Insights on Amorphization of Lithium Aluminate from Atomistic

Mar 20, 2017 - ABSTRACT: We simulated amorphization of lithium aluminate by atomic displacement using molecular dynamics to understand the effect of ...
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Insights on Amorphization of Lithium Aluminate from Atomistic Simulation Wahyu Setyawan,* David J. Senor, and Ram Devanathan Energy and Environment Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States ABSTRACT: We simulated amorphization of lithium aluminate by atomic displacement using molecular dynamics to understand the effect of defects on fast lithium ion transport in disordered ceramics. We analyzed the evolution of the AlO4, LiO4, and OLi2Al2 tetrahedral clusters as a function of damage dose calculated in displacements per atom (dpa). The amorphization was associated with the loss of long-range ordering in the network of AlO4 tetrahedra, even though each AlO4 cluster remained tetrahedrally coordinated. The crystalline−amorphous transition occurred gradually within a dose range from 0.1 to 0.2 dpa. The structural damage also induced chemical composition separation, resulting in (Al + O)-rich and Li-rich regions. As a result of the disorder, the Li diffusion coefficient was found to increase to the order of 10−6 cm2/s.

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INTRODUCTION The formation of atomic-level defects and their influence on Li transport in Li-containing ceramics is of great interest for many energy technologies.1−3 In particular, lithium aluminate (LiAlO2) has potential applications in lithium polymer batteries,4 molten carbonate fuel cells,5 fusion reactor blankets,6−11 and tritium production using a nuclear reactor.12 γ-LiAlO2, along with Li2O, Li4SiO4, and Li2ZrO3, is attractive as a solid breeder material for tritium because of good thermophysical and chemical stabilities at elevated temperatures in addition to good tritium release characteristics.13,14 However, the phase stability can be compromised under neutron irradiation. In addition, defects and structural disorder may enhance the diffusion of Li within energy storage materials and breeders. In the case of the former, enhanced transport is desirable, while in the latter, it is detrimental to the chemical integrity of the materials and the tritium release characteristics. Therefore, it is essential to understand the effects of defect accumulation in γ-LiAlO2 and how the Li transport changes as the structural disorder increases. In this report, we focus on structural changes due to defect accumulation in γ-LiAlO2. Readers interested in the advantages of γ-LiAlO2 over other breeder materials can refer to the work of Roux et al.13 There are quantitative experimental studies on damage accumulation in γ-LiAlO2.15−17 For instance, Katsui et al. reported the accumulation of displaced O and Al atoms during irradiation with 10 keV deuterium ions or 10 keV helium ions at room temperature.16,17 Jiang et al. examined the accumulation of displaced Al atoms at higher temperatures, up to 773 K, during irradiation with 40 keV hydrogen ions and 90 keV helium ions.15 Experimental studies of defect accumulation in materials often report macroscopic effects and are limited in their ability to capture atomic level phenomena or transient © XXXX American Chemical Society

processes. Computer simulation using the molecular dynamics (MD) technique can provide information at length and time scales that are difficult to access in experiments and shed light on the atomistic processes governing defect accumulation and ion transport. There have been limited simulation studies18,19 of defect production in LiAlO2 using MD simulations, but the effects of damage accumulation in γ-LiAlO2 on Li transport have not been reported. In this work, we present such simulations and describe the structural changes of γ-LiAlO2 leading to amorphization.

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METHODS There is a limited set of interatomic (or interionic) potentials to model LiAlO2.20,21 Note that for simplicity, atoms and ions are used interchangeably throughout this paper. The more recent potentials by Tsuchihira−Oda−Tanaka (TOT)21 have been shown to sufficiently reproduce important properties, including lattice constants, elastic properties, defect formation energies, thermal expansion coefficients, and melting temperature. For our purpose of examining defect accumulation and the amorphization process, the melting behavior is particularly relevant. We verified the melting behavior by simulating a solid−liquid interface. The melting temperature is found to be 2000 K, in excellent agreement with experimental value of 1973 ± 20 K.22 Therefore, we employ the TOT potentials for our simulations. The potentials include the interpolation functions to transition to the Ziegler−Biersack−Littmark (ZBL) potentials23 needed to describe the short-range repulsion, Received: December 13, 2016 Revised: February 23, 2017 Published: March 20, 2017 A

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EEL denotes the electronic loss energy of a Li, Al, or O PKA impinging on a LiAlO2 crystal obtained from SRIM simulations. EPKA = Erecoil − EEL denotes the damage energy.

