Modeling Radiation Damage in Materials Relevant for Exploration and Settlement on the Moon

Abstract

Understanding the effect of radiation on materials is fundamental for space exploration. Energetic charged particles impacting materials create electronic excitations, atomic displacements, and nuclear fragmentation. Monte Carlo particle transport simulations are the most common approach for modeling radiation damage in materials. However, radiation damage is a multiscale problem, both in time and in length, an aspect treated by the Monte Carlo simulations only to a limited extent. In this chapter, after introducing the Monte Carlo particle transport method, we present a multiscale approach to study different stages of radiation damage which allows for the synergy between the electronic and nuclear effects induced in materials. We focus on cumulative displacement effects induced by radiation below the regime of hadronic interactions. We then discuss selected studies of radiation damage in materials of importance and potential use for the exploration and settlement on the Moon, ranging from semiconductors to alloys and from polymers to the natural regolith. Additionally, we overview some of the novel materials with outstanding properties, such as low weight, increased radiation resistance, and self-healing capabilities with a potential to reduce mission costs and improve prospects for extended human exploration of extraterrestrial bodies.

1. Introduction

Preparing for life on another planet or a planetary object requires an enormous effort from scientists and engineers [1]. The first steps toward extraterrestrial life are the crewed missions to the Moon, aiming to build the basis for the future long-term presence of humans beyond Earth. A remarkable amount of research and feasibility studies are being done by the European Space Agency (ESA) in Europe [2] and the National Aeronautics and Space Administration (NASA) in the USA [3, 4] on how to construct a “new home in space,” in a manner to eliminate the need for supply materials from Earth.

In this context, the use of space resources is one of the key directions in preparation for future human missions to the Moon. The so-called in situ Resource Utilization (ISRU) program by ESA and NASA explores the possibility of converting local resources of space bodies into valuable products and materials [5, 6, 7, 8]. ISRU will ensure the sustainability and energy efficiency of space exploration, reduce the cost of delivery from Earth, and minimize mission risks. Among the topics of current ISRU research are producing metals and construction materials by transforming local regolith and rocks [9, 10], harvesting oxygen and hydrogen from minerals and water [10, 11], and growing plants [12, 13]. In this sense, the development of structurally sound composite materials with superior properties that can benefit from ISRU is crucial for preparing missions to the Moon. Many aspects of habitat construction, from large-scale infrastructure (e.g., communication and energy generation and storage) to manufacturing (e.g., equipment, tools, and machinery), would benefit from ISRU.

In space and on the lunar surface, there are many factors potentially leading to damage in materials, such as exposure to vacuum, extreme thermal conditions, impact collisions with micrometeoroids, and radiation [14]. Among these, radiation is considered particularly harmful for different functional components and instruments of spacecraft and lunar surface missions. Radiation can induce structural defects that evolve from nanoscale to micro- and macro-damage, causing degradation of the mechanical, thermal, and electrical properties of materials or can even lead to direct failure in electronic signals before interacting with the very structural composition of the material. Therefore, improving the radiation resistance of materials to be used in space missions and searching for more radiation-resistant materials is of utmost importance. The research effort is directed toward finding composite materials that can better withstand radiation and other challenges faced by mission components in space and on space bodies and exhibit self-healing capabilities [15].

In this chapter, we first introduce some relevant materials for two of the most critical applications on the Moon, i.e., habitat construction and energy production. Then, we provide an overview of the radiation environment on the lunar surface and different radiation effects that can be induced in materials by such an environment. We then discuss the ways of combining traditional methods commonly used to study radiation effects with recent advanced approaches in materials modeling and provide examples of radiation-effects modeling studies on different materials. Additionally, we discuss the possibilities of using novel promising materials with exceptional properties relevant for space exploration, with an emphasis on their radiation resistance.

2. Materials for practical applications on the Moon

NASA has identified the most important components of the lunar mission as (i) design and construction of habitats and (ii) resource and power management [16]. In particular, the emphasis is on lightweight materials that will be critical for mass reduction and thus increase the science return of the mission. Both components mentioned above will strongly rely on ISRU, i.e., in situ regolith processing and recycling [8, 17]. Below we provide examples of materials that will be of use for both habitat construction and power generation.

2.1 Materials for habitats

Constructing a habitat on the Moon can be done in two ways, by delivering materials from Earth and by using local resources. Although the latter option is more sustainable, the first one cannot be completely avoided. An important consideration that needs to be made when choosing materials is the type of habitat. NASA considers several types of habitat for different use, namely rigid (metals, alloys, and concrete) [18], inflatable (e.g., inflatable concrete [19]), or hybrid structures, as well as underground construction [20]. Depending on the type of habitat, different materials will be used [16, 21]. For example, unprocessed lunar regolith may be used for radiation shielding of habitat (e.g., lunar regolith geopolymer) [22, 23, 24, 25], as well as for construction when converted into concrete [26, 27], 3D-printed [28, 29, 30], or processed into other construction material (e.g., bricks and glass) [16, 21]. For materials delivered from Earth, it is crucial to ensure their low weight, as well as resistance to very high and very low temperatures (which change from 127°C in the daytime to −173°C at night on the Moon surface) and radiation, durability, reusability, and structural reliability [16].

Metals and alloys are essential structural materials for construction given their compressive strength and good tensile properties and for other applications, such as energy carrier/storage (wires) [31] or equipment (e.g., excavation tools, molds, and rovers) [32]. Al, Ca, Fe, Ti, and Mg are the most abundant metals in the lunar regolith, which also contains smaller amounts of Ni, Cr, Mn, Zr, and V [5, 20]. These metals—together with Si, also abundant on the Moon—can be used to produce alloys. However, only Fe can be easily separated from regolith (using magnets). Other metals are present in the form of oxides and thus have to be obtained by manufacturing. Metal and alloy manufacturing will be extremely important for the exploration of the Moon as they represent an essential part of the construction and are critical ingredients for most technologies.

2.2 Materials for energy production

One of the crucial steps toward the Moon exploration and settlement is a reliable energy technology for electricity generation and power storage [33, 34] that would withstand the temperature gradients, high levels of radiation, and impact. The primary energy sources considered for future crewed lunar missions are solar power [35, 36], nuclear power [37], and fuel cells [38, 39]. Other ways may include the production of electricity from the excess heat from the sunlight collected by an “evergreen” inflatable dome [40]. In this chapter, we focus on solar cells, a safe and reliable source of electricity in space.

In the past decades, solar cells for space applications have evolved from single-crystalline Si-based cells to multi-junction (MJ) ones based on GaInP, GaAs, and Ge [41, 42, 43]. A promising class of materials for next-generation lightweight and high-power-conversion efficiency [44] solar cells are hybrid organic-inorganic perovskites (HOIPs) [45, 46, 47], which are considered as potential candidates for use on future lunar bases [34].

HOIPs possess a unique combination of properties, such as enhanced charge carrier mobility [48, 49, 50, 51], diffusion length, and lifetime [48, 52, 53], high optical absorption [54, 55], and low production costs [56], representing a paradigm shift in solar cell technology [57] on Earth [58] and for space applications [59, 60, 61, 62]. Given their flexibility [63], low weight, small dimensions (0.5 μm as compared to 200 μm for Si solar cells), the possibility of in situ manufacturing via 3D-printing techniques [60, 64, 65] at low temperature, and their high resistance to radiation [60, 66, 67, 68, 69, 70, 71], HOIPs qualify as exceptional candidates for easily deployable and resilient solar cells in space missions.

