One-dimensional yttrium silicide electride (Y₅Si₃:e⁻) for encapsulation of volatile fission products

Spent nuclear fuel is reprocessed to extract the unused fissile ²³⁵U and reduce waste volumes.^1–5 This gives rise to a substantial volume of fission product containing effluents. If fission products can be separated, the effluent can be treated as a lower hazard material. The fission products (Xe, Kr, Br, I, Rb, Cs, and Te) are of particular concern as they can escape from the fuel as a consequence of various issues, including nuclear power plant accidents and natural crisis. Radioactive iodine (¹³¹I) is important because it can be absorbed at high concentration by the human thyroid gland leading to several thyroid disorders.^3,6,7 Radioactive cesium (¹³⁷Cs) is also of concern as it causes damage to human organs, such as kidney and lungs.^8–10 Thus, special provision must be made for effective and safe disposal of volatile fission products in order to reduce the risk of release.

Impregnated carbon or charcoal filters are most commonly used to trap iodine in a nuclear plant.¹¹ The preference for this type of filter is due to its large trapping surface area and low production cost.¹¹ Alternative materials, such as silica, zeolites, alumina, silver nitrate, metal organic frameworks, and porous organic polymers, have been examined in order to find a more efficient trapping medium.^12–15 The efficiency of the filters depends upon the properties of the filter material: their thermal and mechanical stability, surface area, and chemical species specificity. The search for alternative filter materials continues in order to reduce the potential impact on the environment and humans.

Electrides are a class of materials where electrons serve as loosely bound anions.¹⁶ Based on electron localization, they fall into three categories: zero-dimensional (electrons residing in cavities),^17,18 one-dimensional (electrons in a channel),^19,20 and two-dimensional (electrons localizing in a layer).²¹ A zero-dimensional “mayenite” type electride, [Ca₂₄Al₂₈O₆₄]⁴⁺•(e⁻)₄, has been widely studied due to its utility as a catalyst for NH₃ synthesis and CO₂ depletion, an electron emitter, and a superconductor.^22–28 Different types of atoms and molecules have been encapsulated experimentally to examine the effectiveness of encapsulation and studied theoretically to understand how encapsulation modifies the electronic properties of this electride.^27–32 

Zhang et al.²⁰ first reported the structure of the apatite based one-dimensional electride [La₈Sr₂(SiO₄)₆]⁴⁺•(e⁻)₄, though its practical utility had not yet been established. An experimental report of the two-dimensional dicalcium nitride electride [(Ca₂N)⁺•e⁻] by Lee et al.²¹ shows that this electride is stable at room temperature and exhibits an open layer structure with high electron concentration and a low work function of 2.6 eV. This electride has been tested with regard to application in sodium ion batteries³³ and solid lubricants.³⁴ 

The air and water stable one-dimensional electride yttrium silicide (Y₅Si₃:e⁻) was first reported by Lu et al.³⁵ This material is a candidate for trapping volatile fission products due to its chemical stability, facilitated by the strong hybridization between yttrium 4d electrons and anionic electrons available in the quasi-one-dimensional channels. The number of anionic electrons per formula is predicted to be 0.79 with the effective formula of the electride then described as [Y₅Si₃]^0.79+:0.79e⁻.³⁵ Ru-loaded Y₅Si₃:e⁻ is catalytically highly efficient for ammonia synthesis because the anionic electrons enhance the nitrogen cleavage and reduce the associated activation energy.³⁵ 

In this study, spin-polarized mode density functional theory (DFT) is used to calculate the structures associated with volatile fission products (Kr, Xe, Br, I, Rb, Cs, and Te) encapsulated in Y₅Si₃:e⁻, their associated encapsulation energies, charge transfer, electronic structures, and charge densities.

