The dysprosium carbide Dy₄C₃ was synthesized at 19, 55, and 58 GPa (Supplementary Table S1). This compound was hitherto unknown. It has the anti-Th₃P₄-type structure (space group I-43d) shown in Figures 1A–C, which has been described for scandium carbide, Sc₄C₃, but not observed in lanthanide carbides or Y carbides (Adachi et al., 1991; Babizhetskyy et al., 2017). At 19 GPa its unit cell parameter is equal to a = 7.4774 (8) Å.

In the structure of Dy₄C₃ (Figures 1A–C; Table 1), dysprosium and carbon atoms occupy the 16c and 12a Wyckoff sites, respectively (Supplementary Tables S2–S4). The coordination polyhedron of Dy cations is an irregular octahedron formed by the six nearest carbon atoms at distances of either 2.3819 (5) Å or 2.8240 (5) Å at 19 GPa (Figure 1B). Carbon atoms are surrounded by eight Dy atoms forming strongly distorted cubes (octaverticons) (Figure 1C).

The cubic Dy₂C₃ sesquicarbide was synthesized in this work at 19 GPa (Supplementary Table S1). It has the Pu₂C₃-type structure (space group I-43d) with the unit cell parameter a = 7.9208 (5) Å at 19 GPa (Figures 1D–F; Table 1). The Dy₂C₃ sesquicarbide was earlier reported at ambient conditions with the lattice parameter equal to a = 8.198 (2) Å at 1 bar (Spedding et al., 1958). The dysprosium and carbon atoms occupy the 16c and 24d Wyckoff sites, respectively (Supplementary Table S5). The structure of Dy₂C₃ contains [C₂] dumbbells with a length of ∼1.27 Å at 19 GPa.

The structures of Dy₂C₃ and Dy₄C₃ (described above) are closely related (see Figure 1): they have the same space group (I-43d), and the former can be easily derived from the latter, as the positions of the centers of [C₂] dumbbells in Dy₂C₃ coincide with the positions of single carbon atoms in Dy₄C₃, whereas the coordinates of Dy atoms are the same in both structures. Thus, the coordination number of Dy atoms in Dy₂C₃ increases to nine (Figure 1E), whereas the coordination environment of [C₂] dumbbells (Figure 1F) is similar to that of a single carbon atom in Dy₄C₃ (Figure 1C).

One more dysprosium carbide, Dy₃C₂, with a tetragonal unit cell (space group P4/mbm), was discovered at 55 GPa (Supplementary Table S1). At this pressure it has the following unit cell parameters: a = 5.9896 (13) Å, c = 3.3880 (12) Å (Figure 2; Table 1). Rare-earth metal carbides of such a stoichiometry have not been previously observed (Babizhetskyy et al., 2017), but the structure of the new Dy₃C₂ was found to be of the U₃Si₂-type, which is common for silicides (Zachariasen, 1948), borides (Riabov et al., 1999), and intermetallides (Chai and Corbett, 2011). Such structure was also theoretically predicted for a high-pressure calcium carbide Ca₃C₂ (Li et al., 2015).

In the structure of Dy₃C₂ (Figure 2; Table 1) carbon atoms occupying a single 4 g Wyckoff position and form [C₂] dumbbells. Two dysprosium atoms are crystallographically distinct, occupying the Wyckoff positions 2a (Dy1) and 4h (Dy2). Figure 2A shows the structure of Dy₃C₂, as viewed along the c direction. Dy1 atoms lie in the same ab plane as the [C₂] dumbbells, forming together the Cairo pentagonal tiling comprised of (Dy1)₂C₃ pentagons (Figure 2B). Such a structural motif is known in nickel diazenide NiN₂, whose structure possesses atomic-thick layers comprised of Ni₂N₃ pentagons (Bykov et al., 2021), and in other compounds (Shao et al., 2018; Deng et al., 2020; Duan et al., 2022). Dy2 atoms are located in a parallel plane, separated from the described one by ½ c (Figure 2C). The Dy2-C inter-layer distances are of 2.413 (9) Å or 2.574 (10) Å (Figure 2D). As seen in Figure 2B, the Dy1 atoms are four-fold coordinated by C atoms with the Dy1-C distance equal to 2.519 (12) Å at 55 GPa. The length of the [C₂] dumbbell is equal to 1.51 (3) Å (Figure 2E).