3. Radiation environment on the Moon and its effect on materials

3.1 Radiation environment on the lunar surface

The radiation environment on the Moon is constituted, apart from solar electromagnetic radiation, by three radiation “populations”—the constant solar wind, the intense but sporadic Solar Energetic Particles (SEPs), and the constant background of Galactic Cosmic Rays (GCRs). A summary of the radiation environment on the lunar surface is given in Table 1.

Source	Particles	Energy, MeV/nuc	Flux, nuc/cm^2/s
Solar Wind	Protons & electrons $\sim$95%, $\alpha$-particles $\sim$4%, heavy ions $\sim$1%	$\sim {10}^{-3}$	$\sim {10}^8$
SEPs	Protons $>$90%, electrons, $\alpha$-particles, heavy ions $<$1%	$\sim$1–10^2	0 – ${10}^6$
GCRs	Protons $\sim 87\%$, $\alpha$-particles $\sim$12%, heavy ions $\sim$1%	$\sim$10^2–10^4	2–4

Table 1.

Radiation particle types, their flux, and energies on the lunar surface [72, 73, 74, 75, 76, 77, 78].

The solar wind is a constant flux of plasma from the upper atmosphere of the Sun. It consists mainly of ionized hydrogen (protons and electrons), a small percentage of $\alpha$-particles, and trace amounts of heavier ions, with kinetic energy between 0.5 and 2 keV/nucleon [75]. The solar wind flux, temperature, density, and speed vary over time and solar longitude and latitude. The lunar surface is under continuous bombardment by the solar wind, as the Moon does not have a significant global geomagnetic field that could deflect solar particles. Particles penetrate the surface and undergo collisions with the ions of the lunar regolith. Their penetration depth depends on the impact energy, angle of incidence, and composition of the target surface. For a proton with a nominal energy of 1 keV, the penetration depth is typically about 20 nm [79]. The implanted protons diffuse and chemically combine with the regolith atoms, such as oxygen, or become trapped in physical defects. Recent studies have suggested that the implantation of solar wind protons in the lunar regolith is a major source of hydrogen in the formation of OH/H₂O [80, 81], whose presence is confirmed by experimental measurements [82].

SEPs originate from solar transient events, such as coronal mass ejections or flares, and consist in a sudden intense flux of high-energy protons and electrons (and a small amount of $\alpha$-particles and heavier ions) [76, 78]. Typical energies of SEPs range from ten to hundreds of MeV. Such transient events have a higher occurrence probability during solar maximum, but they may also occur during solar minimum. Studies have shown that the lunar surface can charge to a high negative potential up to a few kV during SEP events [83, 84]. Such values of the potentials are much higher than the typical night-side potentials of a few hundred volts negative and may increase the risk of electrostatic discharge. The latter represents an additional hazard to the already dangerous radiation environment on the lunar surface.

GCRs constitute the slowly varying, low-intensity (few particles/cm²(m²) per second), highly-energetic radiation background in space. They are mainly associated with supernova explosions in the galaxy, but extra-galactic contributions also exist. GCRs are constituted by $\sim$87$\%$ of hydrogen ions (protons), 12$\%$ of $\alpha$-particles, 1–2$\%$ of high-energy and highly charged ions (high-charge Z and energy (HZE)-particles), and 1$\%$ of electrons and positrons [85]. The energy spectrum of GCRs covers a wide range, extending roughly up to 10¹⁸ eV, with higher energies (up to 10²¹ eV) being associated with ultrahigh-energy GCRs originating from extra-galactic sources. GCRs are modulated by the heliospheric field linked to solar activity. At solar maximum, the solar magnetic field increases, shielding the heliosphere from the lowest energy component of GCRs [86], thus decreasing the overall GCRs flux. At the solar minimum, the reduced solar magnetic field leads to a more intense GCRs flux in our interplanetary space [87, 88].

The annual exposure caused by GCRs on the lunar surface is $\sim$380 mSv during solar minimum and $\sim$110 mSv during solar maximum, as compared to the annual dose of natural ionizing radiation of 2.4 mSv on Earth [89] (1 Sv—1 Sievert, represents the equivalent biological effect of the deposit of a Joule of radiation energy in a kilogram of human tissue). The worst-case scenario studies suggest that SEPs may lead to a much higher exposure of $\sim$1 Sv or even reach $>$2 Sv per event [90]. Studies of the radiation dose of GCRs and SEPs at the lunar surface and in a lava tube [90, 91] have shown that the exposure may be reduced to values similar to Earth in horizontal lava tubes.

3.2 Radiation-induced effects in materials

The effects of radiation on materials and devices can be cumulative (long term) and noncumulative (caused even by a single particle). The so-called Single Event Effects (SEEs) can occur when an ionizing particle passing through an electronic device carries a charge large enough to affect the device’s performance. SEEs in aerospace technology can lead to errors, corrupt the data, create noise, reset the device, or even cause fatal part failure [92, 93, 94, 95]. Cumulative radiation damage, on the other hand, occurs through continuous radiation exposure or exposure to intense flux due to SEPs events and can lead to the degradation of optical components and solar cells, eventually causing permanent damage. The total ionizing dose experienced by an electronic device can cause variations in threshold voltage or leakage current.

Cumulative non-ionizing damage in materials due to protons, electrons, and neutrons (originating from the interaction of energetic protons and electrons with the lunar surface) leads to defect formation (displacement damage) [94]. The types and sources of radiation, as well as the effects it can cause in materials, are summarized in Table 2.

Particle type	Energy	Sources	Radiation effects
Electrons	$>1$ MeV	SEPs	Ionization radiation damage
Protons	$0.1-1$ MeV	SEPs	Surface damage to materials
Protons	$1-10$ MeV	SEPs accelerated in shocks	Displacement damage in solar cells
Protons	$>10$ MeV	SEPs and GCRs	Ionization and displacement damage, background counting in sensors
Protons	$>50$ MeV	SEPs and GCRs	Single event effects
Ions	$>10$ MeV/nuc	SEPs and GCRs	Single event effects

Table 2.

Sources and types of radiation and the effects it causes in materials and devices [96].

Cumulative radiation damage is a multiscale process in terms of time and length. A schematic representation of the so-called displacement damage cascade is shown in Figure 1. At first, an energetic external particle approaches (Figure 1(1)) and enters the target (Figure 1(2)). As the particle passes through the material, it first transfers its kinetic energy to electronic degrees of freedom of the target (electronic stopping) (Figure 1(3)). Electronic excitations happen at a very short time scale ($\sim$100 as). After the particle has been slowed down by the target’s electrons, it undergoes nuclear elastic collisions, displacing atoms in the target (Primary Knock-on Atoms, PKAs) that constitute themselves additional projectiles (Figure 1(4)). The PKA collides with other atoms creating a cascade of collisions [97] (Figure 1(5)). Atomic displacements induce the creation of different types of point defects, such as vacancies and interstitials (Frenkel pairs) and defect clusters (Figure 1(6)) and happen on a much longer time scale (up to ns). Eventually, many defects are healed due to the thermal motion of atoms (annealing stage, Figure 1(7)), leaving a finite number of defects in the structure (Figure 1(8)).

