Chemical and Physical Properties of YHg3 and LuHg3

Amalgams have played an important role in fundamental and applied solid-state chemistry and physics because of the diversity of crystallographic features and properties that they have to offer. Moreover, their peculiar chemical properties can sometimes give rise to unconventional superconducting or magnetic ground states. In the current work, we present an in-depth analysis of single crystals of YHg3 and LuHg3 (Mg3Cd structure type, space group P63/mmc). Both compounds show superconductivity below Tc = 1 ± 0.1 K (YHg3) and Tc = 1.2 ± 0.1 K (LuHg3). Given the high air-sensitivity and toxicity of these compounds, this study was only possible using a number of dedicated experimental techniques.


■ MATERIALS AND METHODS
All sample preparation and handling was performed in a dedicated laboratory, equipped with an argon-filled glovebox system [MBraun, p(H 2 O/O 2 ) < 0.1 ppm]. 43 Single crystals of YHg 3 and LuHg 3 were synthesized from Y/Lu (pieces, Ames Laboratory, >99.9%) and Hg (ChemPur, 99.999%) using the self-flux method. In order to separate crystals from the flux, a custom three-piece alumina crucible was used (see Figure 2b). In order to prevent mercury evaporation during synthesis, a thread was added to both the crucible and the strainer, compared with the earlier version. 44 The Y/Lu chunks and Hg droplets, mixed in the 5:95 mass ratio (excess Hg), were sealed in Ta tubes under Ar atmosphere (Tantalum tubes were closed shut using an arc-melter, which was located inside a glovebox; Figure 2a). For other ratios of Y/Lu to Hg, single crystals could not be obtained. The volume of the Ta tubes was minimized so to exclude Hg loss (∼5 cm 3 for a total sample mass of ∼10 g). The sealed Ta tubes were heated to 500°C and then cooled to room temperature with a rate of 10°C/ hour (YHg 3 and LuHg 3 ) or 2°C/hour (YHg 3 ). Excess Hg flux was separated at room temperature via centrifugation. Some residual mercury could not be completely removed from the surface of the crystals. The resultant crystals had silver luster and needlelike morphology (see Figure 2c,d). Similar to the other mercury-based compounds, 15,16,36−42 the YHg 3 and LuHg 3 phases exhibited extreme air-and moisture-sensitivity, thereby resulting in an immediate decomposition even after short exposure to air ( Figure 4).
Powder X-ray diffraction was performed on a Huber G670 Image plate Guinier camera with a Ge-monochromator (Cu K α1 , λ = 1.54056 Å). Phase identification was done using the WinXPow software. 45 The lattice parameters were determined by a least-squares refinement using the peak positions extracted by profile fitting (WinCSD software 46 ). Differential thermal analysis (DTA) was performed on a Netzsch DTA 404 PC in the range from 30 to 700°C in a sealed tantalum ampule in a steady Ar flow with a heating/cooling rate of 5°C per minute. The resultant data are shown in Figure 5.
Small single crystals of YHg 3 on the order of ∼50 μm were used for single-crystal diffraction experiments. Single-crystal diffraction data were collected using a Rigaku AFC7 diffractometer, equipped with a Saturn 724+ CCD detector and a Mo K α radiation source (λ = 0.71073 Å). The WinCSD software 46 was used for data analysis. The results of the crystallographic characterization are provided in Tables  S1−S3. Magnetic properties were studied using a Quantum Design (QD) Magnetic Property Measurement System for the temperature range from T = 1.8 K to T = 300 K and for applied magnetic fields up to μ 0 H = 7 T. Single crystals of YHg 3 and LuHg 3 were sealed inside quartz tubes, both to protect the sample from oxidation and to ensure sample orientation, with an example shown in Figure 2d. The specific heat data were collected on a QD Physical Property Measurement System (PPMS) in the temperature range from T = 0.4 K to T = 10 K for magnetic fields up to μ 0 H = 9 T. Extra grease was used to cover the sample in order to prevent decomposition. The corresponding contribution of the grease to the overall heat capacity was subtracted on the basis of the mass of the grease. The dc electrical resistivity measurements in a temperature range from T = 0.4 K to T = 300 K were carried out using a specially designed resistivity cell, shown in Figure 3. It consists of two sheets of poly(methyl methacrylate) (PMMA), which are held together by screws. Platinum wires are placed under the sample and then pressed against the sample surface. Grease is used to protect the samples from the environment. The other end of the wires is soldered onto a standard QD PPMS puck. An electric current was applied along the c axis of the single crystals, given the fixed position of the crystal with respect to voltage and current pairs. In mercury-based materials, a surface layer of mercury is frequently presenting an obstacle when measuring electrical resistivity.  As summarized in Figure S1a, the intrinsic electrical resistivity of YHg 3 and LuHg 3 is different from that of pure Hg. In particular, in the case of pure mercury measurement, not only the superconductivity of mercury but also the structural transition of mercury from liquid to solid at T = ∼240 K can be observed. The H−T phase diagram of YHg 3 and Hg is also significantly different, as summarized in Figure  S1b.
Electronic structure calculations were performed by using the allelectron, full-potential local orbital (FPLO) method. 47 All results were obtained within the local density approximation (LDA) to the density functional theory through the Perdew−Wang parametrization for the exchange−correlation effects. 48 Application of the generalized gradient approximation did not reveal essential differences in the electronic structure below and in the vicinity of the Fermi level.

