The management of nuclear waste is a complex and multifaceted issue that requires meticulous attention to safety for long-term sustainability. Nuclear energy produces sizeable quantities of nuclear waste (World Nuclear Association, 2021; U.S. Energy Information Administration, 2022), which can impose danger if not properly contained. In this context, materials science plays a vital role in developing innovative solutions for the safe storage and study of nuclear waste (Beierschmitt et al., 2017).

Rare-earth (RE) compounds, a class of materials with unique properties, play a pivotal role in forming substances to solve the nuclear waste challenges the country faces (Chong et al., 2022). Depending on the level of waste, the primary types of materials used include glass, ceramics, cement, and various composites (Hyatt and Ojovan, 2019; Rafiuddin et al., 2022). Stored nuclear waste holds varying levels of lanthanides and actinides that can form unknown compounds depending on their environment. As actinides exhibit high radioactivity, studying their compounds can pose safety risks that prevent a thorough analysis. Lanthanides offer a safer alternative. As both are in the f-block, actinides can be modeled by their lanthanide counterpart to safely study potential formations occurring in stored waste.

Among the 4f elements, or the lanthanides, neodymium has been of particular interest due to its remarkable magnetic properties (Behrendt et al., 1957), ductility (Wu et al., 2013), and its influence as a dopant in various compounds (Roy et al., 2012; Butenkov et al., 2023). More notably, neodymium is commonly known for its involvement in the permanent magnet Nd₂Fe₁₄B (Boller and Oesterreicher, 1984) and in the lasing medium of an Nd:YAG laser. Alongside its popular uses, neodymium can be used to substitute the actinide uranium. Since the two hold the same number of electrons within the outermost shell, they may exhibit similar bonding formations in their respective compounds. In addition, rhenium can be used to study compounds formed between technetium and actinides during containment. Technetium, a long-lived radioactive element produced during nuclear fission, is specifically targeted for immobilization due to its radioactive nature and potential environmental impact (Hartmann et al., 2011). Technetium shares similar chemistry to rhenium (Darab and Smith, 1996), allowing rhenium to model technetium during experiments. As uranium and technetium are radioactive, direct studies prove to be challenging due to the inherent safety risks. Using similar nonradioactive elements allows us to mimic the radioactive compounds found in nuclear waste for further study.

Laves phase compounds have previously been of immense interest due to their potential applications, such as usage in superalloys and high-temperature steels (Stein and Leineweber, 2021). A large portion of known Laves phase compounds hold an RE element (Villars and Calvert, 1991), and while many are known, there may be an abundance of unknown compounds. Within the neodymium rhenium system, only the hexagonal NdRe₂ (space group P6₃ /mmc) (Elliott, 1964) has been previously synthesized. This hexagonal structure is common among the lanthanides (excluding La, Ce, Pm) (Elliott, 1964; Savitskii and Khamidov, 1965) and some actinides (Th, U, Np, Pu) (Giorgi and Szklarz, 1970; Lam and Mitchell, 1972; Haines et al., 1976). It is also seen in several RE-Tc (Darby et al., 1962; Darby et al., 1964; Szklarz and Giorgi, 1981) and actinide-Tc (Darby et al., 1965) compounds. RE-Re alloys have been previously synthesized through arc-melting and liquid-phase sintering (Elliott, 1964). While useful, these methods often have difficulties in providing pure crystalline phases. High-pressure high-temperature (HPHT) synthesis could be a great alternative. Compared to other methods, HPHT synthesis allows for greater control of sample composition and enables us to obtain metastable materials. In addition, its ease of use and compatibility with X-ray diffraction and spectroscopy tools encourage extensive exploration of material behavior under extreme conditions.

Multiple high-pressure studies were conducted on various compounds holding RE and transition metal elements. This includes the HPHT synthesis of YbZn₂ (Salamatin et al., 2023) and REFe₂ (RE = Pr, Nd, Yb) (Cannon et al., 1972), the pressure-induced structural transitions in R_1-xNi₂ (R = Y, Sm, Gd, Tb) (Gratz et al., 1996), and the pressure-induced disordering of vacancies in RNi₂ (R = Y, Sm, Gd, Tb) (Lindbaum et al., 2002). While useful, detailed studies on the HPHT synthesis of RE rhenium alloys have been scarce; therefore, it is essential to determine how the system behaves and develops at elevated conditions.

In this work, we used the advantages provided by single-crystal high-pressure crystallography (Bykova, 2014; Bykova et al., 2015) to synthesize NdRe₂ for the first time and determine its crystal structure at 24 (1) GPa and 2,200 (100) K. In situ X-ray diffraction (XRD) was used in a laser-heated diamond anvil cell (DAC) to characterize the synthesized single-crystal compound.

