A Comparative Study of Electron Radiation Responses of Pu2Zr2O7 and La2Zr2O7: An ab initio Molecular Dynamics Study

In this study, the response of Pu2Zr2O7 and La2Zr2O7 to electronic radiation is simulated, employing an ab initio molecular dynamics method. It is shown that Pu2Zr2O7 undergoes a crystalline-to-amorphous structural transition with 0.3% electronic excitation, while for La2Zr2O7, the structural amorphization occurs with 1.2% electronic excitation. During the microstructural evolution, the anion disorder further drives cation disorder and eventually results in the structural amorphization of Pu2Zr2O7 and La2Zr2O7. The difference in responses to electron radiation between Pu2Zr2O7 and La2Zr2O7 mainly results from the strong correlation effects between Pu 5f electrons and the smaller band gap of Pu2Zr2O7. These results suggest that Pu2Zr2O7 is less resistant to amorphization under local ionization rates that produce a low level of electronic excitation, since the level of the concentration of excited electrons is relatively low in Pu2Zr2O7. The presented results will advance the understanding of the radiation damage effects of zirconate pyrochlores.


Introduction
With the growing demand for nuclear power, the problem of how to treat nuclear waste safely, especially long-lived transuranic (TRU) elements such as plutonium (Pu) and minor actinides (Np, Am) that are generated through spent fuel, has become extremely important [1][2][3]. Pyrochlore-structured oxides with the general formula A 2 B 2 O 7 (A = Y or another rare earth element; B = Ti, Zr, Sn, or Hf) [4] exhibit a wide range of physical, chemical, and electrical properties, including high ionic conductivity, superconductivity, luminescence, and ferromagnetism [3]. A 2 B 2 O 7 pyrochlores, thus, are taken as attractive candidates for a variety of applications, including hosts for oxidation catalysts, solid electrolytes, oxygen gas sensors, as well as ceramic thermal barrier coatings [5][6][7]. Particularly great efforts have been devoted to evaluating the potential of pyrochlores as host matrices for immobilization of TRU elements [4,8,9].
Zirconate pyrochlores possess high thermal stability, high chemical durability, and remarkable resistance to radiation-induced amorphization, therefore being of special interest [10][11][12][13]. Wang et al. reported that Gd 2 (Zr x Ti 1−x ) 2 O 7 systems (x = 0, 0.25, 0.5, 0.75, 1) become increasingly radiation resistant with increasing zirconium content under 1 MeV Kr + irradiation [14]. Lian et al. found that among a series of A 2 Zr 2 O 7 pyrochlores (A = La, Nd, Sm, and Gd), only La 2 Zr 2 O 7 can be amorphized under ion-beam irradiation [15]. Sickafus and coworkers studied the irradiation response of Er 2 Zr 2 O 7 at a dose as high as 140 dpa by 350 KeV Xe + at room temperature and found that Er 2 Zr 2 O 7 cannot be amorphized [16]. Therefore, zirconate pyrochlores would be excellent candidate host matrices for the immobilization of plutonium (Pu) and minor actinides. 2 of 10 In the literature [17][18][19][20][21][22], atomic collision, electronic excitation, and ionization arising from the electronic energy loss of energetic ions have been used to explain the mechanisms of irradiation-induced amorphization. Sattonnay et al. investigated how the composition affects the behavior of pyrochlores under swift heavy ions irradiation and proposed that the susceptibility to amorphization by high electronic excitation is proportional to the cation radii ratio r A /r B [23]. Theoretically, the influence of low electronic excitation on microstructural evolution in titanate pyrochlores was explored by Xiao et al., who, using an ab initio molecular dynamics (AIMD) method, predicted that structural amorphization occurs under 2% electronic excitation at room temperature [24]. Sassi et al. investigated the interplay between electronic excitation, structure, and composition in lanthanumbased ceramics employing a similar method. They found that when monoclinic-layered perovskite La 2 Ti 2 O 7 is exposed to a lower degree of electronic excitation, the amorphous transition occurs, whereas a similar phenomenon does not occur in cubic pyrochlore La 2 Zr 2 O 7 [25]. Furthermore, their results show that La 2 Zr 2 O 7 can be amorphized at 200 K under 1.6% electronic excitation. These studies demonstrate that electronic excitation may have substantial effects on the microstructural evolution and physical properties of materials.
Thus far, it is not clear how Pu 2 Zr 2 O 7 pyrochlore, which is a product for immobilization of Pu in zirconate pyrochlores [26][27][28][29], responds to electronic excitation. In this study, a comparative study of the responses of Pu 2 Zr 2 O 7 and La 2 Zr 2 O 7 to electronic excitation is made to explore the behaviors of Pu 2 Zr 2 O 7 under electronic radiation. It is noted that discrepancies exist in microstructural evolution under electronic excitation between Pu 2 Zr 2 O 7 and La 2 Zr 2 O 7 . The possible reasons have also been explored. The presented results thus gain fundamental insights into the radiation damage effects of Pu 2 Zr 2 O 7 and may promote related experimental investigations.