Figure 1.

Schematic representation of different stages of the damage cascade in a crystalline material under irradiation.

Atomic displacements described above lead to defect clustering and eventual amorphization in crystalline materials. Consequently, mechanical, physical, and other properties of the irradiated material can be significantly altered. The scale of the changes depends on the energy of incoming particles and the actual number and spatial distribution of survived defects after eventual self-healing [98].

The radiation-induced effects after atomic displacements strongly depend on the type of material. For metals and metallic alloys, the main effect of radiation is the generation of dislocation loops and point defects which cause significant radiation-induced strengthening or hardening. As a result, the ductility and fracture toughness of the metals (alloys) can be reduced, leading to brittle behavior [99]. Ductile-to-brittle transition is especially pronounced at low temperatures at which the defect mobility, and consequently the annealing of defects, is reduced.

As to other materials, such as semiconductors in solar cells, cumulative exposure to space radiation or high SEPs fluxes can strongly affect the performance of MJ solar cells [100]. Moreover, the impacting radiation can reduce the transmittance of the protective SiO₂ cover-glass on top of MJ cells by inducing color centers in the oxide material. The color centers appear when electrons excited by radiation become trapped by impurities in the oxide to form stable defect complexes. On the other hand, the radiation which is not blocked by the cover-glass causes damage in the functional layers of MJ solar cells by displacing atoms. Different energy levels can be created within the bandgap as a consequence of such structural defects. Such electronic defect levels affect the electrical performance of MJ solar cells acting as traps, recombination centers, or carrier removal sites which reduce free carrier concentration [100, 101].

Below, we will present different methods used to describe radiation-induced effects in materials focusing on the description of cumulative effects related to atomic displacements.

4. Monte Carlo particle transport modeling of radiation effects in materials

High-energy charged particles undergo a daunting number of interactions with target materials. Such interactions include:

1. electronic collisions leading to ionization and excitation;

2. multiple Coulomb scattering at small angles (elastic deflection without energy loss, or minimal inelastic loss);

3. inelastic nuclear reactions, that is, high-energy reactions in which a nucleus in the target struck by an incident particle (with energy $>10$ MeV) undergoes fragmentation into secondary lighter nuclei and other lighter particles;

4. elastic nuclear interactions ($<$10–20 MeV) in which atoms are displaced from their initial positions creating point defects.

The most commonly used approach to study radiation-induced effects in materials is the Monte Carlo (MC) particle transport method [102, 103]. In MC particle transport, the interactions of individual primary ions and their secondaries are sampled to build a history of charged particle passage and energy deposition in the target [104], with a large enough statistical sample of trajectories. The energy- and angle-dependent cross sections for different interactions are provided by theoretical models of the elementary interactions and/or experimental data, depending on the energy window. Codes, such as Geant4 [105], MCNP6 [106, 107, 108], FLUKA [109], PHITS [110], and HETC-HEDS [111], have been successfully applied to study the radiation at a hemispherical dome made of lunar regolith used to simulate a lunar habitat [112, 113] and the radiation environment around the Moon [114, 115].

Several relevant radiation-induced effects in materials are due to particles with an energy of a few MeV to a few tenths of MeV, as can be seen in Table 2. In this regime, below hadronic interactions causing fragmentation/spallation, atomic displacements are induced in the target by elastic nuclear interactions. Two concepts describe the slowing down of the impacting particles (and the induced secondaries), (i) the electronic stopping power, that is, the energy loss of the moving particle to the electronic degrees of freedom of the target (a concept valid in the whole energy range) and (ii) the nuclear stopping power, that is, the energy lost to elastic nuclear interactions causing atomic displacements (a concept only used for the regime below hadronic interactions). MC particle transport modeling is a very convenient approach to deal with the enormous amount of interactions that a high-energy particle can induce in a target. However, the approximations used for intermediate and low energies (few MeV and lower) may pose some challenges for the applicability of MC particle transport. At such energies, the atomic-scale structure and the electronic properties of the target system should be taken into account for a reliable description of the radiation-induced effects. In MC particle transport, however, the target materials are amorphous and the macroscopic interaction cross sections, as well as electronic and nuclear stopping power, are obtained by a simple stoichiometric averaging of the elemental cross sections and stopping power. The electronic stopping in MC particle transport simulations is calculated for a uniform electron gas with the same density as the target within the perturbative linear approach not appropriate at low energies [116]. Since the crystal structure of the target is ignored, the effects due to ion channeling (i.e., when the ion path is confined within the crystallographic planes), that have been shown to significantly influence the electronic stopping power [117, 118], are not taken into account.

A displacement cascade in MC particle transport simulations is generally modeled within the Binary Collision Approximation (BCA) [119] which assumes a series of independent two-body collisions. Between collisions, particles travel in a straight line. The BCA is valid when (i) the projectile energy is higher than 1 keV per nucleon, which, for PKAs, could be relevant energy, and (ii) the target material has low density, in which case the collisions between the incoming particle and the target atoms occur rarely. BCA allows reducing the computational complexity of the ion-matter interactions compared to a full many-body simulation (e.g., molecular dynamics, discussed in Section 5) and allows for reaching large dimensions with reduced computational needs. However, this method is valid for linear collisions only and describes only primary damage, that is, it does not account for the dynamic evolution of induced defects at later times (Figure 2).

Figure 2.

Time and length scales and corresponding methods can be applied to study different stages of radiation damage.

One of the most popular tools in which the BCA is implemented is the Stopping and Range of Ions in Matter (SRIM) code [120]. Besides containing semiempirical data for the electronic stopping power of a variety of targets, SRIM can be applied to model the linear cascades and estimate the number of defects in any material and any ion energy up to 1 GeV. Nuclear stopping in very low-energy intervals uses the so-called ZBL (Ziegler-Biersack-Littmark) universal potential that combines classical Coulomb potential with a semiempirical screening function [120]. The electronic and nuclear degrees of freedom are completely separated in SRIM as well as in other MC particle transport tools used by the particle physics community and the space radiation effects community. Finally, it is important to remark that materials are static in MC particle transport methods—there is no dynamics induced in them by the impact of primaries and the generation and passage of secondaries. Thus, more accurate methods are needed to get access to the processes missing in MC particle transport calculations. Such methods are described in the next section.

5. Multiscale approach to modeling radiation damage in materials

There is a large variety of methods used in condensed matter physics and materials science to study radiation effects in materials, each of them describing a particular aspect of the damage process. Figure 2 shows a schematic representation of the different time and length scales with the corresponding computational methods that can be applied to study different stages of radiation damage [97, 121, 122]. The very first stage, at the smallest time-length scale, is the electronic stopping regime. For decades, the semiempirical SRIM code discussed in the previous section has been the most widely used tool to calculate electronic stopping power. Nowadays, the electronic stopping power (and the induced electronic excitations in the target) can be described by ab initio (parameter-free) methods relying on a realistic description of the electronic and ionic properties of the target system. One of the most accurate methods for treating electronic excitations in materials is time-dependent density functional theory (TDDFT) [123] which allows accessing the electronic effects accompanying the ion dynamics. Ab initio molecular dynamics (AIMD) [124] based on density functional theory (DFT) [125, 126] can be applied to study point defect formation. At longer time scales and larger length scales, when atomic displacements start to dominate, classical molecular dynamics (MD) and the BCA are usually applied to perform collision cascade simulations. The kinetic Monte Carlo (KMC) [127], the dislocation dynamics (DD) [128], and the finite element method (FEM) [129] are used to study the evolution of defects at the even longer time and larger length scales.