All calculations were performed using the DFT code VASP (Vienna ab initio Simulation Package).³⁶ This code solves standard Kohn–Sham equations using plane wave basis sets and projected augmented wave (PAW) pseudopotentials.³⁷ In the PAW method, projectors and auxiliary functions are introduced similar to the ultra-soft pseudopotential method and the total energy function includes auxiliary functions. Furthermore, this method keeps the full all-electron wave function as opposed to the other pseudopotential methods in which only valence pseudowave functions are kept. In all calculations, a plane wave basis set with a cutoff of 500 eV and an 4 × 4 × 8 Monkhorst–Pack³⁸ k-point mesh were employed. Further increase in the k-points to 6 × 6 × 12 resulted in a total energy difference of only 0.8 meV per atom. The exchange–correlation energy was modeled using the generalized gradient approximation (GGA) scheme as defined by Perdew, Burke, and Ernzerhof (PBE).³⁹ All defect calculations were performed using a 2 × 2 × 2 supercell containing 128 atoms (Y:80 and Si:48). The conjugate gradient algorithm⁴⁰ was used to perform full geometry optimization (both atom positions and lattice constants were relaxed simultaneously). In all relaxed configurations, forces on the atoms were less than 0.001 eV/Å. The following equation was used to calculate single atom encapsulation energies within Y₅Si₃:e⁻:

where $E(X@Y5Si3:e−)$ is the total energy of a single fission atom encapsulated in a 2 × 2 × 2 supercell of $Y5Si3:e−$⁠, $E(Y5Si3:e−)$is the total energy of a 2 × 2 × 2 supercell of $Y5Si3:e−$⁠, and $E(X)$ is the energy of an isolated gas phase fission atom. A semiempirical dispersion term was used to describe short-range interactions.⁴¹ 

At room temperature, yttrium silicide exhibits an hexagonal phase with the space group P6₃/mcm (193), a = b = 8.403 Å, c = 6.303 Å, α = β = 90°, and γ = 120°, as shown in Fig. 1(a).⁴² There are two non-equivalent Y sites. The first Y site forms three coordination with adjacent Si atoms. The second Y is bonded to six nearest neighbor Si atoms forming a six-coordinate geometry. The crystal structure of Y₅Si₃:e⁻ was relaxed under constant pressure to obtain equilibrium lattice constants to validate the quality of the basis sets and pseudopotentials. Table I reports the calculated lattice parameters together with experimental values: it is evident that there is a good agreement between the calculated and experimental values.

The one-dimensional electron distribution and the total density of states (DOS) plots are shown in Figs. 1(b) and 1(c), respectively. Y₅Si₃:e⁻ exhibits metallic behavior in agreement with a DFT study performed by Lu et al.³⁵ 

Relaxed structures of Y₅Si₃:e⁻ with encapsulated Kr and Xe are shown in Fig. 2. Endoergic encapsulation energies are calculated for both Kr and Xe inferring their instability within the lattice (see Table II). The encapsulation energy calculated for Kr is less unfavorable than Xe due to the smaller atomic radius of Kr than Xe.⁴³ This is further evidenced by the shorter Y–Kr bond length and smaller volume change predicted for Kr (see Table II). According to Bader charge analysis,⁴⁴ both noble gas atoms gain a small negative charge (Kr: −0.40 and Xe: −0.48) due to the polarization between the one-dimensional holes along the c axis and the noble gas atoms. The smaller value for Kr reflects the smaller polarizability of Kr.

Total DOS plots predicted for structures with Xe and Kr are almost identical to the DOS plot of encapsulant free Y₅Si₃:e⁻ (compare Figs. 1 and 2). Atomic DOS plots show that p-states belonging to Kr and Xe appear deep (∼−5 eV) in the valence band. Charge density plots show that encapsulation resulted in no charge transfer from the lattice to Kr (or Xe).

The encapsulation energies for Br and I are highly negative (favorable) with respect to their isolated atom reference states. This is due to the strong electron affinities of these species (see Table III), reflected in the negative Bader charges. Both Br and I gain almost one electron from the extra-framework electrons localized in the one-dimensional channel, meaning that both Br and I are tending toward Br⁻ and I⁻, respectively, close to completing their p-shells (p⁶). The encapsulation energy of Br is more favorable than that of I due to its smaller atomic radius.⁴³ This is reflected in the shorter bond length of Y–Br than Y–I.