Computational Details
Our calculations are carried out by the ab initio molecular dynamics (AIMD) method, as implemented in the Vienna Ab Initio Simulation Package (It was developed by the University of Vienna) (VASP) code [30,31]. In order to describe the exchange-correlation effects between electrons, the generalized gradient approximation (GGA) as parametrized by Perdew and Wang is used [32]. Because AIMD simulation is computationally very expensive, a 1 × 1 × 1 Monkhorst-Pack grid was generally employed in the AIMD simulation [24,33,34]. Hence, a 1 × 1 × 1 Monkhorst-Pack grid is employed in this study as a compromise between computational efficiency and computational accuracy. Computations are performed with a cutoff energy of 300 eV for the plane wave basis set. In our calculations, we employ a 2 × 2 × 2 supercell containing 88 atoms. The Hubbard U correction [35] is considered to modify the strongly correlated Pu 5f electrons, and a U eff value of 4 eV is employed [36].
To study the effect of electronic excitation, we remove several electrons from high-lying valence band states. A jellium background is used to compensate for the loss of charge due to electron removal. Within this approximation, one assumes that electrons move in the presence of a neutralizing background consisting of uniformly spread positive charge [37]. After the system reaches equilibrium states, the removed electrons are placed back to mimic the recombination of electrons and holes. This method has made it possible to simulate the role of electronic excitation and has been applied to simulate the structural amorphization of Ge-Sb-Te alloys [38] and pyrochlores [24,25]. For La 2 Zr 2 O 7 and Pu 2 Zr 2 O 7 , the considered electronic excitation concentrations are 0.3%, 0.6%, and 1.2%. Here, the percentage of electronic excitation concentration corresponds to the number of excited valence electrons to the number of total electrons. The intensity of the e-h pairs that are generated can be estimated by N e-h = [39], where F and ω 0 are the laser fluence and frequency, and R and α e f f are the reflectivity and effective absorption coefficient for the sample [40][41][42][43]. Under laser beam irradiation, the laser fluence at 400 nm for 1% excitation in La 2 Zr 2 O 7 is about 8.6 × 10 2 -4.9 × 10 3 mJ/cm 2 . The AIMD simulation is conducted employing an isothermal-isochoric ensemble, and the temperature is controlled by the Nosé-Hoover thermostat. The simulation time is 6 ps, and the time step is 3 fs. Structural optimization is first performed on Pu 2 Zr 2 O 7 and La 2 Zr 2 O 7 . The Schematic view of the geometrical structures of La 2 Zr 2 O 7 is shown in Figure 1. The calculated lattice constants, oxygen positional parameter x O8f , as well as bonding distances for Pu 2 Zr 2 O 7 and La 2 Zr 2 O 7 , are summarized in Table 1, along with the available theoretical and experimental results for comparison. For Pu 2 Zr 2 O 7 , the obtained lattice constant of 10.802 Å is slightly larger than the experimental value of 10.70 Å [44], whereas it is consistent with the theoretical result of 10.802 Å [36]. The lattice constant of La 2 Zr 2 O 7 is determined to be 10.879 Å, which is in reasonable agreement with the experimental value of 10.805 Å [45] and comparable to the calculated value of 10.696 Å [2]. The relatively larger lattice constant for La2Zr2O7 is mainly due to its larger ionic radius, i.e.,~1.16 Å for La 3+ and~1.1 Å for Pu 3+ [46]. With regard to oxygen positional parameter x O48f , the calculated value of 0.335 for Pu 2 Zr 2 O 7 is the same as other calculations of 0.335 [36]. For La 2 Zr 2 O 7 , the calculated value of 0.333 agrees well with the experimental and other calculated values [2,45]. Generally, the pyrochlores with the x O48f value being closer to 0.375 are more resistant to structural amorphization under ion irradiation [26,47]. It is noted that the x O48f value for Pu 2 Zr 2 O 7 is slightly larger than that of La 2 Zr 2 O 7 , suggesting that Pu 2 Zr 2 O 7 and La 2 Zr 2 O 7 may have different responses to ion irradiation.

