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

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.


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, UO 2 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) [4-6], good oxidation resistance, and chemical compatibility [1,7].However, the poor thermal conductivity of UO 2 (2∼6 Wm −1 K −1 ) in the temperature range of 273∼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 UO 2 , other types of nuclear fuels, including mixed oxides ((U,Pu)O 2 , (U,Th)O 2 , (Pu,Th)O 2 ) [11,12], alloys (U-Al, U-Mo, U-ZrH) [13], UC [14], UN [15], and uranium silicides such as U 3 Si [16] and U 3 Si 2 [17,18], have been used or proposed for different reactors.Among these nuclear fuels, the U 3 Si 2 and U 3 Si, due to their high uranium density [19] and large thermal conductivity [20], are considered potential accident-tolerant fuels.The U 3 Si has a thermal conductivity of approximately 15∼25 Wm −1 K 1 under 300∼1100 K [21] and a maximum uranium loading of 14.6 g-U/cm 3 , which is much higher than that of UO 2 (9.7 g-U/cm 3 ) [16,22].To date, the U 3 Si 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 UO 2 under 4 MeV Au and 390 keV Xe ions irradiation with fluences of 0.5 × 10 15 ∼1.0 × 10 15 ions/cm 2 and found several dislocation loops and dislocation lines [24].Miao et al. studied the high-burnup structure in UO 2 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 U 3 Si 2 to 84 MeV Xe ion irradiation at 600 • C and found that the U 3 Si 2 is strongly resistant to radiation-induced amorphization [29].Theoretically, Owen studied amorphous UO 2 systems using classical molecular dynamics methods and reported that the amorphous structure of UO 2 , 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 UO 2 and ThO 2 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 SiO 2 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-toamorphous structural transition is induced by electron excitation in these pyrochlores [40].Zhao et al. performed finite-temperature density functional theory and AIMD simulations on SrTiO 3 and reported that there is a charge redistribution in Ti-O bonds and that the SrTiO 3 undergoes a phase transition from crystalline to an amorphous state under electron excitation [33].Thus far, the microstructural evolution of UO 2 and U 3 Si under electron excitation still remains unclear.In this work, the structural evolution of UO 2 and U 3 Si 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 U 3 Si is more resistant to electron excitation than the insulating UO 2 due to its metallic character, suggesting that the U 3 Si has excellent structural stability under electron and laser irradiation.

Computational Methods
Because of the existence of U 5f electrons in UO 2 and U 3 Si, 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 UO 2 and U 3 Si 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 eff = U − J is employed to be 4.0 eV [44] for UO 2 and 1.5 eV [45] for U 3 Si.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 × 1 × 1 K-point sampling in the Brillouin zone created by the Monkhorst-Pack [49] technique is used in AIMD calculations.Uranium dioxide (UO 2 ) 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 U 3 Si crystal is of a tetragonal structure with the space group I4/mcm [50].The UO 2 has 12 atoms in the unit cell and the U 3 Si 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 UO 2 and U 3 Si, respectively, and periodic boundary conditions are applied along three directions.Figure 1 shows a schematic view of the geometrical structures of UO 2 and U 3 Si.For UO 2 , 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 UO 2 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 U 3 Si 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 , where F and ω 0 represent the laser fluence and frequency, respectively, and R and α e f f represent the sample's reflectivity and effective absorption coefficient, respectively [52].Under laser beam irradiation, employing volume = 1.31 × 10 −21 cm 3 , ω 0 = 5 eV, R (248 nm) = 22% [53], and α e f f (248 nm) = 0.43 × 10 5 cm −1 , the predicted laser fluence at 248 nm for 3.6% excitation in UO 2 is 2.27 × 10 3 mJ/cm 2 .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.
Materials 2023, 16, x FOR PEER REVIEW 3 of energy for the plane-wave basis is set to 400 eV.A 1 1 1 K-point sampling in t Brillouin zone created by the Monkhorst-Pack [49] technique is used in AIMD calcu tions.Uranium dioxide (UO2) is of a fluorite structure in which the cations are located a face-centered cubic (fcc) sublattice and the anions are in a cubic sublattice [30].The U crystal is of a tetragonal structure with the space group I4/mcm [50].The UO2 has 12 atom in the unit cell and the U3Si has 16 atoms in the unit cell.In the AIMD simulation, a 2 × 2 (96 atoms) and a 2 × 2 × 1 (64 atoms) supercell are employed for UO2 and U3Si, resp tively, and periodic boundary conditions are applied along three directions.Figure shows a schematic view of the geometrical structures of UO2 and U3Si.For UO2, anti-f romagnetic ordering is considered, and the magnetic moment is determined to be 2.06 µ which agrees well with the experimental value of 2 µB [51].Electron excitation can achieved by removing several electrons from the valence band states during the AIM simulation, and the charge loss due to electron removal is compensated by a jellium bac ground [36].The electronic excitation concentration is defined as the ratio of the numb of excited electrons to the total number of electrons.For a 2 × 2 × 2 supercell of the U crystal, the total number of electrons is 3456, and the number of removed electrons rang from 83 to 208, corresponding to an excitation concentration of 2.4~6%.For a 2 × 2 × supercell of U3Si crystal, the total number of electrons is 4640, and the number of remov 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