Dysprosium carbide Dy₄C₃ was synthesized at three different pressures (19, 55, and 58 GPa) that enabled us to analyse its structural response to compression. As expected, the shorter Dy-C contacts are less flexible than the longer ones: those being 2.3819 (5) Å and 2.8240 (5) Å at 19 GPa (Figure 1B) contract by ∼3.6% and ∼9.7%, respectively, upon compression to 58 GPa. The results of our DFT calculations agree well with the experimental data, suggesting ∼3.3% and ∼8.5%, correspondingly (Supplementary Tables S2–S4). Due to the anisotropy of compression, DyC₆ polyhedra become less distorted with the distortion indices (D) equal to 0.085 and 0.053 at 19 and 58 GPa, respectively. A distortion index characterizes the average deviation of interatomic distances and angles from their mean values (Baur, 1974). Ab initio calculations reproduced well the experimental data with D = 0.084 at 19 GPa vs. D = 0.057 at 58 GPa.

In order to obtain the pressure dependence of the volume for the three dysprosium carbides and to determine the parameters of their equations of states (EOSes), we would need to measure volumes on decompression. However, as we performed our experiments in a solid pressure transmitting medium (NaCl), such data could not be reliable because of stresses. Due to that, we instead performed ab initio density functional theory (DFT) calculations in the pressure range up to 100 GPa. Their results are shown in Figure 3, and the parameters of the 3rd order Birch-Murnaghan (BM3) EOS, based on DFT calculations for Dy₂C₃, Dy₃C₂, and Dy₄C₃, are summarised in Table 2.

Dysprosium sesquicarbide Dy₂C₃ contains [C₂] dumbbells with a length of ∼1.27 Å at 19 GPa, which is slightly shorter than the length of the double bond in ethylene and sesquicarbides Y₂C₃ and La₂C₃ at ambient pressure (Gready, 1984; Craig et al., 2006; Kim et al., 2007; Kobayashi et al., 2019). This suggests a formal charge of 4- for the [C₂] dumbbell, so that the formula of Dy₂C₃ can be written as Dy³⁺ ₄ [C₂]^4– ₃, and the compound can be called dysprosium (III) ethenide. The [C₂] units in Dy₃C₂ have a length of ∼1.51 Å at 55 GPa, which is just a bit shorter than the C-C bond length in ethane (Gready, 1984). The compound may be described as Dy²⁺ ₃ [C₂]⁶⁻ and called dysprosium (II) ethanide. The Dy₄C₃ consists of single carbon atoms. With the formula Dy³⁺ ₄C⁴⁻ ₃ it is dysprosium (III) methanide.

In order to get a deeper insight into the crystal chemistry of the novel compounds, we performed a detailed charge and bond order analysis. Mulliken charge analysis (Müller et al., 2021) for the dysprosium atoms in carbides synthesized in this work yields the values of 1.62 in Dy₄C₃, 1.72 in Dy₂C₃, and 1.01 for Dy1 and 1.12 for Dy2 in Dy₃C₂ (Supplementary Table S7). The values for Dy₄C₃ and Dy₂C₃ are in agreement with Mulliken charges known for other dysprosium-containing compounds (Gupta et al., 2016; Ahuja et al., 2017). Our calculations of Mulliken charges for trivalent Dy carbides known at ambient conditions (DyC₂ and Dy₄C₅ (Spedding et al., 1958; Adachi et al., 1976; Czekalla et al., 1997); are in a good agreement with those obtained for Dy₄C₃ and Dy₂C₃ (Supplementary Table S8). For Dy₃C₂, Mulliken charges of dysprosium are obviously lower, thus supporting our assessment of the cation in this compound as Dy²⁺ (see above). Notable is that at the same pressure of 55 GPa, the Dy-C distance in Dy₃C₂ is larger than in Dy₄C₃ (Supplementary Tables S3, S6), which also speaks in favor of a lower charge of dysprosium in the novel ethanide.