Microstructural Evolution in La2Zr2O7 under Electronic Excitation
In order to explore the response of La2Zr2O7 to electronic radiation, AIMD simulations are first carried out with an electronic excitation concentration of 0.3%. Figure 2 shows a variation of temperature and total energy with time for La2Zr2O7 with 0.3% electronic excitation at 300 K. It is obvious that the simulation time of 6 ps is long enough so that the system can reach equilibrium states.

Microstructural Evolution in La 2 Zr 2 O 7 under Electronic Excitation
In order to explore the response of La 2 Zr 2 O 7 to electronic radiation, AIMD simulations are first carried out with an electronic excitation concentration of 0.3%. Figure 2 shows a variation of temperature and total energy with time for La 2 Zr 2 O 7 with 0.3% electronic excitation at 300 K. It is obvious that the simulation time of 6 ps is long enough so that the system can reach equilibrium states.

Microstructural Evolution in La2Zr2O7 under Electronic Excitation
In order to explore the response of La2Zr2O7 to electronic radiation, AIMD simulations are first carried out with an electronic excitation concentration of 0.3%. Figure 2 shows a variation of temperature and total energy with time for La2Zr2O7 with 0.3% electronic excitation at 300 K. It is obvious that the simulation time of 6 ps is long enough so that the system can reach equilibrium states. To investigate how the electronic excitation concentration affects microstructural evolution in La2Zr2O7 at 300 K, electronic excitation concentration of 0.3%, 0.6%, 1.2%, and 1.6% are considered. Based on each equilibrium state, the radial distribution function (RDF) analysis is then carried out. Figure 3 shows the RDF for La2Zr2O7 with 0.3%, 0.6%, 1.2%, and 1.6% electronic excitations. For electronic excitations of 0.3%, 0.6%, and 1.2%, it To investigate how the electronic excitation concentration affects microstructural evolution in La 2 Zr 2 O 7 at 300 K, electronic excitation concentration of 0.3%, 0.6%, 1.2%, and 1.6% are considered. Based on each equilibrium state, the radial distribution function (RDF) analysis is then carried out. Figure 3 shows the RDF for La 2 Zr 2 O 7 with 0.3%, 0.6%, 1.2%, and 1.6% electronic excitations. For electronic excitations of 0.3%, 0.6%, and 1.2%, it is noted that the structure is ordered at both short-range and long-range distances, meaning that La 2 Zr 2 O 7 still remains a pyrochlore structure. Here, the short-range correlation means the bonding interaction, and the long-range correlation corresponds to a nonbonding interaction. In the case of 1.6% electronic excitation, the structure retains a short-range order but has lost its long-range order, suggesting that 1.6% electronic excitation can induce a crystalline-to-amorphous transition in La 2 Zr 2 O 7 at room temperature. In the literature, a similar phenomenon was observed by Sassi et al. [25]. Variation of RDF with time for La 2 Zr 2 O 7 with 1.6% electronic excitation is displayed in Figure 4a. It is shown that the structural amorphization starts at t = 0.075 ps and the structure is completely amorphized at t = 0.3 ps, i.e., under 1.6% electronic excitation the crystalline-to-amorphous transition occurs very fast. Figure 4b shows a schematic view of the