Y 4 Be 33 Pt 16 – a non-centrosymmetric cage superconductor with multi-centre bonding in the framework †

The new ternary compound Y 4 Be 33 Pt 16 was prepared from elements by arc melting, and its crystal structure was determined from single-crystal X-ray di ﬀ raction data (space group I 4¯3 d , a = 13.4849(3) Å). The material is the ﬁ rst representative of a new structure type of complex intermetallic compounds and reveals a cage-like crystal structure. Analysis of chemical bonding by means of the electron localizabilty approach indicates ionic interaction of yttrium with the rest of the crystal structure, characteristic for cage compounds, in particular for clathrates. In contrast to the mostly two-centre bonding in the framework of clathrates, the new compound is characterized by a multi-centre interaction within the framework, caused by the demand of the valence electrons in the system. The non-centrosymmetric material enters the superconducting state at T C = 0.9 K.


Introduction
The diversity of intermetallic structures is fascinating. These compounds can have unit cells with one atom as in α-Po (Pearson symbol cP1) or with more than twenty thousand atoms as in Ta 9063 Al 12827.56 Cu 1244.05 (Pearson symbol cF23134). [1][2][3] The reasons for such complex behaviour are still under discussion. The compounds with crystal structures containing more than ca. 100 atoms in the unit cell are notated as complex metallic alloys (CMA) or complex intermetallic compounds. 4 One of the characteristic features for CMA (but not for all) is the presence of different types of crystallographic disorder in crystal structures, which de facto means the violation of the translational symmetry in the strict sense. Recently, this was shown on examples of o-Al 13 Co 4 (oP102-x) 5 and ternary clathrate Ba 7.81 Ge 40.67 Au 5.33 (cP54-x) 6 by the combination of X-ray diffraction on single crystals with high-resolution transmission electron microscopy. One of the possible reasons for such complex behaviour may be the low valence electron concentration in these materials, which (i) does not allow to use traditional electron counting schemes for understanding the composition and the crystal structure, and (ii) leads to multi-centre atomic interactions in the structures, recently shown e.g. for Be 21 Pt 5 . 7 Intermetallic compounds with complex crystal structures often show unusual physical behaviours. Physics and chemistry of CMA are discussed on the basis of the complexity of their crystal structures, whereby the latter is considered to be the origin of some specific behaviour of these substances. For instance, the intermetallic clathrates reveal unusual functionality in heat transport as a kind of phonon filters with the mean free path of phonons 10-100 nm. 6,8,9 From the position in the Periodic Table, beryllium contributes only two valence electrons for the formation of bonds, thus the compounds with high beryllium content should be a suitable field to search for new complex intermetallic materials. The recently described binary Be 21 Pt 5 has a large unit cell with 416 atoms (cF416), but does not reveal any crystallographic disorder. 7 The information about the ternary compounds of Be with other metals is rather scarce in the literature. 10 Our initial phase diagram studies showed, thatdespite the clear electronic demandthe R-Be-T systems are characterized by formation of several ternary compounds similar to the R-E-T systems with R being alkaline-or rareearth metals, Ep-block elements, and Tlate transition metals. In this work, we present crystal structure and bonding analysis of the new superconductor Y 4 Be 33 Pt 16 .