Assuming all Dy atoms to have integer charges, one can analyse carbon charges and the C-C chemical bonds in carbon dimers in different dysprosium carbides. The integrated crystal orbital bond indexes (ICOBI) obtained for DyC₂ (Adachi et al., 1976), Dy₄C₅ (Czekalla et al., 1997), and Dy₂C₃ are close to 2 (Supplementary Table S8). The small deviations can be explained by shared-electron interactions due to the metallicity of the studied solids. This suggests a C=C double bond in these compounds, which is in a good agreement with its C-C distance (Supplementary Table S9). For Dy₃C₂ the ICOBI index for the C-C bond in the [C₂] dimer differs significantly from those in other carbides (1.116) and suggests the bond order of 1, which is also consistent with the C-C bond length. Additionally, the assigned bond orders are well reflected in individual charges of C atoms and their anions, as obtained in both Mulliken and CHARDI approximations (Supplementary Table S8) (Nespolo and Guillot, 2016; Müller et al., 2021).

The character of the chemical bonding can be judged from calculated electron localization functions (ELF) (Savin et al., 1991). Relevant cross sections of ELFs at 19 GPa for Dy₄C₃ and Dy₃C₂ are shown in Figures 1G, H. They reveal ionic bonding between Dy and C in both compounds and strong covalent bonding in the [C₂] dimers of Dy₂C₃. The 2D ELF for Dy₃C₂ at 55 GPa is shown in Figure 2F. It gives evidence of strong covalent bonding between carbon atoms in dimers and ionic bonds between Dy and C atoms.

For 19 simple binary metal-nitrogen compounds containing [N₂] ^x–species, a linear correlation was found between the length of the N–N dimers and their formal charges (Laniel et al., 2022). We used the literature data on 12 metal carbides studied at ambient conditions (Atoji et al., 1958; Spedding et al., 1958; Atoji, 1967b; 1967a; Krupka et al., 1969; Adachi et al., 1976; Czekalla et al., 1997; Vohn et al., 2000; 1999; Yosida, 2002; Babizhetskyy et al., 2014; Aslandukova et al., 2021) and our own results to analyse the relationship between the length of carbon dimers and their formal charges. For the novel Dy₃C₂, the C-C length at ambient pressure was obtained by DFT calculations, as well as for γ-Y₄C₅ in (Aslandukova et al., 2021); for Dy₂C₃ we included both the experimental value (Spedding et al., 1958) and the one DFT-calculated in this work, as they are a bit different. It appeared that the linear correlation holds also for carbides featuring [C₂]^x− dimers at ambient conditions (Figure 4).

According to ab initio simulations of the phonon densities of state (pDOS) (Togo and Tanaka, 2015) in the harmonic approximation at 0 K, Dy₄C₃ and Dy₂C₃ compounds are dynamically stable at their synthesis pressure of 19 GPa (Figures 5A, B), whereas Dy₃C₂ is unstable both at its synthesis pressure of 55 GPa and at 1 bar (Figures 5C, F).

According to our calculations at 1 bar, Dy₂C₃ is not dynamically stable (Figure 5E), although it is known to exist at ambient conditions (Spedding et al., 1958). These inconsistency indicates some limitations of the theoretical analysis method we apply. Therefore, the predicted dynamical stability of Dy₄C₃ (Figure 5D) at ambient pressure should be considered with caution.

To explore the thermodynamic stability of Dy₄C₃, Dy₂C₃, and Dy₃C₂ in comparison to other Dy carbides, convex hull diagrams were constructed considering known carbides [Dy₂C (Atoji, 1981), Dy₄C₅ (Czekalla et al., 1997; Babizhetskyy et al., 2019; The Materials Project, 2020b), Dy₃C₄ (Hüfken and Jeitschko, 1998; The Materials Project, 2020a), DyC₂ (Adachi et al., 1976)] at various pressures. Structure models for Dy₄C₅ (α-Y₄C₅ type) (The Materials Project, 2020b) and Dy₃C₄ (Sc₃C₄ type) (The Materials Project, 2020a) were acquired from Materials Project database, while those for Dy₂C (Atoji, 1981) and DyC₂ (Adachi et al., 1976)–from CIFs deposited in the ICSD database. The formation enthalpies were computed relative to the DFT total energies of the end-member elements Dy and C according to the equation: ΔH_f = (H_DyCx—H_Dy—x‧H_C)/(1 + x). The results are shown in Figure 6. As seen, pressure has a very significant effect on the chemistry of the Dy-C system. Some phases (e.g., Dy₂C and Dy₄C₅), which are stable at ambient pressure, become unstable already at 20 GPa. According to the convex hull diagram computed at 60 GPa, only those phases, which we observed in this work (Dy₄C₃, Dy₂C₃, and Dy₃C₂), are expected to be thermodynamically stable at such a high pressure.