Article Cite This: Acc. Chem. Res. 2018, 51, 214−222
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Cluster Formation in the Superconducting Complex Intermetallic Compound Be21Pt5 Published as part of the Accounts of Chemical Research special issue “Advancing Chemistry through Intermetallic Compounds”. Alfred Amon,† Alim Ormeci,† Matej Bobnar,† Lev G. Akselrud,†,‡ Maxim Avdeev,∥ Roman Gumeniuk,§ Ulrich Burkhardt,† Yurii Prots,† Christoph Hennig,⊥ Andreas Leithe-Jasper,† and Yuri Grin*,† †
Max-Planck-Institut für Chemische Physik fester Stoffe, 01187 Dresden, Germany Ivan-Franko National University, Lviv 79000, Ukraine ∥ Australian Nuclear Science and Technology Organisation, Sydney, NSW 2232, Australia § Technische Universität Bergakademie Freiberg, 09599 Freiberg, Germany ⊥ Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany ‡
S Supporting Information *
CONSPECTUS: Materials with the crystal structure of γ-brass type (Cu5Zn8 type) are typical representatives of intermetallic compounds. From the electronic point of view, they are often interpreted using the valence electron concentration approach of Hume−Rothery, developed previously for transition metals. The γ-brass-type phases of the main-group elements are rather rare. The intermetallic compound Be21Pt5, a new member of this family, was synthesized, and its crystal structure, chemical bonding, and physical properties were characterized. Be21Pt5 crystallizes in the cubic space group F4̅3m with lattice parameter a = 15.90417(3) Å and 416 atoms per unit cell. From the crystallographic point of view, the binary substance represents a special family of intermetallic compounds called complex metallic alloys (CMA). The crystal structure was solved by a combination of synchrotron and neutron powder diffraction data. Besides the large difference in the scattering power of the components, the structure solution was hampered by the systematic presence of very weak reflections mimicking wrong symmetry. The structural motif of Be21Pt5 is described as a 2 × 2 × 2 superstructure of the γ-brass structure (Cu5Zn8 type) or 6 × 6 × 6 superstructure of the simple bcc structural pattern with distinct distribution of defects. The main building elements of the crystal structure are four types of nested polyhedral units (clusters) with the compositions Be22Pt4 and Be20Pt6. Each cluster contains four shells (4 + 4 + 6 + 12 atoms). Clusters with different compositions reveal various occupation of the shells by platinum and beryllium. Polyhedral nested units with the same composition differ by the distance of the shell atoms to the cluster center. Analysis of chemical bonding was made applying the electron localizability approach, a quantum chemical technique operating in real space that is proven to be especially efficient for intermetallic compounds. Evaluations of the calculated electron density and electron localizability indicator (ELI-D) revealed multicenter bonding, being in accordance with the low valence electron count per atom in Be21Pt5. A new type of atomic interactions in intermetallic compounds, cluster bonds involving 8 or even 14 atoms, is found in the clusters with shorter distances between the shell atoms and the cluster centers. In the remaining clusters, four- and five-center bonds characterize the atomic interactions. Multicluster interactions within the polyhedral nested units and threecenter polar intercluster bonds result in a three-dimensional framework resembling the structural pattern of NaCl. Be21Pt5 is a diamagnetic metal and one of rather rare CMA compounds revealing superconductivity (Tc = 2.06 K).
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INTRODUCTION Intermetallic compounds offer vast structural diversity, where the majority of phases adopt crystal structures with very different numbers of atoms per unit cell.1,2 A subset of intermetallic compounds termed complex intermetallic compounds, also known under the term Complex Metallic Alloys (CMAs), form large periodic structures with several hundreds to thousands of atoms per unit cell, for example, NaCd2 (Pearson symbol cF1157, a = 30.56 Å) or Al55.4Cu5.4Ta39.1 (cF23256-x, a = 71.49 Å).1,3−7 The atomic arrangements in CMAs often mimic structural motifs of simpler compounds, for © 2018 American Chemical Society
example, by hierarchical replacement of atomic positions in the simpler structures by larger atomic clusters in the complex ones.1,8,9 Several factors that are unfavorable for efficient cluster packing, like strong preference of specific first shell coordination environments or the stabilization of a more favorable band structure, can lead to a reduction of symmetry or to the formation of superstructures with large translational periods.9 The discovery of quasicrystals has refueled interest in Received: November 9, 2017 Published: January 9, 2018 214
DOI: 10.1021/acs.accounts.7b00561 Acc. Chem. Res. 2018, 51, 214−222
Article
Accounts of Chemical Research CMAs.1,3,4,10 The quasicrystal approximants typically have a composition close to the quasicrystalline phase and display closely related local atomic arrangements (clusters), for example, the icosahedral quasicrystal YbCd5.7 and its cubic approximant YbCd6.11,12 Most reported CMAs are binary or ternary compounds, formed mainly by metals from groups 12 to 14. CMAs have unique properties and application potential in catalysis, thermoelectrics, and magnetocalorics.13−16 The derivatives of the Cu5Zn8-type (γ-brass) structure, often called γ-phases, are at the border between the small-unit-cell intermetallic compounds and CMAs with giant unit cells.17 Their structures can be understood as consisting of polyhedral cluster units where the relative arrangement of these clusters determines the observed translational periodicity. The crystal structures and electronic configurations of γ-phases have been intensively studied, leading to the development of the theory about electronic stabilization mechanisms for metallic alloys, also known as Hume−Rothery rules.18−21 The γ-phases exist for metals from group 10 or 11 with groups 12 to 14 and also for alkaline and alkaline earth metals. Detailed investigations of the binary systems of group 10 with group 12 metals have shown that, in addition to the cubic γ-phases, several new compounds with related structures were obtained.22−25 Small deviations in stoichiometry, as in the Ni−Zn system, lead to the appearance of two orthorhombic phases next to the γ-phase Ni4Zn22.26 The majority of the γ-brass phases are formed by late transition metals, very often with zinc as majority component. Among the main-group elements, Li, Mg, Al, and Ga serve as components of the compounds of this family.27 Zinc and beryllium often show similar chemical behavior in inorganic compounds as they both contain an s2 valence shell configuration (e.g., see ref 28). Beryllium-rich compounds often exhibit interesting structural motifs with large coordination numbers as in the structure of Ru3Be17,29 which is closely related to the above-mentioned YbCd6. However, the preparation and, especially, structural characterization of Berich compounds remain challenging due to the low X-ray scattering power of Be. So, an early report on the Pt−Be system mentions a Be-rich compound with large unit cell, but no further structural investigation was performed.30,31 Thus, the goal of the present study was the synthesis and investigation of the crystal structure and physical properties of the γ-phase Be21Pt5 - as well as the analysis of the concomitant chemical bonding. Details of experimental work and calculation procedures are described in the Supporting Information.
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Figure 1. Thermal behavior of Be21Pt5 (DTA). During the first heating cycle, the exothermal decomposition is visible at 790 °C, followed by the endothermal effect at 1190 °C visualizing the equilibrium Be21Pt5 ↔ Be5Pt + Be23Pt7.
the eutectoid decomposition of the remaining Be21Pt5 phase is observed around 1050 °C. The subsequent heating and cooling cycle shows only the eutectoid reaction above. No melting point was observed up to 1490 °C. Thus, the phase Be21Pt5 is formed congruently from the melt above 1500 °C and decomposes eutectoidally at 1190 °C. Crystal Structure Determination
The X-ray powder diffraction pattern of the single-phase sample (Figure 2, top) was indexed in a cubic F-centered cell with the lattice parameter a ≈ 15.90 Å. The reflection conditions (0kl observed only with k,l = 2n, k + l = 4n; hhl observed only with h + l = 2n; 00l observed only with l = 4n) suggested the space groups Fd3̅ (No. 203) or Fd3̅m (No. 227). The growth of
RESULTS AND DISCUSSION
Phase Formation of Be21Pt5
Single-phase polycrystalline specimens of nominal composition Be21Pt5 were obtained by arc melting of the elements. The ascast samples were found to be single-phase. These samples were annealed at 900 °C. However, the powder X-ray diffraction pattern showed that only the neighboring phases in the phase diagram, Be5Pt and Be23Pt7, were obtained with this treatment. The microstructure analysis confirmed the formation of these two phases but not Be21Pt5 (Figure S1). In order to clarify the formation conditions of Be21Pt5, the thermal behavior of the single-phase as-cast sample was investigated. During the first heating cycle, the exothermal decomposition of the high-temperature phase Be21Pt5 was observed around 790 °C (Figure 1). The effect at 1190 °C was ascribed to the eutectoid equilibrium Be21Pt5 ↔ Be5Pt + Be23Pt7. On cooling,
Figure 2. Synchrotron X-ray powder diffraction pattern (upper panel) and neutron powder diffraction patter (lower panel) of Be21Pt5. Insets: reflections (002) and (0010) or (068) appear extinct in the diffraction pattern. Experimental points are drawn as black circles and peak positions in the space group F4̅3m as black ticks. Calculated profile and difference plot are shown in red and blue, respectively. 215
DOI: 10.1021/acs.accounts.7b00561 Acc. Chem. Res. 2018, 51, 214−222
Article
Accounts of Chemical Research Crystal Structure
single crystals suitable for X-ray diffraction experiments turned out to be very difficult due to the complex phase diagram (see above and Supporting Information). Therefore, synchrotron powder diffraction data were recorded first on the polycrystalline specimen. The structure solution was then attempted in both space groups. The calculated intensities of the obtained model, for example, in the space group Fd3̅m, containing 80 Pt atoms per unit cell (Wyckoff positions 48f and 32e), showed strong deviations from the experimental data. Only by splitting of the 32e Pt position into two with half occupancies a reasonable agreement was obtained. This partial Pt structure was described without split positions in the space group F43̅ m (No. 216). However, it should be noted that the calculated intensities of the reflections 0kl with k,l = 2n and k + l = 2n, which distinguish between the extinction conditions of Fd3̅m and F4̅3m, have very low intensity and appear practically extinct in the powder diffraction data (Table S1 and inset of Figure 2) simulating another Laue class. Further analysis of the available single crystal data confirmed the observed reflections 0kl with k = 2n and l = 2n being in agreement with the extinction symbol F--- for this compound (see Supporting Information). Structure solution in F43̅ m from synchrotron powder data (WinCSD software, see Supporting Information) yielded four Pt positions (2 × 16e, 24f, and 24g). After refinement of profile parameters, atomic coordinates, and isotropic atomic displacement parameters (ADPs) for Pt, four Be positions were obtained from subsequent difference Fourier maps. The composition of the sample suggested an approximate unit-cell content of Be340Pt80, while the preliminary model above corresponded to Be96Pt80. In the difference Fourier map calculated on the synchrotron diffraction data, no further Be atoms were located due to the large difference in X-ray scattering power between Pt and Be. To determine the positions of the remaining Be atoms, neutron powder diffraction data were recorded (Figure 2, bottom) as the coherent neutron scattering length is of similar magnitude for both elements. After refining the atomic parameters of the partial structural model against the neutron powder pattern, eight more Be positions were located in the difference Fourier map resulting in the unit cell content of Be336Pt80 = 16 × Be21Pt5. The atomic coordinates of all atoms and overall ADPs for Pt and Be atoms were refined. The refinement converged at RB = 4.1%, Rp = 7.1% and Rwp = 8.7%. The structural model obtained from neutron diffraction data was finally refined against the high-resolution synchrotron data. All beryllium positions were refined with one common ADP. The Pt positions were refined with anisotropic ADPs while applying a microabsorption correction to the data. The refinement converged at RB = 3.5%, Rp = 12.8%, and Rwp = 12.6% (crystallographic data in Tables S2, S3, and S4 in the Supporting Information). For samples with Be or Pt excess, in which Be21Pt5 is in equilibrium with its neighboring phases, the lattice parameter of Be21Pt5 changes from 15.8946(2) Å at the Be-poor side to 15.9074(2) Å at Be-rich side, which indicates the existence of a small homogeneity range. The close values of isotropic atomic displacement parameters for the Pt atoms indicate full occupancies of these crystallographic positions. Thus, the homogeneity range may originate from the partial occupancy of some Be sites.
Be21Pt5 crystallizes in the structure type Li21Si5, an F-centered 2 × 2 × 2 superstructure of the γ-brass structure (Cu5Zn8 type17) and 6 × 6 × 6 superstructure of the bcc structure. The interatomic distances between Pt and Be (Table S5) are similar to those observed in other beryllium-rich transition metal compounds. The Pt positions are coordinated with 13 Be atoms and the Pt−Be distances in the first coordination shell range from 2.28 to 2.62 Å, with most of them being shorter than the sum of atomic radii of the elements (rPt = 1.37 Å, rBe = 1.11 Å). The Be atoms have coordination numbers ranging from 9 to 12. The Be−Be distances in the first coordination shell range from 2.18 to 2.70 Å. The structural pattern is described using the nested polyhedral units or “clusters”, which consist of 26 atoms each and have been recognized as the basic building blocks of several complex intermetallic structures.32 Such a cluster is also known as a γ-brass unit, as it is the elemental building block of all γbrass phases with different ordering of atoms on the vertices of the polyhedral shells. The clusters in Be21Pt5 are built around the unoccupied centers at the special positions 4a, 4b, 4c, and 4d, located at (0, 0, 0), (1/2, 1/2, 1/2), (1/4, 1/4, 1/4), and (3/4, 3/4, 3/4), respectively (point symmetry 4̅3m). The first cluster shell is an empty regular “inner tetrahedron” (IT). It is followed by its dual “outer tetrahedron” (OT) as the second shell forming together a tetrahedral star (Figure 3a). The OT is
Figure 3. Atomic arrangement in the 26-atom nested polyhedral unit in Be21Pt5: (a) the first shell inner tetrahedron (IT, purple) and the second shell composed of its dual outer tetrahedron (OT, green); (b, c) the 26-atom cluster, composed of inner tetrahedron, outer tetrahedron, octahedron (OH, blue), and distorted cuboctahedron (CO, red) in two different views.
embedded in a regular octahedron (OH) where the four outer tetrahedron vertices cap four of the eight triangular faces of the octahedron. The other four OH faces are capped by the vertex atoms of the inner tetrahedron. The outermost shell is formed by a distorted cuboctahedron (CO, Figure 3b,c).32 The four observed symmetrically inequivalent cluster types found in Be21Pt5 feature the same shell structure (Table 1) but differ in the composition and shell occupation. The clusters A and A′ have the composition Be20Pt6, and the clusters B and B′ have composition Be22Pt4. The first two shells of the cluster A′ (B′) are closer to the cluster center than that in the cluster A (B); the third shell is more distant in A′ (B′) as in A (B), see Table 1. Clusters A and B form a rock salt like arrangement with the clusters A′ and B′ at the centers of the formed cubes (upper panel in Figure 4). The structure is seen as two 216
DOI: 10.1021/acs.accounts.7b00561 Acc. Chem. Res. 2018, 51, 214−222
Article
Accounts of Chemical Research
γ-phases containing one significantly larger constituent (here Pt), contacts between the larger atoms should be avoided.34,36 In accordance with these empirical observations, the only ordering that allows for no Pt−Pt contacts in Be21Pt5 is achieved by distributing Pt atoms on the OT and OH sites of two different cluster types. The arrangement of Pt on successive clusters in the [111] direction is −OH−OT−OT−OH− (corresponding to cluster sequence ABB′A′ in Figure 4) leading to the larger F-centered unit cell. In the archetype structure Cu41Sn11, the distribution of Cu and Sn on the cluster shells differs from Be21Pt5 to account for stoichiometry.33,37 Similar to the behavior of the smaller Be atoms in Be21Pt5, solely the smaller Cu atoms compose the inner tetrahedra in Cu41Sn11.36 On the IT, OT, and CO sites, some degree of substitutional disorder was found. In another Cu 41 Sn11 derivative with the approximate composition Zn21Pt5 (Pearson symbol cF416-6, a = 18.128 Å),23,38 clusters of compositions Zn22Pt4 and Zn20Pt6 were also found. The former are completely ordered, while the latter show strong substitutional disorder in the shells in contrast to fully ordered Be21Pt5. Related γ-phases with the approximate composition Zn21TM5 have been reported for TM = Ni, Pd, and Pt and for Be25−35Ni5.23,24,26 Our preliminary experiments indicate a possible metastable γ-phase also in the Pd−Be system. Thus, Be21Pt5 completes the family of γ-phases formed by the group 10 transition metals and illustrates the similar behavior of Zn and Be in these compounds.
Table 1. Polyhedral Shells of the 26-Atom Clusters in Be21Pt5 cluster (Wyckoff site) center coordinates composition ITa OTa OHa COa
A (4a)
A′ (4c)
B (4b)
B′ (4d)
000 Pt6Be20 Be3 (1.78) Be2 (2.37) Pt4 (2.83) Be9 (3.59)
1
1
3
1
1
/4 /4 /4 Pt6Be20 Be6 (1.50) Be1 (2.17) Pt3 (2.90) Be12 (3.47)
1
1
/2 /2 /2 Pt4Be22 Be5 (1.68) Pt1 (2.46) Be8 (2.71) Be11 (3.58)
/4 3/4 3/4 Pt4Be22 Be4 (1.33) Pt2 (2.40) Be7 (2.84) Be10 (3.35)
a
Shell notation: IT = inner-tetrahedron, OT = outer-tetrahedron, OH = octahedron, CO = cuboctahedron. Entries indicate shell occupation and distance (in Å; given in parentheses) between the shell atom and the cluster center.
Electronic Structure and Chemical Bonding
The electronic density of states (DOS) of Be21Pt5 (Figure 5) is dominated by Be(2p) states from the Fermi level (EF) until
Figure 4. Crystal structure of Be21Pt5: (upper panel) space-filling arrangement of the clusters in the unit cell, represented by capped cuboctahedrons; (lower panel) arrangement of the four cluster types on the Wyckoff positions 4a (blue), 4b (orange), 4c (green), and 4d (red), represented as pseudoatoms.
interpenetrating fcc lattices of “pseudoatoms” similar to the NaTl structure type (lower panel in Figure 4), similar to the arrangement found in Cu41Sn11.33,34 The clusters fill the unit cell with no voids large enough to accommodate additional atoms. Descriptions like above have often been used as a convenient way to describe compounds of the γ-brass and CMA family. However, from a geometrical point of view, the clusters are not to be seen as separated chemical entities as no significant difference between intracluster and intercluster atomic distances was found. Different ordering of atoms on the polyhedral shells leads to four structure types of γ-phases: Cu9Al4 with the primitive lattice (space group P4̅3m), body-centered Cu5Zn8 (space group I43̅ m), and face-centered Cu41Sn11 (space group F43̅ m) and Li21Si5 (space group F4̅3m, the prototype for Be21Pt5). All four are considered as superstructures to the simple bcc structure with characteristic distribution of the vacancies.2,35 In
Figure 5. Electronic density of states (DOS) of Be21Pt5: partial contributions are drawn as lines; inset shows detailed view around EF.
−3.0 eV, while between −3.0 eV and −6.5 eV, the Pt(5d) states are most prominent. Be21Pt5 can be considered a γ-brass phase in the classical Hume−Rothery formalism with an electron per atom ratio e/a = 21/13 ≈ 1.62. To achieve this ratio, only the 2s electrons of Be are taken into account, disregarding the s- or d-electrons of Pt. The seemingly arbitrary electron counting scheme applied for γ-phases has been rationalized by ab initio calculations on Cu−Al and Cu−Zn γ-phases revealing that primarily the itinerant electrons close to the Fermi level are decisive for the structure stabilization.21 From this viewpoint, the counting scheme is reasonable as the DOS around EF is 217
DOI: 10.1021/acs.accounts.7b00561 Acc. Chem. Res. 2018, 51, 214−222
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Accounts of Chemical Research
characteristic for ionic interactions; compare Mg in magnesium diboride.40 In this case, the QTAIM shape includes mostly the inner shells of an atom. Deviation from a spherical shape (Be2, Be4, Be5, Be6, Be8, and Be10) points toward a direct covalentlike interaction. Integration of the electron density within the QTAIM atoms yields their electronic populations and subtraction of the atomic numbers from the latter yields their effective charges. Platinum atoms reveal high negative charges between −4.8 and −5.7, whereas beryllium atoms play the role of cations (charges between +1.0 and +1.3). Strong charge transfer is in agreement with the large electronegativity difference between beryllium and platinum. Further details of atomic interactions were obtained from the analysis of the Electron Localizability Indicator in its ELI-D representation41,42 (Figure 7, see Supporting Information).
dominated by Be states. The stabilization by Fermi-surface/ Brillouin-zone interactions and the frequently found formation of a pseudogap in the DOS around EF have been argued to be important for the stabilization of complex metallic compounds and γ-phases of the transition metals.4,21 In Be21Pt5, the DOS markedly decreases at +0.45 eV (0.3 states eV−1 fu−1); however, the Fermi level lies well below this pseudogap (DOS(EF) = 5.0 states eV−1 fu−1, inset in Figure 5). The calculated value agrees closely with that obtained from specific heat measurements (5.94 states eV−1 fu−1). The difference between EF and the pseudogap yields 16 electrons per unit cell, that is, 4 Be atoms. In addition to the good agreement between DFT calculations and specific heat measurements, the diffraction data have been examined in detail for the possibility of an additional Be position, but none has been found. In order to analyze the atomic interactions in Be21Pt5, analysis of chemical bonding was performed applying the electron localizability approach, a quantum chemical technique operating in real space and combining the evaluation of electron density and electron-localizability indicator. This concept is proven to be especially efficient for intermetallic compounds. The total electron density was calculated and evaluated according to the Quantum Theory of Atoms in Molecules (QTAIM,39 Figure 6). The atomic shapes of beryllium atoms Be11 and Be12 are nearly spherical, which is
Figure 7. Electron localizability indicator in Be21Pt5 presented in the segment of the cubic unit cell with 0 ≤ x ≤ 0.5; 0 ≤ y ≤ 0.5, and 0 ≤ z ≤ 1.0 (black lines). Distribution of ELI-D in the (220) plane is shown together with the framework of the shortest Pt−Be contacts (