For a complete and accurate description of every aspect of radiation damage, as well as the interplay between them, one has to adopt a combined approach. In recent years, researchers have realized the importance of a multiscale approach to studying radiation damage, as follows from many publications and reviews [121, 122, 130, 131, 132, 133, 134]. Each of the methods presented in Figure 2, as well the ways of combining them, will be discussed below in the order of increasing complexity. The main focus will be on classical MD, AIMD, and TDDFT, which are fundamental for the description of primary radiation damage at the atomic scale.

5.1 Classical molecular dynamics and beyond: the collision cascade

The most widely used approach in materials science to study the interaction of ions with matter (collision cascades) is MD [135]. MD offers a picture of the ion–ion interaction beyond the linear cascade of the pure BCA by including many-body effects. In MD, atoms are treated as classical particles, and their motion is described by Newtonian dynamics. No electronic effects are thus included.

Cascade simulations need large samples consisting of up to a million atoms (depending on the PKA’s energy), which prohibits using parameter-free methods (such as DFT, see Section 5.2) to compute the interatomic forces. Instead, in MD, the forces on atoms are calculated from empirical or semiempirical interatomic potentials (also called force fields) [136, 137, 138]. MD with empirical potentials proved to work well for large systems and long time scales [139].

In an MD cascade simulation, the system is usually modeled using periodic boundary conditions, that is, by replicating a small unit cell in all directions. Typically, prior to the cascade simulation itself, a regular MD simulation is done to thermally equilibrate the target system at the desired initial temperature. Then, with the equilibrated configuration, the cascade simulation is initiated by changing the velocity of one of the atoms (the PKA), giving it the desired amount of kinetic energy in the intended direction. The system is then evolved in time as in regular MD, that is, by integrating Newton’s equations along with a series of time-steps, which involves computing the atomic forces, velocities, and positions at each time-step (see Refs. [140, 141] for classical texts on MD). At the end of the cascade simulation, the number of defects is obtained by evaluating the final geometry of the system. Usually, cascade simulations are repeated several times, choosing a different PKA and/or a different direction of the PKA’s movement to obtain a statistical average of the number of final defects.

MD has been successfully applied to simulate radiation cascades in a variety of materials [139], from simple metals [142, 143] and compounds [144, 145, 146] to complex nanostructures [147], 2D materials [148], and novel multicomponent alloys [149, 150]. MD simulations can afford to access the processes taking place on a relatively long time scale up to ps or even ns which is enough to describe the damage cascade until the thermal spike of the collision has dissipated. Most of the MD codes, however, describe only elastic collisions between atoms and disregard the energy loss mechanisms such as electronic excitation and ionization. The possibility of including electronic excitations is discussed in Section 5.3.

After the primary damage has been formed, defects may continue diffusing, thus annihilating or forming defect clusters. Such processes occur on a much longer time scale, reaching at least seconds, not accessible via regular MD. The problem of simulating a process not accessible in a feasible amount of computational time has motivated the development of several enhanced sampling techniques [151], which in the case of MD simulations of materials have allowed to observe otherwise challenging processes, such as phase transitions.

KMC [127] simulations are commonly used to access long-time effects of radiation in materials [152, 153, 154, 155]. KMC is designed to model the time evolution of an atomic system. However, instead of solving the equations of motion, as it is done in MD, the KMC method is based on the assumption that the long-time dynamics of a system consists of diffusive jumps from state to state. Each of the states is treated independently, which makes KMC a very efficient method. The dynamics of the system, that is, the probability of transition from one state to another does not depend on the history of the system. The probability of a state-to-state transition is assigned randomly and the most probable transition is statistically chosen. This allows avoiding the complications related to the choice of interatomic potentials, thus overcoming the time limitations of MD simulations (usually $t<1$ μs) and accessing the macroscopic length scale. KMC is used as an extension of MD to further evolve the damage cascade in time and study the diffusion, accumulation, and annihilation of defects after a collision cascade took place [155].

To further extend the problem into the macro-domain, the DD [128] and FEM [129, 156] methods, based on dividing a geometrical space on a number of finite (non-overlapping) segments, are usually applied. FEM has been used to study the response of a macro-object to external stress in engineering and has also been applied to study the behavior of solids under irradiation by extrapolating the known displacements and evaluating the geometry of a 3D object. DD method allows for calculating the motion of dislocations as well as evaluating the plastic deformation in the material induced by the collective motion of dislocations.

5.2 Ab initio molecular dynamics: coupling MD with density functional theory

AIMD is one of the most important tools in quantum physics and chemistry [157]. In a typical AIMD simulation, it is assumed that the system consists of $N$ nuclei and $N_e$ electrons for which the Born-Oppenheimer (BO) approximation is applied [158]. The BO approximation implies that the dynamics of the electronic and nuclear subsystems can be treated separately given the fact that the nuclei are much heavier than the electrons and thus the time scales of their motion are very different. In AIMD, the nuclei are evolved using classical mechanics, while the electronic ground state is adapted to the instantaneous nuclear positions at each step of the dynamics (i.e., the adiabatic approximation). The ground-state electronic problem is taken into account through advanced methods, most commonly from DFT [125, 159], a quantum-mechanical method that is used to calculate the electronic structure of many-body systems. Given its importance in describing physical and physicochemical properties of materials, and as it is functional to the understanding of the next section, a brief introduction to the main concepts of DFT is given here.

Practical DFT calculations are based on the Kohn-Sham (KS) formalism [126], which replaces the complex problem of interacting electrons in the standard Schrödinger equation by a problem of non-interacting electrons moving in an effective potential $V_{\mathrm{eff}}$:

$$\left\{-\frac{1}{2}{\nabla }^2+V_{\mathrm{eff}}(\left[n\right],\mathbf{r})\right\}{\psi }_i^{\mathrm{KS}}\left(\mathbf{r}\right)={\epsilon }_i{\psi }_i^{\mathrm{KS}}\left(\mathbf{r}\right),$$E1

where ${\epsilon }_i$ is the eigenvalues of the KS equations and ${\psi }_i^{\mathrm{KS}}$ is the one-electron KS wave functions. Here, the effective potential $V_{\mathrm{eff}}\left(\left[n\right],\mathbf{r}\right)=V_{\mathrm{ext}}\left(\mathbf{r}\right)+V_{\mathrm{H}}\left(\left[n\right],\mathbf{r}\right)+V_{\mathrm{xc}}\left(\left[n\right],\mathbf{r}\right)$ includes the external potential $V_{\mathrm{ext}}\left(\mathbf{r}\right)$ in which the electrons move (i.e., the electron-nuclei Coulomb attraction), the exchange-correlation (XC) potential $V_{\mathrm{xc}}\left(\left[n\right],\mathbf{r}\right)$, in which all the many-body effects are included, and the Hartree potential $V_{\mathrm{H}}\left(\left[n\right],\mathbf{r}\right)$ which is the electrostatic potential created by the electron density. The solution to self-consistent KS equations Eq. (1), is the exact electron density of the system of interacting electrons, provided that $V_{\mathrm{eff}}$ is known exactly: $n\left(\mathbf{r}\right)={\sum }_{i=1}^N{\left|{\psi }_i^{\mathrm{KS}}\left(\mathbf{r}\right)\right|}^2.$ All the properties of the system (e.g., electronic structure and ground-state energy) can be determined from the electron density, according to the Hohenberg-Kohn theorem [125].

