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Abstract
Neutron irradiation induced degradation of porous silica film is studied by Molecular Dynamics and Density-Functional theory-based methods. The degradation of microscopic structure, thermal property, and optical property of porous silica film are systematically investigated. Low-energy recoil is used to simulate the neutron irradiation effect. The pair and bond angle distributions, and coordination number distributions reveal that, under neutron irradiation, the microscopic structure of porous silica film is obviously modified, and the coordination defects are induced. We find that the higher recoil energy, the more coordination defects are formed in the film. The increased defects lead to a decrease in thermal conductivity. In addition, neutron irradiation induces additional optical absorption peaks in UV region and increasement in refractive index, resulting in a noticeable reduction in light transmittance. The detailed calculation of density of states reveals that these optical absorption peaks originate from the irradiation induced defect states in band gap. Our work shows that low-energy neutron irradiation can induce obvious defect density and degrade thermal and optical properties of porous silica film, which are responsible for subsequent laser-induced damage.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Antireflective films are widely applied in laser systems to reduce the optical reflective losses and accommodate the highest possible power densities [1,2]. Sol-gel-derived porous silica film is a conventional antireflection film, which shows many good properties such as continuously adjustable refractive index, easy preparation for large size, and high damage resistance in the ultraviolet regime [3–6]. Due to these advantages, Sol-gel-derived porous silica film has been employed in high-power laser systems for pursuing inertial confinement fusion (ICF), such as National Ignition Facility (NIF) in the United States [7,8], Shenguang (SG) - III laser facility in China [9], Laser Mégajoule (LMJ) in France [10] and high-power laser energy research facility (HIPER) in Europe [11].
However, when porous silica films suffer from the multi-pulse laser and ray irradiations in the ICF facilities, the damage and decrease of the laser-induced damage threshold (LIDT) are observed, limiting the optical lifetime of the films and the stable operating flux of ICF systems [12,13]. This phenomenon is similar to “fatigue” in many materials such as glass [14], thin film [15–17], metal [18], etc., indicating that irreversible modifications happened in the structure of materials [19]. These modifications can be point defects, stress, high temperature, and so on [20,21]. For porous silica films, the neutron radiation from the fusion target can cause modifications and defects in the structure, which possibly responsible for the laser damage and lower LIDT. Although the neutron radiation effect has been studied for many materials of different classes: transition metal carbides [22], silicon dioxide [23], tungsten and copper alloys [24,25], the neutron radiation effect – which is related to the performance degradation of radiated materials – on porous silica films remain poorly understood.
This work aims to give a comprehensive insight into the neutron radiation effect on the microscopic structure, thermal, mechanical, and optical properties of porous silica films by Density-Functional theory (DFT) and Molecular Dynamics (MD)-based methods. In our work, we prepare a porous silica film model with ∼50% porosity and simulate the neutron irradiation effect on the film by MD simulations. Our results show that, under neutron irradiation, the microscopic structure of porous silica film is obviously modified, and coordination defects are induced. The higher irradiation energy, the more coordination defects are formed in the film. The increased defects lead to a decrease in thermal conductivity. In addition, neutron irradiation induces additional optical absorption peaks in UV region and increment in refractive index, resulting in a noticeable reduction in light transmittance. Our work shows that neutron irradiation is one of the potential sources of inducing defects and leading to performance degradation for porous silica films, which are responsible for subsequent laser-induced damage.
2. Method
Simulation software based on MD and DFT methods has studied many disordered systems [26–30], such as Vienna abinitio Simulation Package (VASP) [31] and LAMMPS [32]. Hence, we select VASP for DFT and LAMMPS for MD to study the neutron irradiation effect on amorphous porous silica.
MD method is selected to generate the disordered structure. The disordered structure of 96-atom porous silica is generated under charge-scaling method with Teter potential [33]. The time step is set as 1.0 fs. First, the supercell (14.22 × 14.36 × 14.22 Å3) of 32 Si and 64 O atoms are thermalized in the NVT ensemble at 300 K. Then, the system is equilibrated at 300 K and stabilized at 1.1 g/cm3, which eventually achieved a porosity of 50%, which is close to the porosity of sol-gel silica films on the ICF optics [34]. The molecular structure of amorphous porous silica in Fig. 1 shows several channeled pores exist in the amorphous Si–O network. And we scale the recoil simulations in MD method to consider the neutron irradiation effect. Two Si and two O atoms are randomly chosen from the amorphous Si–O network as the primary knock-on atom (PKA) to guarantee recoils. The energy of neutrons in fusion is nominally on the order of 10 keV. Because of the shielding materials (e.g., the window of target chamber, fused silica shields) in the light path of ICF, the kinetic energy of neutrons reaching porous silica of the terminal optical assembly can be reduced to the order of keV, through inelastic scattering interactions. Therefore, the recoil energy for PKAs in porous silica is sub 100 eV, which can be calculated by collision formula. The kinetic energy of the PKA is set in the range of 0 ∼ 100 eV to study the effect of recoil energy on the microcosmic structure and other properties of porous silica film. The lattice thermal conductivity κ is estimated by the Green−Kubo (G-K) method in equilibrium molecular dynamic simulations (EMD) for amorphous porous silica.
