Ab Initio Molecular Dynamics Study of Electron Excitation Effects on UO₂ and U₃Si

Abstract

In this study, an ab initio molecular dynamics method is employed to investigate how the microstructures of UO₂ and U₃Si evolve under electron excitation. It is found that the U₃Si is more resistant to electron excitation than UO₂ at room temperature. UO₂ undergoes a crystalline-to-amorphous structural transition with an electronic excitation concentration of 3.6%, whereas U₃Si maintains a crystalline structure until an electronic excitation concentration reaches up to 6%. Such discrepancy is mainly due to their different electronic structures. For insulator UO₂, once valence U 5f electrons receive enough energy, they are excited to the conduction bands, which induces charge redistribution. Anion disordering is then driven by cation disordering, eventually resulting in structural amorphization. As for metallic U₃Si, the U 5f electrons are relatively more difficult to excite, and the electron excitation leads to cation disordering, which eventually drives the crystalline-to-amorphous phase transition. This study reveals that U₃Si is more resistant to electron excitation than UO₂ under an irradiation environment, which may advance the understanding of related experimental and theoretical investigations to design radiation-resistant nuclear fuel uranium materials.

1. Introduction

As one of the significant sources of carbon-free energy, nuclear energy has been used on a massive scale. The selection of nuclear fuel is key to deciding the safety of nuclear energy technology, as well as its stability and economic efficiency [1]. In the past decades, uranium has been used as nuclear fuel in fission reactors, and some uranium complexes have been investigated for long-term nuclear waste disposal and the storage of highly radioactive waste materials [2,3]. Throughout the world, UO₂ has been employed in a large number of commercial light water reactors because of its superior properties, such as high melting point (3147 ± 20 K) [4,5,6], good oxidation resistance, and chemical compatibility [1,7]. However, the poor thermal conductivity of UO₂ (2$\sim$6 Wm⁻¹K⁻¹) in the temperature range of 273$\sim$1673 K [8] can cause a large temperature gradient during operation [1,7]. Therefore, extensive studies have been conducted to search for alternative fuels with better thermal performance in reactors [7,9,10]. In addition to UO₂, other types of nuclear fuels, including mixed oxides ((U,Pu)O₂, (U,Th)O₂, (Pu,Th)O₂) [11,12], alloys (U-Al, U-Mo, U-ZrH) [13], UC [14], UN [15], and uranium silicides such as U₃Si [16] and U₃Si₂ [17,18], have been used or proposed for different reactors. Among these nuclear fuels, the U₃Si₂ and U₃Si, due to their high uranium density [19] and large thermal conductivity [20], are considered potential accident-tolerant fuels. The U₃Si has a thermal conductivity of approximately 15$\sim$25 Wm⁻¹K¹ under 300$\sim$1100 K [21] and a maximum uranium loading of 14.6 g-U/cm³, which is much higher than that of UO₂ (9.7 g-U/cm³) [16,22]. To date, the U₃Si is a potential nuclear fuel in low-temperature and low-power reactors such as the Miniature Neutron Source reactors [19,23,24].

During the past decades, researchers have striven to investigate the response of microstructural change in nuclear materials under ion, electron, and pulsed laser irradiation [25,26]. Barthe et al. irradiated sintered UO2 disks with electrons and α particles at different fluences [27]. The results showed the formation of U-related vacancy defects after a 2.5 MeV electron irradiation, whereas no defects were detected for irradiation at 1 MeV. Experimentally, Onofri et al. characterized the microstructural evolution of poly-crystalline UO₂ under 4 MeV Au and 390 keV Xe ions irradiation with fluences of 0.5 × 10¹⁵$~$1.0 × 10¹⁵ ions/cm² and found several dislocation loops and dislocation lines [24]. Miao et al. studied the high-burnup structure in UO₂ under 84 MeV Xe ion irradiation and found that radiation-induced dislocations result in grain polygonization [28]. In addition, Miao et al. investigated the response of U₃Si₂ to 84 MeV Xe ion irradiation at 600 °C and found that the U₃Si₂ is strongly resistant to radiation-induced amorphization [29]. Theoretically, Owen studied amorphous UO₂ systems using classical molecular dynamics methods and reported that the amorphous structure of UO₂, i.e., oxygen ions, are coordinated with 3.65 uranium ions and uranium ions are coordinated with 7.31 oxygen ions [6]. Moreover, ab initio molecular dynamics (AIMD) computer simulations of low-energy recoil events in UO₂ and ThO₂ were carried out by Xiao et al., who determined the threshold displacement energies and revealed a number of novel point defects [30,31].