geometrical structure for La 2 Zr 2 O 7 with 1.6% electronic excitation. Compared with the pyrochlore structure presented in Figure 1, it can be seen that the structure is disordered after 1.6% electronic excitation. Furthermore, the degree of anion disorder is much larger than that of cation disorder. We also explore the variation of mean square displacement (MSD) with time for La 2 Zr 2 O 7 with 1.6% electronic excitation, and the results are presented in Figure 4c. It is found that the mean square displacement of oxygen is considerably larger than that of La and Zr. These results indicate that the displacement of oxygen drives the pyrochlore of La 2 Zr 2 O 7 to undergo a crystallineto-amorphous transition under 1.6% electronic excitation. Theoretically, Xiao et al. also suggested that the amorphization of titanate pyrochlores is mainly contributed by the displacement of oxygens [24]. Experimentally, Lian et al. found that under ion irradiation, anion disorder precedes cation disorder in Gd 2 Ti 2 O 7 , Er 2 Ti 2 O 7 , and La 2 Ti 2 O 7 [48]. In this study, it is noted that the MSD increases with the increasing time rather than vibrates slightly after the system reaches equilibrium states. A similar phenomenon has been found in the literature [49], where the La/Zr/O atoms in the amorphous structure also diffuse rather than vibrate at their equilibrium sites.
is noted that the structure is ordered at both short-range and long-range distances, meaning that La2Zr2O7 still remains a pyrochlore structure. Here, the short-range correlation means the bonding interaction, and the long-range correlation corresponds to a nonbonding interaction. In the case of 1.6% electronic excitation, the structure retains a short-range order but has lost its long-range order, suggesting that 1.6% electronic excitation can induce a crystalline-to-amorphous transition in La2Zr2O7 at room temperature. In the literature, a similar phenomenon was observed by Sassi et al. [25]. Variation of RDF with time for La2Zr2O7 with 1.6% electronic excitation is displayed in Figure 4a. It is shown that the structural amorphization starts at t = 0.075 ps and the structure is completely amorphized at t = 0.3 ps, i.e., under 1.6% electronic excitation the crystalline-to-amorphous transition occurs very fast.  Figure 4b shows a schematic view of the geometrical structure for La2Zr2O7 with 1.6% electronic excitation. Compared with the pyrochlore structure presented in Figure 1, it can be seen that the structure is disordered after 1.6% electronic excitation. Furthermore, the degree of anion disorder is much larger than that of cation disorder. We also explore the variation of mean square displacement (MSD) with time for La2Zr2O7 with 1.6% electronic excitation, and the results are presented in Figure 4c. It is found that the mean square displacement of oxygen is considerably larger than that of La and Zr. These results indicate that the displacement of oxygen drives the pyrochlore of La2Zr2O7 to undergo a crystalline-to-amorphous transition under 1.6% electronic excitation. Theoretically, Xiao et al. also suggested that the amorphization of titanate pyrochlores is mainly contributed by the displacement of oxygens [24]. Experimentally, Lian et al. found that under ion irradiation,