Al, and 37 eV for O based on a previous simulation.18 This approximation is necessary because the electronic effects are not directly included in MD simulations. The amount of energy available for MD atomistic damage is taken as the EPKA and calculated from Erecoil − EEL. Table 1 summarizes the value of Erecoil, EEL, and EPKA from this calculation. On the basis of the value of EPKA from Table 1, we performed a set of displacement cascade simulations using 4 keV Li, 2 keV Al, or 3 keV O PKAs. The simulation started with system equilibration at zero external pressure and temperature of 573 K for 10 ps with a time step of 0.25 fs. Then, a PKA was selected and given an initial kinetic energy (EPKA) with a random direction to initiate the collision cascade. To follow the collision cascade, we employed a variable time step algorithm that constrained the maximum displacement per time step to be 0.01 Å. The size of the simulation cell varied depending on the PKA energy and was large enough to contain the cascade within the cell. The collision cascade was simulated with constant number of atoms, volume, and energy (the NVE ensemble) except for atoms at the boundaries of the cell, which were coupled to a thermostat at 573 K to extract heat from the system. Defects were determined based on the occupancy of the Wigner−Seitz cells (constructed from an undamaged crystal), and the simulation was stopped when the number of surviving defects stayed unchanged, typically between 5 to 10 ps. For each type of PKA and EPKA, 10 simulations were performed to obtain good statistics. The number of defects produced is shown in Table 2. From Table 2, we averaged the defect production over different PKAs based on the concentration of Li, Al, and O in LiAlO2, i.e. (Li + Al + 2 O)/4, and denoted this average PKA as ⟨PKA⟩ to represent the concentration-weighted average. With a ⟨PKA⟩, the number of interstitials + antisites yielded a preferential displacement ratio of 16:9:13 between Li:Al:O surviving defects. We simplified this ratio as 2:1:2, which is also the proportion found by Tsuchihira et al.,18 as previously described. Our results confirmed that this ratio is relatively invariant with respect to PKA energies and PKA type, at least for the energy ranges that were explored in our study. On the basis of the above results, we simulated damage accumulation via sequential atomic displacements. In this method, a group of 5 atoms with a proportion of 2 Li, 1 Al, and 2 O atoms (the 2:1:2 proportion) was displaced with random displacement vectors within the simulation cell. The system was then equilibrated for 10 ps with a time step of 0.25 fs. The next group of atoms was randomly selected, and the process was repeated. The displacement procedure does not require the existence of a crystalline lattice. Therefore, one can continue to displace atoms by a certain distance from their position even after the system becomes amorphous. The equilibration was performed at zero pressure and 573 K (i.e., in an NPT ensemble) within a cubic box of 5 × 5 × 5 lattice units, containing 2000 atoms. Damage accumulation was simulated up to 1 dpa (i.e., 2000 atoms have been displaced). In the following section, we describe the results of the damage accumulation simulations.

each type of PKA (Li, Al, or O) with the corresponding Erecoil as the initial energy, we performed irradiation simulations with the SRIM code,28 which uses binary collision approximation to determine the amount of energy loss due to electronic effects (EEL). We considered the minimum energy to displace an atom, the displacement threshold energy, to be 22 eV for Li, 84 eV for

RESULTS AND DISCUSSION The structure of crystalline γ-LiAlO2 is depicted in Figure 1. The unit cell is tetragonal with lattice vectors (a, 0, 0), (0, a, 0), and (0, 0, c), where a = 5.12 Å and c = 6.17 Å at 0 K (obtained from simulations). These values agree well with experimental lattice constants a = 5.17 Å and c = 6.27 Å.29 Every ion is

allowing for high-energy atomic displacement cascade simulations.18 We performed all simulations using the LAMMPS code.24 There are a few ways to simulate damage accumulation. One may perform successive displacement cascades using primary knock-on atoms (PKAs) with a given initial velocity. Another way is to displace atoms individually, in which the distribution of displaced atoms is based on the distribution of surviving defects from a limited set of displacement cascade simulations. From our initial exploration, we found that Li PKAs or subsequent Li recoils often exhibit channeling in LiAlO2. The energetic atoms passed through the crystal along certain directions with minimal collisions. This phenomenon proves to be very costly when it comes to simulating damage accumulation via displacement cascades in ionic systems such as in LiAlO2 because of the need for an unusually large simulation cell and the expensive evaluation of the long-range Coulombic forces. Moreover, at high recoil energies, an extremely small time step (on the order of 0.003 fs) may be needed, and the recoil can travel a long distance (>250 Å) before it finally collides and undergoes a decrease in velocity. An important finding, however, is that the surviving defects in LiAlO2 were individual defects rather than defect clusters or loops that routinely occur in irradiated metals.25,26 For these reasons, we followed the latter method. We performed the simulations at 300 °C (573 K) based on the temperature of the tritium producing burnable absorber rod at the Watts Bar Unit 1 nuclear power plant.15 We visualized the atomic configurations using the OVITO software.27 To simulate the effects of atomic displacements, one needs to know the distribution of the surviving defects to be introduced into the simulation box to represent the effect of energetic recoils. Tsuchihira et al. simulated displacement cascades with their TOT potentials using oxygen PKAs.18 A range of PKA energies from 1 to 5 keV was explored. The results showed that the number of displaced atoms (i.e., interstitials + antisite defects) had a proportion of approximately 2 Li:1 Al:2 O. This ratio appears to depend rather weakly on the PKA energy. We explore more regimes of damage production by using Li, Al, or O PKAs. To model the PKA energies (EPKA), we considered a recent irradiation experiment in which 40 keV H+ ions were used.15 If we take a 40 keV H atom and collide it with a Li atom, we can calculate the average recoil energy (Erecoil) of the Li atom. We performed a similar calculation for Al and O recoils. Table 1 shows the value of Erecoil. Subsequently, with Table 1. Values of Average Recoil Energy, Erecoil, of Li, Al, or O If These Atoms Collide with a 40 keV Ha PKA

Erecoil (keV)

EEL (keV)

EPKA (keV)

Li Al O

8.9 2.8 4.5

4.6 0.7 1.4

4.3 2.1 3.1

a

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B

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The Journal of Physical Chemistry C Table 2. Defect Production for MD Displacement Cascade Simulationsa vacancies PKA 4 keV Li 2 keV Al 3 keV O ⟨PKA⟩

Li 9.5 7.5 11.8 10.2

± ± ± ±

interstitials + antisites

Al 0.9 0.8 1.4 1.2

1.7 2.2 2.3 2.1

± ± ± ±

O 0.6 0.6 0.7 0.7

10.7 9.2 14.3 12.1

± ± ± ±

Li 1.1 0.8 1.2 1.1

14.8 13.3 18.2 16.1

± ± ± ±

Al 1.3 0.9 2.7 1.9

7.8 8.3 10.2 9.1

± ± ± ±

O 1.3 0.9 2.7 1.9

11 ± 1.2 9.8 ± 0.8 15.0 ± 1.6 12.7 ± 1.3

a

Interstitials + antisites represent the number of atoms of a given type that are not at their own sublattice. The standard errors were calculated from 10 simulations. ⟨PKA⟩ denotes a concentration-weighted average PKA in LiAlO2.

(Al−O). Note that a LiO4 tetrahedron and an AlO4 tetrahedron share a common edge, while between LiO4 tetrahedra or AlO4 tetrahedra, there is a common vertex. A complete list of bond lengths and angles within those tetrahedra has been reported by Marezio.29 Figure 2 shows the evolution of the structure as a function of dose at 0.05, 0.1, and 0.2 dpa. LiO4 tetrahedra are shown in the top panels, while the AlO4 tetrahedra are shown in the bottom panels. The corresponding radial distribution function (RDF) for each type of bond in these structures is plotted in Figure 3. At 0.05 dpa, the RDF of all bond types exhibited well-defined peaks reminiscent of a crystalline phase. Clearly, long-range order was still preserved at this damage level. Correspondingly, the arrangements of the tetrahedra at 0.05 dpa (Figure 2) reveal that most of the material remained undamaged. Increasing the dose to 0.1 dpa significantly altered the structure. At 0.1 dpa, the peaks beyond 6 Å mostly disappeared in all of the RDFs. Evidently, the structure had lost long-range order. On the other hand, the RDFs of the Li−O and Al−O pairs still exhibited a dominant peak at around 2 Å. This indicates that the short-range ordering within the tetrahedra was still intact. The arrangements of the tetrahedra at 0.1 dpa reveal that the orientations of the tetrahedra became random. These randomly oriented tetrahedra resulted in the loss of long-range order. Nevertheless, there was a small region, shown in the lower right corner, where the tetrahedra were still

Figure 1. Structure of γ-LiAlO2 crystal with Li, Al, and O ions plotted as green, gray, and red spheres, respectively. The structure consists of an infinite network of Li-, Al-, and O-centered tetrahedra.

tetrahedrally coordinated. Each Li ion is surrounded by four O ions and forms a LiO4 tetrahedron. In a LiO4 tetrahedron, two O ions are 2.06 Å from the Li, and the other two are 1.95 Å away from the Li. Similar to Li, each Al forms an AlO4 tetrahedron. Because Al has an electropositive charge larger than that of Li, the AlO4 tetrahedron is more compact than the LiO4. In an AlO4 tetrahedron, the lengths of the Li−O bonds are 1.77 and 1.76 Å, and there are two bonds each. In an oxygen-centered tetrahedron, each O ion has 2 Li and 2 Al neighbors. The bond lengths in this OLi2Al2 tetrahedron are 2.06 Å (Li−O), 1.95 Å (Li−O), 1.77 Å (Al−O), and 1.76 Å

Figure 2. Snapshots of the structure of γ-LiAlO2 as a function of irradiation dose. Li, Al, and O ions are drawn as green, gray, and red spheres, respectively. In the top panels, Li-centered tetrahedra are shown, while the Al-centered tetrahedra are depicted in the bottom panels. C

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Figure 3. Radial distribution function of Li−Li, Li−Al, Li−O, Al−Al, Al−O, and O−O pairs at doses of 0.05, 0.1, 0.2, and 1 dpa.

Figure 4. Partitioning of the four nearest neighbors of Li, Al, and O, indicating that even though the structure had become amorphous, the tetrahedral clusters remained intact. In addition, it suggests compositional separation into (Al + O)-rich and Li rich regions.

relatively ordered, suggesting that the structure was not fully disordered. Increasing the dose to 0.2 dpa resulted in a complete randomness in the arrangement of the tetrahedra. Nevertheless, the RDFs of the Li−O and Al−O still exhibited a sharp first peak, i.e. the tetrahedral coordination was still preserved. We extended the analysis to 1 dpa and found the RDFs at 1 dpa (Figure 3) to be practically the same as those at 0.2 dpa. This finding indicates that the material had undergone a phase change from a crystalline structure to an amorphous state during irradiation and had been fully amorphized at 0.2 dpa. The amorphous state itself can be seen as a structure consisting of randomly oriented tetrahedra. The phase transition did not occur homogeneously throughout the material but rather over localized regions, as seen in the structure for a dose of 0.05 dpa shown in Figure 2. The gradual process of amorphization will be more evident in the following discussion.

