Neutron Radiation Shielding of C-PC and Geopolymers

Concrete is one of the most common material used for radiation shielding purposes. It involves using the material's density and atomic composition to protect both against gamma and neutrons and reduce their harmful effects on individuals and equipment in the vicinity of a radiation source. While the protection against the high energy electromagnetic gamma rays is rather simple, the shielding against neutrons is more complex. For gamma rays density is the main factor influencing the effectiveness of the shielding. For neutron shielding, density is of marginal importance due to the different nature of the neutrons. When neutrons are emitted from a radiation source, as they have no charge, they can travel through until they interact with the nuclei of a target atom. The absorption of fast, high energy neutrons, is practically impossible, so to stop a fast neutron, first its energy has to be decreased to the level of a thermal neutron.

Following the laws of mechanics if a neutron of a limited mass hits a large nucleus, it will lose a small part of its energy. But if it collides with a nuclei whose mass is close to the mass of a nucleus, the energy loss will be large. That is why the best moderators are light elements in concrete like hydrogen which is present in the chemically bounded water [1] and oxygen that is from aggregate and cement used to make concrete. The other elements contributed by aggregate have relatively smaller effectiveness but due to big total mass can create an important share in total neutron attenuation efficiency. The second step of neutron shielding is to absorb thermal neutrons. It is independent from the atomic number of the target nuclei or any other simple relation. The best absorbers are neither the light elements (moderators) nor the heavy atoms which are efficient in gamma radiation shielding. The best neutron absorbers in concrete are chloride (Cl) and iron (Fe). Unfortunately, chloride as a component of reinforced concrete is not recommended as it can induce the corrosion of the reinforcing steel. Iron is not ideal either, as thermal neutron absorption in iron results in the emission of high-energy secondary gamma radiation and can cause significant activation of the concrete. For this reason, it is beneficial to use other elements such as gadolinium (Gd), cadmium (Cd), boron (B) or cobalt (Co).

Recently a number of researches have been performed for geopolymers [2]. Geopolymers are a type of inorganic polymer material that can be synthesized from various industrial waste materials such as fly ash, slag, and clay. They are formed by the reaction of these waste materials with alkaline activators such as sodium silicate and sodium hydroxide. Geopolymers have a unique chemical structure that gives them properties such as high strength, low porosity, and fire resistance, making them a promising alternative to traditional cement and concrete. The chemical structure of geopolymers consists of a three-dimensional network of tetrahedral and octahedral units, which are linked together by covalent bonds. This structure is similar to that of natural minerals such as zeolites and feldspars. The use of industrial waste materials to produce geopolymers not only provides a sustainable solution for waste management but also reduces the environmental impact of traditional cement and concrete production. Geopolymers have a wide range of applications, including as a binder in construction materials, such as concrete, mortar, and tiles, as well as in the production of refractory materials, composites, and coatings. They also have potential for use in waste immobilization, catalysis, and energy storage.

The aim of the paper is to evaluate the neutron shielding efficiency of concretes and geopolymers modified by epoxy resin. It has been assumed that polymer is added in 5, 10, 15 and 20% in relation to cement or geopolymer precursors mass [3]. Such content of epoxy can create a separate phase in composite so they can be named C-PC (Cement-Polymer Composite) and G-PC (Geopolymer-Polymer Composite). The evaluation is based on neutron shielding efficiency calculation of fast neutron effective removal cross-section and additionally on the macroscopic cross-section calculation for compositions - Evaluation was based on neutron shielding efficiency calculations – a method adopted from the fast neutron effective removal cross-section calculation allowing for evaluation of fast neutron attenuation and thermal neutron absorption reactions separately.

The calculation has been performed on ordinary concrete with dolomite aggregate (density 2520 kg/m³), heavy-weight concrete with magnetite aggregate (density 4090 kg/m³) and geopolymer concrete with silica based aggregate (density 2000 kg/m³). Cement for concrete was CEM III/B 42,5 N-LH/SR and its oxide composition was obtained from XRF analysis. Dolomite aggregate was 87% pure dolomite with 10% of calcite and 3% of iron sulfide. Magnetite aggregate contained more that 90% of Fe₃O₄ with minor content of Silica, Calcium and Aluminum oxides. Geopolymer precursors were fly ash, zeolite, metakaolin and calcium hydroxide. The secondary components were limestone powder, cenospheres, perlite powder. The silica based aggregate and silica glass with NaOH solution in water has been used in geopolymers as well.