Results and discussion
The powder X-ray diffraction pattern of Y 4 Be 33 Pt 16 , shown in Fig. 1, was indexed using a cubic cell with a = 13.4849(3) Å. The structure was solved and refined from single-crystal diffr-action data in the non-centrosymmetric space group I43d. The main crystallographic information is presented in Table 1, the atomic coordinates and isotropic atomic displacement parameters are shown in Table 2, the anisotropic displacement parameters for Y and Pt atoms as well as the interatomic distances are listed in ESI (Tables S1 and S2, † respectively).
The atoms in the crystal structure of Y 4 Be 33 Pt 16 reveal coordination polyhedrons characteristic for intermetallic compounds in the ternary systems of rare-earth and related metals as R component with transition metals and p-block elements. The yttrium atoms are located within a spacious polyhedron with 20 vertices, being very similar to that of Ca in the CaCu 5 structure type and its several derivatives 11,12 (Fig. 2, top panel). Interestingly, there are three additional Be1 ligands at the distance of 3.666 Å, which is much longer than other yttrium contacts (Table S2 †) andfrom distance analysisthese three do not necessarily belong to the first coordination sphere (cf. analysis of chemical bonding below). While the platinum atoms have environments derived from the Frank-Kasper polyhedrons with coordination numbers of CN(Pt1) = 14 and CN(Pt2) = 13, Be1 has a bisdisphenoid-like environment with eight closer neighbours (and additional four yttrium species at a much longer distance), all remaining beryllium species have 12 or 13 ligands with their coordination environments derived from an icosahedron (Fig. 2, top panel).
The crystal structure of Y 4 Be 33 Pt 16 can be visualized by considering the coordination environment of yttrium. Adjacent coordination polyhedrons of Y are vertex-sharing via the Pt1 position. This results in the formation of a linear rod-like arrangement of interpenetrating Y and Pt1 polyhedrons, as shown in Fig. 2 (middle panel), along the three-fold axes of the cubic unit cell ({111} directions). The resultant rod packing is presented in Fig. 2 (bottom panel) and was first described as crystallographic object in ref. 13. The existence of voids between the rods is due to an incomplete space filling. These voids are located at ( 7 8 0 1 4 ) (Wyckoff site 12b) and ( 3 8 0 1 4 ) (Wyckoff site 12a). The former are empty in Y 4 Be 33 Pt 16 , as they are too small to contain an atom. The voids located at ( 3 8 0 1 4 ) having the shape of a bisdisphenoid are occupied by Be1.
Among the CaCu 5 derivatives, the crystal structure of Y 4 Be 33 Pt 16 is closely related to the ferromagnet Nd 2 Fe 23 B 3 (space group I43d, a = 14.19 Å). 14-16 For a comparison, the compositions can be written as Nd 4 Fe 30 (B 2 ) 3 Fe 16 and Y 4 Be 30 Be 3 Pt 16 . In the Nd 2 Fe 23 B 3 structure, the Y site is occupied by Nd, all other positions beside Be1by iron. While the bisdisphenoid in Y 4 Be 33 Pt 16 is occupied by a single Be1 atom (Wyckoff site 12a), the same coordination environment is occupied in Nd 2 Fe 23 B 3 by a B 2 pair with the centre at the 12a site ( Fig. S1 †). In this way, the B atoms belong to the coordination sphere of Nd with d(B1-Nd1) = 3.32 Å in Nd 2 Fe 23 B 3 , in contrast to Be1 in Y 4 Be 33 Pt 16 which shows much longer distance of d(Be1-Y) = 3.666 Å.
The complex intermetallic structures with large cubic unit cell, in particular derivatives of the gamma-brass structural pattern, can often be interpreted from the crystallographic a Lattice parameter refined from the X-ray powder diffraction data (CuK α1 radiation).  Atom point of view as packings of nested polyhedrons. 18 Recently, this was explained on example of Be 21 Pt 5 by the formation of multi-atomic bonding interactions centred at the middle points of the nested polyhedrons. 7 Interestingly, this approach does not work reasonably well for Y 4 Be 33 Pt 16 . This observation was the starting point for the analysis of chemical bonding in Y 4 Be 33 Pt 16 employing the electron localizability approach.
As for most intermetallic beryllium compounds, a characteristic feature of Y 4 Be 33 Pt 16 is the very low valence electron concentration (VEC) of ca. 1.4 e per atom, which is even lower than in the gamma-brass derivative Be 21 Pt 5 (1.62 e per atom). An important factor stabilizing the latter structure was found to be the charge transfer from Be to Pt. 7 In order to study the role of the ionic contributions to the bonding, the electron density in Y 4 Be 33 Pt 16 was investigated applying the QTAIM (Quantum Theory of Atoms In Molecules 19 ) approach. The zero-flux surfaces in the distribution of electron density define the shape of the atoms in the QTAIM representation. Integration of electron density within the atomic shapes yields their electronic populations and effective charges (Fig. 3). The yttrium atoms in Y 4 Be 33 Pt 16 in the QTAIM representation have a shape close to a spherical one, which is characteristic for cage compounds, e.g. clathrates of Ba or Sr. 9,20 Their effective charge of +1.70 is also characteristic for the earth-alkaline and rare-earth atoms in intermetallic clathrates. 20,21 The shapes of the QTAIM atoms of platinum and beryllium are far from a sphere. They have closer to plane or even concave faces. While beryllium atomsas expected from the electronegativity differencesreveal positive effective charges between +1. 