material in question is effective at shielding radiation. At the Physics Department of Karadeniz Technical University, the gamma irradiation attenuation factors of the examined composites were obtained for a wide variety of energy spectrums emitted from a 152Eu source using an high-purity germanium (HPGe) detector framework. These energy spectra were measured using gamma rays released from a 152Eu source. To acquire experimental outputs throughout the surveying method, they profited from the computer program Gamma Vision, which maintains powerful multi-channel analyzer capabilities. This allowed them to acquire the outputs of the experiments.

**Figure 2.** *Diagram of the HPGe detector for gamma irradiation attenuation experiments.*

**Figure 2** shows the representation of the HPGe detector for gamma irradiation attenuation experiments.

Mixing PbO in the crosslinked PS-b-PEG block copolymers and the PS-b-PEG-BN nanocomposites matrix increases the odds of contact between the incoming gamma irradiation and the shielding material atoms. It can be determined that their samples can treat as shieldings as opposed to the low dosage fractions from gamma irradiation origins. The LACs values fall together with a surge in gamma radiation energies. The occasion for that circumstance is the interaction of gamma radiation with materials *via* a photoelectric effect, Compton scattering, and pair creation. The photoelectric effect is especially significant in the low gamma energy regions; hence, μL values are higher in the gamma radiation energy zones in which they are found. The Compton effect is predominant in locations with a medium level of irradiation energy, whereas pair creation is predominant in places with an elevated level of gamma irradiation energy; hence, μL worthies begin to decrease with the increase of gamma energies. In addition, it was observed that the radiation protection capacities of the samples improved when PbO or BN percentages of the produced materials were modified. The present study reports on the mass attenuation coefficients (MACs) measured at discrete gamma-ray energy intervals ranging from 121.782 keV to 1408.006 keV. The findings reveal a negative correlation between gamma-ray energy and attenuation aptitude, indicating that as the gamma-ray energy increases, the attenuation of all samples gradually decreases. This is the case. The mixing of PbO in the crosslinked PS-b-PEG block copolymers and the PS-b-PEG-BN nanocomposites matrix results in an increase in the possibility of interaction between the incoming gamma radiation and the gamma-ray shielding atoms. This is because it is more difficult to shield

#### *Boron and Boron Compounds in Radiation Shielding Materials DOI: http://dx.doi.org/10.5772/intechopen.111858*

photons with high gamma energies than it is with low gamma energies of photons. It is possible to conclude that the samples can act as shields even when exposed to gamma irradiation sources that produce the modest dose rates. When there is an increase in the amount of gamma radiation present, the values of the μms go down. In addition, it was found that the PbO and BN percentages of the manufactured materials had an effect on the radiation protection capacities of the samples and that these percentages had an improvement in the radiation protection capacities of the samples. When they examine all of the samples side by side, they can conclude that the larger μms and optimal absorption of gamma rays are due to the increased percent rates of the PbO element in the various compounds. It may be underlined that the samples generated in the research disclose significant and dependable results to enlighten radiation shielding studies if the μm results of all of the samples are examined with a broad viewpoint. This is because these samples were developed in the course of the research. The HVL, TVL, and MFP values that were obtained for these samples are the most important indications of the radiation shielding ability of the newly created materials for radiation shielding at intervals of gamma-ray energy ranging from 121.782 keV to 1408.006 keV. The value of these coefficients determines how significant their radiation protection efficiency is. The lower the value, the more significant their radiation protection efficiency is. The HVL, TVL, and MFP values all scale up or down about a single property. The TVL value, which is the shielding thickness value required to stop 90% of the emitted photons, that is, to absorb them, increases as the photon energy increases. This is because the shielding thickness value is proportional to the value required to stop 90% of the photons. Their findings are an extremely useful indicator of the radiation shielding capacity of the material in question; more specifically, one may conclude that the lower the TVL value of any given sample is, the greater the radiation shielding efficiency will be as a result of the reduced thickness requirements. The HVL values of the samples provide convincing guidance regarding the shielding capacity of the materials in decreasing the photon quantities to half of what they are currently at for the sample thickness. One of the main characteristics that clearly explain the gamma radiation degrading abilities of the shielding substances that are used is the MFP value. The better a substance's ability to shelter other particles from radiation, the lower the MFP value should be. The results that they obtained show that the MFP rates of the other samples increase as the photon energy increases. The success of the materials that were created to measure the attenuation of the gamma photons in the various energy intervals can be monitored by computing the RPE. Therefore, the RPE values for the PbO doped the crosslinked PS-b-PEG block copolymers and the PbO-doped PS-b-PEG-BN nanocomposite materials have been monitoring the densities of the photons as a function of different gamma-ray energy intervals. In their research, it can be seen that the RPE values tend to decrease with increasing energy for all the evaluated composites. According to these findings, the PbO-doped polymer-based composites that they developed have a good performance in shielding gamma radiation. That is to say, the recent adjustments to the doping ratios are proving to be quite successful in lowering the intensity of gamma photons. In addition, it was found that the PbO and BN percentages of the manufactured materials had an effect on the radiation protection capacities of the samples and that these percentages had an improvement in the radiation protection capacities of the samples. When one looks at the HVL and TVL values of those samples, one can see that the sample with the PS-PEG (1000)-BN-S0 has the best HVL value for 121.782 keV with 1.336 cm, and the sample with the TVL value of 4.439 cm has the best value for 121.782 keV. It can be seen that the PS-PEG (1500)-BN-S0 sample has the best HVL

value, which is 7.801 cm, and the best TVL value, which is 25.913 cm. Both of these values come from the energy level 1408.006 keV. When they compare these values with previously indicated values, which are solely polymers in their structure, the contribution of adding BN to the composite is visible. In addition, BN is thought to be a good neutron absorber. Based on this concept, it is simple to conclude that the contribution of BN is significant, given that one expects that the mineral that was added will also be useful for neutron radiation. This conclusion can be reached since one thinks that the mineral will be useful for neutron radiation. As a consequence of this, the materials from their investigation show that PbO doping occurred in the crosslinked PS-b-PEG block copolymers and PbO doping occurred in the PS-b-PEG-BN. Nanocomposite materials are excellent choices for achieving radiation protection objectives for gamma rays. These materials are particularly advantageous as a shielding substance for transporting radiation sources and as an insulating substance for radioactive waste administration facilities or the building industry. When it comes to boosting the hardness, durability, and radiation absorption capacities of the shielding materials, the connecting of several sorts of contributions (such as cement, polymer, and metal oxide, among others) is of the utmost importance. As a result of their low cost and low weight, polymer structures are a significant class of substances that are utilized in radiation shielding research. In addition, polymer structures will be the starting point for many different types of research utilizing composites acquired by suffixing micro or nano-oxide, etc., to investigate radiation attenuation both theoretically and experimentally.

#### **2.3 The gamma-ray shielding properties of the polymer-nanostructured selenium dioxide (SeO2) and boron nitride (BN) nanoparticles**

The gamma-ray shielding properties of crosslinked PS-b-PEG block copolymers combined with nanostructured SeO2 and BN nanoparticles were investigated by Cinan et al. [2] in their work. The PS-b-PEG copolymer as well as nanostructured SeO2 and BN particles, all had a substantial impact on the enhancement of the resistance of the nanocomposites, and the samples with high additive rates demonstrated superior resistance than the other nanocomposites. As a result of the accomplishments, it is possible to conclude that the polymer-based nanocomposites can be utilized as a viable option in the gamma-irradiation-shielding sector of the industry. Their nanocomposites' irradiation properties were studied using rays from a 152Eu source in an HPGe detector setup, and the results were evaluated using Gamma Vision software. In addition, the theoretical calculus was used to determine all of the radiation shielding factors, and these were compared to the findings of the experiments. Because different rays of different energy and wavelengths have varied interactions with the atoms in the material, the 152Eu radioactive source was utilized to offer the most thorough data. The comparability between the experimental findings and the theoretical predictions was found to be satisfactory in all of the nanocomposites.

The PS-b-PEG copolymer as well as nanostructured SeO2 and BN particles had a key role in the enhancement of the resistance of the nanocomposites, and the samples with high additive rates displayed superior resistance than the other nanocomposites did. **Figure 3** presents SEM images of the crosslinked PS-b-PEG block copolymer with BN nanocomposites. BN nanoparticles mixed homogeneously with PS-b-PEG block copolymer. There are roughnesses, particles, pores, and elevations on the surface. Based on the results that were obtained, it is possible to conclude that polymerbased nanocomposites are a good option for use in the gamma-irradiation-shielding

*Boron and Boron Compounds in Radiation Shielding Materials DOI: http://dx.doi.org/10.5772/intechopen.111858*

#### **Figure 3.**

*SEM photographs of the crosslinked PS-b-PEG (10,000) block copolymer+BN nanocomposite (50% PS-PEG (10,000)+50% BN+0% PbO): (a) PS-PEG (10,000)-BN-S0 (12,000× magnification); (b) PS-PEG (10,000)-BN-S0 (4480× magnification).*

discipline in many different applications (such as flexible and durable gamma-radiation-protective systems for the transportation of radioactive materials, isolation for the operations of radioactive waste, and radiation services in hospitals, nuclear power plants (NPPs), the defense industry, the building industry, and many other applications). The theoretical and experimental mL values of the studied nanocomposites were found to be in satisfactory concordance with one another. In particular, the PS-b-PEG block copolymers blended with the nanostructured SeO2 and BN particles' nanocomposite matrix resulted in a significant enhancement in the possibilities of reciprocal influence between the arriving gamma rays and the shielding nanocomposite atoms. This was the case since the PS-b-PEG block copolymers were blended with the nanocomposite matrix. They can conclude that the nanocomposites they have researched can also be employed as materials that guard against low and large doses of gamma radiation. They demonstrated that the μL rates tended to fall when the gamma energy was increased. It was determined that the experimental and theoretical μ<sup>L</sup> rates exhibited good harmony and improved shielding behavior with the change in the polymer type utilized to manufacture gamma-ray-absorbing nanoparticles. This was one of the conclusions that were reached. Moreover, they discovered that the gamma-ray protection properties of the nanocomposites increased when the amounts of nanostructured SeO2 and BN particles contained in the nanomaterials were adjusted. This was another finding made by the researchers. The μm values of the PBSNC5, PBSNC9, PBSNC6, PBSNC8, and PBSNC12 nanocomposites [2] were lower than the mm values of their respective copolymers when the composites including copolymers, SeO2, and BN nanoparticles were tested at 121.782 keV. These nanocomposites had μm values of 0.151, 0.142, 0.242, 0.263, and 0.329, respectively. At this energy, the mm values of the PSNC6 and PSNC11 copolymers [2] dropped from 0.283 to 0.151 and from 0.177 to 0.142, respectively, after the addition of 50 wt% nanostructured BN to the PSNC6 and PSNC11 copolymers. This change was caused by the addition of nanostructured BN. It was determined that the experimental and theoretical μm rates exhibited good harmony; more specifically, it was determined that the PS-b-PEG copolymers combined with nanostructured SeO2 and BN particles in a nanocomposite matrix showed good attenuation and protective outcomes against gamma irradiation. It is possible to conclude that the nanocomposites have

the potential to be used as shielding materials against low and high gamma doses in a variety of settings. For all of the nanocomposites' outcomes, it has been thoroughly emphasized that the experimental and theoretical values demonstrate changes when the type of copolymer that was used to build the nanomaterial for the attenuation of and protection against the impacts of gamma rays is changed. These variations can be seen in both the attenuation and protection that the nanomaterial provides. In addition to this, it was observed that the radiation shielding performance of the other nanocomposites increased when the nanostructural proportions of SeO2 or BN particles included in the nanocomposites were raised. When the μL and μm values of all of the nanocomposites are examined, it is clear that the nanostructured composites cultured in this work demonstrate significant and reliable outcomes in terms of radiation absorption and protection. These findings can be seen when the nanocomposites are examined.

The HVL, TVL, MFP, and RPE rates that have been determined for the nanocomposites are the factors that have the largest impact on the gamma-shielding effectiveness. The gamma-ray shield's qualities have a greater influence on the environment when the HVL, TVL, and MFP rates are reduced. In addition, the performance of the polymer-based nanocomposites that were manufactured to develop the shield for protection against gamma rays over a wide energy range may be seen by calculating the RPE rates. This will show the performance of the nanocomposites. Additionally, it was discovered that the gamma irradiation protective properties of the nanocomposites rose when the amounts of nanostructured SeO2 and BN particles present in the nanomaterials were increased. This was another finding that was made. The TVL rates of the PS-b-PEG block copolymers blended with the nanostructured PbO particles changed from 5.799 cm to 30.725 cm. On the other hand, the TVL rates of the PS-b-PEG (1000) block copolymer blended with the nanostructured SeO2 particles did not change. Furthermore, the HVL rates of the PS-b-PEG copolymers blended with the nanostructured PbO and BN particles changed from 0.967 cm to 7.347 cm (for 15% PS-b-PEG (10,000) copolymer, 15% nanostructured BN, and 70% PbO particles) [8], and the HVL values of the PS-b-PEG (10,000) block copolymer blended with the nanostructured SeO2 and BN particles changed from 0.843 cm to 7.203 cm (for 15% PS-b-PEG (10,000) copolymer, 15% nanostructured BN, and 70% SeO2 nanoparticles). To be more specific, the nanostructured SeO2 additive decreased the thickness while simultaneously improving the radiation absorption efficiency. In addition, the ability of the polymer-based nanocomposites that were designed to detect the attenuation behaviors of the gamma rays in a wide energy range can be detected by computing the RPE rates. When confronted by gamma rays, the copolymers that were combined with nanostructured SeO2 and BN nanocomposites had excellent shielding efficacy (see **Figure 4**). This conclusion may be drawn from all of the researchers' findings. The shielding properties of these composites were comprehensively obtained with the 152Eu gamma radioisotope source by detecting the outputs of nanostructured SeO2 and BN particles blended or unblended in PS-b-PEG-based composite tablets with the experimental system. The infrastructure of this system was created with theoretical calculations *via* the radiation parameters. In addition to this, the morphological and temperature degradation features were examined. It has been observed that increasing the amount of nanostructured SeO2 and BN particles in PS-b-PEG copolymer-structured composite materials results in an increase in the amount of radiation shielding and protection from dangerous gamma rays given by the materials. In this context, the behavior of SeO2 and BN blended and unblended nanocomposites against a gamma radioisotope source with a wide energy range was

*Boron and Boron Compounds in Radiation Shielding Materials DOI: http://dx.doi.org/10.5772/intechopen.111858*

**Figure 4.**

*The μm rates and HVL values of the PS-b-PEG copolymers blended with the nanostructured SeO2 and BN particles under a wide range of gamma irradiation energies.*

investigated. Additionally, an application-oriented study that can be used in fields such as nuclear technology was carried out, and the results of this study can contribute to the scientific literature. The TEM photos also revealed another significant finding, which was that the addition of BN nanoparticles to the nanocomposite brought about a discernible shift in the distribution as well as the particle structure of the SeO2 nanoparticles present in the composite.

#### **2.4 Design and fabrication of high-density borated polyethylene nanocomposites as a neutron shield**

Mortazavi et al. [9] have shown that neutron shielding using polyethylene composites containing boron can be accomplished in a very efficient manner. Their investigation is centered on the manufacturing of borate polyethylene nanocomposites. The purpose of this research is to develop a radiation shield that can be employed effectively in situations in which the user is subjected to both neutron and gamma radiation. They started by making borate polyethylene shields that had 2 and 5% by weight of boron nanoparticles, and then, they compared the neutron attenuation of those shields to that of pure polyethylene. In order to determine the amount of attenuation that Am-Be neutrons experience when traveling through the shields, they used polycarbonate sheets. The mean (standard deviation) of the number of traces induced by neutrons traveling through shields was 1.048810 3 128.98 for polyethylene with 5% by weight, and 289.5610 3 1.1972, and 1.534010 3 206.52 for polyethylene with 2% by weight boron nanoparticles and pure polyethylene. The tensile strength of borate polyethylene nanocomposites was found to be greater than that of pure polyethylene. Neutron attenuation was compared between a borate polyethylene nanocomposite that had 5% by weight boron in it and pure polyethylene, and the results showed that there was a statistically significant difference between the two.

However, there was not a statistically significant difference between having 5% by weight of boron borate in a polyethylene nanocomposite and having 2% by weight of boron. It was also established in this research that the tensile strengths of boron carbide nanocomposites are significantly greater than those of pure polyethylene. It is important to note that the findings of Mortazavi et al.'s earlier research on photon shielding show that the use of nano-sized materials in radiation shielding can only provide better attenuation results in very particular circumstances, such as a limited photon energy range or a limited concentration of nanomaterials in the matrix. This is something that should be kept in mind.

#### **2.5 The nuclear shielding of iron-boron alloys**

Iron-boron alloys play a significant role in powder metallurgy, and Aytac and coworkers [10] looked at their nuclear radiation shielding properties for this study. When bombarded with 152Eu, Fe(100-x)B(x) alloys (where x is 1, 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20) produce photons with energies of 0.0810, 0.1218, 0.2764, 0.3029, 0.3560, 0.3443, 0.3839, and 0.7789 MeV, respectively. The photon intensities were measured with an Ultra-Ge detector. Half-value layers, mean free routes, effective atomic numbers, and effective electron densities were all computed using experimentally observed μm. The results demonstrate that the HVL and MFP values are best for the Fe-B alloy with 20% boron. Research has demonstrated that the addition of boron does not improve Fe-B alloys' photon-shielding properties. However, it was shown to be quite effective in terms of gamma attenuation in the chosen energy range when compared to previously reported shield materials. Neutron dose transmission studies were conducted as well, with removal cross-sectional values (∑R) determined. In contrast to their gamma-shielding properties, Fe-B alloys' neutron reduction capability increased with increasing boron content. The findings from each of the gamma shielding parameters demonstrated that an increasing quantity of boron had a detrimental effect on the alloys' capacity to cut down on gamma radiation. In addition to that, measurements of the equivalent neutron dosage were carried out, and the effective removal cross sections of the alloys were gathered. Based on these factors, it was determined that the alloy's neutron-holding capacity rose along with the percentage of boron present in the alloy. It is anticipated that as a consequence of this, it will be possible to conclude that Fe-B alloys are more effective at absorbing neutron radiation than gamma radiation.