Fig. 1. The molecular structure of amorphous porous silica. Si and O atoms are represented by yellow and red spheres, respectively.
DFT-based method is used to compute the elastic constants and optical properties. Perdew–Burke–Ernzerhof (PBE) pseudopotential with generalized gradient approximation (GGA) is adopted to describe the electron correlation. The cutoff energy of the plane-wave basis is at 500 eV. The Brillouin zone integration was performed over 1 × 1 × 1 Gamma grid k-point. The force convergence criterion in optimization is at 0.01 eV/Å, and the self-consistent convergence of the total energy is at 1 × 10−5 eV per atom. Bathe–Salpeter equation (BSE) based upon the quasi-particle G0W0 calculations is adopted to obtain optical properties of amorphous porous silica.
3. Results and discussion
3.1 Modification of the microscopic structure
Figure 2 illustrates the pair distribution functions for the porous silica with recoils of Si and O atoms to reveal changes in bond lengths. The energy of atoms selected as PKA is chosen in the 0–100 eV range to compare the recoil effects. For the initial structure, the Si-O peaks at 1.65 Å, consistent with the result reported in experiments [35]. The Si-Si and O-O peaks are at 3.1 Å and 2.6 Å, respectively. After recoils in different energies, there is a conspicuous increase occurring on the left of the Si-Si and O-O peak (2.4 ∼ 2.8 Å for O-O peak and 2.0 ∼ 2.3 Å for O-O peak), suggesting shorter Si–Si and O–O bonds appear. The primary peaks of Si-O pairs shift to lower values from 1.65 Å, indicating the average Si-O bond distance of porous silica is shortened after neutron irradiation. On the other hand, the decrease in peak value of three pairs caused by irradiation indicates that the disorder degree of amorphous porous silica is increasing. The Si-O-Si bond angle distribution is presented in Fig. 3. It can be clearly seen that the range of Si-O-Si primary peaks is broadened to a lower angle and the toe near 100° increases after recoils, reducing the average Si-O-Si angle. Several experimental studies have demonstrated that amorphous silica suffers densification during neutron irradiation [36–38] and the increased mass density has been correlated with a reduction in the average Si-O-Si angle [39,40]. Hence, we calculate the relative change of mass density for porous silica after neutron irradiation listed in Table 1. As can be seen from the table, the mass density of porous silica increases after irradiation, which is in accordance with experiment results.
Fig. 2. Pair distribution functions of amorphous porous silica at different recoil energies (a) Si-O and (b) Si-Si (c) O-O.
Fig. 3. Si-O-Si bond angle distribution functions of amorphous porous silica at different recoil energies.
Table 1. The relative change of mass density of porous silica before and after neutron irradiation (positive values represent increase).
In addition, we perform the coordination number distribution of Si and O atoms in Fig. 4. It is found that higher energy recoils lead to a decrease in the coordination number of Si and O atoms, which indicates the formation of more coordination defects in the structure. To account for the increasement of coordination defects, the number of coordination defects nonbridging oxygen (NBO, an O atom only bonded to one Si atom) and three-coordinated silicon (Si3+, a Si atom bonded to 3 O atom) are shown in Fig. 5. It can be seen that the number of NBO and Si3+ increases with the increase of recoil energy. These results indicate that recoil leads to obvious changes in the silicate structure, and more NBO and Si3+ coordination defects can be formed in porous silica film with higher recoil energy.
Fig. 5. The number of coordination defects in the amorphous porous silica with different recoil energies.
3.2 Degradation of thermal conductivity
The porous silica material possesses strong anisotropic characteristic on account of the distribution of the pores [35–37], so we computed thermal conductivity κ in three directions. The varies of thermal conductivity κ (at T = 300 K) in three directions as functions of energy of recoils are plotted in Fig. 6. We find that the magnitude of kx, ky, kz decrease with the rising energy of recoils, indicating the poorer capacity of heat-transmission. Since neutron irradiation leads to lower thermal conductivity, the heat produced by UV laser irradiation cannot escape faster, thus forming a high-temperature area in the irradiation area and causing laser-induced damage. Moreover, we notice that the transport quantity has directional dependence in the amorphous porous silica systems, and kz is significantly higher than kx (ky). Indeed, the pore in Z-direction in amorphous porous silica is larger than those in the X, Y-direction, which leads to higher κ.