The exothermic endoergic encapsulation energy calculated using ½X₂ (X = Br and I) as the reference indicates that both Br and I are still stable inside Y₅Si₃:e⁻, despite there being an energy penalty to dissociate their diatomic molecules. The calculated dissociation energies (per atom) for Br₂ and I₂ are 1.26 and 1.12 eV, respectively. Despite the higher dimer dissociation energy for Br than I, Br exhibits a strong encapsulation energy.

Although encapsulation of Br and I results in a reduction of states associated with free anionic electrons at the Fermi level in the total DOS plots, at this concentration of encapsulation, these materials retain their metallic character (see Fig. 3). There is, however, an accumulation of charge density around the encapsulated atoms in the one-dimensional channel. Encapsulation introduces a slight increase in the overall volume. The larger atomic radius of I is reflected in a larger increase in the total volume (see Table III).

Te demonstrates a strong negative (favorable) encapsulation energy (see Table IV). This is due to the transfer of 1.42 electrons to Te. The large Bader charge of 1.42 |e| means that Te is tending to the stable Te²⁻ ion electronic configuration. A highly exothermic encapsulation energy is also calculated with respect to the dimer, despite the strong Te₂ dissociation energy of 1.46 eV per atom.

At this level of Te encapsulation, the material maintains its metallic character [see Fig. 4(b)]. That is, free electrons are left in the one-dimensional channel. Though a single Te atom can gain only part of the electron density from the channel, the volume increase for Te is larger than for I, due to the larger size of Te²⁻ than I⁻. The accumulation of electrons by Te is confirmed in the charge density plot where charge density is more localized on Te than the remaining lattice.

The relaxed configurations associated with Rb and Cs encapsulation are shown in Fig. 5 with the encapsulation energies and the Bader charges reported in Table V. Both Rb and Cs exhibit positive encapsulation energies (2.28 and 2.51 eV, respectively). This is due to their low electron affinities and large size. Bader charge analysis shows that both Rb and Cs are polarized with small positive charges (0.29 and 0.01, respectively). While Rb and Cs readily donate their outmost s¹ electrons to form stable noble gas electronic configurations, this is not the case in this electride material as channel space has already accommodated electrons.

The total DOSs calculated for Rb and Cs containing materials remain metallic (see Fig. 5). Both total DOS and charge distributions are not significantly altered in either case.

The relaxed structures of Br₂, I₂, and Te₂ dimers occupying channel positions are shown in Fig. 6. The encapsulation energies and Bader charges are reported in Table VI. Encapsulation energies calculated using the molecular reference state predict that the encapsulation is favorable and only slightly less favorable than when these anions are encapsulated as separated species (compare with energies in Tables III and IV). The molecular dimer bond lengths inside the channel are significantly longer than their corresponding gas phase dimers (which are 2.31, 2.69, and 2.58 Å for Br₂, I₂, and Te₂, respectively). Furthermore, negative Bader charges (see Table VI) on the atoms of dimers confirm the formation of adjacent anion pairs rather than molecules. Nevertheless, this suggests that the electride is capable of accommodating high concentrations of Br and I as anions.

The encapsulation of fission products is expected to take place via the surface of the Y₅Si₃:e^– with the involvement of kinetic barrier. There is lack of experimental date available on the surface structure of this electride leaving the modeling of surface structures difficult for this electride. Future work should model the surface structures and calculate the activation energies and the diffusion pathways for these fission products.

Atomic scale simulation based on DFT has been used to examine the thermodynamic efficacy of Y₅Si₃ as a filter material to encapsulate volatile fission products. It is found that encapsulation is unfavorable for Kr, Xe, Rb, and Cs. Conversely, strong encapsulation energies are predicted for Br, I, and Te with significant charge transfer from this electride's confined electrons to the encapsulated species. This results in the formation of stable Br⁻, I⁻, and Te²⁻ anions. Encapsulation of Br₂, I₂, and Te₂ dimers resulted in the dissociation of molecules and the formation of separated anion pairs. In conclusion, Y₃Si₃ electride is a promising filter material to trap Br, I, and Te from effluent gases released in the processing of spent nuclear fuel.

Computational facilities and support were provided by the High Performance Computing Centre at Imperial College London. The authors declare that there is no competing financial interest.

The data that support the findings of this study are available from the corresponding author upon reasonable request.