#### **2.6 Boron nitride nanosheet-reinforced WNiCo-FeCr HEAs**

WNiCo-FeCr high entropy alloys (HEAs) were the subject of research conducted by Kavaz et al. [11], who investigated the synthesis and complete characterization of these alloys. These alloys were reinforced with newly created boron nitride nanolayers (BNNSs). In this work, a comprehensive investigation was conducted into the effect of B4C on the structural, physical, mechanical, and nuclear protective features of synthesized HEAs. The investigation focused on the effect of B4C's monotonous behavior modifications. They were able to ascertain the characteristics of protection against nuclear radiation through the use of experimental gamma-ray and neutron assemblies. In addition, the properties of nuclear radiation shielding for gamma rays and fast neutrons were carefully compared with the properties of many other kinds of shielding materials, both those already in use and those of the next generation. They concluded that an elevated level of B4C directly adds to the

shielding qualities of nuclear radiation after reviewing the relevant evidence. They state that the B4C that is formed within the structure of BNNS will contribute to the overall properties of HEAs. This is highly essential for nuclear applications, as HEAs are now being examined as a component of potential future nuclear reactors. In addition, they concluded that B4C is a versatile material that can be utilized in settings where the mechanical and nuclear shielding qualities need to be improved for a variety of radiation intensities. This led them to the conclusion that B4C is a versatile material.

#### **2.7 B4C particle-reinforced Inconel 718 composites**

Gokmen [12], in his work, wanted to offer a computational tool that would perform calculations of critical physical variables for the gamma-ray attenuation in the B4C (0.25 wt%) particle-reinforced Inconel 718 superalloy. Specifically, the purpose of this study was to determine the gamma-ray attenuation in the material. It was the first time that the shielding qualities of the B4C (0.25 wt%) particle-reinforced Inconel 718 superalloy were investigated for use in nuclear technology as well as other technologies such as nanotechnology and space technology. The relationship between the weight percentage of the B4C component in these superalloy materials and the attenuation of gamma rays was investigated. The LAC, MAC, Exposure Buildup Factors (EBF), TVL, HVL, MFP, Zeff, and fast neutron removal cross sections (FNRC) values of the B4C (0e25 wt%) particle-reinforced Inconel 718 superalloy composites (which contains special alloy elements such as Ni, Cr, Nb, Mo) were theoretically calculated for the first time in order to evaluate the effectiveness of gamma and neutron radiation shielding using the PSD software. The attenuation performance of the materials, which may be utilized as shielding materials, improved as a result of a decrease in the weight fraction of the B4C compound in the Inconel 718 superalloy composites, as evidenced by the computed values of the MAC. The MFP, HVL, and TVL values were found to increase as the gamma-ray energy and the weight percent of the B4C component found in the Inconel 718 superalloy composites was increased. This was observed to be the case. This occurred because of the density as well as differences in the chemical makeup of certain superalloy compounds. Due to the greater values of MFP, HVL, and TVL, it can be deduced that thicker materials are necessary to attenuate radiation to a level that is considered safe. Because of this, it is preferable to choose materials with lower HVL values rather than those with higher HVL values in order to cut down on both the cost and the size. As a consequence of this, the Inconel 718 superalloy materials with B4C addition are incapable of successfully absorbing a wide variety of gamma rays. This is because these materials have a low gamma absorption cross section. Because of this, the superalloy Inconel 718 material known as S6 which contains B4C in a weight percentage of 25% was discovered to be the most effective neutron shielding material. Because the energy of the incident gamma rays influences both the selection of the shielding material and the determination of the required thickness of the shielding material, this study reveals that each quantity is dependent on the energy.

#### **2.8 Borate glasses**

The expanding applications of gamma radiation in fields such as health, industry, and agriculture call for the research and development of radiation shielding materials that are see-through. According to Kirdsiri et al. [8], glass materials are perfect

for this purpose since they can be recycled completely, they do not have an opaque appearance, and they can be modified and transformed by adding new components.

Nuclear radiation attenuation and mechanical characteristics were inspected by Lakshminarayana et al. [13] for 10 lithium bismuth borate glasses with varying levels of Bi2O3 concentration (ranging from 10 to 55 mol% and denoted as glasses A to J). This was done in order to gain an understanding of how these properties would change with an increase in Bi2O3 content. At a selection of twenty-five energies ranging from 15 KeV to 15 MeV, photon shielding abilities in respect to μ, μ/ρ, Zeff, Neff, HVL, TVL, MFP, and RPE have been investigated. At each energy level, it was found that the μ/ρ values that were calculated using theoretical (Py-MLBUF [14] and WinXCOM [15]) and computational (MCNPX [16], FLUKA [17, 18], and PHITS codes [19]) methods were in qualitative agreement with one another. For example, each Py-MLBUF, WinXCOM, MCNPX, FLUKA, and PHITS algorithms got a different /g value for sample J at 0.6 MeV energy. These values were 0.119, 0.1186, 0.1126, 0.1183, and 0.1174 cm2 /g, respectively.

In this research work, Almuqrin et al. [20] aim to evaluate the radiation shielding capabilities of a Yb3+-doped calcium borotellurite glass system as part of their investigation. The system's fundamental components are CaF2–CaO–B2O3–TeO2–Yb2O3, but for convenience's sake, one is referring to it as TeBYbn. It was determined what would happen if the amount of TeO2 in the glasses was increased from 10 to 54 mol% by experimenting with five distinct combinations of compositions and densities. Investigation into the μm (μ/ρ) of the samples was carried out with the help of the Phy-X/PSD program [21]. The mass attenuation coefficients were calculated theoretically by using an online program that was designed to calculate shielding characteristics. Other metrics, such as the μL, transmission factor (TF), RPE, Zeff, and MFP, were then computed and studied after that. TeBYb5, the glass with the highest TeO2 content, was demonstrated to have the highest μ/ρ; however, at higher energies, the variations between the values became essentially insignificant. It was discovered that density increases with density, such as going from 0.386 to 0.687 cm−1 for TeBYb1 and TeBYb5 at 0.284 MeV, respectively. It was determined that there is an inverse association between the thickness of the sample and the TF because it was discovered that samples with a thickness of 1.5 cm had the lowest TF. Because both the HVL and the TVL of the samples declined as the density of the samples dose, one can conclude that TeBYb1 is the least effective of all of the glasses that were studied. These five samples were able to demonstrate their effectiveness as radiation shields by having an MFP that was lower than that of certain other types of shielding glasses. TeBYb5 appeared to have the greatest capacity to attenuate photons based on the parameters that were determined.

Lakshminarayana et al. [22] investigated the gamma-ray and neutron attenuation properties of both the B2O3-Bi2O3-CaO and the B2O3-Bi2O3-SrO glass systems in their research. This was done for both of the glass systems. Within the energy range of 0.015 to 15 MeV, linear attenuation coefficients (μ) and mass attenuation coefficients (μ/ρ) were estimated by using the Phy-X/PSD program. The obtained numbers fit up quite well with the respective simulation results computed by the MCNPX, Geant4 [23–25], and Penelope [26] programs. The inclusion of Bi2O3, rather than B2O3/CaO or B2O3/SrO, results in increased gamma-ray shielding competency. This is indicated by an increase in the Zeff as well as a decrease in the HVL, TVL, and MFP. Within the range of 0.015 to 15 MeV, a geometric progression (G-P) fitting approach was utilized to determine EBFs and energy absorption buildup factors (EABFs) at 1 to 40 mfp penetration depths (PDs). The RPE values that have been computed show that they have a high capacity for shielding photons with lower energies, comparatively greater

density (7.59 g/cm3 ), larger μ/ρ, Zeff, equivalent atomic number (Zeq), and RPE, along with the lowest HVL, TVL, MFP, EBFs, and EABFs derived for 30B2O3-60Bi2O3-10SrO (mol%) glass, implying that it could be an excellent gamma-ray attenuator. Additionally, 30B2O3-60Bi2O3-10SrO (mol%) glass holds a commensurably bigger macroscopic removal cross section for fast neutrons. <sup>−</sup> ∑= <sup>1</sup> 0.1199 *cm* obtained by

*R*

applying Phy-X/PSD for fast neutron shielding, owing to the presence of a larger wt% of 'Bi' (80.6813 wt%) and moderate "B" (2.0869 wt%) elements in it. Because it has a high weight percentage of the "B" element, the sample with the composition 70B2O3- 5Bi2O3-25CaO (mol%) (B: 17.5887 wt%, Bi: 24.2855 wt%, Ca: 11.6436 wt%, and O: 46.4821 wt%) has a high potential for the capture or absorption of thermal or slow neutrons and intermediate energy neutrons.

During the course of their research, Madbouly and colleagues [27] looked at bismuth-borophosphate glasses. One type of glass known as borophosphate glass contains phosphorus and boron oxide as components. Borophosphate glass is an important category of glass that can be distinguished by several useful qualities that it contains. Borophosphate glass has been demonstrated to have excellent ionic conductivity, and its preparation is very straightforward. Despite its low melting point and high glassforming capacity, the application of borophosphate glass has been limited because of its hygroscopic character. This is even though it has a relatively low melting point. It is recommended that a heavy metal oxide (HMO) be added to the produced glass in order to increase its potential for radiation shielding. The metal oxide with the highest density is known as HMO. In addition to this, the high atomic number of Bi contributes to the enhanced gamma shielding capabilities of the glass [28]. In applications that make use of radiation, protective glasses are increasingly being utilized to absorb incoming photons that could potentially harm employees and patients in the area surrounding the radioactive source. Radiation is currently being utilized in hundreds of applications spanning a variety of industries, such as the medical area and the production of energy. Even though radiation has certain positive effects, extra caution is required while working with radioactive sources since photons with a high energy level pose a significant threat to the human body. In this work, they investigate the effect that Bi2O3 has on the structure of borophosphate glasses as well as the optical and radiation shielding properties of these glasses. They measured the photon transmissions, μLs, HVL, TVL, and MFP values of bismuth-borophosphate glasses experimentally. The gamma-ray energies they employed were 662, 1173, 1275, and 1333 keV. After that, the results of the measurements were checked against the FLUKA code. The conclusions from the FLUKA code were in good agreement with the results of the experiments. In addition, the data demonstrate that increasing the amount of Bi2O3 in the glass network improves the quality of shielding. According to the data they currently have, the absorbance increases in tandem with a rising Bi2O3 level. Bismuth-borophosphate glasses have excellent gamma-ray shielding capabilities, making them a good choice for shielding applications.

For shielding applications against the energies emitted by 22Na and 131I isotopes, Al-Buriahi [29] used FLUKA to examine the radiation of gamma and fast-neutron shielding performance of borate glasses containing zinc, bismuth, and lithium (as modifier). Glasses ranging from 0 to 20 mol% xBi2O3-(25-x) Li2O-60B2O3-15ZnO were analyzed. For the 22Na isotope, the simulations are in run for energies of 0.511 and 1.275 MeV, and for the 131I isotope, the energies of 0.365, 0.637, 0.284, and 0.723 MeV. In addition, the report explored the borate glasses' capacity to deflect fast neutrons, thermal neutrons, and charged particles. The results show that the 22Na isotope emits photons with energies as low as 0.284 MeV and that the borate glasses of BLBZ1, BLBZ2, BLBZ3, BLBZ4, and BLBZ5 have values of 0.282, 0.349, 0.887, 1.103, and 1.397 cm−1 and values of 0.108, 0.198, 0.251, 0.286, and 0.310 cm2 /g. At 0.2 MeV, the borate glasses BLBZ1, BLBZ2, BLBZ3, BLBZ4, and BLBZ5 had maximum total SP of electron interaction values of 2.292, 2.076, 1.949, 1.865, and 1.807 MeV cm<sup>2</sup> /g, respectively. Furthermore, for the current borate glass samples, the effect of Bi2O3 content on the dosage rate was quite minimal. The removal cross sections for fast neutrons in the borate glasses of BLBZ1, BLBZ2, BLBZ3, BLBZ4, and BLBZ5 were 0.112, 0.111, 0.103, 0.100, and 0.106 cm−1, respectively. It is concluded that BLBZ5 glass has the potential to be developed as a viable option for gamma applications. **Table 1** shows the glass code, chemical formula, and weight fraction (wt %) for each component in the current glass specimens.

Borotellurite glasses with the molar compositions of 60TeO2–20B2O3–(20-x)Bi2O3– xPbO, where x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 mol%, were synthesized with the help of a typical melt quenching procedure and investigated in terms of their physical, optical, structural, and gamma shielding capabilities. Marzuki and colleagues [30] researched these spectacles. After being mixed, the powder was subsequently melted in an electric furnace at a temperature of around 1000°C for approximately 60 minutes. After being quenched by pouring it into a preheated parallel plate brass mold, the molten metal was subsequently annealed at 350°C for roughly 180 minutes before being cooled to room temperature at a rate of 1°C per minute. When the concentration of PbO is increased from 0 to 10 mol%, the density of the current samples decreases from 6.08 to 5.93 g/cm3 , and the molar volume decreases from 33.37 to 30.27 cm3 /mol. This is because there is a decrease in the concentration of the element Bi2O3. Because PbO is used throughout the network rather than Bi2O3, the optical packing density has increased from 71.91 to 72.67% as a direct result of this change. When the concentration of PbO increases, the refractive index, molar refractivity, and ionic polarizability all decrease. Specifically, the refractive index drops from 1.9137 to 1.8306, the molar refractivity drops from 18.531 to 16.884 cm3 , and the ionic polarizability drops from 7.3534 to 6.7000 3. An increasing fraction of the glass network will be formed of [TeO3] (tp) and [TeO3+1] polyhedra as the amount of lead oxide present in the glass increases. The Phy-X PSD software [21] was used in the theoretical research of the gamma radiation shielding qualities, and the photon energy was varied from 0.015 to 15 MeV throughout the study. When considering all glasses, the values of the μ<sup>L</sup> that are observed to be the highest are found at 0.015 MeV, while the values that are observed to be the values that are observed to be lowest are found around 5 MeV. At this stage of the gamma photon-electron interaction, the formation of pairs starts to


#### **Table 1.**

*Glass code, chemical formula, and weight fraction (wt%) for each component in the current glass specimens.*

#### *Boron and Boron Compounds in Radiation Shielding Materials DOI: http://dx.doi.org/10.5772/intechopen.111858*

take precedence over everything else. When there is an increase in the concentration of PbO, there is a corresponding decrease in the concentration of Bi2O3; this causes the LAC values to decrease across all photon energies. The values of the μL change from a high of 413.2183 cm−1 to a low of 12.4962 cm−1 when the potential energy is 0.015 MeV. This dependence on composition is at its most pronounced for photon energy in the range of 0.015–0.04 MeV. When the energy is greater than 0.04 MeV, this dependence is greatly diminished. The outcomes of this experiment at μL suggest that using Bi2O3 as a gamma shielding material rather than PbO is likely to give better results. The experiment was conducted to investigate this hypothesis.

The study conducted by Mahmoud et al. [31] sought to examine the impact of Pr3+ ions on the structural, optical, and gamma-ray shielding characteristics of borosilicate glasses. This study produced a set of borosilicate glass specimens comprising five distinct samples. The samples were composed of a mixture of (55-x) B2O3, 15SiO2, 20CaO, 10Li2O, and xPr6O11. The objective of the study was to investigate the effects of Pr6O11 on the structural, optical, and X-ray shielding characteristics of borosilicate glass. The findings obtained from the UV-Vis IR spectrometer indicate a reduction in the direct energy gap from 3.508 to 3.304 eV, which is accompanied by an elevation in the Urbach energy from 0.335 to 0.436 eV. These changes are observed as the concentration of Pr6O11 is increased from 0 to 1 mol%. Furthermore, the Monte Carlo simulation outcome about the shielding characteristics of X-rays illustrates an increase in the micrometer values as a result of the minor amounts of Pr6O11 reinforcement. At an energy level of 103 keV, the micrometer values experienced a 161% increase, while the 0.5 values decreased by 62% upon increasing the Pr6O11 concentration from 0 to 1 mol%. At higher intermediate and high-energy gamma (E) values, the gamma-ray shielding properties of the produced glasses exhibit a negligible improvement. This study posited that the samples under investigation are suitable for shielding photons possessing energies that are less than 511 keV.

#### **3. Conclusions**

Nanocomposite materials are excellent choices for achieving radiation protection objectives for gamma rays. These materials are particularly advantageous as a shielding substance for the transportation of radiation sources and as an insulating substance for radioactive waste administration facilities or the building industry. As a result of their low cost and low weight, polymer structures are a significant class of substances that are utilized in radiation shielding research. A boron polymer that contains phenylethenylboronic acid has been shown to have a significant neutron absorption cross section. They assessed several different metrics of coherent and incoherent neutron scattering for a variety of boron polymers. In addition, polymer structures will be the starting point for many different types of research utilizing composites acquired by suffixing micro- or nano-oxide, etc., to investigate radiation attenuation both theoretically and experimentally. It has been observed that increasing the amount of nanostructured SeO2 and BN particles in PS-b-PEG copolymerstructured composite materials results in an increase in the amount of radiation shielding and protection from dangerous gamma rays given by the materials. In this context, the behavior of SeO2 and BN blended and unblended nanocomposites against a gamma radioisotope source with a wide energy range was investigated. It was also established that the tensile strengths of boron carbide nanocomposites are significantly greater than those of pure polyethylene. The findings from each of the

gamma shielding parameters demonstrated that an increasing quantity of boron had a detrimental effect on the alloys' capacity to cut down on gamma radiation. In addition to that, measurements of the equivalent neutron dosage were carried out, and the effective removal cross sections of the alloys were gathered. Based on these factors, it was determined that the alloy's neutron-holding capacity rose along with the percentage of boron present in the alloy. It is anticipated that as a consequence of this, it will be possible to conclude that Fe-B alloys are more effective at absorbing neutron radiation than gamma radiation. It is concluded that B4C is a versatile material that can be utilized in settings where the mechanical and nuclear shielding qualities need to be improved for a variety of radiation intensities. This led them to the conclusion that B4C is a versatile material. The Inconel 718 superalloy materials with B4C addition are incapable of successfully absorbing a wide variety of gamma rays. This is because these materials have a low gamma absorption cross section. Because of this, the superalloy Inconel 718 material known as S6 which contains B4C in a weight percentage of 25% was discovered to be the most effective neutron shielding material. Because the energy of the incident gamma rays influences both the selection of the shielding material and the determination of the required thickness of the shielding material, this study reveals that each quantity is dependent on the energy. The boron-doped nanoparticles and boron-based polymers can be effectively used as potential radiation shielding materials in daily life and work-life environments. The use of additives in the boric-oxide matrix is also another promising approach for the development of glass-based composites for radiation shielding materials.