Ion or laser irradiation can substantially deposit energy in solids via elastic and inelastic collisions, as described in [32,33,34], which induces strong electron excitation and ionization [33,35]. In the literature, researchers have demonstrated that electron excitation can induce crystalline-to-amorphous structural transitions and influence material properties significantly. For example, Li et al. studied the response of Ge-Sb-Te alloys to laser irradiation by employing an AIMD method and found that electron excitation results in the structural amorphization of the alloy [36]. The amorphization of crystalline SiO₂ induced by an electron beam in transmission electron microscopes has been reported by a number of researchers [37,38,39]. Furthermore, Xiao et al. carried out AIMD simulations on a series of titanate pyrochlores under electron irradiation and found that a crystalline-to-amorphous structural transition is induced by electron excitation in these pyrochlores [40]. Zhao et al. performed finite-temperature density functional theory and AIMD simulations on SrTiO₃ and reported that there is a charge redistribution in Ti-O bonds and that the SrTiO₃ undergoes a phase transition from crystalline to an amorphous state under electron excitation [33]. Thus far, the microstructural evolution of UO₂ and U₃Si under electron excitation still remains unclear. In this work, the structural evolution of UO₂ and U₃Si under electron excitation is investigated by employing the AIMD method, and the possible origin of their different response behaviors is explored. It is revealed that the U₃Si is more resistant to electron excitation than the insulating UO₂ due to its metallic character, suggesting that the U₃Si has excellent structural stability under electron and laser irradiation.

2. Computational Methods

Because of the existence of U 5f electrons in UO₂ and U₃Si, strong correlation effects cannot be ignored [41]. To correct the on-site Coulomb interaction between the U 5f electrons, the Hubbard U correction proposed by Dudarev et al. [42] is utilized in this work. In this study, the responses of UO₂ and U₃Si to electron excitation are simulated by using the AIMD $+$ U (ab initio molecular dynamics plus Hubbard U correction) method, as implemented in the Vienna Ab Initio Simulation Package (VASP) [43]. The effective Hubbard parameter $U_{\mathrm{eff}}=U-J$ is employed to be 4.0 eV [44] for UO₂ and 1.5 eV [45] for U₃Si. The interactions between ions and electrons are described by the projector-augmented wave (PAW) pseudopotential, as described in [46,47] and the exchange–correlation potential between electrons is described by the Ceperly Alder parameterization under local density approximation (LDA) [48]. With spin-polarized effects taken into account, the cut-off energy for the plane-wave basis is set to 400 eV. A 1 $\times$ 1 $\times$ 1 K-point sampling in the Brillouin zone created by the Monkhorst-Pack [49] technique is used in AIMD calculations. Uranium dioxide (UO₂) is of a fluorite structure in which the cations are located in a face-centered cubic (fcc) sublattice and the anions are in a cubic sublattice [30]. The U₃Si crystal is of a tetragonal structure with the space group I4/mcm [50]. The UO₂ has 12 atoms in the unit cell and the U₃Si has 16 atoms in the unit cell. In the AIMD simulation, a 2 × 2 × 2 (96 atoms) and a 2 × 2 × 1 (64 atoms) supercell are employed for UO₂ and U₃Si, respectively, and periodic boundary conditions are applied along three directions. Figure 1 shows a schematic view of the geometrical structures of UO₂ and U₃Si. For UO₂, anti-ferromagnetic ordering is considered, and the magnetic moment is determined to be 2.06 µB, which agrees well with the experimental value of 2 µB [51]. Electron excitation can be achieved by removing several electrons from the valence band states during the AIMD simulation, and the charge loss due to electron removal is compensated by a jellium background [36]. The electronic excitation concentration is defined as the ratio of the number of excited electrons to the total number of electrons. For a 2 × 2 × 2 supercell of the UO₂ crystal, the total number of electrons is 3456, and the number of removed electrons ranges from 83 to 208, corresponding to an excitation concentration of 2.4~6%. For a 2 × 2 × 1 supercell of U₃Si crystal, the total number of electrons is 4640, and the number of removed electrons ranges from 111 to 278, corresponding to an excitation concentration of 2.4~6%. The intensity of the generated electron-hole pairs can be calculated as $N_{e-h}=\frac{\left(1-\mathrm{R}\right)\times {\alpha }_{eff}\times F}{\hslash {\omega }_0}$, where F and ${\omega }_0$ represent the laser fluence and frequency, respectively, and R and ${\alpha }_{eff}$ represent the sample’s reflectivity and effective absorption coefficient, respectively [52]. Under laser beam irradiation, employing volume = 1.31 × 10⁻²¹ cm³, $\hslash {\omega }_{0 }$ = 5 eV, R (248 nm) = 22% [53], and ${\alpha }_{eff}$ (248 nm) = 0.43 × 10⁵ cm⁻¹, the predicted laser fluence at 248 nm for 3.6% excitation in UO₂ is 2.27 × 10³ mJ/cm². The AIMD simulation is conducted with a time step of 1.5 fs and a canonical ensemble, and the Nosé–Hoover thermostat [54] is employed to control the temperature.

