Alfred Amon‡
,
Eteri Svanidze,
Yurii Prots,
Michael Nicklas,
Ulrich Burkhardt,
Alim Ormeci,
Andreas Leithe-Jasper* and
Yuri Grin
Max-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Straße 40, Dresden 01187, Germany
First published on 25th June 2020
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 diffraction data (space group I3d, a = 13.4849(3) Å). The material is the first 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.
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, that – despite the clear electronic demand – the R–Be–T systems are characterized by formation of several ternary compounds similar to the R–E–T systems with R being alkaline- or rare-earth metals, E – p-block elements, and T – late transition metals. In this work, we present crystal structure and bonding analysis of the new superconductor Y_{4}Be_{33}Pt_{16}.
a Lattice parameter refined from the X-ray powder diffraction data (CuK_{α1} radiation). | |
---|---|
Crystal system | Cubic |
Composition | Y_{4}Be_{33}Pt_{16} |
Space group | I3d |
Pearson symbol | cI212 |
Formula units per u. c. Z | 4 |
Unit cell parameter a | 13.4849(3) Å^{a} |
Unit cell volume V | 2452.1(2) Å^{3} |
Calculated density | 10.22 g cm^{−3} |
Radiation, wavelength | MoK_{a}, 0.71073 Å |
Absorption coefficient | 105.2 mm^{−1} |
Diffraction system | Rigaku AFC7 |
2θ_{max} | 86.2° |
N(hkl) measured | 27218 |
N(hkl) unique | 1477 |
N(hkl) observed | 1446 |
R_{int}; R_{s} | 0.045; 0.032 |
Refined parameters | 28 |
R_{F}; wR_{F}^{2} | 0.044; 0.088 |
Weighting scheme | w_{i} = [ln(F_{obs,i}^{4})]^{−1} |
Extinction coefficient^{17} | 0.000062(9) |
Flack parameter | −0.005(10) |
Residual electron density max; min | +2.3; −1.9 e Å^{−3} |
Atom | Site | x/a | y/b | z/c | B_{eq/iso}^{a} (Å^{−2}) |
---|---|---|---|---|---|
a B_{eq} = ⅓[B_{11} × a*^{2} × a^{2} + ⋯ + 2B_{23} × b* × c* × b × c × cos(α)]. | |||||
Y | 16c | 0.8097(1) | x | x | 0.66(2) |
Pt1 | 16c | 0.93652(4) | x | x | 0.594(6) |
Pt2 | 48e | 0.48917(4) | 0.89865(4) | 0.77608(4) | 0.607(8) |
Be1 | 12a | ⅝ | 0 | ¾ | 1.2(6) |
Be2 | 24d | 0.914(3) | 0 | ¾ | 1.1(4) |
Be3 | 48e | 0.056(2) | 0.989(2) | 0.664(2) | 1.1(3) |
Be4 | 48e | 0.620(2) | 0.919(2) | 0.893(2) | 1.0(3) |
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†) and – from distance analysis – these 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 (⅞ 0 ¼) (Wyckoff site 12b) and (⅜ 0 ¼) (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 (⅜ 0 ¼) 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 I3d, 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 Be1 – by 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 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 atoms – as expected from the electronegativity differences – reveal positive effective charges between +1.30 and +1.40, the platinum species have large negative charges of −2.72 and −3.31 for Pt1 and Pt2, respectively. This confirms strong charge transfer in the compound according to the scheme [Y^{+1.70}]_{4}[Be1^{+1.36}]_{3}[Be2^{+1.30}]_{6}[Be3^{+1.36}]_{12}[Be4^{+1.31}]_{12}[Pt1^{–2.72}]_{4}[Pt2^{−3.31}]_{12}.
Fig. 3 QTAIM atoms and their effective charges in Y_{4}Be_{33}Pt_{16}. The Pt–Pt contacts with 2.82 Å < d(Pt–Pt) < 2.91 Å are shown to emphasize the volume representation. |
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 electrons 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 four-atomic 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 cages – as obtained from the bonding analysis – within 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 two-centre (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.
Fig. 5 Calculated electronic density of states (DOS) for Y_{4}Be_{33}Pt_{16}. The total DOS (black line) is shown together with the contributions of essential atomic states. |
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 the normal state electronic specific heat coefficient γ_{n} = 18 mJ mol_{Y}^{−1} K^{−2}, as well as cubic term coefficient β = 4.5 mJ mol_{Y}^{−1} K^{−3}. Using the value of γ_{n}, it is then possible to estimate the effective mass m* from the following relation:^{22} m* = (γ_{n}ħ^{2}k_{F}^{2})/(π^{2}nk_{B}^{2}) ≈ m_{e}, indicating lack of electron mass enhancement (equivalently, the theoretically computed value of DOS at the Fermi energy yields γ_{calc} = 16.3 mJ mol_{Y}^{−1} K^{−2}). From the value of β, the Debye temperature θ_{D} can be calculated using θ_{D} = [(14π^{4}N_{A}rk_{B})/(5β)]^{1/3} = 358 K.^{22} Consequently, the value of θ_{D} can then be used to estimate the strength of the electron–phonon coupling, employing the McMillan's formula.^{23} Typically, materials with λ_{e–p} → 1 are classified as strongly-coupled 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} (dashed line), further confirms weak coupling in Y_{4}Be_{33}Pt_{16}. The upper critical fields of non-centrosymmetric superconductors are often rather high (on the order of several or even dozens of Tesla), but Y_{4}Be_{33}Pt_{16} belongs to the smaller family of non-centrosymmetric superconductors with the upper critical fields on the order of few hundred Oersted. The other examples are AuBe (H_{c2} = 335 Oe),^{24} Mo_{2}Al_{3}C (H_{c2} = 50 Oe),^{25} or LaRhSi_{3} (H_{c2} = 180 Oe).^{26}
The fact, that – despite of absence of inversion symmetry – no 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.
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.
Footnotes |
† Electronic supplementary information (ESI) available. CCDC 1996617. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/d0dt01374a |
‡ Current address: Department of Chemistry, University College London. |
This journal is © The Royal Society of Chemistry 2020 |