30  Further information about atomic interactions was obtained by applying the electron localizability approach. The distribution of the electron localizability indicator (ELI-D) in the vicinity of the yttrium nuclei is close to a spherical one, whereby the valence shell (4 th ) is absent. The light structuring of the penultimate shell indicates the participation of the elec-  trons from this shell in the bonding. The intersection with the QTAIM yttrium atom reveals that the latter bears only the inner shells, confirming the ionic interaction of yttrium with the Be-Pt framework (Fig. 4, top panel). In the cage wall, there are two bonds involving Be2, Be4 and Pt2. Populations are 1.63 and 1.36 electrons, respectively. The interesting aspect is that Pt1 also contributes to them. Its contribution is comparable to those of Be2 and Be4. Hence, each attractor describes a fouratomic bond, two Pt and two Be. This reflects the characteristic multi-atomic interaction in the whole Be-Pt framework. The distribution of ELI-D in the (Be1-Pt2-Be4) triangle reveals one maximum located within the triangle. The intersection of the ELI-D basin of this maximum with the QTAIM shapes of the neighbouring atoms (Fig. 4, middle panel) shows the Be1, Be4, and Pt2 atoms contributing 0.11, 0.15, and 1.45 of the total population of 1.84 electrons for this basin. This confirms the mainly three-atomic (3a) character of the interaction in this part of the structure. The remaining 0.13 electrons originate from two other Pt2, one Be3, and even one yttrium neighbours, suggesting that even more atoms are participating in this multi-atomic bonding. The Pt atoms contribute the majority of the population for the bonding basins, which makes the multi-centre interactions strongly polar. The bonding analysis reveals that the Be1 atoms should be included into the coordination sphere of yttrium despite a large interatomic distance (cf. distance-based considerations above and comparison of the Y-polyhedrons in Fig. S1(e) †). The Y-centred cagesas obtained from the bonding analysiswithin the three-dimensional Be-Pt framework fill-up the large part of the unit cell of Y 4 Be 33 Pt 16 (Fig. 4, bottom panel). In summary, analysis of the chemical bonding classifies Y 4 Be 33 Pt 16 as a cage compound, e.g. a material with its crystal structure in the form of a 3D framework with large cages. Ionic interaction of cationic yttrium species in the cages of the anionic Be-Pt framework is the bonding characteristic of this cage structure. In contrast to other representatives of cage compounds, e.g. intermetallic clathrates with mainly twocentre (non-polar or polar) bonds in the framework, the framework in Y 8 Be 66 Pt 32 is formed by multi-atomic (polar) interaction. In agreement with the chemical bonding picture, the calculated electronic density of states of Y 4 Be 33 Pt 16 is characterized by the intermixing of Pt and Be states in the whole energy range and shows three main regions (Fig. 5). The low-energy range (E < −6.7 eV) is formed mainly by the s states of Be and Pt with small contributions of the s states of yttrium, reflecting the bonding in the Be-Pt framework. The middle-energy region (−6.7 eV < E < −2.3 eV) is dominated by d states of platinum atoms. The region below the Fermi level (E F ) contains contributions of all essential atomic states. Interestingly, a pseudo gap is found above the Fermi level (due to the band dispersion along Γ-H in the Brillouin zone, Fig. S2 †), in contrast to the typical DOS distribution in cage compounds with two-centre bonds in the framework, where the pseudo gap appears typically close to E F . 9 The presence of non-filled states agrees with the electron-deficient situation in this material.
The non-centrosymmetric compound Y 4 Be 33 Pt 16 enters a superconducting state below T C = 0.9 K, as evidenced by the BCS-like anomaly observed in specific heat data, shown in Fig. 6. A fit to the specific heat data above the superconducting transition (dashed line), can be used to estimate the value of  22 Consequently, the value of θ D can then be used to estimate the strength of the electronphonon coupling, employing the McMillan's formula. 23 Typically, materials with λ e-p → 1 are classified as stronglycoupled superconductors, while λ e-p → 0.5 indicates weak coupling. 23 For Y 4 Be 33 Pt 16 , 0.38 ≤ λ e-p ≤ 0.47, indicating weakly-coupled superconductivity. Once the phonon contribution to the specific heat (βT 3 ) has been subtracted from the specific heat data, an entropy conserving construction (not shown) yields the ratio ΔC e /γ n T C ≈ 1.80, which is comparable to the BCS value of ΔC e /γ n T C = 1.44, consistent with Y 4 Be 33 Pt 16 being a weakly-coupled superconductor. As expected, the critical temperature T C is gradually suppressed by the application of a magnetic field, consistent with type-II superconductivity, allowing to construct the H−T phase diagram (inset of Fig. 6).
A relatively small value of the upper critical field H c2 = 0.44 T, extracted from a Ginzburg-Landau fit 22 26 The fact, thatdespite of absence of inversion symmetryno distinct deviations from BCS theory are observed, points towards the lack of strong correlation effects. 27,28 However, a more comprehensive analysis of the superconducting state in Y 4 Be 33 Pt 16 is currently underway. In particular, because several in-depth muon spin-rotation, relaxation, and resonance experiments performed on another Be-containing non-centrosymmetric superconductor BeAu 24 revealed that not only type-I character, 29 but also a multi-gap nature of superconductivity 30 may exist in such unconventional systems.