#### **Acknowledgements**

The authors thank to Karadeniz Technical University for their support. In addition, the authors also would like to express gratitude to Bilkent University UNAM for their kind hospitality.

*Boron and Boron Compounds in Radiation Shielding Materials DOI: http://dx.doi.org/10.5772/intechopen.111858*

### **Author details**

Ahmet Hakan Yilmaz1 \*, Bülend Ortaç2 and Sevil Savaskan Yilmaz2,3

1 Department of Physics, Faculty of Sciences, Karadeniz Technical University, Trabzon, Turkey

2 UNAM-National Nanotechnology Research Center and Institute of Materials Science and Nanotechnology, Bilkent University, Ankara, Turkey

3 Department of Chemistry, Faculty of Sciences, Karadeniz Technical University, Trabzon, Turkey

\*Address all correspondence to: hakany@ktu.edu.tr

© 2023 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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#### **Chapter 5**

## Some Features of Boron Isotopes Separation by Laser-Assisted Retardation of Condensation Method

*Konstantin A. Lyakhov*

#### **Abstract**

Boron isotopes have many applications in industry: medicine, semiconductor, and solar energy. Especially massive demand is for boron-10 isotopes in nuclear industry for nuclear reactors shielding and control. Various aspects of laser-assisted boron isotope separation by retardation of condensation method, such as irradiation conditions and laser and vacuum system design, have been considered. Irradiation conditions include interaction scheme of laser radiation and supersonic beam, dependence of efficiency of excitation on gas flow temperature and pressure. Basic physical constraints on laser intensity and its spectral properties have been discussed. The relation of gas flow properties, nozzle design, and vacuuming rate has been elucidated as well.

**Keywords:** boron isotopes, laser-assisted isotope separation, overcooled supersonic gas flow, vacuum system design, laser and optical system design, turbomolecular vacuum pump

#### **1. Introduction**

Most important applications of boron isotopes are related to boron additives widely employed in nuclear plants, as boron carbide used in control rods, or as boric acid solution used as a chemical shim in the Pressurized Water Reactors(PWR) and semiconductor industry. Due to the much larger thermal neutron absorption crosssection of boron-10 (*σ<sup>n</sup>* ¼ 3837 barn) than for boron-11 (*σ<sup>n</sup>* ¼ 0*:*005 barn) the use of enriched H3BO3 allows to reduce the total amount of boron-based poison material in the primary reactor coolant system and, therefore, to reduce corrosion and wear on the other components of the reactor core [1]. Boron-10 enriched compounds are also used to increase the efficiency of nuclear reactor emergency shutdown systems and for nuclear fuel transportation. In semiconductor industry, boron is routinely used for producing p-type domains in silica. Decreasing the size of electronic devices makes the problem of heat removal more and more important. Its solution can be using isotopically pure boron, which provides minimal distortion of the crystal structure of silica matrix and minimizes the thickness of boron acceptor layers, and, therefore,

increases the heat conductivity of the acceptor layer and the transistor switching power [2]. Boron-11 can be used in this case, because protection from cosmic and other kinds of radiation becomes important with advancing miniaturization of electronic devices and in solar panels [3, 4]. Moreover, boron isotope enriched boron nitride used in nanotubes and nanoribbons has high potential for applications in nanotechnology [5–7]. As an example, in spacecraft semiconductors boron-10 enriched BN nanotubes, can be used for radiation shielding [8]. Boron-10 can be also used as a neutron-detecting component in self-powered solid-state neutron detectors [9], used in nuclear materials studies and in well logging. Boron-10 in health care is applied in boron neutron capture cancer therapy [10–12], and in studies of food properties aimed at preventing cancer and other diseases [13].

There are three methods for boron isotopes separation commonly used in industry. These methods are based on the chemical exchange reaction [14], low-temperature fractional distillation [15], and gas centrifuging. In these methods, BF3 is used. In gas centrifuging, BCl3 due to its high vapor pressure at room temperature, can be also used, but it is far less efficient, because of presence of three chlorine isotopes. However, using BF3 is not economically justified, because 86% of price for high purity 10B comes from powder extraction from BF3. Hence, other methods, which rely on using BCl3, are needed.

Laser-assisted methods comprise Atomic Vapor Laser-assisted Isotope Separation (AVLIS) [2], and Molecular Laser Isotope Separation (MLIS) methods, also known as Selection of Isotopes by Laser EXcitation (SILEX) [16–18], http://www.silex.com.au/ businesses/silex. MLIS methods can be classified as following: Chemical Reaction by Isotope Selective Laser Activation (CRISLA) [19–21], Condensation Repression by Isotope Selective Laser Activation (CRISLA-2) scheme (this scheme is also known as Separation of Isotopes by Laser-Assisted Retardation of Condensation (SILARC)), and Cold Walls Laser-Assisted Selective Condensation (CWLARC) scheme (this scheme is also known as SILARC-2 [22]). Laser-assisted methods are based on the selective excitation of target isotopes in atomic or molecular form by laser radiation. Selectivity is expressed *via* specific for different target isotopes in atoms or molecules resonantlike photon energy dependence of photoabsorption cross section. In case if multiphoton dissociation is used as isotope selection mechanism, frequency of infrared (IR) laser radiation should be red-shifted [21]. Two lasers (IR + UV) can be used for dissociation or ionization of molecules. In contrast to high selectivity, subsequent chemical reactions in CRISLA method can significantly deteriorate efficiency of the process. CWLARC method has three major disadvantages: Firstly, coaxial nozzle throughout is very low, which makes it only attractive for medicine applications, secondly, wall temperature should be kept at the same low-temperature level in quite narrow interval due to the specific temperature dependence of enrichment factor, and, thirdly, isotope harvesting success strongly depends on the symmetry of selectively excited molecules. As a general advantage of SILARC methods is that only a few photons are needed for selective excitation instead of several dozens of photons required in the methods based on multiphoton dissociation (CRISLA) or ionization (AVLIS). In contrast to popular laser-assisted methods, such as Molecule Obliteration Laser Isotope Separation(MOLIS) and Atomic Vapor Laser Isotope Separation (AVLIS), large laser fluence is not required and even harmful for isotopes harvesting in SILARC methods, due to destructive resonant interaction of strong electric fields with target molecules. Ideally, laser intensity should be just high enough for molecular excitation, and, therefore, able to guide molecular dynamics in needed direction. Moreover, SILARC methods are more efficient because of typically two orders of

*Some Features of Boron Isotopes Separation by Laser-Assisted Retardation of Condensation… DOI: http://dx.doi.org/10.5772/intechopen.111948*

magnitude higher linear photo-absorption cross section, than nonlinear multiphoton absorption cross section [23]. Moreover, the controllability of sequential isotope scrambling effects is more easier. The total energy consumed by vacuum pumps to provide optimal pressure level in discharge chamber ( 10<sup>2</sup> 1 torr), is normally significantly smaller in MLIS methods than in AVLIS, where requirements for vacuum level in discharge chamber are exceptionally high (10<sup>6</sup> <sup>10</sup><sup>7</sup> torr). Therefore, only SILARC method deserves more detailed analysis.

SILARC method conceived by Y.T. Lee in Ref. [24], and developed by Jozef Eerkens in [22, 25]. In this method isotopes harvesting is based upon well established mass separation effect in overcooled supersonic gas flow: monomers escape gas flow core at higher rate than van der Waals clusters (dimers and higher oligomers). The larger mass difference the more separation effect is pronounced. In order to produce gas flow with uniform pressure distribution, specially profiled supersonic nozzle should be designed. Formed oligomers can be drawn from the flow either by some cold surfaces (wavy plates or walls as in SILARC-2) [17, 26], or by skimmer blade as in SILARC scheme [26]. Viability of this method was originally demonstrated on example of sulfur isotope separation in SF6 target gas mixed with argon [27, 28].

At the first glance, the isotope production rate should increase with increasing nozzle throughput, which can be achieved by increasing nozzle dimensions, number of nozzles, or gas flow density. In the latter case, applying the laser radiation to a dense gas flow is not able to change mass distribution of formed clusters, because irreversible cluster growth sets in (in majority of clusters are over-critical [29]), and, therefore, monomer molar fraction available for excitation is rapidly decreasing. If gas flow density is not too high, then quantum optimal control methods can be helpful [30]. Too high gas density corresponds to the case when cluster loading is larger than the critical one, so-called over-critical loading. In this case, clusters are normally ionized by electromagnetic radiation but not decouple [31, 32]. However, if the gas flow dilution is high enough, its temperature is low, and transition time of molecules across irradiation cell (IC) is not too long, then the population of under-critical clusters is decreasing much slower. The upper limit for IC length is given by the condition, that the fraction of under-critical clusters in the gas flow is vanishingly small because most of them escaped gas flow. Apparently, only in the case, when under-critical clusters are still in the gas flow irradiation zone, selective resonant-like absorption of laser photons by target gas molecules can lead to retardation of their further binding with surrounding carrier gas molecules. Here, it will be considered only such gas flow pressures and temperatures that gas flow is mostly represented by monomers and dimers. We demonstrated, that increasing nozzle dimensions will decrease product cut and overall performance of isotope separation process. Therefore, only increasing the number of nozzles is the only option left to control.

Since enrichment factor and product cut are small, isotopes should be extracted by many recirculations of the gas flow. Calculations of the product cut, describing degree of gas flow separation, and enrichment factor, describing isotope content in the separated part of the gas flow, were carried out on the basis of static approximation of the transport model developed in Ref. [26].

In Ref. [33] we developed an iterative scheme for one-stage cascade and in Ref. [34] for two-stage cascade. Each cycle in this scheme corresponds to transition time of gas molecule through IC.

Configuration of the skimmer inlet should correspond to population profile of excited molecules across the separation cell cross section at the end of IC. In order to keep at minimum gas flow disturbance induced by skimmer inlet, it should be also carefully designed [35, 36].

Optimal pressure and temperature fields inside the gas flow can be provided by adequate nozzle wall shape, IC and skimmer chamber geometry, and proper choice of core and rim gas evacuation rates. Also, due to specific pattern of velocity field, yielded by the given nozzle design, the efficiency of isotope extraction is directly related to the skimmer inlet configuration and its distance from the nozzle outlet.

Since optimal enrichment facility design should be a compromise between selectivity (or time spent for extraction of a given amount of isotopes) and related energy consumptions (should be made as small as possible), we suggest that adequate criterion for efficiency of separation should correspond to the minimum of the objective function, which has a meaning of average over time of total energy consumed per unit isotope recovery [37].

In Refs. [38–40], it has been demonstrated that using an irradiation cell for isotope separation in SILARC scheme as an absorber part of CO2 laser resonator can substantially cut electricity consumption. The idea to use a resonator as a multi-pass cavity for isotopes separation is not a novel one. For instance, as shown in Ref. [41], the use of resonator allows to increase production of selectively ionized 168Yb by the order of magnitude. Moreover, in Ref. [42], it has been shown that the selectivity of dissociation of CF2HCl molecules by CRISLA method can be significantly increased, if they are introduced inside resonator cavity of CO2 laser.

In case of overcooled gas flow, photo-absorption spectra are very narrow (only collisional broadening is dominant). Hence, the proper choice of laser pulse spectrum is crucial. In the case of CW-mode irradiation, hitting the target isotopologues is especially problematic for CO2 laser, because it's emission spectrum is only discretely tunable, while the laser emission line should coincide with center of photo-absorption line with accuracy not worse than its full width at half of maximum (FWHM). At room temperature, the fundamental vibrational mode *ν*<sup>3</sup> of BCl3 can be excited by CO2 laser pulses, having emission lines 10P(8)-10P(28) in their spectrum. At laser intensities lower than saturation limit, 10P(8)-10P(16) lines are better absorbed [43], while at larger laser intensities, where multiphoton processes start to play essential role, photo-absorption maximums are more red-shifted 10P(24)-10P(28) [19, 44, 45]. By increasing pressure in the laser medium, frequency mismatches can be compensated due to emission line broadening effects. However, due to high collision rate at room temperature, the rate of excitation loss equals to or even lower than the rate of excitation gain. Hence, in order to diminish it, the gas should be sufficiently dilute and cold. These conditions both can be fulfilled by supersonically expanding rarefied gas flow.

This chapter is of the following structure. In Section 2, the transpart model to describe main features of the SILARC method is presented. In subsection 2.1, some details of evaluation of spectral properties of photo-absorption cross section are given. In subsection 2.2, definitions and results of calculation of product cut and enrichment factor are given. In Section 3, the operational principles of boron isotopes separation facility and physical processes, they are based on, are elucidated. In Section 4, gas flow irradiation conditions, such as laser spectrum choice and beam radius, are given. In subsection 4.1, basic constraints on laser intensity variation range are discussed. In Section 5, gas flow properties and requirements applied on vacuum system to provide their optimal choice are given. In subsection 5.1 examples of calculation of optimal nozzle wall shape are given. In subsection 5.2, the calculation of minimal required vacuum pump rate related to the given nozzle profile is given schematically.

*Some Features of Boron Isotopes Separation by Laser-Assisted Retardation of Condensation… DOI: http://dx.doi.org/10.5772/intechopen.111948*

#### **2. Transport model**

Excitation dynamics of the overcooled gas flow, controlled by selectively tuned laser field for this target gas, can be modeled by the transport equations, describing population dynamics of four characteristic groups of species, presented in dilute enough overcooled gas flow [26]. Molar fractions of these characteristic groups fulfill the following material balance equation:

$$f\_{\rm im} + f\_{\rm i\*} + f\_{\rm i!} + f\_{\rm id} = \mathbf{1},\tag{1}$$

where *fi*m, *fi* <sup>∗</sup> , *fi*! , and *fi*<sup>d</sup> are molar fraction of monomers, excited monomers, epithermal, and dimers of *i*th isotopologue of the target gas molecule, respectively. Population dynamics of these characteristic groups are described by the following system of equations

$$\begin{cases} \frac{df\_{i\*}}{dt} = k\_{\text{df}} - f\_{i\*} \left\{ (1 - e\_{\*}) (k\_{\text{df}} + k\_{\text{VV}} + k\_{\text{VT}} + k\_{\text{se}}) + e\_{\*} k\_{\text{W}} \right\},\\ \frac{df\_{i!}}{dt} = (1 - e\_{\*}) (k\_{\text{df}} + k\_{\text{VT}}) f\_{i\*} - \{ (1 - e\_{1}) k\_{\text{th}} + e\_{1} k\_{\text{W1}} \} f\_{i!},\\ \frac{df\_{\text{id}}}{dt} = k\_{\text{df}} f\_{i\text{m}} - k\_{\text{df}} f\_{i\text{d}}. \end{cases} \tag{2}$$

Here, *k*df and *k*dd are dimer formation and dissociation rates, *k*VT and *k*VV are vibration-translational and vibration-vibrational relaxation rates, *k*se is photon spontaneous emission rate, *k*th is epithermals thermalization rate, *k*W1 is "wall" escape rate for epithermals, *e* <sup>∗</sup> and *e*<sup>1</sup> are to-the-wall survival probabilities for excited monomers and epithermals, respectively. In our calculations, it was taken into account, that transport coefficients depend on the respective isotopologue mass (index *i* will be omitted below when no confusion occurs). In our case with sufficiently low gas flow pressure and target gas molar fraction, vibration-translational *k*VT, vibrationvibrational *k*VV , and photon spontaneous emission rate *k*se are very small and can be neglected. By assuming steady gas flow and continuous wave irradiation, the system transport equations are reduced to the system of algebraic equations, which was solved in Ref. [26].

Laser excitation rate is given by:

$$k\_{\rm A} = \frac{\sigma\_{\rm abs}(\nu\_{\rm ex})}{h\nu\_{\rm ex}} \frac{t\_{\rm int}}{t\_{\rm tr}} \phi\_{L},\tag{3}$$

where *<sup>t</sup>*int <sup>¼</sup> <sup>2</sup>*RL <sup>U</sup>* is gas flow transition time across laser beam in case of continuous wave irradiation and *t*int ¼ *νpτpt*tr in case of pulsed irradiation, and *ϕ<sup>L</sup>* is the laser field distribution, which is assumed to be pencil-like with radius *RL*, which corresponds to full cross-wise overlap with planar gas flow(for higher nozzle throughput):

$$
\phi\_L = \frac{I\_{\rm las}}{\pi R\_L^2},
\tag{4}
$$

where *I*las ¼ *I*CW in case of CW-lasing, and *I*las ¼ *Ip* in the case of pulsed lasing.