The neutron shielding efficiency of compounds can be compared based on an equivalent absorption cross-section called a fast neutron effective removal cross-section, Σ_R [4, 5]. It is a linear attenuation coefficient given in cm⁻¹ and is defined as a probability that a fast energy neutron undergoes on the first collision, which removes it from the group of penetrating, uncollided neutrons. The concept of this phenomena is based on the presence of hydrogen as it is the main moderator that dominates the attenuation of neutrons. Calculation of fast neutron effective removal cross-sections is by analogy to the calculation of mass attenuation coefficients of gamma-ray according to the equation:where: \(W_{i}\) – partial density of i^th constituent, \(\left( {\Sigma_{R} /\rho } \right)_{i}\) – fast neutron mass removal coefficient of i^th constituent

The fast neutron mass removal cross-section of constituents is related to the microscopic nuclear properties and varies smoothly with the atomic weight. The value can be calculated using the empirical equations or measured. For most elements and some compounds, experimental and theoretical values of the fast neutron mass removal cross-sections have been published [6‐8]. In order to estimate the neutron shielding efficiency of concrete in a more detailed way and do not describe not fast neutron attenuation only, a method based on macroscopic cross-sections for a different interaction can be used [9]. In this method, instead of fast neutron attenuation cross-sections, it uses a database of neutron scattering lengths and cross-sections that includes the thermal neutron microscopic cross-section as well [10]. Thus the macroscopic neutron scattering cross-section \({\Sigma }_{s} ,\) or the macroscopic thermal neutron absorption cross-section \({\Sigma }_{a} ,\) and finally their sum named the total macroscopic neutron cross-section \({\Sigma }_{T} ,\) can be calculated using equation:where: \(W_{i}\) – partial density of i^th constituent, \(\left( {{\Sigma }_{j} /\rho } \right)_{i}\) – neutron mass attenuation coefficient of i^th constituent for a specific interaction (j).

The key issue for shielding efficiency evaluation is atomic composition determination. It is presented in elemental weight fractions and partial densities. For concretes it was assumed that only 20% of the water is chemically bound water by cement hydration. Later weight fractions for specific elements of the concrete and the partial densities from oxide composition of the constituents were calculated. In case of geopolymers the calculations were simpler as all constituents with full mass have been taken into account. Weight fractions of concretes and geopolymer has been modified by addition in 5, 10, 15 and 20% of by epoxy resin composed of Carbon (76%), Oxygen (17%) and Hydrogen (7%) (Tables 1 and 2).

Dominating elements in concrete are mainly the income form aggregates that contribution in total unit mass is more than 80%. For ordinary concrete (OC) they were calcite (CaCO₃) and Mg/Ca oxides from dolomite aggregate and for magnetite concrete (MC) it was Fe oxide. In case of geopolymer (GP) due to presence of sand Silica and oxide content is the highest. It can be also found that hydrogen content in geopolymer mortar is f one order of magnitude bigger than in cement based concretes. These remarks from atomic composition can be directly transferred to analysis of contribution in neutron shielding efficiency parameters (Figs. 1, 2, and 3). The highest contribution to fast neutron mass removal cross-section of all composite’s results from aggregates (Fig. 1). It can be also observed much bigger contribution of hydrogen in geopolymer (GP) in comparison to both concretes (OC and MC). This effect is even more visible on macroscopic neutron scattering cross-section values (Fig. 2). It proves that the hydrogen in concrete is the most important component regarding fast neutron shielding efficiency. The next in importance are oxide (O) due to big contribution in total mass and iron (Fe) that is present in magnetite concrete. Iron is also the key factor contributing thermal neutron absorption cross-section (Fig. 3). It is the only peak for magnetite concrete (MC) and for ordinary one (OC) although it is less than 2% in total mass its contribution is visible. Finally, contribution to total macroscopic neutron cross-section (Fig. 4) is similar to macroscopic neutron scattering cross-section (Fig. 2) as the cross-section values for absorption are of two magnitudes less than for scattering and they do not change the total value significantly. The last remark from the contribution analysis is that an addition of epoxy to every composite slightly increases hydrogen and carbon content and thus their importance in the shielding efficiency parameters.

The comparison of radiation shielding parameters absolute values shows that ordinary concrete (OC) is the worst from every point of view (Fig. 5). Geopolymer mortar (GP) is the best when fast neutron scattering and total macroscopic neutron cross section is compared. Magnetite concrete (MC) has the highest values of thermal neutron absorption cross-section and surprisingly fast neutron mass removal cross-section as well. It is probably due to the fact that in fast neutron mass removal cross-section calculation issues other than simple fast neutron scattering also have some influence. They simply decide about fast neutron mass removal coefficient value of each atomic constituent.

The positive influence of epoxy addition on every parameter is clearly visible by positive value of slope coefficients in trend line equations. It doesn’t differ much between composites but changes regarding the type of parameter. The smallest influence it has on thermal neutron absorption (Fig. 5c) and the highest for fast neutron scattering (Fig. 5b) and total neutron macroscopic neutron cross-section (Fig. 5d). Moderate effect is noted in case of fast neutron mass removal cross-section (Fig. 5a).

The following conclusions from the research described above can be drawn: