Molecular dynamics simulations of radiation response of LiAlO2 and LiAl5O8
Introduction
LiAlO2 pellets are a critical component of tritium (T or ) producing burnable absorber rods (TPBAR) [1,2] where a specific loading per unit length of enriched 6Li is used in the pellets for a variety of national security applications. It also finds important applications in composite electrolytes where it is used as an additive [3], a substrate for the growth of III-IV semiconductors like GaN [4] and as a membrane for molten carbonate fuel cells [5]. When γ-LiAlO2 is enriched with 6Li, this isotope absorbs neutrons when irradiated in a light water reactor (LWR) and produces tritium through the reaction . The tritium can be retained in the pellet or diffuse to its surface. This reaction causes a substantial loss of Li atoms under irradiation resulting in the formation of a Li-poor secondary phase of the type LiAl5O8 [6,7] via the reaction, 5 LiAlO2 → LiAl5O8 + 4 Li (displaced) + 2 O (displaced), which was also confirmed by a recent report [8]. The precipitated LiAl5O8 participates in further T generation and diffusion. Since the displacement of Li from the lattice may cause structural damage to the ceramic, we investigate the Li diffusion and atomic displacement processes in the two ceramics to gain a perspective of the radiation response of these materials. Radiation damage is a consequence of energetic recoils in a solid material where an atom gets knocked off from its original site leaving behind a vacancy. The minimum energy required to transfer an atom from its original site, leaving behind a permanent defect is called the displacement threshold energy, Ed. Experimentally it is difficult to measure Ed as it is challenging to isolate the displacement of a particular type of atom in a multi-element system. Computational investigations, especially MD simulations, can play a crucial role in determining Ed for each sublattice. The goal of the present work was to compare the Li diffusion and cation threshold displacement energies in the two ceramics to assess their radiation tolerance by using MD simulations.
Before delving into the calculations, a thorough understanding of the structures of the two ceramics is required. γ-LiAlO2 has a tetragonal structure derived from beta beryllia [9]. The γ-LiAlO2 crystal consists of a three-dimensional network of distorted XO4 tetrahedra (X = Li, Al) where each tetrahedron is composed of a Li/Al metal atom at the center and oxygen atoms at the corners, as shown in Fig. 1(a). Each Li (Al) tetrahedron has one edge shared with an Al (Li) tetrahedron. In addition, each oxygen at the vertex is shared by four tetrahedra, two each of Li and Al. Such an arrangement creates quadrangular channels along the [001] direction giving rise to a linear order of octahedral voids as shown in Fig. 1(b).
LiAl5O8 has a Spinel-like cubic crystal [9]. It is composed of a three-dimensional network of Li/Al-O6 octahedra that share edges. This network of octahedra has corners linked by Al-O4 tetrahedra as depicted in Fig. 2. A unit cell of LiAl5O8 consists of 4 Li, 20 Al and 32 O atoms. The formula can be expressed as (Al)tet(Li1/2Al3/2)octO4 where every Li ion is always enclosed in an octahedron and located at 4d Wyckoff sites, 3 out of 5 Al ions are enclosed in octahedra and are located at 12d Wyckoff sites while the other 2 Al are enclosed in tetrahedra thereby being located at 8c Wyckoff sites [9]. Every Li-O6 octahedron shares an edge with 6 Al-O6 octahedra while 6 other Al-O4 tetrahedra form the second nearest neighbors of the Li ion.
A thorough understanding of diffusion of Li species in these ceramics is essential to characterize the tritium release of the material because tritium diffusivity is, to some extent, correlated to the Li migration mechanism [10]. There have been several experimental [11], [12], [13], [14] and computational [15], [16], [17] efforts that have investigated Li ion migration in γ-LiAlO2 and calculated its diffusion coefficients and activation barriers. One study found Li ion diffusion to be the cause of extrinsic conductivity at temperatures of 200 °C [11]. Another study investigated the dynamics of Li ions experimentally and found its activation energy to be between 0.7 and 1.26 eV [12]. This study proposed that the actual migration path may be more convoluted and longer than the distance to the next closest Li vacancy, and that it may be taking place via interstitial sites that are octahedrally coordinated or via channels existing in the crystal. A more specific study on γ-LiAlO2 revealed that Li-O bonds break on heating and Li atoms can migrate from one tetrahedral site to the next with an activation energy of 0.5–0.8 eV [13]. This investigation has been supported by results from a neutron diffraction study indicating a rather curved jump path between adjacent lithium sites [18]. On the computational side, the first ever work using MD found a Li diffusion coefficient of 2.8 10−11 m2/s at 600 K and an activation energy of 0.52 eV [15]. Other recent MD works carried out by Setyawan et al. investigated irradiation damage processes in γ-LiAlO2 and found that Li defects account for about 70% of the damage and LiO4 tetrahedra are more prone to damage as compared to the AlO4 tetrahedra [19] with the diffusion coefficient of Li ions in the crystalline state lying in the order of 10−10 m2/s at 573 K [20]. Furthermore, density functional theory computations carried out by Islam and Bedrow [17] have shown that Li diffusion is strongly determined by the presence of Li point defect and Frenkel defect. An in-situ study with 25 keV He+ ion irradiation with fluence on the order of 1017 He+/cm2 [21] on polycrystalline γ-LiAlO2 found that at a depth of < 50 nm from the surface, the Li concentration approaches to zero, indicating that almost all Li atoms were released to vacuum during the ion implantation. This evinces that Li mobility is orders of magnitude larger than that of Al under irradiation damage.
Regarding the displacement threshold energy, MD has previously been used to determine Ed in a variety of systems ranging from pure metals like Mo [22], Fe [23] and V [24] to metal oxides like MgO [25], Gd2Ti2O7 [26] and MgAl2O4 [27]. While there have been extensive computational and experimental investigations into the atom displacement energetics of γ-LiAlO2, much less is known about defects and diffusion in LiAl5O8. With regards to γ-LiAlO2, Tsuchihira et al. [28] calculated the threshold displacement energies for Li, O and Al by using a MD potential developed by the same group earlier in 2009. They complemented the investigation by performing cascade simulations and found that Li formed the greatest number of defects owing to its low displacement energy of 22 eV as compared to 84 eV for Al and 37 eV for O.
While there have been extensive computational and experimental investigations into the diffusion and radiation response of γ-LiAlO2, much less is known about the same in LiAl5O8. A major reason for the lack of MD efforts on LiAl5O8 is the unavailability of interatomic potential for this system. As stated earlier, radiation causes rapid transmutation of Li into T and helium, γ-LiAlO2 is deprived of Li and the sub-stochiometric composition leads to the formation of considerable amount of the secondary phase LiAl5O8 [7]. Devaraj et al. [7] found that there is a loss of ∼ 50% 6Li enrichment in neutron irradiated LiAlO2 pellets in tritium producing burnable absorber rods (TPBAR) when the pellets were irradiated for a period of 18 months. Therefore, it is compelling to investigate the diffusion and radiation response of both these ceramics, as they coexist in the same component in the application area. We are not aware of any previous work that investigates lithium transport or displacement energetics in LiAl5O8.
Therefore, in the present work, we have proposed and established the validity of an existing Li-Al-O potential for MD calculations of LiAl5O8. This validation opens possibilities for further MD based investigations into irradiation-induced defects in these ceramics. Leveraging this potential, we performed MD simulations to calculate the lithium diffusion and displacement energetics in LiAlO2 and LiAl5O8. The results reveal higher lithium vacancy migration barrier and lower lithium interstitial migration barrier in LiAl5O8 leading to superior dynamic annealing in the latter crystal. The displacement energetics reveal that lithium displacement energies are higher in LiAl5O8 leading to superior damage tolerance than LiAlO2. The present work predicts that radiation tolerance of LiAl5O8 will be superior to that of LiAlO2 based on differences in defect production and Li diffusion observed in the two ceramics.
Section snippets
Proposed potential selection
There are only a few interatomic potentials for modeling the Li-Al-O system, namely the Jacob et al. potential developed in 1996 [15], the Tsuchihira−Oda−Tanaka (TOT) [29] potential developed in 2009, and the interactions proposed by Kuganathan et al. [30] in 2019. Jacob's potential is not suitable to our study because it has not been found to be very accurate in terms of generating a stable structure [19]. The TOT potential has been well established for the LiAlO2 system. But for our work we
Results and discussions
The optimized structural properties of γ-LiAlO2 and LiAl5O8 are shown in Fig. 3(a) and (c) respectively. The densities obtained were 2.48 gm/cc for LiAlO2 and 3.42 gm/cc for LiAl5O8 which are close to the experimental densities of 2.53 gm/cc [9] and 3.52 gm/cc [9] respectively thereby providing a good initial validation of the potential used for both systems. The bond distances obtained with these potentials are listed in Table 2 for LiAlO2 and Table 3 for LiAl5O8. For LiAlO2 the results are in
Conclusions
It is known that under neutron irradiation of LiAlO2 containing 6Li, LiAl5O8 can form due to orders of magnitude higher mobility of Li than Al or O atoms. We have used molecular dynamics simulations to compare, for the first time, defect production, Li defect migration energies, and Li diffusion in LiAlO2 and LiAl5O8. Li diffusion by the vacancy mechanism was one order of magnitude slower in LiAl5O8 (D0 = 3.17 × 10−11 m2/s) compared to that in LiAlO2 (D0 = 4.02 × 10−10 m2/s) at a temperature of
CRediT authorship contribution statement
Ankit Roy: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing – original draft, Writing – review & editing, Visualization. David J. Senor: Methodology, Resources, Writing – review & editing, Funding acquisition. Andrew M. Casella: Writing – review & editing. Ram Devanathan: Conceptualization, Methodology, Funding acquisition, Writing – review & editing, Project administration, Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The research was supported by the National Nuclear Security Administration of the US Department of Energy (DOE) through the Tritium Technology Program at Pacific Northwest National Laboratory.
The authors thank Professor Julian D. Gale (Curtin University, Australia) for valuable discussion, comments, and advice.
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