Results and Discussion
The RDF defines variations in the surrounding matter density as a function of d tance from a point, as well as the frequency with which specific distances occur [55], whi is obtained in the simulation model by counting the number of atom pairs separated particular distances.Figure 2 illustrates the RDFs of UO2 and U3Si with and without el tron excitation at a temperature of 300 K.When a material is crystalline, its structure

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 UO 2 and U 3 Si 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 UO 2 and U 3 Si as a function of the electronic excitation concentration at 300 K.For UO 2 , 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 SrTiO 3 , 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∼1.3Å, which can be attributed to the formation of O 2 molecules.In the case of U 3 Si, it is noticeable that the situation is somewhat different.U 3 Si 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, U 3 Si is more resistant to electron excitation than UO 2 .
Materials 2023, 16, x FOR PEER REVIEW 4 of ordered at both short-range and long-range distances; when the material is amorphou its structure is ordered at short-range distances and disordered at long-range distanc The strong and weak RDFs (with peak values approaching 1) correspond to structu ordering and disordering, respectively.Figure 2a presents the radial distribution fun tions of UO2 and U3Si as a function of the electronic excitation concentration at 300 K. F UO2, it is noted that its structure remains ordered at both short-range and long-range d tances under electronic excitation concentrations of 0% and 2.4%, as indicated by t strong peaks in the whole considered interatomic distance range; however, as the el tronic excitation concentration increases to 3.6%, structural short-range ordering a long-range disordering are observed, i.e., a crystalline-to-amorphous phase transfo mation is induced.A similar phenomenon has been observed in SrTiO3, titanate pyr chlores, and nickel oxide [33,40,56] for which electron excitation also causes a crystallin to-amorphous phase transformation.In particular, new peaks appear at 1.17~1.3Å, whi can be attributed to the formation of O2 molecules.In the case of U3Si, it is noticeable th the situation is somewhat different.U3Si is shown to be strongly tolerant to electron ex tation and maintains a crystalline structure under electronic excitation concentrations 0.0%, 2.4%, 3.6%, and 4.8%, as indicated by the strong RDF peaks in the whole interatom distance range in Figure 2b.When the electronic excitation concentration is as high 6.0%, a crystalline-to-amorphous phase transformation occurs.Obviously, U3Si is mo resistant to electron excitation than UO2. Figure 3 illustrates the geometrical configurations of UO2 after electron excitation different electronic excitation concentrations.It is shown that the UO2 remains in a cry talline structure when no electrons are excited.For an electronic excitation concentrati of 2.4%, there is a slight lattice disordering for anions, and the cations maintain the latt ordering well.When the electronic excitation concentration reaches 3.6%, the structure UO2 changes significantly.In particular, the anions are dramatically disordered, and O like molecules are formed.The <O-O> distances are determined to be approximately 1 Å, which is close to the bond length of 1.24 Å for O2 [40].As the electronic excitation co centration further increases to 4.8% and 6.0%, more and more O2-like molecules a formed.Moreover, cation disordering has become increasingly significant.Obvious during the electron excitation process, anions are first disordered, which drives cation d ordering and eventual structural amorphization.Such an amorphization mechanism found to be similar to that of titanate pyrochlores [40].In comparison to UO2, electr excitation with 2.4~6.0%concentration has a more limited influence on the geometri structure of U3Si.As can be seen from Figure 4b-d, for electronic excitation concentratio of 2.4%, 3.6%, and 4.8%, the structures of U3Si are well ordered; in the case of 6.0 Figure 3 illustrates the geometrical configurations of UO 2 after electron excitation at different electronic excitation concentrations.It is shown that the UO 2 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 UO 2 changes significantly.In particular, the anions are dramatically disordered, and O 2 -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 O 2 [40].As the electronic excitation concentration further increases to 4.8% and 6.0%, more and more O 2 -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 UO 2 , electron excitation with 2.4∼6.0%concentration has a more limited influence on the geometrical structure of U 3 Si.As can be seen from Figure 4b-d, for electronic excitation concentrations of 2.4%, 3.6%, and 4.8%, the structures of U 3 Si 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 U 3 Si is driven by cation disordering instead of anion disordering.This is different from the amorphization mechanism of UO 2 .Experimentally, the microstructural evolution in UO 2 and U 3 Si 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].