Structure Description
The single crystals prepared as described above were characterized by X-ray diffraction techniques. Carefully ground crystals yielded a powder XRD pattern, which was fully interpreted with the hexagonal unit cell (P6 3 /mmc space group). The lattice parameters for YHg 3 [a = 6.5443(5) Å and c = 4.8732(4) Å] and for LuHg 3 [a = 6.465(1) Å and c = 4.848(2) Å] were in a good agreement with the values reported earlier (a = 6.541 Å and c = 4.87 Å, 10 a = 6.546 Å and c = 4.871 Å, 8 respectively). The indexing of the powder diffraction data of YHg 3 was confirmed by the Rietveld refinement, which resulted in low residuals (R P = 0.007 and wR P = 0.012). The (010) and (011) reflections indicate the ordering of Y and Hg in the basic atomic arrangement of the Mg type (space group P6 3 /mmc, a ≈ 3.27 Å, c ≈ 4.87 Å) and are clearly visible in the PXRD pattern ( Figure 5).
The PXRD pattern of pristine LuHg 3 does not show the characteristic reflections [e.g., (010) and (011)], which indicates formation of the ordered Mg 3 Cd-type superstructure ( Figure 6, top panel). This was also confirmed by the single crystal X-ray diffraction   The subsequent DTA study of the single crystals revealed a complex temperature-dependent behavior with several thermal effects ( Figure 6e). Most of the phase transformations detected by DTA should be−at least partially−solid-state ones, e.g. formation of the polytype variants of the Mg 3 Cd type. Because the temperatures are relatively low, the reaction rates may, therefore, be reduced significantly. This should result in incompletely transformed structure patterns, thereby hindering the ordering of the crystal structure and requiring much smaller crystallization rates in comparison with those of YHg 3 .
After increasing the cooling time, the formation of the Mg 3 Cd-type superstructure was observed in the powder XRD pattern (Figure 6f). Nevertheless, additional weak diffraction reflections (Figure 6f, green arrows) were observed, which do not belong to any of the known binary phases. All attempts to index them using the structure data for the known superstructures of the Mg-type lattice (e.g., TiNi 3 structure type, or apply automatic indexing) failed. This may indicate the presence of new phase(s) obtained as byproducts of the temperaturedependent reactions (cf. DTA data) or as result of sample decomposition during grinding. Additionally, this can signal the presence of some minor structural defects in the single crystals of LuHg 3 .
The single-crystal diffraction images for YHg 3 are shown in Figure  5 a−d. Because of the high chemical activity and mechanical fragility of single crystals, they have to be used for experiments as grown, i.e., without any mechanical fragmentation (Figure 5a). This consequently requires a careful absorption correcting (linear absorption coefficient of 1450 cm −1 ). The details of the data collection and refinement are listed in Table S1, while the refined atomic coordinates and anisotropic displacement parameters are listed in Table S2. The obtained atomic displacement parameters show two striking features: strong anisotropy for the Y position (B33 ≫ B11) and larger displacement parameter for Hg with respect to the one of Y. Refinement of the crystal structure with the Y position shifted from the mirror plane on the [001] axis (z.ne.3/4) and the attempt to refine the occupancy of the Hg position are possible but both do not yield statistically relevant reduction of the residuals. Thus, the observed unusual features of the atomic displacement parameters may be caused mainly by the incompletely accounted influence of very high X-ray absorption (cf. huge value of the linear absorption coefficient). The structure refinement confirmed the atomic arrangement of the Mg 3 Cd structure type (ordered variant of the Mg structure type with a = 2a Mg and c = c Mg ; Y and Hg at the positions of Cd and Mg, respectively; R F = 0.030, wR F = 0.031).
The structural motif of YHg 3 employs the hexagonal close-packed phase with the AB stacking sequence along the [001] direction. An ordered arrangement of Y and Hg atoms in the 1:3 ratio within each hexagonal layer (superstructure formation) requires doubling of the hexagonal lattice a in comparison with the "uni-color" packing (Mg structure type). This is evidenced by the appearance of superstructure reflections both in the single crystal and powder X-ray diffraction patterns (see Figures 5 and 6).
Both species in the YHg 3 structure have a coordination number of 12 and hexagonal analogues of cuboctahedra as their coordination polyhedra. Whereas Y atoms are surrounded exclusively by Hg atoms located at distances of 3.1085(6) and 3.2777(9) Å, the coordination polyhedron around Hg consists of 4 Y and 8 Hg species. The Hg−Hg distances of 3.0678(8) Å (4×), 3.219(1) Å (2×), and 3.335(1) Å (2×) are comparable with the values of 2.993 and 3.465 Å observed for octahedrally coordinated atoms in α-Hg (at T = 78 K). 49 Calculation of the electron density (ED) and its analysis within the QTAIM approach reveal essential charge transfer from yttrium to mercury (Figure 7). The shapes of the atomic basins, obtained from the topological analysis of ED, show features characteristic of a charge transfer scenario. All faces of the QTAIM basin of the yttrium atom are convex toward the Hg ligands, which reflects in this way the difference in electronegativity (EN Hg > EN Y ). This behavior is similar to the recently investigated Mg 3-x Ga 1+x Ir 50 and Mg 29-x Pt 4+y , 51 where the more electropositive component Mg shows QTAIM basins with solely convex faces. Integration of the ED within the atomic QTAIM basins yields their electronic populations. Subtraction of the electron number for the neutral atom from the population yields the effective charge. The resultant charges of +1.59 for Y and −0.53 for Hg are in good agreement with the difference in electronegativities between these components. This also indicates that the possible disorder in the structure is most probably not caused by an exchange of Y and Hg at the respective crystallographic sites. This would be a clear energetic disadvantage as a result of an enhanced electrostatic contribution to the total energy of the system. Therefore, the origin of the disorder observed in the X-ray diffraction experiments is most probably coming from the stacking faults of the closest packed layers along the [001] direction.