3. Results and Discussion

The RDF defines variations in the surrounding matter density as a function of distance from a point, as well as the frequency with which specific distances occur [55], which is obtained in the simulation model by counting the number of atom pairs separated by particular distances. Figure 2 illustrates the RDFs of UO₂ and U₃Si with and without electron excitation at a temperature of 300 K. When a material is crystalline, its structure is ordered at both short-range and long-range distances; when the material is amorphous, its structure is ordered at short-range distances and disordered at long-range distances. The strong and weak RDFs (with peak values approaching 1) correspond to structural ordering and disordering, respectively. Figure 2a presents the radial distribution functions of UO₂ and U₃Si as a function of the electronic excitation concentration at 300 K. For UO₂, it is noted that its structure remains ordered at both short-range and long-range distances under electronic excitation concentrations of 0% and 2.4%, as indicated by the strong peaks in the whole considered interatomic distance range; however, as the electronic excitation concentration increases to 3.6%, structural short-range ordering and long-range disordering are observed, i.e., a crystalline-to-amorphous phase transformation is induced. A similar phenomenon has been observed in SrTiO₃, titanate pyrochlores, and nickel oxide [33,40,56] for which electron excitation also causes a crystalline-to-amorphous phase transformation. In particular, new peaks appear at 1.17$~$1.3 Å, which can be attributed to the formation of O₂ molecules. In the case of U₃Si, it is noticeable that the situation is somewhat different. U₃Si is shown to be strongly tolerant to electron excitation and maintains a crystalline structure under electronic excitation concentrations of 0.0%, 2.4%, 3.6%, and 4.8%, as indicated by the strong RDF peaks in the whole interatomic distance range in Figure 2b. When the electronic excitation concentration is as high as 6.0%, a crystalline-to-amorphous phase transformation occurs. Obviously, U₃Si is more resistant to electron excitation than UO₂.

Figure 3 illustrates the geometrical configurations of UO₂ after electron excitation at different electronic excitation concentrations. It is shown that the UO₂ remains in a crystalline structure when no electrons are excited. For an electronic excitation concentration of 2.4%, there is a slight lattice disordering for anions, and the cations maintain the lattice ordering well. When the electronic excitation concentration reaches 3.6%, the structure of UO₂ changes significantly. In particular, the anions are dramatically disordered, and O₂-like molecules are formed. The <O-O> distances are determined to be approximately 1.13 Å, which is close to the bond length of 1.24 Å for O₂ [40]. As the electronic excitation concentration further increases to 4.8% and 6.0%, more and more O₂-like molecules are formed. Moreover, cation disordering has become increasingly significant. Obviously, during the electron excitation process, anions are first disordered, which drives cation disordering and eventual structural amorphization. Such an amorphization mechanism is found to be similar to that of titanate pyrochlores [40]. In comparison to UO₂, electron excitation with 2.4$~$6.0% concentration has a more limited influence on the geometrical structure of U₃Si. As can be seen from Figure 4b–d, for electronic excitation concentrations of 2.4%, 3.6%, and 4.8%, the structures of U₃Si are well ordered; in the case of 6.0% electronic excitation concentration, it is noted that lattice disordering occurs on U atoms rather than Si atoms (see Figure 4e), suggesting that the structural amorphization in U₃Si is driven by cation disordering instead of anion disordering. This is different from the amorphization mechanism of UO₂. Experimentally, the microstructural evolution in UO₂ and U₃Si under electron excitation has not been investigated yet, since they are radioactive materials and direct experimental study is not easy. However, electron excitation-induced structural amorphization has been experimentally observed in alloys, semiconductors, and ceramics [38,57,58,59].