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].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 UO 2 and U 3 Si 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 UO 2 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 UO 2 disappears for melted UO 2 , implying that no O 2 -like molecules are formed during the melting process.In the case of U 3 Si (see Figure 5b), the peak intensity of RDF at short-range distances for melted U 3 Si is much stronger than that for excited U 3 Si, 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 UO 2 and U 3 Si 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 UO 2 are approximately six and ten times larger than those of excited UO 2 , respectively.As for U 3 Si, after a simulation time of 6 ps, the displacements of U and Si atoms in melted U 3 Si are over thirty times larger than those in excited U 3 Si, as illustrated in Figure 5d.These results suggest that the electron excitation-induced phase transition in UO 2 and U 3 Si 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 In 2 Se 3 nanowires [61].To evaluate if the structural amorphization is a solid-liquid transition, an AIMD proach is utilized to simulate the structural evolution of UO2 and U3Si at 5000 K, whic much higher than their respective melting temperatures of 3147 ± 20 K [4,5] and ~125 [60].Figure 5a compares the RDFs of melted and excited UO2 with an electronic excitat concentration of 6.0%.As shown in Figure 5a, the RDF peak located at an interatomic d tance of ~1.13 Å for excited UO2 disappears for melted UO2, implying that no O2-like m ecules are formed during the melting process.In the case of U3Si (see Figure 5b), the p intensity of RDF at short-range distances for melted U3Si is much stronger than that excited U3Si, indicating strengthened short-range ordering.Obviously, the structu amorphization induced by high-temperature melting is different from that induced electron excitation.Figure 5c,d compares the mean square displacements of cations a anions in melted and excited UO2 and U3Si with a 6% electronic excitation concentrati As shown in Figure 5c, with a simulation time of 3 ps, the displacements of O and U ato in melted UO2 are approximately six and ten times larger than those of excited UO2, spectively.As for U3Si, after a simulation time of 6 ps, the displacements of U and Si ato in melted U3Si are over thirty times larger than those in excited U3Si, as illustrated in F ure 5d.These results suggest that the electron excitation-induced phase transition in U and U3Si is different from the thermal melting-induced phase transition, and the form is a solid-solid transition rather than a solid-liquid transition.In the literature, a sim 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 UO 2 and U 3 Si, the total and projected density of state distributions of UO 2 and U 3 Si 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 UO 2 , 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 U 3 Si, 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 UO 2 is very different from that of ground state U 3 Si, which may result in different responses of UO 2 and U 3 Si to electron excitation.For UO 2 , 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 O 2 -like molecules.As for U 3 Si, the U 5f electrons dominate the Fermi level.Therefore, the structural amorphization in U 3 Si 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 U 3 Si are more difficult excite than those in UO 2 .Consequently, the U 3 Si is more resistant to electron excitation than the UO 2 .
To explore the origin of the discrepancy in microstructural evolution under el excitation between UO2 and U3Si, the total and projected density of state distributi UO2 and U3Si with and without an electronic excitation concentration of 6.0% are trated in Figure 6.The Fermi level is set to be 0 eV.For ground state UO2, the band determined to be 1.89 eV without spin-orbital coupling compared with the experim value of ~2.1 eV [62].In the case of ground state U3Si, electrons are distributed Fermi level, indicative of metallic character, which agrees well with the experimen sults [24].Clearly, the electronic structure of ground state UO2 is very different fro of ground state U3Si, which may result in different responses of UO2 and U3Si to el excitation.For UO2, the valence band maximum is mainly contributed by U 5f or indicating that the valence electrons located at U 5f orbitals are relatively more eas cited.When the number of excited electrons is large enough, the excitation of U 5 trons induces charge redistribution, resulting in cation disordering and the genera O2-like molecules.As for U3Si, the U 5f electrons dominate the Fermi level.Therefo structural amorphization in U3Si is also driven by cation disordering.Since the el work function of the U element is as high as 3.63 eV, as described in [63,64], the ele in U3Si are more difficult excite than those in UO2.Consequently, the U3Si is more re to electron excitation than the UO2.