#### **2.1 Evaluation of photo-absorption cross section**

According to Refs. [44, 46, 47], BCl3 molecules photo-absorption spectra in gaseous state are regularly blue-shifted by � <sup>8</sup> � 9 cm�<sup>1</sup> in respect to their values for BCl3 isolated in argon matrix [48]. Since BCl3 belongs to one of two symmetry groups, *D*3*<sup>h</sup>* or *C*2*v*, depending on whether the masses of chlorine isotopes are the same or not, the lines, corresponding to ~*λ*<sup>1</sup> and ~*λ*<sup>4</sup> are contributed by both, so that respective absorption peak intensities are proportional to the following probabilities<sup>1</sup> :

$$p^{(1)} = P\left( (\mathfrak{B}5)^3 \right) + \mathbf{1.5P\left( (\mathfrak{B}5)^2 (\mathfrak{X}7) \right)} = \mathbf{0.64}; p^{(4)} = P\left( (\mathfrak{B}7)^3 \right) + \mathbf{1.5P\left( (\mathfrak{X}7)^2 (\mathfrak{X}5) \right)} = \mathbf{0.08}; p^{(4)} = \mathbf{0.08}; p^{(5)} = \mathbf{0.08} \tag{5}$$

$$p^{(2)} = \mathbf{1.5P\left( (35)^2 (37) \right)} = \mathbf{0.21}; p^{(3)} = \mathbf{1.5P\left( (37)^2 (35) \right)} = \mathbf{0.06}. \tag{6}$$

Measured distances between neighbor peaks are

$$
\Delta\tilde{\lambda}\_{12} = \mathbf{1.41} \text{ cm}^{-1}; \Delta\tilde{\lambda}\_{23} = \mathbf{1.189} \text{ cm}^{-1}; \Delta\tilde{\lambda}\_{34} = \mathbf{1.301} \text{ cm}^{-1}.\tag{6}
$$

Linear photo-absorption cross sections for each line can be extracted from Naeperian infrared intensity

$$\begin{split} I\_{IR} &= \frac{2}{\pi} \frac{1}{27.648} \int \sigma\_{abs} \left(\ddot{\lambda}, \ddot{\lambda}\_k\right) d\ddot{\lambda}, \\ \sigma\_{abs} \left(\ddot{\lambda}, \ddot{\lambda}\_k\right) &= \sigma\_{abs} \left(\ddot{\lambda}\_k\right) \frac{\Delta \ddot{\lambda}}{4 \left(\ddot{\lambda} - \ddot{\lambda}\_k\right)^2 + \Delta \ddot{\lambda}^2}. \end{split} \tag{7}$$

According to experimental data for <sup>11</sup>*ν*<sup>3</sup> absorption band from [47]: *IIR* ¼ 231*:*3 km*=*mole.

Since overcooled gas flow is irradiated cross-wise in opposite directions, Doppler broadenings in respect to laser beam outgoing from laser source and reflected from retro-mirror will compensate each other. Hence, photo-absorption cross section can be approximated by Lorentzian, having FWHM

$$\text{L2}\Delta\nu\_P = \frac{4p\_{\text{tot}}\sigma\_{\text{QG}}}{\pi\sqrt{\pi k\_B T\_{\text{flow}} M\_{\text{Q}}\varepsilon}} = c\Delta\tilde{\lambda} = 2.31 \text{ MHz}.\tag{8}$$

Thus, the total cross-section of isotopologues of sort *k* is given by:

$$\begin{aligned} \sigma\_{\text{abs}}^{(k)} &= \sigma\_{\text{max}}^{(k)} \frac{\Delta \nu\_P^2}{\left(\nu - \nu\_k\right)^2 + \Delta \nu\_P^2}, \\ \sigma\_{\text{max}}^{(k)} &= \frac{27.648 I\_{IR}}{\Delta \bar{\lambda}} p^{(k)}, \end{aligned} \tag{9}$$

where

$$\left\{\sigma\_{\text{max}}^{(1)}, \sigma\_{\text{max}}^{(2)}, \sigma\_{\text{max}}^{(3)}, \sigma\_{\text{max}}^{(4)}\right\} = \{\textbf{17.72}; \textbf{5.74}; \textbf{1.84}; \textbf{2.23}\} \times \textbf{10}^{-16} \text{ m}^2. \tag{10}$$

<sup>1</sup> probability to find combination of <sup>35</sup>*Cln* and <sup>37</sup>*Cl*<sup>3</sup>�*<sup>n</sup>* is denoted by *<sup>P</sup>* ð Þ <sup>35</sup> *<sup>n</sup>* ð Þ <sup>37</sup> <sup>3</sup>�*<sup>n</sup>* � �.

*Some Features of Boron Isotopes Separation by Laser-Assisted Retardation of Condensation… DOI: http://dx.doi.org/10.5772/intechopen.111948*

#### **2.2 Product cut and enrichment factor evaluation**

Product cut can be evaluated as a fraction of escaped target gas molecules and oligomers from the gas flow core

$$
\theta = \frac{Q\_{\text{esc}}}{Q\_{\text{feed}}},
\tag{11}
$$

where *Q*feed ¼ *yQN*feed, *N*feed ¼ *Qf t*tr is the number of target gas molecules in the feeding gas flow and *Q*esc is the number of escaped specied. The product cut can be transformed to *θ* ¼ a þ b, where

$$\begin{aligned} \mathfrak{a} &= \sum\_{k=1 \atop k \neq i}^{2} \mathfrak{x}\_{k} a\_{k}, & a\_{k} &= \left(\mathbb{1} - f\_{\mathrm{kd}}\right) \Theta + f\_{\mathrm{kd}} \Theta\_{\mathrm{d}}; \\ \mathfrak{b} &= \mathfrak{x}\_{i} a\_{i}, & a\_{i} &= \left(\mathbb{1} - f\_{i!} - f\_{\mathrm{id}}\right) \Theta + f\_{i!} \Theta\_{1} + f\_{\mathrm{id}} \Theta\_{\mathrm{d}}, \end{aligned} \tag{12}$$

relative isotope abundance of excited *i*th isotope is denoted as *x* (for definiteness we assume that only 11BCl3 isotopologues are excited, i.e., *<sup>i</sup>* <sup>¼</sup> 2), and

$$
\Theta = \mathbf{1} - e^{-k\_{\rm W}t\_{\rm tr}} \tag{13}
$$

is a fraction of escaped from gas flow core monomers,

$$
\Theta\_1 = \mathbb{1} - e^{-\mu\_1 k\_{\rm W} t\_{\rm tr}} \tag{14}
$$

is a fraction of escaped epithermals, and

$$
\Theta\_d = \mathbf{1} - e^{-\boldsymbol{\wp}\_d k\_{\rm W} t\_{\rm tr}} \tag{15}
$$

is fraction of escaped dimers, where

$$\boldsymbol{\mu}\_d = \frac{\sigma\_{cQ/G} \mathbf{M}\_{Q/G}^{1/2}}{\sigma\_{cQG/G} \mathbf{M}\_{QG/G}^{1/2}}.\tag{16}$$

Enrichment factor by *i*th isotope is given by

$$\beta = \frac{{}^i \mathcal{Q}\_{\text{esc}} / \mathcal{Q}\_{\text{esc}}}{{}^i \mathcal{Q}\_{\text{feed}} / \mathcal{Q}\_{\text{feed}}} = \frac{a\_i}{\theta},\tag{17}$$

where *<sup>i</sup> Q*feed*=Q*feed and *<sup>i</sup> Q*esc*=Q*esc are relative abundances of *i*th isotope in the escaped and feed gas flows, respectively.

Product cut and enrichment factor as functions of gas flow core temperature (other parameters are fixed to their optimal values) were calculated in Refs. [37, 49]. Significant descrepancy between the maximal values of enrichment factors 1.0043 (*ptot* <sup>¼</sup> 10 mTorr, *<sup>T</sup>* <sup>¼</sup> 24 K, *<sup>σ</sup>abs* <sup>¼</sup> <sup>13</sup>*:*75 Mb, *<sup>ϕ</sup><sup>L</sup>* <sup>¼</sup> <sup>39</sup>*:*31 W*=*cm2, *LIC* <sup>¼</sup> 67 cm) and 1.25 (*ptot* <sup>¼</sup> 10 mTorr, *<sup>T</sup>* <sup>¼</sup> 25 K, *<sup>σ</sup>abs* <sup>¼</sup> <sup>0</sup>*:*071 Mb, *<sup>ϕ</sup><sup>L</sup>* <sup>¼</sup> 10 kW*=*cm2, *LIC* <sup>¼</sup> 20 cm), obtained in [37, 49] respectively, can be explained by that the formula (32) from [26] should be multiplied by the vibration-translational(VT) transition probability, as it should be in order to get proper equilibrium dimer concentration (Eq. (124) in [25]). Here, *LIC* is gas flow length from nozzle outlet to skimmer inlet.

#### **3. Operational principles**

At the beginning of operation, the mixing tank is occupied only by carrier gas, while target gas molecules, having natural relative isotope abundance, are stored in the feed chamber. Then, the target gas is injected into the mixing tank. Target gas is seeded at a very low molar fraction(*yQ* 0*:*02) into carrier gas, in order to minimize nearly resonant VV excitation loss caused by collisions among BCl3 molecules. Gas flow should be diluted as well in order to minimize nearly resonant excitation loss due to VT (vibration-translational) relaxation. In order to provide pressure *pflow* ≈10 mtorr and temperature *Tflow* ≈24 K, that correspond to maximum of enrichment factor, provided Ar is chosen as a carrier gas, the total pressure in the mixing tank should be *P*<sup>0</sup> ≈ 6 torr [38], provided expansion remains isentropic at least along the gas flow core axis.

The scheme shown in **Figure 1** allows multifrequency boron isotopes excitation in the absorber part of CO2 laser resonator (in Ref. [39] the same scheme was proposed, but for orthogonal gas flow irradiation). From the mixing tank gas expands

#### **Figure 1.**

*The principal scheme of boron isotope enrichment setup (edges, links, and details, that are invisible from the frontal surface, are displayed by dashed lines). The laser beam passes through a semi-transparent window and cross-wise impinges the gas flow. In order to increase excitation rate, the laser beam oscillates within a resonant multi-pass cavity between opposite mirror strips in order to interact with whole length of supersonic jet. Core gas is boron-10 enriched by selective laser evaporation of* 11BCl3 *isotopologues. It is circulated from the mixing tank and back in order to compensate pressure loss and to achieve a higher degree of target isotope recovery.*

*Some Features of Boron Isotopes Separation by Laser-Assisted Retardation of Condensation… DOI: http://dx.doi.org/10.5772/intechopen.111948*

continuously into the separation chamber, where it is irradiated cross-wise by the laser beam confined between mirror strips placed on opposite walls of resonator, three (one flat and two concave) mirrors outside the resonator cavity and grating.

Multiple reflections from mirrors may lead, however, to the instability of laser power and frequency<sup>2</sup> . As shown in Refs. [38, 39], the use of resonant absorber cavity for isotope separation will lead to 4–6.5 times increase of laser pulse peak intensity.

In order to provide the largest gas flow irradiation volume, having the optimal static pressure and temperature distributions, a uniform velocity profile can be provided by slit nozzle design, which is discussed in more detail in subsection 5.1.

Skimmer blade divides the gas flow into target isotope (boron-11) enriched (rim) and desired isotope (boron-10) enriched (core) fractions by the end of chamber. Core and rim gas flow fractions, having laser-controlled target isotopologue populations, are evacuated separately by two separate vacuum pumps, having appropriate pumping down rates. Before redirecting them back into mixing tank or exhausting into atmosphere, they are captured in respective Zeolite cold traps as shown in **Figure 1**. Roughly speaking, pumping out speeds should be chosen proportional to corresponding stagnation pressures. The larger the initial pressure loss, the less demanding requirements for vacuum pumps. Material, momentum, and energy balance equations for skimmer partition have been solved in Section 5.2. Besides evaluating required minimal levels for pumping down rates for core and rim gas flows, it helps to clarify contributions and relations between various parameters, affecting gas flow deceleration, and, therefore, stagnation pressures, corresponding to each vacuum pump.

#### **4. Irradiation conditions**

According to experimental data, the gaseous state 11BCl3 photo-absorption line center position ranges from ~*λ* ð Þ1 max <sup>¼</sup> <sup>957</sup>*:*67 cm�1, as of [44], to <sup>~</sup>*<sup>λ</sup>* ð Þ1 min <sup>¼</sup> <sup>954</sup>*:*2 cm�1, as of [47], according to different physical conditions (more red-shifted spectra correspond to higher gas temperatures). The value 944*:*194 cm�1, measured in Ref. [19], corresponds to multiphoton absorption.

If photoabsorption takes place at physical conditions, corresponding to ~*λ* ð Þ1 max, then FWHM, corresponding to 10P(4)-10P(10) emission lines, should be:

$$
\Delta \tilde{i}\_{\text{FWHM}}^{(k)} = \{-0.26; 0.142; 1.05; 1.77\} \text{ cm}^{-1},\tag{18}
$$

where 10P4 line (1-st entry) is almost vanishing, and line 10P6(2-nd entry) is very weak, so only line 10P8 can be used for one (Δ~*λ* max FWHM <sup>¼</sup> <sup>1</sup>*:*05 cm�1) or two (Δ~*λ* max FWHM <sup>¼</sup> <sup>1</sup>*:*31 cm�1) isotopologues excitation. In case, if photoabsorption takes place at physical conditions, corresponding to ~*λ* ð Þ1 min, then FWHM, corresponding to 10P(8)-10P(14) emission lines, should be:

<sup>2</sup> As a possible ways to overcome this problem, adaptive retro-mirror surface automatic adjustment or its displacement by piezoelectric transducer (PZT), which is activated by generator, that is controlled by phase-shift sensitive detector.

$$
\Delta \tilde{\lambda}\_{\text{FWHM}}^{(k)} = \{-0.69; -0.19; 0.81; 1.632\} \text{ cm}^{-1}.\tag{19}
$$

10P(8)-10P(12) lines can be used for simultaneous excitation of all three most abundant chlorine isotopologues, provided laser medium pressure is 5.75 bars, which corresponds to Δ~*λ* max FWHM <sup>¼</sup> <sup>0</sup>*:*81 cm�<sup>1</sup> and laser pulse width *<sup>τ</sup><sup>p</sup>* <sup>¼</sup> 334 ps.

#### **4.1 Admissible laser intensity variation range**

Absorbed energy, corresponding to pulsed excitation of chlorine isotopologues of 11BCl3, can be estimated from the formula for excitation rate, deduced in Ref. [39]:

$$k\_A(t) = \frac{1}{2\pi^2 R\_L^2} \sum\_{k=1}^{N\_l} \int\_{-\infty}^{\infty} \frac{d\alpha}{\hbar \alpha} e^{\alpha t} \frac{dE\_A^{(k)}}{d\alpha},\tag{20}$$

where it was assumed, that laser beam is pencil-like (*RL* ¼ 2*:*8 mm is laser beam radius, corresponding to the thickness of gas flow core with optimal pressure and temperature inside). It can be represented as:

$$k\_A(t) = \frac{1}{\pi R\_L^2} \sum\_{i=1}^{N\_l} \sum\_{j=1}^{N\_l} F^{-1} \left[ \frac{d\lambda^{(j)}}{d\alpha} \right],\tag{21}$$

where

$$\frac{d\lambda^{(\vec{y})}}{d\alpha} = \frac{1}{\hbar \nu} \frac{dE\_A^{(\vec{y})}}{d\alpha} \tag{22}$$

is absorbed photons spectral density. As shown in Ref. [39], laser pulse spectral density can be represented as:

$$\frac{dE\_A^{(j)}}{d\alpha} = E\_0^{(i)} E\_0^{(j)}\, ^{(i)}(t) \sigma^{(j)}(\alpha) \, ^\star \mathcal{V}^{(j)}(\alpha). \tag{23}$$

Let us see what is the average number of resonantly absorbed photons per BCl3 molecule, provided laser pulse intensity *I ref <sup>p</sup>* corresponds to some reference CW-mode intensity *I ref CW* <sup>¼</sup> 1W and BCl3 absorption spectrum, corresponding to <sup>~</sup>*<sup>λ</sup>* ð Þ1 min, was chosen. According to the formula, derived in Ref. [39], average numbers of photons in pulsed mode, absorbed by each isotopologue excitable by different lines, are:

$$\left\{N\_{\rm ph}^{(1)}, N\_{\rm ph}^{(2)}, N\_{\rm ph}^{(3)}, N\_{\rm ph}^{(4)}\right\} = \{4.5, 77.8, 0.26, 0.57\} \times 10^{-3}.\tag{24}$$

It is seen, that majority of photons are absorbed by *ν*<sup>2</sup> line, which is in the closest proximity to 10P8. However, the number of photons, absorbed within the excitation loss characteristic time interval, should be less than *Nmax crit* ¼ 34 � 39 [50], in order to avoid multiphoton dissociation. Excitation loss time coincides with gas flow transition time across laser beam, because all other relaxation times, such as dimer formation, vibration-vibrational, and vibration-translational transfers as

*Some Features of Boron Isotopes Separation by Laser-Assisted Retardation of Condensation… DOI: http://dx.doi.org/10.5772/intechopen.111948*

well as spontaneous emission, are bigger [38]. Thus, the upper limit for laser intensity should be

$$I\_{\text{max}} = I\_{\text{ref}} \frac{N\_{\text{crit}}^{\text{max}}}{\text{Max} \left\{ N\_{\text{ph}}^{(k)} \right\}} = 437 - 501 \text{ W.} \tag{25}$$

The lower limit for applicability of SILARC method is, apparently, given by the following condition:

$$I\_{\rm min} = \frac{I\_{\rm ref}}{\rm Max \left\{ N\_{\rm ph}^{(k)} \right\}} = 12.8 \text{ W.} \tag{26}$$

In the case, when BCl3 absorption spectrum, corresponding to ~*λ* ð Þ1 max, was chosen, the average number of photons, absorbed by each absorption line, from 10P8 emission line are:

$$\left\{N\_{\rm ph}^{(1)}, N\_{\rm ph}^{(2)}, N\_{\rm ph}^{(3)}, N\_{\rm ph}^{(4)}\right\} = \{0.02, 0.1, 0.41, 0.29\} \times 10^{-3}.\tag{27}$$

Thus, the upper and lower limits for laser intensity should be *I*max ¼ 83*:*2 � 94*:*4kW,*I*min ¼ 2*:*45 kW*:*

#### **5. Gas flow properties and vacuum system design**

Apparently, the main goal in vacuum system design is to provide the largest overlap of laser beam with gas flow core, having optimal pressure and temperature for isotope separation. This condition in the case of cross-wise irradiation can be fulfilled, provided gas flow is planar (interaction region with cross-wise directed laser beam is large), and preserves its shape over all its extension. This can be implemented, if the gas flow is perfectly expanded. Thus, the vacuum chamber pumping down speed should be carefully chosen. The pumping out speed is provided by two vacuum pumps. High-rate one evacuates the central part of the gas flow, and low-rate one evacuates the peripheral gas flow. The main gas flow stream is divided into two parts by the wedge-like inlet of the skimmer chamber, which is placed on the opposite side of the irradiation cell.