Radiation damage not only induces structural modification but can also drive phase separation. To study the propensity for phase separation, we analyzed the chemical species of the four nearest neighbors (nn4) for each ion as shown in Figure 4. For example, in Figure 4a, the partition of the nn4 for a Li ion is presented. The plotted data was averaged over all Li ions. A similar averaging was done for the nn4 of Al and O ions. For a Li ion, where it has four O ions in a perfect material, the nn4 curve shows that Li started to lose some of the O neighbors and started to approach other Li ions as the dose increased. At about 0.15 dpa, the nn4 partition became 3.6 O + 0.4 Li. A closer examination revealed that a Li ion had either 4 O neighbors or 3 O + 1 Li neighbors. Therefore, the 3.6 O + 0.4 Li partition corresponds to a structure in which 60% of the Li had 4 O ions as their nn4, while 40% of the Li had 3 O neighbors +1 Li neighbor (i.e., 0.6 × 4 + 0.4 × 3 = 3.6 O and 0.4 × 1 = 0.4 Li). These results suggest phase separation took D

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The Journal of Physical Chemistry C place and that about 40% of the material became Li-rich. The same value of partition persisted to the amorphous state. Practically 100% of Al remained with four O ions as their nn4. Hence, compared to LiO4, the AlO4 tetrahedra were more stable against radiation damage. The nn4 partition of the O ions (Figure 4c) also suggests phase separation, in fact, a different region of phase separation compared to the Li-rich region. Starting from an ideal partition of two Al and two Li neighbors, the number of Al neighbors increased to 2.6, while the number of Li neighbors decreased to 1.4 as the dose reached 0.15 dpa. A careful look at the structure revealed that this partition corresponds to a structure in which 40% of the O ions still had the ideal partition (2 Li + 2 Al), 54% had 1 Li + 3 Al, 0.02% had 3 Li + 1 Al, and 0.04% had 4 Al neighbors. The trend of the partition evolution of O and Li (as described above) suggests that the structure had undergone a phase separation toward (Al + O)-rich region and Li-rich region. The same trend persisted to 1 dpa. Such compositional separation can be the precursor to the formation of LiAl5O8 as observed by Jiang et al.,15 Al2O3, or Li2O precipitates. From the above analysis, it is apparent that the gradual process of amorphization occurred within a dose range approximately from 0.1 to 0.15 dpa. The full amorphization was achieved at 0.2, and the amorphous structure persisted to the highest dose that is considered here (1 dpa). We note that the damage rate in the simulation (2.5 × 108 dpa/s) is much higher than a typical damage rate in experiments. Due to the high dpa rate, dynamic annealing of defects does not occur in the simulation. In comparison, there is a competition between damage accumulation and defect annealing in experiments. Thus, a simulated dose of 0.2 dpa is likely to correspond to a much higher experimental dose. The focus of the study is not to determine the amorphization dose but to study the structural disorder in an amorphous system and the effect of this disorder on Li transport. We have studied only one interionic potential and one simulation procedure. The amorphization dose may vary with the choice of potential and does not correspond to a specific experimental dose. We expect minimal variation with temperature except at very high temperatures near the melting point because of the high dpa rate used in the simulation. In Figure 5, a snapshot of the structure at 1 dpa is presented. First, the bonds clearly indicate tetrahedral coordination in this amorphous state. Second, local density variation can be seen throughout the material, showing hollow channels in some regions and denser network of ions in other regions. Nevertheless, the preservation of the tetrahedral coordination

throughout the material prevented the structure from completely phase separating or from forming voids. In the future, we will investigate the fate of this structure in the presence of H and He gas atoms. Phase transition from a crystalline to an amorphous state is often accompanied by swelling or densification,30−33 which can have an important effect on the physical stability and chemical reactivity of the materials. Figure 6 shows the changes in the

Figure 6. Increased density and decreased lattice constant of LiAlO2 as a function of dose. The unit cell is tetragonal, and the c/a ratio was invariant with dose; hence, only the value of a is shown.

density of LiAlO2 as a function of dose. The density increased from about 2.65 g/cm3 in the undamaged state (experimental value = 2.62 ± 0.01 g/cm3)22 to about 3.30 g/cm3 at 0.15 dpa. The density remained constant from 0.15 to 1 dpa. Evidently, the amorphous state was about 1.25 times denser than the crystalline state. Below 0.15 dpa, the material consisted of undamaged regions that were relatively open structures and damaged regions that were denser, as indicated in the snapshots of the structure at 0.05 dpa, shown previously in Figure 2. Clearly, the structure collapsed into a denser amorphous state upon prolonged irradiation. In neutron irradiated LiAlO2, the presence of helium gas and tritium will counteract this tendency toward densification. An experimental He and H ion irradiation study15 showed that there is negligible volume swelling in the amorphous LiAlO2. The gas bubbles in experiments will contribute to swelling that will counter the densification observed here. The net effect could be negligible volume swelling seen in experiments. In an amorphous state, the notion of point defects is no longer valid because the lattice sites can no longer be defined. However, we can study which displaced atom is more critical in driving the amorphization by looking at the number of point defects at the early stages of amorphization, i.e., below a dose of 0.1 dpa. Figure 7 shows the defect analysis based on the occupancy of the Wigner−Seitz cells. Note that the number of defects has been normalized with the number of the corresponding sublattices for each defect species. For example, in the 5 × 5 × 5 supercell, there are 500 Li, 500 Al, and 1000 O sublattices. The accumulation of vacancies, interstitials, and antisite defects as well as the number of ions that remain in their sublattices are shown in Figure 7. Among these accumulation curves, the accumulation of vacancies is particularly straightforward to relate to how the displacement of each type of ion influences the early stage of the

Figure 5. Snapshot of the structure of LiAlO2 at a dose of 1 dpa, revealing that tetrahedral coordination remained intact. E

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Figure 7. Partitioning of defects as a function of dose. The number of defects for each species is normalized with respect to the number of sublattices for that species in a perfect crystal.

measurements of the relative Al disorder in LiAlO2 subjected to H ion irradiation.15 In that experiment, the relative Al disorder increased sharply around 0.1 dpa and reached a saturation value of 0.3 when the dose levels exceeded 0.15 dpa. In the experiment, however, a second stage of increase was observed from 0.3 to 0.6 dpa. At 0.6 dpa, the relative Al disorder reached 0.5, which then saturated at this value beyond 0.6 dpa. To understand the driving force for the second stage increase, we note two phenomena that were observed in the experiment but absent in our simulations. These are the loss of Li to the surface and the subsequent formation of LiAl5O8 phase. The loss of Li will increase the fraction of Al compared to that in undamaged LiAlO2. Because the relative Al disorder was calculated based on the LiAlO2 molecular unit, the Al disorder appears to increase as the fraction of Al in the Lidepleted damaged structure increases. This could explain the second stage increase between 0.3 to 0.6 dpa. The subsequent formation of LiAl5O8 in the Li depleted damaged state effectively prevents additional Li loss because LiAl5O8 is stable and hence radiation tolerant at doses above 0.6 dpa. The radiation tolerance of LiAl5O8 could also explain the second plateau from 0.6 to 1 dpa. If the experiments were to be continued beyond 1 dpa, a third stage increase could potentially appear associated with the amorphization of the LiAl5O8 phase and further loss of Li. Therefore, it appears that the first stage increase is because of amorphization of LiAlO2, while the second stage increase is due to Li depletion mediated by enhanced Li transport after LiAlO2 becomes amorphous (as will be shown in the following paragraphs). While Li depletion has been commonly thought of as the cause of the formation of LiAl5O8, our simulations show that the phase separation

amorphization process. First, recall that the damage accumulation is simulated by displacing ions with a 2:1:2 proportion of Li:Al:O. In the early stage of damage where defect recombination is negligible, this would correspond to a vacancy/sublattice proportion of 2:1:1 because there are 1 Li, 1 Al, and 2 O per molecular unit of LiAlO2. As the damage increases, the proportion will change because of disproportionate interstitial-vacancy recombination. At about 0.1 dpa, we observed a proportion of about 0.2:0.34:0.2 = 1:1.7:1. In other words, there was a smaller proportion of Li vacancies (about twice as small) than what was introduced, while there was a larger proportion of Al vacancies (about twice as large). This suggests that the amorphization process was mostly driven by the displacement of Al ions from their sublattice. To verify this observation, we performed ad hoc simulations in which only one type of atom was displaced. We found that displacing only Li or only O did not cause amorphization, i.e., the crystalline phase was preserved practically throughout the material even at 1 dpa. On the contrary, displacing only the Al ions clearly induced amorphization, and the material was fully amorphized at about 0.06 dpa. These ad hoc simulations clearly show that the amorphization was mainly driven by the Al displacement. Because the displacement of Li or O alone practically does not induce amorphization, the effect of Li depletion (as in systems with free surfaces or interfaces with other materials) on the amorphization process is expected to be negligible. During the peak rate of the amorphization process near 0.1 dpa, the number of accumulated Al vacancies increased rapidly to 0.3 vacancies/sublattice. This number remained the same for higher doses. The Al interstitial curve also corroborates this trend. This finding is consistent with the experimental F