AIMD is used to simulate any physicochemical process where the electronic structure of the system changes significantly or when a detailed description of the structure is needed. A typical example would be the simulation of chemical reactions, where chemical bonds are formed or broken, which cannot be described via classical force fields.

5.3 Time-dependent density functional theory for electron dynamics and its coupling to MD

Although the adiabatic BO approximation is the usual approximation in the methods described above, its applicability is only justified in near-equilibrium situations. However, under ion impact, the electronic subsystem is rapidly driven out of equilibrium.

A realistic description of the dynamics of the electrons in the target during the passage of fast ions can be obtained in the framework of TDDFT which gives access to the electron dynamics out of the electronic ground state. In particular, real-time TDDFT [160] provides a non-perturbative description of the electronic excitations upon an external perturbation and can be combined with the Ehrenfest MD scheme [161], which allows for coupling between electron and ion motion, contrary to the BO picture.

TDDFT consists in solving the time-dependent KS equations [123]:

$$i\mathrm{\hslash }\frac{\partial }{\partial t}{\psi }_i^{\mathrm{KS}}\left(\mathbf{r},t\right)=\left\{-\frac{{\mathrm{\hslash }}^2{\nabla }^2}{2m}+{\widehat{V}}_{\mathit{ext}}\left(\left\{R_I\left(t\right)\right\}\right)+{\widehat{V}}_{\mathit{HXC}}\left[n\right(\mathbf{r},t\left)\right]\right\}{\psi }_i^{\mathrm{KS}}\left(\mathbf{r},t\right),$$E2

where ${\widehat{V}}_{\mathit{HXC}}$ describes both the electrostatic (Hartree) electron-electron interaction and the quantum-mechanical XC potential, ${\widehat{V}}_{\mathit{ext}}$ is the potential arising from the ions (both the fast-moving impacting particle and the target atoms), and $\left\{R_I\left(t\right)\right\}$ are the atomic positions. The force on the nuclei in Ehrenfest dynamics is defined as

$$F_I\left(t\right)=-\sum _i⟨{\psi }_i^{\mathrm{KS}}\left(t\right)|{\nabla }_{R_I}{\widehat{H}}_e|{\psi }_i^{\mathrm{KS}}\left(t\right)⟩$$E3

where ${\widehat{H}}_e$ is the Hamiltonian, that is, the operator on the r.h.s. of Eq. (2). Ehrenfest dynamics is a mean-field method, meaning that the nuclei move on an effective potential energy surface (a mathematical function that describes the energy of the system and whose value depends on the coordinates of all the atoms), which is an average of all adiabatic states involved, weighted by their populations. Other methods exist, in particular, one allowing for electronic transitions, that is, switches between adiabatic states when their population changes [162].

The solution of the time-dependent KS equations in real time can be obtained by applying the so-called time-evolution operator, evolving the KS states in time [123]. The time-step of this propagation must be of the order of attoseconds to describe the fast dynamics of the electrons, in contrast to what occurs in AIMD and MD where the time-step is of the order of femtoseconds. The time-dependent electron density is calculated at each step, from which the total energy of the system is obtained. Knowing the total energy as a function of time, the electronic stopping power can be calculated as $S_e=-\mathit{dE}/\mathit{dx}$, where $\mathit{dE}$ is the energy loss and $\mathit{dx}$ is the distance traveled by the projectile inside the target.

Many examples of accurate first-principles calculations of the electronic stopping power are available in the literature [117, 118, 163, 164, 165, 166, 167, 168]. Recent studies have demonstrated that electronic excitations (induced by both the primary impacting ion and especially by PKAs and further displaced atoms) affect the cascade evolution [118, 169, 170, 171] and thus, they need to be accounted for. The electronic stopping effects can be included in MD cascade simulations through the so-called two-temperature (2T) model [118, 172]. In 2 T-MD, the electrons are included as a thermal bath. Each particle is subject to a friction force representing the electronic stopping and a stochastic force representing the coupling between the vibrational degrees of freedom of the lattice and the electrons. This model considers constant electronic density in the entire system and thus, the electronic stopping power is independent of the crystal direction. Recent studies have extended the 2T model by coupling the electronic and nuclear effects via many-body forces that act in a correlated way. This allowed for the construction of a unified model for ion-electron interactions [170, 171, 173, 174] with a complex energy-exchange process between the ionic and electronic subsystems [174].

6. Selected cases of radiation damage studies in materials relevant for exploration of the Moon

The previous section provided an overview of computational methods that can be applied to study radiation damage in materials and discussed the advantages of combining such methods into a multiscale approach. This section mainly focuses on the effects of radiation on materials of practical use on the Moon, including several novel and promising materials. We overview the existing radiation damage studies for these novel materials, emphasizing multiscale modeling when available.

6.1 Improving the model for solar cell degradation via a multiscale approach

Generally, degradation of solar cells is modeled via the non-ionizing energy loss (NIEL) approach, the NIEL being the portion of energy loss per unit path length of the projectile converted into displacement damage. According to Akkerman et al. [175] (the definition used in most simulation tools), the NIEL is defined as:

$$\text{NIEL}\left(E\right)=\frac{N_A}{A}{\int }_{T_d}^{E_{\max }}Q\left(E_R\right)E_R{\left(\frac{\mathit{d\sigma }}{{\mathit{dE}}_R}\right)}_E{\mathit{dE}}_R=\frac{N_A}{A}D\left(E\right),$$E4

where $E$ is the total kinetic energy of the external particle, $E_R$ is the portion of kinetic energy which turns into displacement damage, $Q\left(E_R\right)$ is the partition factor giving the fraction of kinetic energy to be lost to NIEL mechanisms, $N_A$ is Avogadro’s number, $A$ is the atomic mass of the lattice atom, $\mathit{d\sigma }/{\mathit{dE}}_R$ is the partial differential cross section for creating a recoil atom with energy $E_R$, and $D\left(E\right)$ is the displacement damage function. The integral runs from the minimum energy required to permanently displace an atom to a defect position, that is, the threshold displacement energy $T_d$, to $E_{\max }$, which is the maximum energy transferred to a recoil atom in a particular interaction. Although the NIEL concept differs from the nuclear stopping power, as it includes also the energy loss to non-ionizing events induced by hadronic interactions, as already mentioned above (see Table 2), relevant non-ionizing effects are induced by particles with energies from few to few tenths of MeV, which is the regime of Coulomb interactions.