#### **5.1 Nozzle design**

Nozzle wall shape was found as a friction-free(isentropic) region corrected by the boundary layer. According to experimental data from Ref. [51], gas flow deceleration (full pressure drop) across the nozzle practically does not depend on angle of nozzle inlet, if *θ*<sup>0</sup> <850. The larger radius of the nozzle throat curvature *R*2, the larger gas flow uniformity, and, therefore, the smaller deceleration. According to boundary layer theory, in order to take into account dissipative effects, nozzle contour, corresponding to isentropic gas flow expansion, should be corrected by displacement layer thickness (DLT).

In order to figure out which gas flow regime takes place-laminar or turbulent, one needs to know Reynolds number evolution along the nozzle axis. Since boundary

**Figure 2.**

*(a) Cross-section of nozzle profile in zx plane (gas flow temperature at the nozzle outlet along its axis (it's minimal value) corresponds to optimal value for boron isotopes separation) and (b) break down parameter distribution along the nozzle axis for boron isotopes separation.*

layers from opposite walls do not interfere with each other, Reynolds number to characterize the transition from laminar to turbulent flow can be introduced as:

$$Re\_{\chi} = \frac{\rho v \infty}{\mu}.\tag{28}$$

If *Re <sup>x</sup>* <sup>&</sup>gt;<sup>5</sup> � <sup>10</sup><sup>5</sup> , then gas flow gets certainly turbulent for most commercial surfaces. Therefore, for our nozzle design, it should be definitely stable, since *Re <sup>x</sup> Xfin* � � <sup>¼</sup> 2615.

The boundary layer corrected nozzle profile for argon used as a carrier gas and break down parameter is shown in **Figure 2a**.

Calculations of continuous gas flow are only valid until breakdown parameter *B* ¼ *M* ffiffiffi *πγ* 8 q *<sup>λ</sup> ρ dρ dz* � � � � � � is lower than its critical value *Bcrit* <sup>¼</sup> <sup>0</sup>*:*05. As seen in **Figure 2b**, gas flow departs from continuous regime practically overall nozzle extension. Therefore, caution must be exercised relative to obtained results on nozzle profile.

#### **5.2 The model for estimation of minimal requirements for vacuuming rate**

Influence of gas flow deceleration, caused by interaction with ambient gas and irradiation chamber-vacuum pump inlet tract, on temperature distribution in gas flow can be tolerated, if pressure builds up at vacuum pump inlet still provides an acceptable variation of static pressure for isotope separation in the discharge chamber. This condition can be fulfilled if vacuum tract resistance to the gas flow is reduced to a minimum and pumping out speed is accurately chosen. As well known, during gas flow transition across vacuum tract, gas pressure rises due to friction with walls, or, in the case of gas flow injected in the pipe of much larger diameter, with ambient gas, due to shock waves caused by hydrodynamic discontinuities.

Let us consider subsequent stages of gas flow evolution. In the beginning, gas chamber is pumped down until some pressure level, which is smaller than the pressure at nozzle outlet. In this case, gas flow gets under-expanded, and occupies the space between irradiation chamber walls, according to pressure of residual gas. On the next stage, ambient gas pressure increases accordingly to pumping down rate applied, so that angle between gas flow direction and oblique shock at nozzle outlet decreases.

*Some Features of Boron Isotopes Separation by Laser-Assisted Retardation of Condensation… DOI: http://dx.doi.org/10.5772/intechopen.111948*

Since we need perfectly expanded gas flow, vacuum pump characteristics should be such that this angle vanishes after some time and then does not change.

As pointed out in Ref. [36], the large decrease in stagnation pressure across a normal shock wave may be reduced by decelerating the free-stream flow by means of one or more oblique shock waves, followed by a weak normal shock wave, produced by central body, placed at skimmer inlet. By employing that principle, an efficient external compression of the gas flow is achieved before the gas flows into a subsonic internal compression diffuser (skimmer partition of discharge chamber). Larger stagnation pressure recoveries are obtainable if several successive weak shock waves instead of one relatively strong conical shock wave are utilized for decelerating the gas flow.

To find gas density, one needs to solve a system of material, momentum, and energy conservation equations. For sake of simplicity, this system of equations can be transformed, according to hydraulic approximation, to the system of balance equations, where taking an average of conservation equations is carried out over cross sections at the characteristic intermediate stations *i*: The first station(*i* ¼ 1) corresponds to inlets of the pipes, connected to the port of rim or core gas flow evacuating vacuum pumps, the second one(*i* ¼ 2) corresponds to core gas flow evacuating vacuum pump inlet or to two pipe into one pipe connection, assigned for rim gas flow evacuation, the third one(*i* ¼ 3) corresponds to rim gas flow evacuating vacuum pump inlet. This system of balance equations is following:

$$\begin{cases} \begin{aligned} &d\mathcal{N}^{a;i} \\ &d\boldsymbol{t} \\ &d\boldsymbol{t} \\ &d\boldsymbol{t} \\ &\partial\boldsymbol{t}^{a;i} \\ &\partial\boldsymbol{t}^{a;i} \\ &\partial\boldsymbol{t}^{a;i} \\ &\partial\boldsymbol{t}^{a;i} \\ &\partial\boldsymbol{t}^{a;i} \\ \end{bmatrix} \frac{d\mathcal{S}^{a;i}}{dt} + A^{a;i}\_{in} \left(\mathcal{P}^{a;i}\_{in} + m\_{0}\rho^{a;i}\_{in}\left[\boldsymbol{v}^{a;i}\_{in}\right]^{2}\right) + \delta\mathcal{P}^{a;i} = A^{a;i}\_{out}\left(\mathcal{P}^{a;i}\_{out} + m\_{0}\rho^{a;i}\_{out}\left[\boldsymbol{v}^{a;i}\_{out}\right]^{2}\right), \\ &\frac{d\mathcal{S}^{a;i}}{dt} + \rho^{a;i}\_{in}\rho^{a;i}\_{in}A^{a;i}\_{in} \left(\frac{m\_{0}\left[\boldsymbol{v}^{a;i}\_{in}\right]^{2}}{2} + C\_{p}T^{a;i}\_{out}A^{a;i}\_{out}\left(\frac{m\_{0}\left[\boldsymbol{v}^{a;i}\_{out}\right]^{2}}{2} + C\_{p}T^{a;i}\_{out}\right), \\ &P^{a;i}\_{out} = \rho^{a;i}\_{out}b\_{B}T^{a;i}\_{out}. \end{aligned} \tag{29}$$

In order to close this system of equations, it should be supplemented by the ideal gas equation of state

$$P\_a^{out;i} = \rho\_a^{out;i} k\_B T\_a^{out;i},\tag{30}$$

and by equation for friction coefficient *f i <sup>a</sup>*. We assume that gas friction with pipe wall surface is laminar

$$Re\_D^{a;i} = \frac{\rho\_a^{out;i} \upsilon\_a^{out;i} D\_i}{\mu} < 2300,\tag{31}$$

where *Di* is pipe diameter. Hence, the friction coefficient can be estimated as:

$$f\_a^i = \frac{\mathbf{64}}{\mathrm{Re}\_D^{a;i}}.\tag{32}$$

The total number of molecules in rim and core gas flow fractions, accumulated over its transition time across the irradiation chamber are:

*Boron, Boron Compounds and Boron-Based Materials and Structures*

$$\mathbf{Q}\_{\rm core} = (\mathbf{1} - \mu \theta) \mathbf{Q}\_{\rm f} \tag{33}$$

and

$$Q\_{rm} = \mu \theta Q\_f \tag{34}$$

respectively, where *μ* ¼ 0*:*02 is target gas(BCl3) molar fraction. Product cut, or fraction of molecules escaped the gas flow core, was calculated on the basis of the transport model, developed in Ref. [26]. It's value, corresponding to optimal conditions *Tin*; 0 *<sup>a</sup>* <sup>¼</sup> 25 K, *Pin*; 0 *<sup>a</sup>* ¼ 10 mtorr, calculated in Ref. [38], is *θ* ≈0*:*2.

Heat transfer intensity can be phenomenologically approximated as:

$$q = h|T\_w - T|,\tag{35}$$

where wall temperature is fixed at *Tw* ¼ *Tatm* ¼ 300 K, and *T* is average temperature over gas flow volume. A coefficient of proportionality *h* is introduced as *h* ¼ *ρvCpNSt*, where Stanton number *NSt* is related to momentum transfer due to friction by Reynolds analogy, which, however, yields satisfactory results only for gases:

$$N\_{\rm St} = \frac{1}{2} P \eta^{\rm f} \tag{36}$$

Friction factor *f* is introduced as:

$$f = \frac{\text{wall shear stress}}{\frac{1}{2}\rho v^2}.\tag{37}$$

The total heat transfer can be approximated as:

$$
\delta Q\_a^i = \frac{\overline{f}\_a^i}{2} Pr(T) \rho\_a v\_a \mathcal{C}\_p |T\_w - T| \mathcal{S}\_a. \tag{38}
$$

Average values are approximated as *<sup>o</sup>* <sup>¼</sup> *oin*þ*oout* <sup>2</sup> *:* We assume, that momentum transfer to the wall surface can be approximated by the formula for gas flow pressure build-up due to friction over planar surface:

$$\delta P\_a^i = \frac{f\_a^i}{8} m\_0 \overline{\rho}\_a \overline{\nu}\_a{}^2 \mathbb{S}\_a \tag{39}$$

Since the efficiency of pumping down speed depends on the gas density at the vacuum pump inlet, one needs to know which model of vacuum pump is able to provide the required pumping out speed. Then, given that what gas is pumped down and provided it's hold at room temperature, this dependence can be transformed into the following relation to inlet density:

$$\frac{d\mathbf{U}^{a}}{dt} = \kappa \mathbf{f}\_{pump}(\rho^{a}),\tag{40}$$

where factor *κ* fits reference vacuum pump interpolated dependence on gas density to desired pumping down speed at a given density. We have used pressure *Some Features of Boron Isotopes Separation by Laser-Assisted Retardation of Condensation… DOI: http://dx.doi.org/10.5772/intechopen.111948*

dependence of pumping speed of the turbo-molecular pump (TMP) TURBOVAC MAG 3200C [52], as a reference, which is shown in **Figure 3a**, where different gases at room temperature are pumped down. Thus, the performance curve for pumping out of the air can be taken from interpolation:

$$f\_{pump} = 3.07 - 3.09 \times 10^{-21} \rho(t) + 9.5 \times 10^{-43} \rho(t)^2. \tag{41}$$

Moreover, it can be estimated pressure evolution within the pumped-down vessel. According to the Reynolds transport theorem, particle balance condition leads to the following equation for average gas density *ρ<sup>a</sup>* in the inter-chamber connector:

$$\begin{cases} V\_{ch} \frac{d\rho\_a(t)}{dt} = \frac{dN\_a}{dt} - \rho\_a(t) \frac{dU\_a}{dt}, \\ \rho\_a(0) = \rho\_{in}, \\ \rho\_{in} = \frac{p\_{in}}{k\_B T\_0}. \end{cases} \tag{42}$$

The vacuum pump should provide such pumping speed, that asymptotic gas density *<sup>ρ</sup>as* <sup>¼</sup> lim*<sup>t</sup>*!<sup>∞</sup> *<sup>ρ</sup>*ð Þ*<sup>t</sup>* is within the range:

$$
\rho\_{\rm out} < \rho\_{\rm at} < \rho\_{\rm in}, \tag{43}
$$

where *T*<sup>0</sup> is room temperature.

Solution of the balance equation at the initial condition, that stagnant gas resides in the feed chamber at room temperature and pressure 10 mtorr, for core gas flow is shown in **Figure 3b** and for rim gas in **Figure 3c**. It is seen from this figure, that after rather short period of time stationary condition is reached (it depends on the volume of intermediate chamber). Pumping speeds were chosen from the condition that asymptotic density is ranged as (43).

Inter-chamber connector geometry and pipe length and diameter for core and rim gas flows respectively should be chosen so, that separated species are not driven due to high pressure back into irradiation chamber: *P<sup>a</sup> out* <*Pin*. We have the following solutions of the system of Eqs. (29) *Pcore out* <sup>¼</sup> <sup>0</sup>*:*27 Pa, *<sup>T</sup>core out* <sup>¼</sup> <sup>187</sup>*:*7 K, *vcore out* ¼ 44*:*68 m*=*s, *ρcore out* <sup>¼</sup> <sup>3</sup>*:*<sup>34</sup> � <sup>10</sup><sup>19</sup> <sup>m</sup>�3, *<sup>P</sup>rim out* <sup>¼</sup> <sup>1</sup>*:*95 Pa, *<sup>T</sup>rim out* <sup>¼</sup> <sup>96</sup>*:*43 K, *vrim out* ¼ 11*:*32 m*=*s, *ρrim out* <sup>¼</sup> <sup>7</sup>*:*<sup>49</sup> � <sup>10</sup><sup>20</sup> <sup>m</sup>�3, corresponding to given geometry for core and

**Figure 3.**

*(a) TURBOVAC MAG 3200C pumping speed as a function of inlet gas pressure, [52], (b) Core gas flow density evolution, provided TMP-3403LMC with flange VG300 is used, [53], and (c) rim gas flow density evolution, provided HiPace 300 DN100 is used.*

rim gas flows. For core and rim gas flows one obtains *Recore*; 1 *<sup>D</sup>* <sup>¼</sup> 69 and *Re rim*,1 *<sup>D</sup>* ¼ 37 , respectively. Thus, *f* 1 *rim* ¼ 0*:*3 and *f* 1 *core* ¼ 0*:*2.

Thus, we obtain the following values for pumping down speeds for core and rim gas flows *dUcore dt* <sup>¼</sup> 3300 l*=*s, *dUrim dt* ¼ 310 l*=*s.

Since the system of Eqs. (29) along with approximation for heat transfer (38), momentum loss (39), and friction coefficient (37) is valid only if gas flow is continuous along the wall surface and shock-free, while in real situations gas flow is rather injected in the pipe due to its significantly smaller cross section, comparing to the pipe area, especially in the case of rim gas flow, found pipe geometry is expected to be just a lower limit (pipe length can be larger), the same concerns to found pumping speeds for rim and core gas flows evacuation, which in turn can serve as an upper limit for pumping speed requirements.

#### **6. Conclusions**

In this chapter, physical constraints such as gas flow core temperature and pressure distributions, oblique shocks configuration in the course of gas evacuation from discharge chamber, condensation rate, pressure in CO2 laser medium, and spectral properties of BCl3 at different temperatures and pressures on the efficiency of SILARC method have been discussed. In particular, it has demonstrated the possiblity to extract boron isotopes from BCl3 gas flow more efficiently by applying a three-mirros scheme for multiline excitation. Recommendations on laser system design, optimal nozzle design, and parameters of the corresponding vacuuming system are given.

#### **Author details**

Konstantin A. Lyakhov Steklov Mathematical Institute, Moscow, Russia

\*Address all correspondence to: lyakhov2000@yahoo.com

© 2023 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Some Features of Boron Isotopes Separation by Laser-Assisted Retardation of Condensation… DOI: http://dx.doi.org/10.5772/intechopen.111948*

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#### **Chapter 6**

## Effect of Capping Agents on the Nanoscale Metal Borate Synthesis

*Fatma Tugce Senberber Dumanli*

#### **Abstract**

Boron compounds are beneficial additives for industrial applications due to their superior physical, chemical, mechanical, and thermal features. The common use of boron compounds can be listed as ceramic, glass, glazes, metallurgy, lubricating agents, non-linear optical devices, and nuclear processes. Metal borates can be classified in accordance with the metal atom in the structure. According to the metal borate type, each compound exhibits different properties and is preferred for various applications. The other significant factor of a material that makes it preferable for the industry is its morphological characteristics. With the developing technology and novel synthesis procedures, metal borates can be fabricated at different morphologies. The characteristics of the metal borates can be improved by the modification of their surfaces. Capping agents are additive materials that are used to control particle growth and/or modify the morphological features of compounds. There is a recent increase in the number of studies based on metal borates prepared by using capping agents. In this chapter, the theoretical background on metal borates, synthesis procedures of metal borates, classification of the capping agent, the effect of capping agent on particle growth and examples of capping agent use on metal borates preparation were explained. Also, the characteristics of the same metal borates at different morphological features were compared.

**Keywords:** borate, capping agent, nanoparticle, morphology, synthesis, particle growth

#### **1. Introduction**

Boron is a rare portion element of earth's crust, and it is generally found in nature as the complexes of oxygen (O), hydrogen (H) other metal atoms. More than 150 boron minerals have been identified until today [1, 2]. Since including similar composition of most of the natural boron reserves (B, O, H, and metal atoms), "boron minerals" and "metal borates" might be considered synonymous words.

The majority of the boron reserves are found in Turkey (72.8%), Russia (7.6%), and South America (6.1%). Also, the smaller reserves could be seen in China, Kazakhstan, Argentina, Italy, Mexico, and Germany. The most abundant examples of the boron minerals can be listed as Borax (Na2B4O7·10H2O), Tincalconite (Na2B4O7·5H2O), Colemanite (Ca2B6O11·5H2O), and Ulexite (NaCaB5O6(OH)6·5H2O). In the reserves of boron minerals, particles commonly form in microcrystalline [3, 4].