Fig. 6. Thermal conductivities (κ) of amorphous porous at different recoil energies in 300 K. The kx, ky, and kz represent κ along x, y, and z axis, respectively. Dash lines show linear fits of kx, ky, and kz.
3.3 Degradation of optical properties
The optical absorption of porous silica under different energy recoils evaluated using the G0W0 + BSE calculations is shown in Fig. 7(a). The exciton effect is considered in the BSE method. Without the recoil, the optical band gap of porous silica is located at about 5 eV, and there are no obvious optical absorption peaks in the 3 ∼ 4 eV range. With the recoil, optical absorption peaks appear in the 3 ∼ 4 eV range, indicating that porous silica has strong absorption to UV laser after irradiation. Such as, with 40 eV recoil, one obvious absorption peak appears at 3.3 eV. To relate the computed optical properties to electronic structure, we obtained the density of states (DOSs) for porous silica under different energy recoils. As shown in Fig. 7(b), with recoils, the band gap is reduced and the occupied defect states - which are contributed by coordination defects - exist in band gap (The red marks represent occupied defect states in band gap). The electrons in these defect states can absorb laser energy and transit to the conduction band under the narrowing band gap and the action of the exciton effect, resulting in the optical absorption in the 3 ∼ 4 eV.
Fig. 7. The optical absorption and the density of states (DOSs) of amorphous porous silica at different recoil energies. (a) The optical absorption of amorphous porous silica at different recoil energies. The black dotted lines marked the energy range between 3 eV and 4 eV. (b) The DOSs of amorphous porous silica at different recoil energies. The black dotted line represents the Fermi level, and the red triangle marks represent occupied defect states in band gap.
Figure 8 presents the refractive index of porous silica in the range of 3 ∼ 4 eV with different recoil energies. The refractive index at 3.5 eV of unirradiated 50% porosity silica is 1.18, agreeing well with experiment data [5,6]. As shown in Fig. 8, the refractive index gradually increases with higher recoil energies. Under 100 eV recoil, the refractive index increases to 1.21 from 1.18. This result is consistent with several reports that the narrowing energy band causes a higher refractive index [41], and the increase of refractive index is accompanied by irradiation-induced structure densification [42].
As one of the important optical properties of the antireflective films, the transmittance of porous silica is obtained. We assume that the incident laser is at normal incidence on the interfaces of air - porous silica film - fused silica lens, and the transmittance T is calculated using the formula [43]:
Fig. 9. The optical transmission rate of amorphous porous silica in the range from 3 eV and 4 eV at different recoil energies.
4. Conclusion
In this work, the influences of neutron irradiation on the microscopic structure, thermal and optical properties of amorphous porous silica are systemically studied by MD and DFT-based methods. Low-energy recoil is used to simulate the neutron irradiation effect. The pair distribution functions and coordination number distributions reveal that, under neutron irradiation, the bonds of Si-O, Si-Si, and O-O, the average Si-O-Si bond angle are reduced, and coordination defects are formed in porous silica. The densification of porous silica is found. Moreover, we find that neutron irradiation can increase refractive index and induce additional optical absorption in UV region (3 ∼ 4 eV), leading to the notable reduction in transmittance of porous silica film. The increment of refractive index and additional optical absorption is attributed to the shrinkage of energy band and modification of electronic density states after neutron irradiation. Our results indicate that neutron irradiation can cause performance degradation and is responsible for possible subsequent laser-induced damage to porous silica films in the ICF systems. Our work would help to understand the mechanism of neutron irradiation induced degradation of amorphous porous silica and the decreased damage threshold of the subsequent laser.
Funding
Key Project of National Natural Science Foundation of China-China Academy of Engineering Physics Joint Foundation (U1830204); Key Laboratory Opening Topic Fund (JCKYJCKY2022210C005); National Natural Science Foundation of China (11804046, 12105037, 61505023).
Acknowledgments
This work is supported by the Key Project of National Natural Science Foundation of China-China Academy of Engineering Physics joint Foundation (NSAF, No. U1830204), the Key Laboratory Opening Topic Fund (JCKYJCKY2022210C005) and the National Natural Science Foundation of China (No. 61505023, No. 11804046, No. 12105037).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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