On the basis of a large set of experimental observations, it is assumed that the degradation of a semiconductor device under irradiation can be linearly correlated with the NIEL [176]. In practice, this means that the number of defects should give a measure of the damage irrespective of their distribution, whether clustered in high density in small regions (as in the case of neutron damage) or homogeneously scattered over a relatively wide volume (as in the case of the low-energy proton or $\gamma$-ray-induced damage) [177]. Thus, in principle, the damage produced by different particles (with different energies) should be scalable via their NIEL (i.e., the number of displacements), as indeed has been shown in several studies [176, 178, 179, 180, 181, 182]. The NIEL scaling is a powerful method for dealing with displacement damage predictions in complex radiation environments, such as on the Moon and in space missions in general. However, deviations from the linearity exist and seem to be associated with the “quality” of the radiation damage at the microscale as induced by different kinds of particles and (or) as influenced by intrinsic defects in the target [183].

Generally, the NIEL is calculated via MC particle transport codes, assuming amorphous target materials, a static $T_d$ that is constant for each element in all the materials where such element is found (thus, not considering the underlying electronic structure), and a simple linear collision cascade model for the number of final defects [184]. Several quantities in the NIEL formula and, more generally, the overall understanding of radiation damage can be strongly improved via AIMD and TDDFT+MD studies. $T_d$, for example, is an important quantity that can significantly affect the NIEL [185, 186] and its accurate estimation can be accessed by AIMD simulations [187, 188]. Recent results for $T_d$ in semiconductors have shown that the electronic excitations can, in general, reduce their value [122], in line with previous experimental results [189]. The effect of electronic excitations consists in weakening the atomic bonds making it easier to displace an atom from its equilibrium position. On the other hand, the “heating” effect of electronic excitations has the consequence of facilitating the healing of the structure. Even a small change in $T_d$ affects the calculated NIEL, as can be seen in Figure 3 showing the NIEL for a proton and an electron in GaAs. The NIEL is affected by the choice of $T_d$ in an energy window of the lunar radiation environment (see Table 1). These findings raise an important question about the role of electronic excitations in defect formation that deserves more attention in future works.

Figure 3.

NIEL for protons and electrons in GaAs for different values of the threshold displacement energy $T_d$ calculated with the online SR-NIEL tool [190].

Another example of possible improvement in the NIEL model is a more precise calculation of the number of radiation-induced defects and of the “quality” of radiation-induced damage (which type of defects are induced). It has been observed that point-like and clustered defects contribute differently to some degradation parameters [191]. Recent MD studies [192, 193, 194] and experimental works [181, 195, 196] have proposed an effective or $\mathit{\text{adjusted}}$ NIEL to correct the deviations from a linear dependence of degradation parameters on the NIEL and restore a linear relationship. Other MD studies [197] proposed new metrics for counting defects including the effect of a “heat spike”, which leads to a much lower rate of final defects as compared to predictions from a simple linear collision cascade model as commonly used in the NIEL calculations based on MC particle transport [184, 198].

On a parallel research stream, multiscale studies in a number of materials combining MD simulations of collision cascades with the electronic stopping from TDDFT offer a more accurate description of both the number and the nature of defects created under realistic conditions. The electronic degrees of freedom and their coupling to the phonons of the target affect the cascade evolution and morphology [170, 171, 173, 174]. This is of relevance for the NIEL which includes a part of energy dissipated to phonons. This fraction depends on the energy of the impinging particle but also on the properties of the material. Some studies have shown that the direction-dependence of the electronic stopping can influence the collision cascades [118]. Other studies have demonstrated that the formation of thermal spikes and therefore of amorphous pockets is sensitive to the electronic specific heat [199] and others that the choice of the model employed for the inclusion of the electronic effects and in particular the overestimation (or underestimation) of electron-phonon coupling can have a significant influence on the number of defects created [171].

6.2 Radiation effects in the next-generation lightweight photovoltaic panels

As discussed in Section 2, HOIPs have a unique combination of properties particularly interesting for lunar exploration. The general chemical formula for perovskites is ABX₃, where A and B are two metal ions with different ionic radii and X is an anion that is six coordinated to the B-site [200]. HOIPs, in particular, comprise a negatively charged lead-halide inorganic skeleton where B is a metal cation (Sn²⁺ or Pb²⁺), X is a halide anion (I⁻, Br⁻, and/or Cl⁻) and A is a monovalent positively charged organic cation, such as methylammonium (MA⁺ = CH₃NH₃X⁺, where X = I, Br, Cl) or formamidinium (${\mathrm{FA}}^{+}=\mathrm{CH}{\left({\mathrm{NH}}_2\right)}_2^{+}$ (Figure 4).

Figure 4.

Structure of a HOIP: methylammonium cation (${\mathrm{CH}}_3{\mathrm{NH}}_3^{+}$) occupies the central A site surrounded by 12 nearest-neighbor iodide ions in corner-sharing PbI₆ octahedra [201] (available under the terms of the creative commons CC BY license).

Despite many advantages, several external factors, such as air, moisture [202], UV light [47, 203], heat, light soaking [204], and partially also radiation [205, 206], induce considerable structural instabilities in HOIPs. An intrinsic instability is also present, caused by a relatively weak cohesion between the organic cation and the inorganic octahedra and predominantly by the low-energy barriers for the migration of halide anions and organic cations, with halide migration being the most prevalent [201, 207, 208, 209, 210]. Phase segregation can be induced by large-scale ion migration [211]. However, some of the challenges that HOIPs-based solar cells face on Earth, such as degradation caused by moisture, are not relevant for space applications [212]. Thermal and vacuum stability, high power-conversion efficiency, and radiation resistance are the main challenges in the space context. A sensible choice of the chemical composition, of eventual use in tandem devices [212] (which also helps to reach an efficiency of up to 30%) or incorporation of a functionalized 2D metal-organic frameworks (MOFs) [213], can improve the long-term operational stability of HOIPs.

A relevant collection of DFT studies for HOIPs can be found in Ref. [214]. A recent study based on DFT + compressed sensing-symbolic regression has shown that mitigation of the propensity of halogens to migrate could be achieved by selectively strengthening specific bonds [215]. The study also unveiled the reasons for improved stability given by specific halogens, the origin of the higher stability offered by certain organic cations compared to others, and highlighted in a quantitative and first-principles manner how weak interactions have a significant role in binding the halogens more strongly.

The study of the radiation tolerance of perovskite solar cells is an extremely active field of research. Solar cells based on HOIPs as active layers have been recently sent to space via first campaigns [60, 216]. Several ground-testing experiments have been performed mostly using protons, either with an energy of several tenths of MeV [69, 211, 217] or with an energy of 150 keV, 100 keV, and 50 keV [70, 218, 219], of less relevance for realistic space conditions.

Superior radiation resistance of perovskite solar cells in comparison to commercially available crystalline Si-based cells has been demonstrated [69]. Moreover, experiments have shown that perovskite solar cells have remarkable self-healing capabilities (at room temperature) that lower the number of defects caused by proton irradiation [69]. Another experimental study has shown that the proton irradiation effects on the physical properties of HOIPs are strongly dependent on the synthesis method [220] which appeared to affect the strength of specific chemical bonds. In particular, HOIPs, produced by mechano-chemical synthesis, have shown practically no change in their physical properties after irradiation with a high-energy 10 MeV proton beam with doses of up to 10¹³ protons/cm².