The unique properties of borates could be explained by the high constant elasticity, heat resistance, corrosion resistance, luminescence, and low softening and melting temperatures [5, 6]. Also, recent studies exhibit the biocompatible properties of boron minerals [7, 8]. In the uses of boron compounds, the chemical nature and structure of borates provide multifunctionality [9]. Traditional uses of boron minerals can be seen in ceramics and glazes, detergents, agriculture, metallurgy, and fire retarding materials. With the effect of developed technologies, these compounds can also be utilized in energy storage systems, laser systems, optoelectronics, band gap engineering, tissue engineering, wound healing, bone regeneration, bone formation, antibacterial compositions, adsorption of pollutants from wastewater, and design of biochemical sensors [3–11].

Considering the properties that boron provides to the materials in which it is added and/or doped, its strategic importance emerges. For this reason, studies on the modification of metal borates, synthesis of novel metal borates, and related developments continue around the world. To increase their characteristics, specific types of metal borate compounds such as lanthanum borates or other rare earth-doped borates could be synthesized, or capping agents could be employed to modify their properties.

In the synthesis of specific metal borates, the reserves can be transformed to compounds at higher with high added value by the reaction metal sources with the boron mineral or boric acid (H3BO3) [12–14]. Lithium borates, zinc borates, and aluminum borates can be given as examples.

Capping agents could especially be used in nanoparticle synthesis. In the use of the capping agents, the particle sizes were mostly decreased, and the morphology was homogenized without changing experimental procedures. Also, produced particles become stabilized in the solution and agglomeration can be eliminated [15, 16]. Because of the high surface area to volume ratio of the smaller particle sizes, especially on the nanoscale, the compounds exhibited novel and remarkable features different from their bulk and molecular counterparts [17–19].

The characteristics of the prepared sample are associated with the designed experimental setup. For the effective use of capping agents, their role of them in the particle growth mechanism should be clarified. A detailed understanding of the connection between characteristics and synthesis procedures of the novel borates obtained will increase the correct form of metal borate use in industrial applications.

#### **2. Capping agents**

Capping agents are important additive materials to modify particle shape and size. The uses of the capping agents and modifiers have gradually increased both liquidstate and solid-state conditions. Several types of surfactants, polymers, extracts, ligands, cyclodextrins, dendrimers, and polysaccharides could be utilized with this aim. These organic compounds exhibit the ability to modify the metal surface, provide sufficient dispersion, and prevent the agglomeration of nanoparticle [20, 21].

#### **2.1 Mechanism**

The relationship between the capping agent and the metal surface is related to the electrical forces between the steric features of the surface, interfaces, composition, and chemical features of the ligand [20]. For a typically liquid-state synthesis

#### *Effect of Capping Agents on the Nanoscale Metal Borate Synthesis DOI: http://dx.doi.org/10.5772/intechopen.111770*

procedure, the stages of particle formation include nucleation and growth. The modifying additives of capping agents are effective in both stages. Based on its characteristics, controlling the shape and size of the synthesized particles could be possible. With the addition of the capping agents, a draft could be prepared for the formation of the nucleus. The assumed draft also would be affected by the length of the molecules of the capping compound.

The growth mechanism of the particle can be explained with the steps of diffusion from cluster to particle surface and the bonding and/or reaction between ion and solid particles. Controlling the reaction and/or diffusion rate is also possible with the use of the reaction parameters [22].

Amphiphilic molecules of the capping agents include an apolar hydrocarbon group and a polar head group. The functionality of the capping agent is related to these apolar-polar groups. The apolar group reacts with the liquid medium, whereas the polar group bonded to the metal ion to contribute to the nanostructure [23]. The role of the capping agents on nanoparticle formation is schematized in **Figure 1**.

The capping molecule acts as a barrier for the transferring of ions on the produced particle surface. However, the partial transfer of the ions could be possible in the solution medium [22]. The selectivity of the capping agent is effective on the particle size of the prepared sample. The increasing selectivity will lead to lower mass transfer and limited particle growth. Two essential factors that affect the mass transfer between solution and particle are (i) the adsorption/desorption in the bulk and surfactant system; and (ii) the connection between the surfactant and the surface of the solid particle.

#### **2.2 Classification**

The functional groups of the capping agents are effective in the formation of solid particle–ligand interface, and ligand-solution interface. These groups are commonly

**Figure 1.** *The role of the capping agents on nanoparticle formation.*

**Figure 2.**

*Common examples of the capping agent with the different donor atoms.*

found in polyatomic structures such as carboxylate, amino, and other coordinating groups including heteroatoms. According to the obtained interface between solid particle–ligand and ligand- solution, the fabricated sample could exhibit different properties such as hydrophilicity [24]. Anions or neutral molecules bound to the organic ligand centre are called donor atoms. The most common examples of the capping agent with the different donor atoms are presented in **Figure 2**.

The classification of the capping agents is based on the donor atom of capping agents [23, 25]:


of the extraction process. However, there is no research was seen on the use of green capping agents in the modification of metal borates. This may be due to the effect of the capping agent on the particle growth mechanism that has not been adequately studied for the metal borate modification.

### **3. Metal borate compounds**

#### **3.1 Structure of the metal borates**

Metal borates are well-known materials due to their superior properties such as their resistance to physical, chemical, and thermal conditions, the activities of magnetic and electrical, and antibacterial behavior [12]. Metal atom links to the borate groups at the positions of tetragonal and trigonal, and the compounds exhibit symmetrical and asymmetrical stretching. These symmetric and asymmetric stretchings are typical for a molecule and could be examined by using the Fourier-transform infrared spectroscopy (FT-IR) and/or Raman spectroscopy. The characteristic band values of borates groups for metal borates for the FT-IR and Raman spectrums are summarized in **Table 1**.

Some properties of the metal borate could be intrinsic to the metal atom bonded in structure, the designed experimental procedure, and the crystallinity of the sample. This would lead to specific uses of the metal borates according to their types. The synthesis of modified boron minerals can be beneficial for the special uses of metal borates. The common uses of metal borates according to the metal atom bonded to the borate structure can be seen in **Table 2**.

The modification of the metal borates would also lead to novel applications. Although the traditional uses of magnesium borates are thermoluminescence and neutron shielding, the studies on their novel uses showed that magnesium borates modified by capping agents exhibited the hierarchical porous microspheres in morphology and could be an alternative for the Congo Red adsorption from wastewater [37 – 39].

#### **3.2 Synthesis procedures**

Metal borates could be produced by using both liquid-state (hydrothermal) and solid-state (thermal) methods. The synthesis procedure of metal borate could also be adapted to novel technologies such as ultrasound and microwave methods [40, 41]. Although these technologies provide a minor or major decrease in particle size distribution, there is still a requirement for the homogenization in surface morphology of the obtained samples.


#### **Table 1.**

*The characteristic band values of borates groups for metal borates for the FT-IR and Raman spectrums [26–28].*


#### **Table 2.**

*Examples, chemical formulas, and uses of some metal borates [2, 12, 13, 29–36].*

Liquid-state synthesis of metal borates involves the stages of (i) dissolution of metal and boron sources in liquid mediums, (ii) mixing the prepared solutions at the suitable ratio, reaction temperature, and time, and (iii) filtration and drying if it is necessary. Water is selected as the solution medium in liquid-state conditions; however, other types of fuels could also be used in metal borate preparation. The liquid-state synthesis procedure could also be entitled as hydrothermal, combustion, and co-precipitation methods [42–44]. The capping agent is usually added to the mixture of the dissolved sources. The main point of the liquid-state synthesis procedure is that the selected capping agent should be soluble in the solution for better interaction between the core particle and the capping agent molecules.

Solid-state synthesis of metal borates includes the stages of (i) mixing of metal and boron sources at the suitable mole ratios at powder state, (ii) calcination of prepared mixtures at the suitable reaction temperature and time, (iii) grinding, if it is necessary. The described method can be entitled as the solid-state, calcination or thermal method [45–47]. The capping agent should be added to the powder mixture. The main point of the solid-state synthesis procedure is to obtain a homogeneous mixture of powder at the initial state.

To improve the characteristics of the metal borates, some experimental procedures could also be defined as the combination of both methods. Most of the combinations

#### *Effect of Capping Agents on the Nanoscale Metal Borate Synthesis DOI: http://dx.doi.org/10.5772/intechopen.111770*

include the preparations of metal and boron complexes in hydrothermal conditions and the calcination of the prepared complexes [44].

#### *3.2.1 Effects of capping agents on the produced metal borates*

In the heterogeneous form of processes of adsorption, desorption, surface reaction, and adsorbate lateral diffusion, each process includes bond-breaking and bond-making facts, which are related to the electronic properties of the reactants and surfactant material [20]. The growth-limiting role of the capping agent on particles is also based on the relationship between the particle and the capping agent. The efficiency of the capping agent is mainly based on the suitable matching of material and reaction conditions and the interaction of the capping agent with the core particle. Commonly, the proper amount of capping agent in the reaction medium is assumed as 1% or lower.

#### **Figure 3.**

*The modification of hydrothermally synthesized zinc borates by using (A) without capping agent, (B) CTAB added, (C) triton 114 added, and (D) oleic acid added [36].*

The advantages of the capping agent in metal borate synthesis can be listed as the homogenization of the sample surface, modification of particle shape, and obtaining smaller particle size. By using the cationic surface-active agent of CTAB, nonionic surface-active agent of Triton-114, and anionic surface-active agent of oleic acid, the modification of the surfaces of the hydrothermally synthesized zinc borates was presented in **Figure 3**. As could be seen in the SEM analysis results, in **Figure 3**, the capping agent uses of the CTAB and oleic acid decreased the length of the prepared samples whereas the use of T as a capping agent reshaped the particle appearance. Ipek (2020) also indicated the improvement of the fire-retardant properties of zinc borate by decreasing the particle sizes with the use of capping agents [36]. To overcome the problem of incompatibility of zinc borate in polymer matrixes, Li et al. (2010) produced hydrophobic zinc borate by the modification with oleic acid [47].

Erfani et al. (2012) synthesized ultra fine particles of calcium tetraborate by using the capping agent of PVP to control the particle size and to reduce the agglomeration in a co-precipitation method [17]. Khalilzadeh et al. (2016) experimented that increasing PVP addition up to a certain value in the production of lithium tetraborate narrowed the particle size range, reduced the average particle diameter, decreased agglomeration, and increased the band gap value [33]. Xing et al. (2019) studied the modifying effect of folic acid on the yttrium borate to strengthen its photoluminescence emission intensity features in hydrothermal conditions [48]. Liu et al. (2010) synthesized the nanoscale europium-doped barium borate (Ba–B–O: Eu3+) with the addition of oleic acid as a capping agent and enhanced the emission intensities of products by adjusting the correct ratio of the modifying agent [13].

**Figure 4.** *XRD results of the synthesized magnesium borate hydroxides with different capping agents [49].*

#### *Effect of Capping Agents on the Nanoscale Metal Borate Synthesis DOI: http://dx.doi.org/10.5772/intechopen.111770*

The only drawback of the capping agent usage in metal borate synthesis can be explained by the decrease in crystallinity. A few studies indicated that the use of a capping agent could adversely affect the prepared sample and a decrease in the crystallinity of the product could be seen in some cases. In the fabrication of magnesium borate hydroxide powders, Kumari et al. studied the effects of different capping agents CTAB, SDS, and Triton on the products. The results indicated the well-modified morphology of the sample at lower crystallinity [49]. The XRD results of Kumari et al. were presented in **Figure 4**. As it was given in **Figure 4**, the adverse effect of capping agents on the Triton, SDS and CTAB added magnesium borate hydrates can be seen with the decreasing peaks of the (h k l) values of (0 2 0), (3 2 0), (2 1 1), (2 2 1), (5 1 0), (3 4 0) and (0 5 1). The decrease in crystallinity could be explained by the limited growth of the core particles due to the capping agent effect.

#### **4. Conclusion**

With the help of the nanoscale metal borate productions with the usage of the capping agents, samples with high added value have been obtained compared to the microcrystalline structures. In the use of a capping agent, the type of the capping agent, the amount, being soluble in the selected solvent and the interaction between the capping agent and particle are the key points. For the correct determination of the capping agent, the particle growth mechanism, and effects of the capping agent on it were detailed studied. Also, the advantages and disadvantages of the capping agent usage in metal borate preparation were discussed. The novel uses and changes in characteristics of modified nanoscale metal borates were presented.

It is expected that the significance of metal borates in industrial applications would be expanded with the increase of advanced technologies in their synthesis. In this case, the development of modified synthesis techniques with a novel experimental setup is suggested.

#### **Nomenclature**


### **Author details**

Fatma Tugce Senberber Dumanli Nisantasi University, Istanbul, Turkey

\*Address all correspondence to: fatma.senberber@nisantasi.edu.tr

© 2023 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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#### **Chapter 7**

## Numerical Simulation of the Mechanical Behaviour of Boron Nitride Nanosheets and Nanotubes

*Nataliya A. Sakharova, Jorge M. Antunes, André F.G. Pereira, Bruno M. Chaparro and José V. Fernandes*

#### **Abstract**

Among the compounds formed by an element of the 13th group and nitrogen, boron nitride, also called white graphene, stands out for its high strength and thermal conductivity, transparency to visible light, antimicrobial properties, high resistance to oxidation, and biocompatibility. One-dimensional and two-dimensional boron nitride nanostructures, i.e. nanotubes and nanosheets, respectively, are expected to present innovative advanced characteristics not equal to those of bulk boron nitride, bringing new perspectives to numerous applications in nanoscale electronics and biomedicine. For the correct design of systems and devices consisting of boron nitride nanosheets and nanotubes, understanding the mechanical behaviour of these nanostructures is extremely important. Firstly, because the robustness and functioning of nanosystems and nanodevices based on boron nitride nanostructures are determined by the mechanical behaviour of their constituents and also because deformation can influence the optical, electric, and thermoelectric properties of boron nitride nanotubes and nanosheets. In this context, the current chapter is dedicated to the numerical evaluation of the elastic properties of boron nitride nanosheets and nanotubes, using the nanoscale continuum modelling (also called molecular structural mechanics) approach. With this aim, a three-dimensional finite element model was used to evaluate their elastic moduli.

**Keywords:** boron nitride, nanosheets, nanotubes, elastic moduli, modelling, numerical simulation

#### **1. Introduction**

Hexagonal boron nitride (h-BN) is one of the compounds of the 13th–15th groups, consisting of alternating boron (B) and nitrogen (N) atoms, linked by strong covalent bonds, forming a honeycomb lattice structure similar to that of graphene. For this reason, h-BN is often called "white graphene" [1, 2]. Hexagonal BN is a promising ultra-wide bandgap semiconductor with notable physical properties, chemical and thermal stability, and compatibility with graphene [1–5]. Two-dimensional (2D) h-BN layers have been broadly integrated into van der Waals heterostructures, with the aim to develop novel architectures for 2D electronic devices [5, 6]. The combination of 2D boron nitride layers with those of graphene enables the emergence of new applications and improves the performance of conventional devices. Dean et al. [3] demonstrated that the use of h-BN substrates instead of standard silica brings advantages to highquality graphene electronics, allowing to reduce roughness and chemical reactivity of graphene devices. Among the potential applications envisaged in recent times for 2D BN, resonant nanoelectromechanical systems (NEMS) [7], membranes for the separation of toxic gases [8] and water desalination [9], quantum emitters [10], anodes for magnesium-ion batteries [11]. Considering the diversity of potential applications, the development of methods for synthesised BN nanosheets has received special research attention (see, for example [1, 2, 12–15]). Hexagonal BN nanosheets with few atomic layers were synthesised using the thermal chemical vapour deposition (CVD) method on copper substrate [1, 2], polycrystalline nickel and cobalt substrates [2], and amorphous silica and quartz substrates [13]. The method proposed by Song et al. [1] allowed producing h-BN nanosheets at a large scale. Obtaining 2D BN nanosheets by micromechanical cleavage, a technique that consists of peeling off h-BN layers from bulk crystals, was also reported [3, 12, 15]. Moreover, a low-cost, template-free method for chemical synthesis of single-layer h-BN areas, using different acids as precursors, was recently proposed [14].

Single-walled boron nitride nanotubes (NTs), 1D structures, which can be understood as rolled-up BN nanosheets, are in the research focus due to their perspectives in highly demanded applications such as membranes for gas separation [16] and water filtration [17], osmotic power generators [18], and nanosensors [19]. The structural similarity of boron nitride nanotubes (BNNTs) and carbon nanotubes (CNTs) motivated research in order to replace CNTs with BNNTs in existing applications. Among these, there are the reinforcement of nanocomposites and the improvement of advanced functional materials. But innovative applications have also been sought, where the combination of boron nitride and carbon nanotubes in hybrid nanostructures permits taking advantage of both constituents and achieving better properties and performance of novel devices. After Chowdhury and Adhikari [20] first synthesised boron nitride nanotubes using arc discharge, in 1995, BNNTs were successfully produced by ball-milling [21–23], CVD [24–27], laser ablation [28–32], and thermal plasma jet [33–36] methods. Regarding the intended applications for 1D and 2D boron nitride nanostructures, their mechanical properties play a significant role in reinforced composites, membranes, van der Waals structures, as well as in the functioning and strength of nanosystems and nanodevices. On the other hand, deformation can modify the electronic, thermoelectric, optical, and chemical properties of boron nitride 1D and 2D nanostructures [37, 38].