The newly synthesized NdRe₂ crystallized at 24 (1) GPa in the centrosymmetric cubic F d 3 ¯ m space group with the unit cell parameter a = 7.486 (2) Å. Its structure consists of neodymium atoms surrounded by a network of rhenium tetrahedra (Figure 2A). Common with Laves phase compounds, a Kagome net can be seen along the [111] direction (Figure 2B). The crystallographic data for the newly synthesized NdRe₂ can be found in Table 1 and its atomic coordinates are in Table 2.

During the initial single-crystal structure solution and refinement, we used only neodymium and boron, however, our R₁ value was never lower than 12% and the residual electron density was very high. To solve this problem, we decided to verify the composition of the synthesized compound using the EDS analysis. Figures 1A, B shows the SEM image of the sample and the spectrum of its composition, respectively. Since the EDS analysis was conducted after sample recovery and the sample in the rhenium gasket was attached to the carbon tape, the precise location of the observed reaction was unknown. Consequently, multiple spots on both sides of the sample were analyzed. In addition to neodymium, the EDS spectrum showed the presence of rhenium and aluminum oxide. The sample was placed close to the ruby (Al₂O₃) pressure marker and the rhenium gasket, which led to the present compound formation under high pressure and laser heating. Carbon tape was used in the EDS analysis as a mount, which does not allow us to determine if carbon was involved during the synthesis. Although boron was placed in the DAC during the experiment, its presence is not detectable using EDS. Prior to the synthesized compound NdRe₂, several other compositions were attempted during the structure solution. Despite our best efforts, it was shown that NdRe₂ was synthesized in the experiment.

Due to the limited opening angle of the DAC and, therefore, incomplete datasets, goodness of fit (GOF) values were larger than expected. While additional atom placements were attempted, the GOF value would only marginally decrease while substantially increasing the R₁ value. The atom’s thermal parameters were refined in anisotropic approximation and had a data/parameter ratio of 15.5. The residual electron density peaks ranged between 0.5–1.8 e/ų, indicating that no atoms were missing from the structure.

The compound synthesized in this study is the first single crystal obtained at high pressure conditions and one of two RE-Re compounds with a Laves structure to be observed to crystallize in the space group F d 3 ¯ m . The other compound in the same space group is PrRe₂ (Savitskii and Khamidov, 1965). As the new cubic NdRe₂ was synthesized using HPHT, we can compare how the interatomic distances vary in our structure versus similar compounds synthesized through other methods at ambient pressures (see Figure 3; Supplementary Table S1). In cubic NdRe₂, we have the interatomic distance between Nd and Re as 3.1035 (14) Å and within the Re tetrahedra, the Re-to-Re distance is 2.6467 (11) Å. In comparison to the cubic PrRe₂, the cubic NdRe₂ has shorter Nd-Re and Re-Re bond lengths, which is expected due to HPHT conditions. Relative to all other known RE-Re compounds, the Nd-Re and Re-Re bond lengths are within range.

The calculated mechanical properties of NdRe₂ can be found in Tables 3, 4. As the structure is cubic, only three independent elastic constants were needed to calculate the compound’s mechanical properties, such as the bulk and shear modulus. With a Young’s and shear moduli of approximately 53 GPa and 18 GPa, respectively, NdRe₂ is located between the only two calculated moduli in the RE-Re system, PrRe₂ and YRe₂ (Jain et al., 2013; de Jong et al., 2015). The equation of state (EOS) (Figure 4A) provides a bulk modulus of 191.4 GPa. While NdRe₂ has a moderate hardness and low stiffness, its B/G value shows that it has high ductility. This corresponds to the positive value of the Cauchy pressure, which indicates that NdRe₂ exhibits metallic bonding (Pettifor, 1992; Suetin et al., 2010; Wu et al., 2014). The average wave velocity of 1,275 m/s corresponds to the relatively low Debye temperature of 140.6 K, showing that NdRe₂ has low thermal conductivity.

In addition to the mechanical properties, the band structure at ambient pressure (Figure 4B) of NdRe₂ was calculated. As discussed elsewhere (Jovanovic and Schoop, 2022), Kagome lattices and their band structures can differ depending on the atomic bonding present in the crystal structure of a material. The lattice types are divided between a linked and separated lattice, with the latter being subdivided into categories of interacting, semi-interacting, and isolated compounds. The calculated band structure of NdRe₂ indicates that no Kagome bands are present as it belongs to the cubic MgCu₂ structure type. Despite this, experimental studies are needed to study the magnetic properties of the material.

We report the successful synthesis of a neodymium-rhenium alloy with the formula NdRe₂. The structure was obtained by means of single-crystal X-ray diffraction in a diamond anvil cell at 24 (1) GPa and laser heated up to 2,200 (100) K. Its cubic structure belongs to the F d 3 ¯ m space group. The formation of NdRe₂ lends itself to being an interesting compound of study for nuclear waste immobilization. As NdRe₂ can be used to mimic nuclear waste compounds involving technetium and uranium, the potential behavior and properties of these compounds can be safely studied.