Recently, multi-junction tandem solar cells (combining HOIPs with previous technologies or technologies investigated in parallel) have also been studied under ion irradiation [217]. Lang et al. [217] carried out SRIM simulations of energy loss of high-energy protons as well as the energy transferred to the recoiling nuclei—a measure of the degradation of PV parameters—in tandem solar cells (Figure 5). The study [217] has shown that HOIP/CIGS tandem solar cells possess a high radiation hardness and retain over 85% of their initial performance even after 68 MeV proton irradiation and a dose of $2\times {10}^{12}$ proton/cm², equivalent to 50 years in space at the International Space Station (ISS) orbit.

Figure 5.

3D scatter plots of the straggling of 68 MeV protons within the (A) HOIP/CIGS(Cu(In,Ga)Se${}_2$) and (B) HOIP/SHJ(Si heterojunction) tandem solar cells. The energy loss of the incident 68 MeV protons to recoils is plotted as a function of depth based on SRIM simulations with a total of $5\times {10}^7$ protons. The damage of a real space environment at the orbit of the ISS is shown as a black line. Adapted from [90] (available under the terms of the Creative Commons CC-BY license).

First-principles calculations of the atomic knock-on displacement events in HOIPs have shown that such displacements are significant and highly energy-dependent [221]. The work has shown that only certain types of atoms are prone to displacements suggesting that mitigation strategies should be directed toward some chemical species more than others. Overall, further studies are necessary, but existing research proves that HOIPs-based solar cells have a remarkable potential for power generation on missions to low Earth orbit, the Moon, and beyond [62].

6.3 Novel multi-principal-element alloys with enhanced radiation resistance

6.3.1 Outstanding properties of MPEA for space applications

Another promising class of novel materials for space applications is multi-principal element alloys (MPEAs) [222, 223], which combine superior mechanical properties and enhanced radiation resistance [224]. Also known as high-entropy alloys (HEAs) or concentrated solid-solution alloys (CSSAs), MPEAs consist of at least five principal elements with the concentration of each element from 5 to 35% [222]. Despite the complex composition, MPEAs often form single-phase solid solutions (Figure 6). The interest of researchers in MPEAs has been growing exponentially in recent years, as they exhibit a paradigm shift in alloy development. MPEAs indeed combine a set of outstanding properties, such as high strength, hardness, fracture toughness, corrosion resistance, strength retention at high temperature [226], good low-temperature performance [227], and recently discovered enhanced radiation resistance, superior to conventional alloys and pure metals [149, 222, 223, 228, 229, 230, 231, 232, 233]. Moreover, MPEAs have great potential as 3D printing materials [234]. MPEAs can be printed from a powder, providing manufacturing freedom for lightweight and customizable products of complex geometries for applications in the aerospace, energy, molding, tooling, and other industries, all of the great relevance for the exploration of the Moon.

Figure 6.

Atomic structure of a body-centered cubic (BCC) AlCoCrCuFeNi HEA. The Al, Fe, Co, Cr, Ni, and Cu atoms are shown in red, magenta, green, blue, cyan, and gray colors, respectively [225] (available under the https://creativecommons.org/licenses/by-nc-sa/3.0/Creative Commons Attribution License).

Recent experiments have shown that MPEAs have a higher resistance to defect formation due to high atomic-level stress and chemical heterogeneity [235]. MPEAs also possess lower void swelling and higher phase stability [236, 237] as compared to conventional alloys. Self-healing capability is another remarkable property of MPEAs [227, 236, 238].

The subclass of lightweight (LW) MPEAs have a great potential for space applications due to their high strength-to-weight ratio [239, 240, 241]. The main components of LWMPEAs are low-density elements, such as Al, Mg, Si, and Ti [240]. The latter is of extreme importance for ISRU since 99% of the lunar soil consists of Si, Al, Ca, Fe, Mg, and Ti oxides [5, 242].

Currently, the main focus of computational studies has been on the single-phase random solid-solution (SS) alloys based on transition metals with high densities (Co, Cr, Fe, Ni) for application in radiation environments, in particular in nuclear reactors [148, 149, 232, 236, 243, 244, 245]. MD simulations of displacement cascades applied to pure metals and multicomponent alloys [150, 244, 245, 246, 247, 248] confirm the experimentally observed reduction of the number of defects and defect clusters in MPEAs compared to pure metals (Figure 7).

Figure 7.

The number of defects in Ni, NiFe, and NiCoCr from experiments and MD simulations [150].

The electronic stopping power for a proton in binary alloys has recently been calculated using real-time TDDFT [249]. The study has shown that the electronic stopping power of binary alloys is higher than that of pure Ni, suggesting that alloys more effectively stop the incoming particles. Moreover, the inclusion of the electronic stopping into MD simulations of defect formation significantly reduces the final number of surviving defects, as shown in Figure 8. The inclusion of both the electron-phonon coupling and the electronic stopping in the 2T-MD model not only reduces the actual number of defects but also notably impacts their final arrangement, namely leading to more isolated point defects and reducing the size of defect clusters in binary and ternary alloys [250, 251, 252, 253, 254].

Figure 8.

Average number of surviving defects in the classical MD cascade, MD cascade including electronic stopping force, and the 2 T-MD cascade at the end of the simulation for 50 keV Ni cascade in Ni, Ni₈₀Fe₂₀, and NiFe [224, 250, 251, 252].

The majority of MD studies focus on binary and ternary MPEAs due to the lack of force fields for alloys with more than three elements. However, some studies exist [233] on defect formation in NiCoFeCr alloy in which fewer defects have been found at the end of the displacement cascade with PKA energies from 10 to 50 keV, as compared with pure Ni. The limitations of the classical MD with force fields and the ways of solving this problem are discussed in the following.

6.3.2 Machine-learning assisted materials discovery

Classical MD with empirical potentials is the method that proved to work well for large systems and long time scales [139] for the modeling of collision cascades. However, classical interatomic potentials cannot accurately reproduce interactions between the atoms in MPEAs due to their complex structure and lattice distortions leading to internal strain [149, 255, 256]. On the other hand, ab initio methods relying on quantum mechanics, such as DFT, can accurately reproduce the interatomic potentials in complex structures but are limited to a small length scale.

Recent developments in machine learning (ML) approaches can provide a solution to this problem. ML-enhanced materials discovery is an emerging and extremely rapidly growing field. The combination of a precise model based on quantum mechanics and ML algorithms have the potential for an efficient and accurate description of materials properties [257, 258, 259]. Much progress has been made in recent years in the development of ML-based interatomic potentials with the input from electronic structure calculations. First applications have shown that accurate potentials can be obtained for many relevant systems [260, 261, 262, 263, 264, 265]. ML-assisted calculations have been applied to pure metals, binary, ternary alloys [266, 267], and MPEAs [268, 269, 270].

ML and artificial intelligence (AI) may become powerful tools for more accurate multiscale modeling of materials properties. Artificial Neural Networks (ANN) [271] combined with atomistic KMC have already been used to describe the microstructural changes in metals and alloys induced by irradiation [272]. Machine-learned interatomic potentials have been used to study defect formation in refractory MPEAs [273]. The results confirm experimental findings, showing that the 3D migration and increased mobility of defects in MPEAs promote defect recombination leading to more efficient healing. AI, thus, can provide a bridge between different methods, such as DFT, MD, and KMC, and allow for large-scale atomistic simulations of high accuracy, which will accelerate the discovery of new advanced materials.