The studies devoted at evaluating the mechanical properties of boron nitride nanosheets (BNNSs) and BNNTs are mostly carried out theoretically because experimental techniques at the nanoscale require many resources that are expensive. There are three classes of theoretical approaches (analytical and numerical) used to model and characterise the mechanical behaviour of BNNSs and BNNTs, namely the atomistic, the continuum mechanics (CM), and the nanoscale continuum modelling (NCM) approaches, the latter also called molecular structural mechanics (MSM). With regard to the atomistic approach, there are studies where the elastic properties of BNNSs and BNNTs were evaluated using *ab initio* Density Functional Calculations (DFT) and molecular dynamics (MD). The latter makes use of different potential functions to describe the interactions between B and N atoms in the nanostructures. Ahangari et al. [39] calculated Young's modulus of BNNSs by the *ab initio* DFT

#### *Numerical Simulation of the Mechanical Behaviour of Boron Nitride Nanosheets and Nanotubes DOI: http://dx.doi.org/10.5772/intechopen.111868*

method, and Le [40] and Zhao and Xue [41] used MD simulations with Tersoff potentials for this purpose. Concerning the BN nanotubes, Santosh et al. [42] used MD simulation, with force–constant approach to describe the interaction between B and N atoms, in order to calculate the Young's and shear moduli of the BNNTs. Tao et al. [43] performed MD simulation with Tersoff–Brenner (TB) potential, combining it with the finite element (FE) method to evaluate Young's modulus of BNNTs. Kumar et al. [44] in their MD simulation study used a second-generation reactive empirical bond order (REBO) potential and evaluated the BNNTs Young's modulus. The use of the CM approach, which models the entire nanostructure as a continuum element, is not frequent in the literature. Oh [45] made use of the CM approach combined with the adjusted TB potential to evaluate Young's modulus of the BNNTs.

Unlike the CM approach, the NCM/MSM considers the bonds between B and N atoms as elastic elements (springs or beams), taking advantage of the connection between the molecular structure of the nanosheet or nanotube and the solid mechanics. Tapia et al. [46] used the NCM/MSM approach, in which the B-N bond is replaced by the beam element, to evaluate Young's and shear moduli of the BNNSs. The NCM/ MSM approach has often been chosen as the most suitable for efficient and fast computational simulation of the mechanical response of BNNTs. Genoese et al. [47] evaluated the Young's and shear moduli of BNNTs, relating the "stick-and-spring" (NCM/MSM) and the Donnell (CM) model of continuum thin shell. Li and Chou [48] and Ansari et al. [49] replaced the B-N bond with the beam element for evaluating of BNNTs elastic properties under NCM/MSM approach, while Zakaria [50] used twosectioned beam elements for this purpose. Giannopoulos et al. [51], instead of beam elements, modelled the B-N bond as spring-like elements to calculate the BNNTs Young's modulus. Yan et al. [52] studied longitudinal and torsional free vibrations of BNNTs in a framework of the NCM/MSM approach and derived analytical solutions for Young's and shear moduli.

Although most achievements in evaluating the elastic properties of boron nitride nanosheets (NSs) and nanotubes (NTs) are due to theoretical approaches, many experimental studies have been carried out for this purpose. Song et al. [1] measured Young's modulus of BNNSs with 2–5 layers, using the nanoindentation test carried out by atomic force microscopy (AFM). Arenal et al. [53] used *in situ* uniaxial compression tests performed by high-resolution transmission electron microscopy (HRTEM) and AFM to evaluate Young's modulus of single-walled boron nitride nanotubes (SWBNNTs). Chen et al. [54] evaluated the Young's modulus of multi-walled boron nitride nanotubes (MWBNNTs), with the help of *in situ* axial compression, using a transmission electron microscope (TEM) with a force transducer holder. Chopra and Zettl [55] and Suryavanshi et al. [56] measured Young's modulus of MWBNNTs using the thermal vibrational amplitude of a cantilevered nanotube and the electric-fieldinduced resonance method, respectively, in TEM. Zhou et al. [57] used a high-order resonance technique within HRTEM for this purpose. Golberg et al. [58] and Ghassemi et al. [59] evaluated Young's modulus of the MWBNNTs from *in situ* bending and cycling bending tests, respectively, carried out with the help of AFM set up within TEM. Tanur et al. [60], with a resource to a three-point bending technique in AFM, calculated Young's and shear moduli of MWBNNTs.

The aim of the present study is to evaluate elastic moduli of one-layer boron nitride nanosheets (BNNSs) and non-chiral single-walled boron nitride nanotubes (SWBNNTs) employing the NCM/MSM approach with beam elements to simulate B-N covalent bond. For this purpose, 3D FE model was used, which permits evaluating Young's and shear moduli of 1D and 2D boron nitride nanostructures. The Young's modulus results obtained for SWBNNTs are analysed, bearing in mind those for BNNSs. Moreover, the current study presents a reference to determine the elastic properties of BNNSs and SWBNNTs and the architecture of hybrid 1D and 2D structures based on carbon and boron nitride.

#### **2. Atomic structure of BNNSs and SWBNNTs**

The BNNS has a honeycomb atomic arrangement with planar geometry [61] as shown in **Figure 1**, where the chiral vector, *Ch*, and the chiral angle, θ, are drawn. The unit vectors of the hexagonal BN lattice, *a***<sup>1</sup>** and *a***2**, and the chiral indices, n and m (integers), are also represented in this figure. These parameters allow defining the chiral vector and chiral angle by the following expressions:

$$\mathbf{C}\_{\hbar} = n\mathfrak{a}\_1 + m\mathfrak{a}\_2,\tag{1}$$

$$\theta = \sin^{-1} \frac{\sqrt{3}}{2} \frac{m}{\sqrt{n^2 + nm + m^2}}. \tag{2}$$

Rolling up the h-BN sheet into a cylinder, while varying the chiral angle, θ, from 0° to 30°, results in three types of SWBNNTs configurations, as exemplified in **Figure 1**. When θ ¼ 0° (*m* ¼ 0) and θ ¼ 30° (*n* ¼ *m*), the resulting tubular structures are called ð*n*, 0) zigzag and ð Þ *n*, *n* armchair nanotubes, respectively, and form the symmetry group of non-chiral NTs (see, **Figure 2**). Intermediate NT configurations, for which 0°< θ<30° (*n* 6¼ *m*), are related to the symmetry group of ð Þ *n*, *m* chiral NTs.

The geometric structure of the SWBNNTs is described through the circumference, *LC*, and the diameter, *Dn*, of the nanotube expressed as follows:

$$L\_{\mathbb{C}} = |\mathbb{C}\_{\hbar}| = \mathfrak{a}\sqrt{n^2 + nm + m^2},\tag{3}$$

#### **Figure 1.**

*Schematic illustration of the h-BN sheet with the chiral vector, Ch, chiral angle, θ, and indication of rolling-up for zigzag and armchair BNNTs. B atoms are represented in black; N atoms are in grey.*

*Numerical Simulation of the Mechanical Behaviour of Boron Nitride Nanosheets and Nanotubes DOI: http://dx.doi.org/10.5772/intechopen.111868*

#### **Figure 2.**

*Zigzag and armchair configurations of SWBNNTs, built using the software Nanotube Modeler©. B atoms are represented in black; N atoms in grey.*


**Table 1.**

*B-N covalent bond length values available in the literature.*

$$D\_n = \frac{L\_C}{\pi} = \frac{a\_{B-N}\sqrt{n^2 + nm + m^2}}{\pi},\tag{4}$$

where *a* is the length of the unit vector defined through the equilibrium B-N covalent bond length *aB*�*<sup>N</sup>* by *<sup>a</sup>* <sup>¼</sup> ffiffiffi <sup>3</sup> <sup>p</sup> *aB*�*<sup>N</sup>*.

There is no agreement among researchers regarding the B-N bond length, therefore different *aB*�*<sup>N</sup>* values can be found in the literature as shown in **Table 1**.

#### **3. Molecular mechanics of 1D and 2D BN nanostructures and equivalent properties of elastic beams**

In this study, the NCM/MSM approach was used to evaluate the elastic properties of BNNSs and SWBNNTs. This approach makes use of the equivalence between bonding interactions in the h-BN lattice and the elastic behaviour of beam elements.

As stated by Mayo et al. [66] and Rappé et al. [67], the energy of bonded interactions is defined via those related to bond stretching, *Ur*, bond bending, *U*θ, and bond torsion, *Uτ*, as follows:

$$U\_{bond} = U\_r + U\_\theta + U\_\tau = \frac{1}{2} \Delta k\_r (\Delta r)^2 + \frac{1}{2} k\_\theta (\Delta \theta)^2 + \frac{1}{2} k\_\tau (\Delta \phi)^2,\tag{5}$$

where *kr*, *k*θ, and *k*<sup>τ</sup> are the bond stretching, bond bending, and torsional resistance force constants, respectively, and Δr, Δθ, and Δϕ are the bond stretching increment, bond angle bending variation, and angle variation of the twist bond, respectively.

The term of bond torsion energy, *Uτ*, is a result of merging dihedral angle torsion, *Uϕ*, and out-of-plane torsion (also called improper torsion), *U<sup>ψ</sup>* , energy terms, as follows:

$$U\_{\tau} = U\_{\phi} + U\_{\psi} = \frac{1}{2} \left( 2k\_{\phi} + k\_{\psi} \right) \left( \Delta \phi \right)^{2} = \frac{1}{2} k\_{\tau} \left( \Delta \phi \right)^{2},\tag{6}$$

where *k<sup>ϕ</sup>* and *k<sup>ψ</sup>* are dihedral torsion and inversion force constants, respectively, and *k<sup>τ</sup>* ¼ 2*k<sup>ϕ</sup>* þ *k<sup>ψ</sup>* .

In its turn, the axial, *UA*, bending, *UB*, and torsional, *UT*, strain energies associated with respective elastic deformations of beams are expressed by:

$$U\_A = \frac{1}{2} \frac{E\_b A\_b}{l} \left(\Delta l\right)^2,\tag{7}$$

$$U\_B = \frac{1}{2} \frac{E\_b I\_b}{l} \left(\Delta o\right)^2,\tag{8}$$

$$U\_T = \frac{1}{2} \frac{G\_b I\_b}{l} \left(\Delta\theta\right)^2,\tag{9}$$

where *Eb* and *Gb* are the Young's and shear moduli of the beam, respectively; *l* is the beam length; *Ab*, *Ib* and *Jb* are the cross-section area, the moment of inertia, and the polar moment of inertia of the beam, respectively; Δ*l* is the beam axial tensile displacement, ω is the rotational angle at the ends of the beam, Δϑ is the relative rotation between the ends of the beam.

Consequently, the beam tensile, *EbAb*, bending, *EbIb*, and torsional, *GbJb*, rigidities can be linked to bond stretching, *kr*, bond bending, *k*θ, and torsional resistance, *k*τ, force constants, respectively, equating, *Ur* ¼ *UA*, *U<sup>θ</sup>* ¼ *UB* and *U<sup>τ</sup>* ¼ *UT*, from (Eq. (5)) and (Eqs. (7)–(9)), as follows [68]:

$$E\_b A\_b = k\_r l; E\_b I\_b = k\_\theta l; G\_b I\_b = k\_\tau l. \tag{10}$$

With regard to the *kr*, *k*θ, and *k*<sup>τ</sup> force constants for the 1D and 2D BN nanostructures, dissimilar values were reported in the literature, depending on the calculation method chosen for this purpose. One of the established methods to calculate force field constants of the diatomic nanostructure is based on Universal Force Fields (UFF) [67] and the other combines *ab initio* DFT calculations with the analytical relationships, coming from molecular mechanics (MM), for the surface Young's modulus, *Es*, and the Poisson's ratio, *ν*, [47]. The *Es* and *ν* values to be replaced in the MM expressions are taken from the literature [64, 69] or obtained from DFT calculations [70]. Tapia et al. [46] obtained the bond force constants from *ab initio* DFT computations, without resorting to MM models. The DREIDING force field (FF) approach [66], which is based solely on the hybridization of atoms, provides the force field constants directly. Apart from the well-known molecular FFs, a classical FF, for describing the B-N bonds, was developed using *ab initio* molecular dynamics (AIMD) simulations combined with lattice dynamics (LD) calculations [65]. The *kr*, *k*θ, and *k*<sup>τ</sup> force constants for 1D and 2D BN nanostructures, calculated by different approaches are summarised in **Table 2**. It is worth noting that the bond bending force constant, *k*θ, depends on the effective charges of the B and N atoms (*Z* <sup>∗</sup> 1,2) and the three-body angles between the bond pairs, B – N – B and N – B – N, which results in two different values *<sup>k</sup>*θ<sup>1</sup> and *<sup>k</sup>*θ2, linked by relationship *<sup>k</sup><sup>θ</sup>*1*=k<sup>θ</sup>*<sup>2</sup> <sup>¼</sup> *<sup>Z</sup>* <sup>∗</sup> <sup>2</sup> <sup>2</sup> *=Z*<sup>2</sup> <sup>1</sup> [67].

The values of the bond torsion constant, *k*τ, available in the literature are less frequent and with greater discrepancy than those reported for *kr* and *k*<sup>θ</sup> force constants. Ansari et al. [70] based their calculation on the link between the bending rigidity of the BN sheet and *k*τ, established by molecular mechanics (MM). Genoese et al. [69] calculated the dihedral torsion force constant, *kϕ*, also based on the link between *k<sup>ϕ</sup>* and bending rigidity. Rajan et al. [65] computed two values of the

*Numerical Simulation of the Mechanical Behaviour of Boron Nitride Nanosheets and Nanotubes DOI: http://dx.doi.org/10.5772/intechopen.111868*


#### **Table 2.**

*Force field constants for 1D and 2D BN nanostructures reported in the literature.*

inversion force constants, *kψ*<sup>1</sup> and *kψ*<sup>2</sup> for improper dihedral angles B-N-N-N and N-B-B-B, respectively.

The input parameters for the numerical simulation of 1D and 2D boron nitride nanostructures are calculated based on (Eq. (10)), and assuming the equivalence between the B-N bond length, *a*<sup>B</sup>�N, and the beam length, *l.* The assumption that the beam element has a circular cross-section area, d being its diameter, allows determining the cross-section area, *Ab*, the moment of inertia, *Ib*, and the polar moment of inertia, *Jb*, of the beam, as follows:

$$A\_b = \pi d^2 / 4; I\_b = \pi d^4 / 64; I\_b = \pi d^4 / 32. \tag{11}$$

Regarding **Table 2**, it is possible to conclude that the adequate selection of the values of *kr*, *k*θ, and *k*τ, to calculate the geometrical and elastic properties of beams, which in turn provide input for numerical simulation, is a challenging task. Sakharova et al. [71] studied the influence of input parameters, calculated based on different sets of force field constants, on the elastic properties of BNNTs. It was found that the literature results are in better agreement with the input parameters assessed using values of the force constants close to those reported by Genoese et al. [69] (see **Table 2**). Consequently, in the current study, the bond stretching, *kr*, and bond bending, *k*θ, force constants from the work of Genoese et al. [69] were chosen to calculate the input parameters for the numerical simulation, as shown in **Table 3**. The torsional resistance constant, *k*τ, was calculated by *k<sup>τ</sup>* ¼ 2*k<sup>ϕ</sup>* þ *k<sup>ψ</sup>* , using *k<sup>ϕ</sup>* ¼ <sup>0</sup>*:*052 nN nm*=*rad2 computed by Genoese et al. [69] and *<sup>k</sup><sup>ψ</sup>* <sup>¼</sup> <sup>0</sup>*:*278 nN � nm*=*rad<sup>2</sup> taken from DREIDING FF [66].

#### **4. Geometric characteristics of BN nanosheets and single-walled nanotubes and finite element analysis**

Single-layer BNNS with a size of 14.26�13.94 nm<sup>2</sup> was selected for finite element analysis (FEA). With regard of SWBNNTs, non-chiral NTs, zigzag (θ ¼ 0°), and armchair (θ ¼ 30°) were selected for FEA (see **Table 4**). The aspect ratio between

#### *Boron, Boron Compounds and Boron-Based Materials and Structures*


#### **Table 3.**

*Input parameters for numerical simulations of BNNSs and SWBNNTs: Geometric and elastic properties of beam elements.*


#### **Table 4.**

*Geometric characteristics of the non-chiral SWBNNTs.*

nanotube length, *Ln*, and diameter, *Dn*, was about 30, thus the NTs elastic response is independent of *Ln*.

The FE meshes of the BNNS and SWBNNTs, used in FEA, were obtained with the help of the Nanotube Modeller© software. This software produces the Program Database files, which are then converted, with the *InterfaceNanotubes.NM* in-house application [71], to the appropriate format to be used by the ABAQUS® code.

The mechanical behaviour of the BN nanosheet was studied under numerical tensile and in-plane shear tests, using the ABAQUS® FE code. **Figure 3** shows the geometry of the NS and the boundary conditions of the three studied loading cases.

In the first loading case, the nodes on the left edge of the BNNS were fixed and an axial tensile force, *Px*, was applied on the opposite (right) edge (**Figure 3a**). In the second case, the nodes on the bottom edge of the BNNS were fixed, while an axial transverse force, *Py*, was applied on the top edge of the nanosheet (**Figure 3b**). In the third loading case, the boundary conditions were the same as in the second case, and a shear force, *Nx*, was applied to the upper edge nodes of the BNNs (**Figure 3c**).

Under the applied force *Px*, the BNNS elongates in the x- direction, which leads to axial displacement, *ux*. The Young's modulus along the x-axis, *Ex*, is determined as follows [46]:

*Numerical Simulation of the Mechanical Behaviour of Boron Nitride Nanosheets and Nanotubes DOI: http://dx.doi.org/10.5772/intechopen.111868*

**Figure 3.**

*Schematic representation of: (a) tensile loading in the x - direction (zigzag configuration); (b) tensile loading in the y- direction (armchair configuration); (c) in-plane shear loading in the x-direction for the BNNSs. The geometrical parameters and the boundary conditions of the nanosheet are also presented.*

$$E\_{\mathbf{x}} = \frac{P\_{\mathbf{x}} L\_{\mathbf{x}}}{\mu\_{\mathbf{x}} L\_{\mathbf{y}} t\_n},\tag{12}$$

where *Lx* and *Ly* are the BNNS side lengths as shown in **Figure 3**; *tn* is the nanosheet thickness.

The Young's modulus along the y-axis, *Ey*, is calculated by the following expression [46]:

$$E\_{\mathcal{Y}} = \frac{P\_{\mathcal{Y}} L\_{\mathcal{Y}}}{v\_{\mathcal{Y}} L\_{\mathfrak{x}} t\_n},\tag{13}$$

where *Py* is applied transverse force, *vy* is the displacement of the BNNS in the y-direction, taken from the FEA.