■ SUPERCONDUCTING PROPERTIES
The temperature-dependent magnetic susceptibility data of both YHg 3 and LuHg 3 indicate diamagnetic behavior down to the lowest measured temperature T = 1.8 K. However, a transition associated with an entrance into superconducting state is observed in the temperature-dependent specific heat data, shown in Figure 8a,b for YHg 3 and LuHg 3 , respectively. The transition occurs at T c = 1 ± 0.1 K for YHg 3 and at T c = 1.2 ± 0.1 K for LuHg 3 . Upon application of a magnetic field (Figure 8a), the transition is suppressed; however, given the small signal of the sample compared with that of the grease (which is necessary to prevent the sample from decomposition), the exact values of T c for a given H c value could not be established. Modest values of the Sommerfeld coefficient γ n = 5−6 mJ mol F.U. −1 K −2 for both YHg 3 and LuHg 3 were extracted from the linear fit of the C p /T vs T 2 data in the normal state (dashed lines). Because of the difficulties of the background subtraction, it was not possible to estimate superconducting parameters for YHg 3 and LuHg 3 , which would give more insights regarding the type of superconductivity in these compounds.
Band structure calculations for YHg 3 and LuHg 3 are shown in Figure 9a,b, respectively. For both compounds, a nonzero density of states at the Fermi level is observed, from which the value of γ theory = 5 mJ mol F.U. −1 K −2 is estimated. This agrees well with the value of γ n extracted from the specific heat data. It appears that at the Fermi level, the 4d orbitals of Y and 6p orbitals of Hg are dominant for YHg 3 (see inset of Figure 9a). Similarly, the 5d orbitals of Lu and 6p orbitals of Hg are contributing the most to the overall density of states of LuHg 3 . The value of the density of states around the Fermi level remains constant for an extended energy range for both compounds, thereby suggesting that the ground states of YHg 3 and LuHg 3 are rather robust.
Metallic behavior is observed in the temperature-dependent electrical resistivity data of YHg 3 and LuHg 3 , shown in Figure  10 and S1a. The metallicity of both systems is consistent with the nonzero density of states at the Fermi level observed in the band structure calculations. For both YHg 3 (orange) and LuHg 3 (blue), a high value of the residual resistivity ratio RRR ∼400 signals a good sample quality. The entrance into superconducting state is marked by a drop in the resistivity (Figure 10, inset), which is gradually moved to lower temperature upon application of a magnetic field. From the lower plateau of the transition, the corresponding H−T phase diagram is obtained, see Figure S1b. The resultant value of the critical field μ 0 H c (0) = 80 mT for YHg 3 is estimated using a Ginzburg−Landau fit. Unfortunately, it was not possible to estimate the critical field of LuHg 3 in a similar way, given its high air-sensitivity. However, it is rather likely that the value of the critical field in LuHg 3 would be comparable with that of YHg 3 . Further in-depth analysis of YHg 3 and LuHg 3 using various methods, such as, for example, μSR 52,53 would give more insights regarding their superconducting order parameter. Chemical substitution experiments could also be fruitful. Currently, studies of amalgams of rare-earth and actinides  appear to be scarse. 11,24,38,39,54,55 However, by using modern experimental tools, we are now able to conclusively unveil their peculiar chemical and physical properties.

■ CONCLUSIONS
A detailed characterization of large single crystals of YHg 3 and LuHg 3 has been carried out. Because of the extreme air-and moisture sensitivity of these materials, it has only now been possible to definitively establish their crystallographic and physical properties. Both compounds crystallize in the Mg 3 Cd structure type [P6 3 /mmc space group, a = 6.5443(5) Å and c = 4.8732(4) Å for YHg 3 and a = 6.465(1) Å and c = 4.848(2) Å for LuHg 3 ). Low-temperature specific heat and resistivity measurements revealed the presence of superconductivity in both phases with T c = 1 and 1.2 K, respectively.

■ ASSOCIATED CONTENT Data Availability Statement
The data underlying this study are available in the published article and its Supporting Information.

Notes
The authors declare no competing financial interest.