Synthetic procedures
All sample preparation was performed in a laboratory specialized for work with Be, inside a argon-atmosphere glove box system (MBraun, p(H 2 O/O 2 ) < 0.1 ppm).
Caution! Beryllium is considered (according to UN GHS criteria) a health risk and experiments require appropriate infra structure.
Polycrystalline samples around the composition Y 4 Be 33 Pt 16 were synthesized by arc melting Y ( pieces, Ames, >99.9%), Pt (foil, Chempur, >99.9%), and Be (sheet, Heraeus, >99.9%) in the 10 : 30 : 60 ratio. The samples did not exhibit any marked air or moisture sensitivity. Small amounts of impurities were found to be present in all samples. The minority phases are Be 21 Pt 5 (superconductor with T C = 2.06 K (ref. 7)), Be 5 Pt (semiconductor 31 ), as well as elemental Pt in the amount of <3%. Temperature treatment, as well as slight variation of the initial composition did not result in an improved sample quality.

Crystallography
Powder X-ray diffraction was performed on a Huber G670 Image plate Guinier camera with a Ge-monochromator (CuK α1 radiation, λ = 1.54056 Å). Phase identification was done using the WinXPow software. 32 All crystallographic calculations were done with the WinCSD software package 33 Single-crystal X-ray diffraction data have been collected on a Rigaku AFC7 diffract-  ometer equipped with a Saturn 724 + CCD detector using MoK α radiation (λ = 0.71073 Å).

Chemical analysis
Chemical composition of polished samples was studied using energy-dispersive X-ray spectroscopy (EDS) with an UltraDry EDS detector (ThermoFisher NSS7) attached to a Jeol JSM 6610 scanning electron microscope (SEM). The semi-quantitative analysis was performed with 25 keV acceleration voltage and ≈3 nA beam current.

Physical properties measurements
Heat capacity was measured in the temperature range from 0.4 K to 10 K, in magnetic fields up to H = 9 T using a QD Physical Property Measurement System.

Calculation procedures
Electronic structure calculations were performed by using the all-electron, full-potential local orbital (FPLO) method. 34 All main results were obtained within the local density approximation (LDA) to the density functional theory through the Perdew-Wang parametrization for the exchange-correlation effects. 35 Application of the generalized gradient approximation did not reveal essential differences in the electronic structure below and in vicinity of the Fermi level. Chemical bonding analysis in position space was performed within the approach of combined topological analysis of electron density (ED) and electron localizability indicator (ELI). The former type of analysis forms the basis of the quantum theory of atoms in molecules (QTAIM). 19 ELI was calculated in the ELI-D representation 36-38 by a module implemented in the FPLO package. 39 Topological analysis of the ED and the ELI-D were carried out by the program DGrid. 40

Conclusions
The ternary compound Y 4 Be 33 Pt 16 is the first representative of a new prototype of intermetallic cage compounds with an unusual combination of structural and bonding features. The cubic crystal structure with 212 atoms in the unit cell isin contrast to many other complex intermetallic structurescompletely ordered and does not show violation of the translational symmetry, characteristic for CMA materials. Analysis of chemical bonding in position space reveals mainly ionic interaction of Y with the remaining parts of the structure, indicating an analogy to intermetallic clathrates and classifying the new atomic arrangement as a cage-like one. In contrast to other cage materialsclathrateswith mainly two-centre bonding in the framework, the framework atoms in Y 4 Be 33 Pt 16 participate only in multi-centre interactions. On top of the interesting structure-bonding relationship, the new compound is a non-centrosymmetric BCS-type superconductor with T C = 0.9 K.

Conflicts of interest
There are no conflicts of interest.