To calculate the shear strain, *γxy*, the displacement of the BNNS in the x-direction under the in-plane shear force (*Nx*Þ, *vx*, was taken from FEA. Consequently, the shear modulus, *Gxy*, of the BNNS is calculated by the following expression [46]:


**Table 5.**

*Nanotube wall thickness values, tn, reported in the literature.*

$$G\_{\rm xy} = \frac{N\_{\rm x}}{\chi\_{\rm xy} L\_{\rm x} t\_{\rm n}}, \chi\_{\rm xy} = \tan \frac{v\_{\rm x}}{L\_{\rm y}}. \tag{14}$$

where *Lx* and *Ly* are the NS side lengths, *tn* is the NS thickness.

The ABAQUS® FE code was also used to evaluate the elastic response of SWBNNTs under tensile, bending, and torsion loading. The boundary conditions consisted in fixing the edge nodes at one end of the NT. The axial tensile force, *Fa*, the transverse force, *Ft*, and the torsional moment, *MT*, were applied to the other end of the NT, to carry out tensile, bending, and torsion tests. In the last case, the edge nodes cannot move in the radial direction.

The axial displacement, *ua*, the transverse displacement, *ut*, and the twist angle, *ω*, were obtained from the FEA of the respective test. This allows calculating the tensile, *EA*, bending, *EI*, and torsional, *GJ*, rigidities of the non-chiral SWBNNTs with length *Ln* as follows:

$$EA = \frac{F\_a L\_n}{u\_a}, EI = \frac{F\_l L\_n^3}{u\_l^3}, GJ = \frac{M\_T}{\alpha}. \tag{15}$$

Making use of (Eq. (15)), the Young's, *ENT*, and shear, *GNT*, moduli of the SWBNNTs are determined by the following expressions [72]:

$$E\_{NT} = \frac{EA}{\pi t\_n \sqrt{8\left(\frac{EI}{EA}\right) - t\_n^2}},\tag{16}$$

$$G\_{NT} = \frac{GJ}{2\pi \left(\frac{EI}{EA}\right)t\_n\sqrt{8\left(\frac{EI}{EA}\right) - t\_n^2}},\tag{17}$$

where *tn* is the nanotube wall thickness, the same parameter as the nanosheet thickness in (Eqs. (12)–(14)).

In the present study, the wall thickness value of the SWBNNTs was considered equal to the graphite interlayer spacing, *tn* ¼ 0*:*34 nm. Such value was confirmed experimentally by TEM, *tn* ¼ 0*:*338 � 0*:*004 nm [73], and commonly used by the research community [43, 48, 49, 71]. Still, there is no agreement on the *tn* value as shown in **Table 5**.

#### **5. Elastic moduli of the boron nitride nanosheets (BNNS)**

**Figure 4a** shows Young's modulus of the BNNS, along the x-axis (zigzag direction), *Ex*, and the y-axis (armchair direction), *Ey*, evaluated respectively by (Eqs. (12) *Numerical Simulation of the Mechanical Behaviour of Boron Nitride Nanosheets and Nanotubes DOI: http://dx.doi.org/10.5772/intechopen.111868*

#### **Figure 4.**

*(a) Current Young's moduli, Ex (zigzag) and Ey (armchair), of BNNSs and those by Tapia et al. [46], Le [40], Zhao and Xue [41], Verma et al. [77], and Le and Nguyen [78]; (b) current Young's modulus,ENS, of BNNS and those by Kudin et al. [74], Ansari et al. [49], Ahangari et al. [39], and Song et al. [1].*

and (13)), as well as *Ex* and *Ey* results available in the literature. For cases in which only one Young's modulus was reported, the comparison was carried out with the average value *ENS* ¼ *Ex* þ *Ey =*2, as shown in **Figure 4b**. The value of *ENS*, measured by the nanoindentation test, performed in AFM, in the work by Song et al. [1], is also shown in **Figure 4b**. Since Song et al. [1] reported the surface Young's modulus (the product of Young's modulus by the nanosheet thickness, *EsNS* ¼ *ENStn*), *ENS* was evaluated using *tn* = 0.33 nm, as suggested in their study.

The scatter of Young's moduli results, *Ex* and *Ey*, available in the literature is evidenced in **Figure 4a**. Good agreement was found between the current *Ex* (zigzag direction) and *Ey* (armchair direction) values and those evaluated by Tapia et al. [46], with a difference of 5.4 and 5.7% for *Ex* and *Ey*, respectively. The work by Tapia et al. [46] shares the same modelling (NCN/MSM with beams) and calculation approach as the present study. The values *Ex* and *Ey* reported by Verma et al. [77] in their MD study employing TB potential, are 14.5 and 4.2% higher, respectively, than those obtained in the present study. For Young's moduli along the x-axis and y-axis calculated by Le [40], differences of 23.6 and 26.8% are seen when compared with the current *Ex* and *Ey* moduli, respectively. Le and Nguyen [78] reported *Ex* and *Ey* values of 19.8 and 20.8% lower than those evaluated by (Eqs. (12) and (13)), respectively. Despite the similar values of *Ex* and *Ey* obtained in the works by Le [40] and Le and Nguyen [78], these studies used different modelling methods, which are MD simulations with Tersoff and Tersoff-like potentials and FE simulations under NCM/MSM

approach based on harmonic force fields, respectively. The largest difference of 40.0% (for *Ex*) and 29.8% (for *Ey*) were found between current Young's modulus values and those by Zhao and Xue [41], who employed MD simulations with Tersoff potential.

Particularly good agreement (difference of 0.8%) is observed between the current Young's modulus of the BNNS, *ENS*, and that assessed by Ahangari et al. [39] using ab initio DFT calculations (see, **Figure 4b**). The BNNS Young's moduli reported by Kudin et al. [74] and Ansari et al. [49] are 19.0 and 16.2% smaller, respectively, than *ENS* calculated in the present study. In the work of Kudin et al. [74] Young's modulus was evaluated using *ab initio* calculations. Ansari et al. [49] employed an analytical solution in the framework of the NCM/MSM approach for this purpose. The biggest difference of about 43% is seen when the current BNNS Young's modulus is compared with that obtained by nanoindentation experiments [1]. This comparatively lower value of *ENS*, evaluated in a study by Song et al. [1], can be related to the presence of intrinsic defects and their distribution in boron nitride NS.

The results presented in **Figure 4a** indicate that the BN nanosheets are not transversely isotropic, i.e. Young's moduli in the zigzag and armchair directions are not equal to each other, *Ex* 6¼ *Ey*. The present study, as well as those by Le [40], Zhao and Xue [41], Tapia et al. [46], Verma et al. [77], and Le and Nguyen [78], suggest a mild anisotropy of BNNSs. Such anisotropic nanosheet behaviour can be quantified by the ratio between Young's moduli for zigzag and armchair configurations, *Ex=Ey*. In **Figure 5**, the current ratio *Ex=Ey* is compared with those calculated from the results available in the literature.

The current ratio of *Ex=Ey* ≈1*:*01 is in very good agreement with *Ex=Ey* ≈1*:*01, 1*:*04, 1*:*02 found in the works by Tapia et al. [46], Le [40], and Le and Nguyen [78], respectively. In contrast to other results under analysis, Zhao and Xue [41] reported Young's modulus for the zigzag NS configuration smaller than for armchair, with the ratio *Ex=Ey* ≈0*:*94. Verma et al. [77] indicated the highest anisotropy ratio, among others presented in **Figure 5**, *Ex=Ey* ≈1*:*10. The BN nanosheet anisotropy can possibly be explained by the alignment of the bonds in relation to the loading path, which causes it to lose crystalline symmetry, as there are two types of atoms in each structure.

The evaluation of the BNNS shear modulus has practically not been the research focus so far. **Figure 6** shows the shear moduli of the BNNS, *Gxy*, evaluated by

#### **Figure 5.**

*Comparison of the current Ex=Ey ratio with those obtained from the literature by Tapia et al. [46], Le [40], Zhao and Xue [41], Verma et al. [77], and Le and Nguyen [78].*

*Numerical Simulation of the Mechanical Behaviour of Boron Nitride Nanosheets and Nanotubes DOI: http://dx.doi.org/10.5772/intechopen.111868*

**Figure 6.**

*Current shear modulus, Gxy of BNNSs and those by Tapia et al. [46], Kudin et al. [74], and Le and Nguyen [78].*


#### **Table 6.**

*Current results of Young's and shear moduli for boron nitride nanosheets and those reported in the literature.*

(Eq. (14)), with the *Gxy* results available in the literature. The value of *Gxy* evaluated in the current work is in good concordance (the difference of 4.6%) with that reported by Tapia et al. [46]. On the other hand, the current shear modulus is more than 40% smaller than *Gxy* evaluated by Kudin et al. [74] and Le and Nguyen [78].

To facilitate understanding, the results of the elastic moduli shown in **Figures 4**–**6**, are summarised in **Table 6**.

#### **6. Elastic moduli of the single-walled boron nitride nanotubes (SWBNNTs)**

**Figure 7a** shows Young's modulus, *ENT*, of the non-chiral, zigzag, and armchair SWBNNTs, as a function of the NT diameter, *Dn*. Young's modulus was evaluated by (Eq. (16)), which makes use of the tensile, *EA*, and bending, *EI*, rigidities calculated

#### **Figure 7.**

*(a) Evolution of Young's modulus, ENT, with NT diameter, Dn, for non-chiral SWBNNTs; (b) comparison of the current results of Young's modulus of SWBNNTs with those reported in the literature [42–45, 48, 52].*

with (Eq. (15)) based on the respective numerical test results. Young's moduli of boron nitride NS in zigzag, *Ex*, and armchair, *Ey*, directions are also plotted in **Figure 7a**. **Figure 7b** compares the values of *ENT* obtained in the present study with those reported in the literature, selected so that different modelling and calculation approaches were taken into consideration. The Young's moduli of non-chiral boron nitride NTs with diameters range similar to the one studied in the present work were chosen for comparison purpose.

The *ENT* evolutions with the nanotube diameter for zigzag and armchair boron nitride NTs coincide, which establishes a unique trend for both ð Þ *n*, 0 and ð Þ *n*, *n* nonchiral NTs (see, **Figure 7a**). The Young's modulus of the SWBNNTs, after a slight decrease at the beginning of the trend, converges to a nearly constant value, *ENT*≈ 0.958 TPa, with increasing of *Dn*. This stabilised value, on the one hand, tends to Young's modulus of BNNS in the zigzag direction, *Ex*, and, on the other hand, is equal to the *Ey* value in the armchair direction.

It can be concluded from **Figure 7b** that the current SWBNNTs Young's modulus results are in reasonably good consonance with those reported in the literature. Particularly good agreement (difference of 0.05%) was found between the current value of *ENT* and that evaluated for ð Þ *n*, *n* NTs with *Dn* >3*:*0 *nm* by Oh [45] in a study employing the CM approach. The difference becomes 1.73% when compared with the *ENT* value for ð Þ *n*, *n* NTs in the entire range of diameters considered, obtained in the same work [45]. For Young's moduli calculated by Yan et al. [52], based on the

*Numerical Simulation of the Mechanical Behaviour of Boron Nitride Nanosheets and Nanotubes DOI: http://dx.doi.org/10.5772/intechopen.111868*

analysis of longitudinal vibrations under the NCM/MSM approach, and by Tao et al. [43], employing MD combined with the FE model, the differences for the current value of *ENT* are about 1.5 and 2.5%, respectively. The greatest differences of about 3.9, 4.5, and 5.8% are observed when *ENT* evaluated by (Eq. (16)) is compared with Young's modulus reported by Kumar et al. [44], Li and Chou [48], and Santosh et al. [42], respectively. The works of Santosh et al. [42] and Kumar et al. [44] both used MD simulation, with the difference in the way of describing the interatomic interactions in the h-BN lattice, force-constant method, and REBO potential, respectively. Li and Chou [48] investigated the elastic behaviour of the SWBNNTs within the framework of the NCM/MSM approach with beam elements to model the B-N bond, as in the present study, using only the other force field constants (see, **Table 2**).

It is worth noting that Young's modulus values evaluated in the present study for the BNNS and SWBNNTs are close to those typically obtained for the CNTs (*ECNT* ≈1*:*0 TPa), which indicates that the 1D and 2D BN nanostructures are appropriate candidates to replace carbon counterparts in various technological applications or to envisage the design of hybrid structures, constituted by NSs or NTs of carbon and boron-nitride.

**Figure 8a** shows the shear modulus, *GNT*, of the SWBNNTs, as a function of the NT diameter, *Dn*. The shear modulus was evaluated by (Eq. (17)), using tensile, *EA*, bending, *EI*, and torsional, *GJ*, rigidities derived by (Eq. (15)) from FEA results.

#### **Figure 8.**

*(a) Evolutions of the current shear modulus, GNT, with NT diameter, Dn, for the non-chiral SWBNNTs; (b) comparison of the current results of the shear modulus of SWBNNTs with those reported in the literature [42, 44, 48, 52].*

**Figure 8b** shows the current shear modulus values with those available in the literature, for comparison purposes.

The shear modulus, *GNT*, of the SWBNNTs is almost constant with increasing NT diameter, *Dn*, except at the beginning of the evolution *GNT* ¼ *f D*ð Þ*<sup>n</sup>* , where the insignificant decrease of the *GNT* is observed (see, **Figure 8a**). Regarding the results available in the literature, a reasonable agreement, with a difference ≈ 3.6%, is observed when the current values of *GNT* are compared to those evaluated by Li and Chou [48], who employed the same modelling approach as in the present study but using a different set of force field constants (see, **Figure 8b**). However, greater differences occur for the other available *GNT* values. As previously discussed [71], the


**Table 7.**

*Comparison of current Young's and shear moduli results for BNNTs with those reported in the literature.*

*Numerical Simulation of the Mechanical Behaviour of Boron Nitride Nanosheets and Nanotubes DOI: http://dx.doi.org/10.5772/intechopen.111868*

SWBNNTs shear modulus results are relatively uncommon in the literature so far, in addition to showing a significant scattering of reported values.

To facilitate the understanding of the results of the SWBNNTs elastic moduli presented in **Figures 7** and **8**, they are summarised in **Table 7**, which also includes the experimental results from the literature.

It is possible to conclude from this table that the current Young's modulus results are in reasonable agreement with most of the experimental values of *ENT*. With regard to the shear modulus, as far as we know, only Tanur et al. [60] reported a very low *GNT* value for the case of MWBNNTs, which was explained by the shear effects occurring between adjacent layers.

#### **7. Conclusions**

In the present numerical simulation study, Young's and shear moduli of 1D (nanotubes) and 2D (nanosheets) boron nitride structures were evaluated based on the NCM/MSM approach.

The current result of the elastic moduli points to a mild anisotropy of the boron nitride nanosheets. The Young's modulus of the BNNS in the zigzag direction, *Ex*, is greater than that in the armchair direction, *Ey*, with the anisotropy ratio *Ex=Ey* ≈1*:*01, whose value is in good concordance with those reported in the literature.

The Young's and shear moduli of single-walled boron nitride nanotubes become quasi-constant with increasing nanotube diameter, *Dn*, after a slight decrease at the beginning of the trend. This quasi-constant value of the SWBNNTs Young's modulus tends to the BNNS Young's modulus in a zigzag direction, *Ex*, and coincides with that in the armchair direction, *Ey*.

The current results establish a reference for the evaluation of the elastic properties of the boron nitride nanosheets and nanotubes by numerical methods.

#### **Acknowledgements**

This research is sponsored by FEDER funds through the program COMPETE— Programa Operacional Factores de Competitividade—and by national funds through FCT, Fundação para a Ciência e a Tecnologia, under the projects CEMMPRE— UIDB/00285/2020 and ARISE—LA/P/0112/2020

#### **Conflict of interest**

The authors declare no conflict of interest.

#### **Author details**

Nataliya A. Sakharova<sup>1</sup> \*, Jorge M. Antunes1,2, André F.G. Pereira1 , Bruno M. Chaparro<sup>2</sup> and José V. Fernandes<sup>1</sup>

1 Centre for Mechanical Engineering, Materials and Processes (CEMMPRE) - Advanced Production and Intelligent Systems, Associated Laboratory (ARISE), University of Coimbra, Coimbra, Portugal

2 Abrantes High School of Technology, Polytechnic Institute of Tomar, Tomar, Portugal

\*Address all correspondence to: nataliya.sakharova@dem.uc.pt

© 2023 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Numerical Simulation of the Mechanical Behaviour of Boron Nitride Nanosheets and Nanotubes DOI: http://dx.doi.org/10.5772/intechopen.111868*

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### *Edited by Metin Aydin*

Boron plays a pivotal role in the development of innovative boron-based materials, endowed with properties of paramount significance in both the manufacturing and performance aspects of numerous products crucial to modern society. Over the past few decades, there has been a burgeoning interest in boron, its compounds, and boron-based materials within the scientific and technological communities. This heightened attention stems from their exceptional potential applications across a wide spectrum of fields, spanning from materials science to biomedical research, owing to their remarkable characteristics. These extraordinary properties make them compelling candidates for a diverse array of applications in industry and everyday life. These applications encompass biotechnology, medicine (drug delivery systems and technologies, bioimaging systems, and radiation therapy), agriculture, radiationshielding materials, capping agents, and mechanical strength, among others. However, despite extensive research, many aspects of boron's properties remain shrouded in mystery, presenting practical challenges. This book delves deep into the realm of boronbased nanomaterials, shedding light on their properties and providing an up-to-date overview of the latest breakthroughs in boron and its compounds. It offers insights into the industrial, medical, and everyday applications of boron-containing materials. The book is a comprehensive resource for seasoned professionals, scientists, and scholars in pursuit of cutting-edge technological advancements. Comprising research articles and reviews, it is an invaluable reference for both students and scholars engaged in the exploration of boron and boron-based materials.

Published in London, UK © 2024 IntechOpen © Funtay / iStock

Boron, Boron Compounds and Boron-Based Materials and Structures

Boron, Boron Compounds

and Boron-Based Materials

and Structures

*Edited by Metin Aydin*