Microstructural Evolution in Pu 2 Zr 2 O 7 under Electronic Excitation
To explore how the Pu 2 Zr 2 O 7 pyrochlore responds to electronic excitation, AIMD simulation is also carried out on Pu 2 Zr 2 O 7 , in which 0.3% electrons are excited at 300 K. The corresponding variation of RDF with time for Pu 2 Zr 2 O 7 with 0.3% electronic excitation is illustrated in Figure 5a. We found that at t = 0.3 ps the structure becomes disordered at a long-range distance, and with time evolution, the structure is eventually completely amorphized. Compared with the case of La 2 Zr 2 O 7 , the crystalline-to-amorphous transition occurs more easily in Pu 2 Zr 2 O 7 , since the threshold electronic concentration of 0.3% is much lower than that of 1.6% for La 2 Zr 2 O 7 . These results suggest that the Pu 2 Zr 2 O 7 should be readily amorphized under local ionization rates that produce a low level of electronic excitation. Theoretically, Shen et al. suggested that the influences of different types of point defects on the thermomechanical properties of Pu 2 Zr 2 O 7 and Gd 2 Zr 2 O 7 show somewhat different character, and Pu 2 Zr 2 O 7 has been suggested to be more susceptible to radiationinduced amorphization than other zirconate pyrochlores like Gd 2 Zr 2 O 7 [50].
anion disorder precedes cation disorder in Gd2Ti2O7, Er2Ti2O7, and La2Ti2O7 [48]. In this study, it is noted that the MSD increases with the increasing time rather than vibrates slightly after the system reaches equilibrium states. A similar phenomenon has been found in the literature [49], where the La/Zr/O atoms in the amorphous structure also diffuse rather than vibrate at their equilibrium sites.

Microstructural Evolution in Pu2Zr2O7 under Electronic Excitation
To explore how the Pu2Zr2O7 pyrochlore responds to electronic excitation, AIMD simulation is also carried out on Pu2Zr2O7, in which 0.3% electrons are excited at 300 K. The corresponding variation of RDF with time for Pu2Zr2O7 with 0.3% electronic excitation is illustrated in Figure 5a. We found that at t = 0.3 ps the structure becomes disordered at a long-range distance, and with time evolution, the structure is eventually completely amorphized. Compared with the case of La2Zr2O7, the crystalline-to-amorphous transition To explore the origin of the structural amorphization induced by electronic excitation in Pu 2 Zr 2 O 7 , we plot the variation of mean square displacement with time for Pu 2 Zr 2 O 7 with 0.3% electron excitation in Figure 5c. It is shown that the mean square displacement of anions is considerably larger than that of cations. Figure 5b also shows that the disorder of anions is more significant than that of cations. These results suggest that the structural amorphization is also driven by anion disordering, similar to the case of La 2 Zr 2 O 7 discussed above and the cases of titanate pyrochlores reported by Xiao et al. [24]. occurs more easily in Pu2Zr2O7, since the threshold electronic concentration of 0.3% is much lower than that of 1.6% for La2Zr2O7. These results suggest that the Pu2Zr2O7 should be readily amorphized under local ionization rates that produce a low level of electronic excitation. Theoretically, Shen et al. suggested that the influences of different types of point defects on the thermomechanical properties of Pu2Zr2O7 and Gd2Zr2O7 show somewhat different character, and Pu2Zr2O7 has been suggested to be more susceptible to radiation-induced amorphization than other zirconate pyrochlores like Gd2Zr2O7 [50]. To explore the origin of the structural amorphization induced by electronic excitation in Pu2Zr2O7, we plot the variation of mean square displacement with time for Pu2Zr2O7 with 0.3% electron excitation in Figure 5c. It is shown that the mean square displacement of anions is considerably larger than that of cations. Figure 5b also shows that the disorder of anions is more significant than that of cations. These results suggest that the structural   Figure 6 presents the total and projected density of state (DOS) distributions for idealLa 2 Zr 2 O 7 and Pu 2 Zr 2 O 7 . For La 2 Zr 2 O 7 (see Figure 6a), O 2p orbital dominates and hybridizes with very few La 5d and Zr 4d orbitals at the valence band maximum (VBM), and few Zr 4d and O 2p orbitals contribute to the conduction band minimum (CBM). For Pu 2 Zr 2 O 7 (see Figure 6b), it is shown that the Pu 5f orbital dominates and hybridizes with very few O 2p and Zr 4d orbitals at the VBM, and the CBM are contributed by Pu 5f orbital and very few Zr 4d and O 2p orbitals. On the one hand, because of the strong correlation effects between Pu 5f electrons, the O 2p electrons in Pu 2 Zr 2 O 7 are more readily to be excited than Pu 5f electrons. On the other hand, in spite of the stronger <Pu-O> bonding interaction in Pu 2 Zr 2 O 7 than the <Zr-O> bonding interaction in La 2 Zr 2 O 7 at valence bands, the O 2p electrons in Pu 2 Zr 2 O 7 are more easily to be excited to the conduction bands due to the much smaller band gap. Consequently, anion disorder drives cation disorder and eventually results in structural amorphization.