To evaluate if the structural amorphization is a solid–liquid transition, an AIMD approach is utilized to simulate the structural evolution of UO₂ and U₃Si at 5000 K, which is much higher than their respective melting temperatures of 3147 ± 20 K [4,5] and ~1258 K [60]. Figure 5a compares the RDFs of melted and excited UO₂ with an electronic excitation concentration of 6.0%. As shown in Figure 5a, the RDF peak located at an interatomic distance of ~1.13 Å for excited UO₂ disappears for melted UO₂, implying that no O₂-like molecules are formed during the melting process. In the case of U₃Si (see Figure 5b), the peak intensity of RDF at short-range distances for melted U₃Si is much stronger than that for excited U₃Si, indicating strengthened short-range ordering. Obviously, the structural amorphization induced by high-temperature melting is different from that induced by electron excitation. Figure 5c,d compares the mean square displacements of cations and anions in melted and excited UO₂ and U₃Si with a 6% electronic excitation concentration. As shown in Figure 5c, with a simulation time of 3 ps, the displacements of O and U atoms in melted UO₂ are approximately six and ten times larger than those of excited UO₂, respectively. As for U₃Si, after a simulation time of 6 ps, the displacements of U and Si atoms in melted U₃Si are over thirty times larger than those in excited U₃Si, as illustrated in Figure 5d. These results suggest that the electron excitation-induced phase transition in UO₂ and U₃Si is different from the thermal melting-induced phase transition, and the former is a solid–solid transition rather than a solid–liquid transition. In the literature, a similar phenomenon is reported for titanate pyrochlores [40] and In₂Se₃ nanowires [61].

To explore the origin of the discrepancy in microstructural evolution under electron excitation between UO₂ and U₃Si, the total and projected density of state distributions of UO₂ and U₃Si with and without an electronic excitation concentration of 6.0% are illustrated in Figure 6. The Fermi level is set to be 0 eV. For ground state UO₂, the band gap is determined to be 1.89 eV without spin–orbital coupling compared with the experimental value of ~2.1 eV [62]. In the case of ground state U₃Si, electrons are distributed on the Fermi level, indicative of metallic character, which agrees well with the experimental results [24]. Clearly, the electronic structure of ground state UO₂ is very different from that of ground state U₃Si, which may result in different responses of UO₂ and U₃Si to electron excitation. For UO₂, the valence band maximum is mainly contributed by U 5f orbitals, indicating that the valence electrons located at U 5f orbitals are relatively more easily excited. When the number of excited electrons is large enough, the excitation of U 5f electrons induces charge redistribution, resulting in cation disordering and the generation of O₂-like molecules. As for U₃Si, the U 5f electrons dominate the Fermi level. Therefore, the structural amorphization in U₃Si is also driven by cation disordering. Since the electron work function of the U element is as high as 3.63 eV, as described in [63,64], the electrons in U₃Si are more difficult excite than those in UO₂. Consequently, the U₃Si is more resistant to electron excitation than the UO₂.

4. Conclusions

In summary, an AIMD simulation method is employed to investigate the response behaviors of UO₂ and U₃Si to electron excitation at room temperature. It is found that a crystalline-to-amorphous phase transition can be induced in UO₂ with an electronic excitation concentration of 3.6%, whereas in U₃Si, the threshold electronic excitation concentration for structural amorphization is as high as 6.0%. This structural amorphization induced by electron excitation is a solid–solid transition rather than a solid–liquid transition. The different electronic structures of ground-state UO₂ and U₃Si might result in different responses to electron excitation. The UO₂ is an insulator, for which the U 5f valence electrons are relatively more easily excited, which drives anion disordering and eventually structural amorphization. U₃Si exhibits a metallic character, and the U 5f electrons dominate the Fermi level. Electron excitation causes cation disordering, which leads to structural amorphization. This study reveals that U₃Si undergoes crystalline-to-amorphous structural transitions less easily than UO₂ when electronic excitation occurs, suggesting that U₃Si has better potential under electron or laser irradiation as a nuclear fuel than UO₂.