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least by a factor of 30. The observed structural and compositional transformations have critical implications for tritium retention in breeder blankets and in burnable absorber rods, as well as for the design of novel energy storage materials.

occurring during the amorphization of LiAlO2 may, by itself, facilitate the formation of LiAl5O8. The effect of these structural changes on Li transport can be seen from the plot of the diffusion coefficient of Li as a function of dose in Figure 8. The diffusion coefficient was determined

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Phone: +1-509-371-7692. ORCID

Wahyu Setyawan: 0000-0001-5192-8085 Author Contributions

The manuscript was written through contributions of all authors. W.S. and R.D. designed the simulations, and W.S. performed the simulations. W.S., D.J.S., and R.D. interpreted the results. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the National Nuclear Security Administration of the U.S. Department of Energy through the Tritium Technology Program at Pacific Northwest National Laboratory. Computation was performed using institutional computing resources at Pacific Northwest National Laboratory.

Figure 8. Li diffusion coefficient in LiAlO2 as a function of dose.

from the slope of the mean square displacement of Li as a function of time by annealing the system with constant number of atoms, volume, and temperature (the NVT ensemble) at 1000 K. The diffusion coefficient increased steadily with increasing disorder up to about 0.15 dpa and then remained mostly unchanged as the material became amorphous. The diffusion coefficient increased by about a factor of 30 during amorphization from 0.2 × 10−6 cm2/s at 0.01 dpa (slightly disordered state) to 5.9 × 10−6 cm2/s at 1 dpa (amorphous state). Disorder resulted in a dramatic increase in Li diffusion coefficient to the order of 10−6 cm2/s. Previous ab initio calculations34 have shown that expansion of the structure of a ceramic (rutile) can contribute to anisotropic Li diffusion with values of about 10−6 cm2/s along the c direction and 10−14 cm2/ s in the AB-plane. In addition, density functional theory calculations by Islam and Bredow3 have shown that Li diffusion in γ-LiAlO2 is strongly dependent on the presence of Li vacancies and interstitials. The present study shows that disorder in the crystalline lattice and regions of low density due to radiation damage can provide rapid migration pathways for Li. This finding has implications for the design of nanostructured or disordered materials to enhance Li transport for energy storage. In Li breeders and burnable absorber rods, the migration of Li ions to interfaces and surfaces may lead to unexpected changes in tritium inventory.

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ABBREVIATIONS PKA, primary knock-on atom; dpa, displacements per atom; RDF, radial distribution function; NVT, ensemble with constant number of atoms, volume, and temperature; NPT, ensemble with constant number of atoms, pressure, and temperature; NVE, ensemble with constant number of atoms, volume, and energy

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REFERENCES

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CONCLUSIONS Molecular dynamics simulations have shown that γ-LiAlO2 at 573 K was rapidly disordered at a dose between 0.1 and 0.2 displacements per atom, after which it became fully amorphous. The amorphization was caused by the displacement of Al ions from their lattice sites. However, the tetrahedral coordination within AlO4 clusters remained intact, resulting in an amorphous structure that consisted of randomly oriented AlO4 clusters. The collapse of the ordering of the AlO4 tetrahedra during the amorphization process induced overall densification and phase separation into Al- and O-rich and Li-rich regions. Regions of lower density were found within the disordered structure. As a result of this disorder, Li diffusion was enhanced significantly, at G

DOI: 10.1021/acs.jpcc.6b12562 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

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DOI: 10.1021/acs.jpcc.6b12562 J. Phys. Chem. C XXXX, XXX, XXX−XXX