Origin of the Different Electronic Radiation Responses between
than the values of ~2.635 Å for <La-O48f>, ~2.339 Å for <La-O8b>, and 2.106 Å for <Zr-O48f>, respectively. These results mean that stronger bonding interactions exist in Pu2Zr2O7 than in La2Zr2O7. However, the band gap of 2.12 eV for Pu2Zr2O7 is smaller than the value of 3.52 eV for La2Zr2O7, i.e., the valence electrons in Pu2Zr2O7 are more easily to be excited to the conduction bands if enough energy is provided. Figure 6 presents the total and projected density of state (DOS) distributions for ide-alLa2Zr2O7 and Pu2Zr2O7. For La2Zr2O7 (see Figure 6a), O 2p orbital dominates and hybridizes with very few La 5d and Zr 4d orbitals at the valence band maximum (VBM), and few Zr 4d and O 2p orbitals contribute to the conduction band minimum (CBM). For Pu2Zr2O7 (see Figure 6b), it is shown that the Pu 5f orbital dominates and hybridizes with very few O 2p and Zr 4d orbitals at the VBM, and the CBM are contributed by Pu 5f orbital and very few Zr 4d and O 2p orbitals. On the one hand, because of the strong correlation effects between Pu 5f electrons, the O 2p electrons in Pu2Zr2O7 are more readily to be excited than Pu 5f electrons. On the other hand, in spite of the stronger <Pu-O> bonding interaction in Pu2Zr2O7 than the <Zr-O> bonding interaction in La2Zr2O7 at valence bands, the O 2p electrons in Pu2Zr2O7 are more easily to be excited to the conduction bands due to the much smaller band gap. Consequently, anion disorder drives cation disorder and eventually results in structural amorphization.

Conclusions
In summary, the microstructural evolution in Pu2Zr2O7 and La2Zr2O7 under electron radiation has been investigated by ab initio molecular dynamics simulations. It is shown that Pu2Zr2O7 is more susceptible to electron radiation than La2Zr2O7, since the crystallineto-amorphous structural transition at 300 K occurs at 0.3% electronic excitation for Pu2Zr2O7 and 1.6% for La2Zr2O7. In both compounds, the degree of anion disorder is much larger than the degree of cation, i.e., the structural amorphization is driven by anion disorder. In Pu2Zr2O7, there are strong correlation effects between Pu 5f electrons, resulting in O 2p electrons being more readily excited. Furthermore, the band gap of Pu2Zr2O7 is

Conclusions
In summary, the microstructural evolution in Pu 2 Zr 2 O 7 and La 2 Zr 2 O 7 under electron radiation has been investigated by ab initio molecular dynamics simulations. It is shown that Pu 2 Zr 2 O 7 is more susceptible to electron radiation than La 2 Zr 2 O 7 , since the crystalline-toamorphous structural transition at 300 K occurs at 0.3% electronic excitation for Pu 2 Zr 2 O 7 and 1.6% for La 2 Zr 2 O 7 . In both compounds, the degree of anion disorder is much larger than the degree of cation, i.e., the structural amorphization is driven by anion disorder. In Pu 2 Zr 2 O 7 , there are strong correlation effects between Pu 5f electrons, resulting in O 2p electrons being more readily excited. Furthermore, the band gap of Pu 2 Zr 2 O 7 is much smaller than that of La 2 Zr 2 O 7 . Consequently, the O 2p electrons in Pu 2 Zr 2 O 7 are more easily to be excited to the conduction bands, and Pu 2 Zr 2 O 7 is less resistant to electron radiation than La 2 Zr 2 O 7 .