Conclusions
In summary, an AIMD simulation method is employed to investigate the response behaviors of UO 2 and U 3 Si to electron excitation at room temperature.It is found that a crystalline-to-amorphous phase transition can be induced in UO 2 with an electronic excitation concentration of 3.6%, whereas in U 3 Si, 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 UO 2 and U 3 Si might result in different responses to electron excitation.The UO 2 is an insulator, for which the U 5f valence electrons are relatively more easily excited, which drives anion disordering and eventually structural amorphization.U 3 Si 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 U 3 Si undergoes crystalline-to-amorphous structural transitions less easily than UO 2 when electronic excitation occurs, suggesting that U 3 Si has better potential under electron or laser irradiation as a nuclear fuel than UO 2 .

Figure 1 .
Figure 1.Schematic view of the geometrical structures of (a) UO2 and (b) U3Si.The grey, red, a blue spheres represent the U, O, and Si atoms, respectively.For UO2, anti-ferromagnetic ordering illustrated, and the "↑" and "↓" signs on U atoms denote spin up and spin down, respectively.

Figure 1 .
Figure 1.Schematic view of the geometrical structures of (a) UO 2 and (b) U 3 Si.The grey, red, and blue spheres represent the U, O, and Si atoms, respectively.For UO 2 , anti-ferromagnetic ordering is illustrated, and the "↑" and "↓" signs on U atoms denote spin up and spin down, respectively.

Figure 2 .
Figure 2. The radial distribution functions of (a) UO2 and (b) U3Si as a function of electronic exci tion concentration at 300 K.

Figure 2 .
Figure 2. The radial distribution functions of (a) UO 2 and (b) U 3 Si as a function of electronic excitation concentration at 300 K.

Figure 5 .
Figure 5. (a,b) The radial distribution functions and (c,d) mean square displacements of UO 2 and U 3 Si.The melted UO 2 and U 3 Si are simulated at a temperature of 5000 K above their melting points.The excited UO 2 and U 3 Si are simulated with an electronic excitation concentration of 6.0%.

Figure 6 .Figure 6 .
Figure 6.The total density of state distributions for (a) UO2 and (b) U3Si without and with a tronic excitation concentration of 6.0%; (c) partial density of state distributions projected on bitals of O atom and 5f orbitals of U atom of UO2 without and with an electronic exc Figure 6.The total density of state distributions for (a) UO 2 and (b) U 3 Si without and with an electronic excitation concentration of 6.0%; (c) partial density of state distributions projected on 2p orbitals of O atom and 5f orbitals of U atom of UO 2 without and with an electronic excitation concentration of 6.0%;(d) partial density of state distributions projected on 3p orbitals of Si atom and 5f orbitals of U atom of U 3 Si without and with an electronic excitation concentration of 6.0%.