6.4 Radiation resistance of fiber-reinforced polymers and composites for habitats

Fiber-reinforced polymers (FRPs) are composite materials made of a polymer matrix reinforced with fibers. Typical polymers that are often used include epoxy, vinyl ester, polyester thermosetting plastic, and phenol-formaldehyde resins. Typical fibers include, but are not limited to, glass, carbon, and aramid. In a composite FRP material, the polymer and fiber often have significantly different physical and/or chemical properties, which remain separate and distinct within the finished structure but are complementary for tailored properties [274]. Because of their low density (lightweight), great moldability, specific strength, stiffness [275], excellent mechanical stability, and good thermal properties, FRPs are being increasingly used as structural materials in aerospace, automotive, marine industries, and civil infrastructures. Hence, FRPs are of great interest for many applications for lunar missions as potential structural materials [276]. Glass fibers (also “fiberglass”) can be directly produced from the lunar soil as well as from by-products of metal extraction and can be used to reinforce lunar concrete [277].

The radiation environment on the Moon presents challenges for FRPs with concerns on both the immediate reactions taking place in the materials (short-term effects) and continued post-exposure degradation processes (long-term effects) [276, 278]. In the past decades, many selected FRPs have been ground-tested at different kinds of radiation and particle accelerator facilities for their potential use in space-related radiation environments, including UV-light [279, 280], $\gamma$-rays [281, 282], electron beams [283, 284] and proton beams [285].

Carbon-fiber composites have been widely used in aerospace industries due to their high-temperature stability and low density along with high strength, as well as superior beam-induced shock absorption [285, 286]. A combined modeling and experimental study of the radiation effect on carbon-fiber-reinforced molybdenum-graphite compound (MoGRCF) [285], including MC simulations of the energy deposited into a realistic structure by a 200-MeV proton beam (Figure 9) has show that carbon-fiber-reinforced composites have superior beam-induced shock absorption ability compared to that of graphite.

Figure 9.

MC modeling of the energy deposition for a 200-MeV proton beam interacting with an irradiation target array (MoGRCF) in tandem with the isotope production array downstream [285] (available under the terms of the Creative Commons Attribution 3.0 License).

In the 1980s, the degradation behavior of carbon-fiber-reinforced plastic (CFRP) under electron beam irradiation in various conditions simulating experiments in space has been studied by Sonoda et al. [283]. It has been observed that there is no change in mechanical properties of CFRP when irradiated by up to a dose of 50 MGy. MC simulations of radiation effects in FRPs have shown that by adding lead nanoparticles it is possible to increase their radiation resistance [287]. According to the study, the addition of 15 wt% of lead nanoparticles to FRPs led to a mass reduction of $\sim$64% for the same level of radiation shielding.

An alternative to glass fiber for polymer reinforcement is basalt fiber which offers advantages, such as high specific mechanical and physicochemical properties, biodegradability, non-abrasive qualities, and cost-effectiveness [288]. Arnhof et al. [289] have recently studied mechanical properties of fiber-reinforced geopolymer (FRG) with basalt fiber (i.e., inorganic alumino-silicate polymer) made from lunar regolith simulant as potential shielding and structural material. As basalt fibers can be produced in situ at the lunar surface efficiently, they can be used widely to increase the mechanical strength of geopolymers. Overall, geopolymers are advantageous for lunar construction due to their excellent resistance to extreme temperature fluctuations and adequate shielding from radiation [290], as well as enhanced mechanical properties over conventional cement [291].

The additive-manufacturing (AM) techniques for lunar construction from regolith, including FRP materials, and their suitability for ISRU has recently been reviewed in Refs. [292, 293]. The AM techniques for lunar construction include Cement Contour Crafting (CCC), Binder Jetting (BJ), Selective Solar Light Sintering (SSLS) and Selective Laser Sintering/Melting (SLS/SLM) for 3D printing and metal melting, Stereolithography/Digital Light Processing (SLA/DLP), among others. CCC and BJ technologies could be used for outdoor lunar civil engineering. SSLS could be applied to both direct compacting of lunar regolith to ceramic parts and 3D printing. SLA/DLP-based methods could be used for the indoor manufacturing of ceramic instruments, providing higher precision and printing quality and lower defect rate of the printed parts than other AM methods. In the last decade, studies have clearly shown that the 3D-printing technologies will become one of the cornerstones of lunar exploration, providing future astronauts with all the necessary infrastructure [293].

Lunar concrete consisting of mined regolith with the addition of glass fibers (also made in situ from regolith containing plenty of silicates) has a high strength-to-weight ratio and can be easily 3D-printed, as tests on lunar regolith simulant have shown [294]. Other studies have shown the promising properties of urea from astronauts’ urine as a superplasticizer for lunar geopolymers for 3D-printing applications. The use of urea is expected to reduce the necessary amount of water by about 30% [295].

It is worth mentioning that the 4D printing of a “smart material” with FRPs that responds to radiation-induced damages and aging in a programmable way could be realized in near future [296, 297]. In addition to experiments on the radiation environment in a lab, multiscale computational simulations as mentioned above could be helpful for gaining further insights into the radiation-induced molecular changes occurring in polymers.

7. Conclusions

In this chapter, we introduced some relevant materials for lunar habitat construction and power generation. We discussed the radiation environment on the Moon and the effects that radiation can cause in such materials. We provided an overview of computational methods used to study different stages of radiation damage in materials, focusing on the methods that allow simulating the behavior of materials with extreme accuracy down to the atomic scale. We emphasized that by coupling different methods, it is possible to account for different time and length scales in the evolution of the radiation-induced effects and to combine the electronic effects with atomic displacements.

Several particular examples of radiation damage studies have been discussed with the focus on novel materials with enhanced radiation resistance and other remarkable properties for use on the Moon that can revolutionize space exploration. Such materials include HOIPs for energy production and MPEAs and FRP composite materials for construction. The primary materials considered for lunar construction are FRGs with basalt or glass fibers, which have excellent mechanical properties, can benefit from ISRU, and provide necessary radiation shielding. We emphasized that researchers’ effort is mainly directed toward the development of additive manufacturing techniques, such as 3D printing for habitat construction from lunar regolith. 3D printing will allow producing complex and customizable products in a shorter time and with a lower cost and material consumption.

Nowadays, the radiation-induced effects in materials for space missions are mainly studied by MC particle transport modeling, inheriting the remarkable modeling and computational efforts by the high-energy physics community. However, with the development of first-principles methods and multiscale simulations, a more accurate understanding of radiation effects in materials can be achieved for the regime below hadronic interactions, with details down to atomic scale. It can be expected that the combination of first-principles methods, MC particle transport, and ML will contribute further to the investigation of materials to unravel their full potential for the application in harsh space radiation environments, in particular for what concerns the resistance and resilience to cumulative displacements effects.

Acknowledgments

The authors are grateful for the funding provided by the project ESC2RAD within the Horizon 2020 Research and Innovation program (grant agreement ID: 776410) and by the project PROIRICE within the program H2020-MSCA-IF 2016 of the Horizon 2020 program of the European Union (grant agreement ID: 748673).