Open Access Article
Qiang
Zheng
a,
Walter
Schnelle
a,
Yurii
Prots
a,
Matej
Bobnar
a,
Ulrich
Burkhardt
a,
Andreas
Leithe-Jasper
a and
Roman
Gumeniuk
*ab
aMax-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Str. 40, 01187 Dresden, Germany. E-mail: roman.gumeniuk@physik.tu-freiberg.de
bInstitut für Experimentelle Physik, TU Bergakademie Freiberg, Leipziger Str. 23, 09596 Freiberg, Germany
First published on 2nd February 2016
A new intermetallic compound AlPd15B7 was synthesized by arc-melting the stoichiometric mixture of the elements. Single crystal X-ray diffraction data of ternary metal-rich boride reveal a new type of structure with the space group Ia
d and the lattice parameter a = 16.4466(3) Å. It adopts a filled anti-Yb3Rh4Sn13-type structure, where the positions corresponding to 3Yb, 4Rh and 13Sn atoms are occupied by 3Pd, 4B, and 1Al + 12 Pd, respectively and 3B additionally at interstitial sites. Magnetic susceptibility, electrical resistivity, and specific heat measurements reveal bulk superconductivity with a critical temperature Tc ≈ 2.9 K. Electronic structure calculations show that Pd 4d and B 2p states dominate the density of states (DOS) at the Fermi level EF.
n).1–4 They became an object of numerous studies, mostly owing to the interesting interplay between magnetic and superconducting properties.1,5–9 The crystal structures of both Remeika M3T4X13 phases and filled-skutterudites10,11 are derivatives of the simple perovskite-type structure, and show similar arrays of corner-sharing trigonal prisms/antiprisms (octahedra) enclosing icosahedral voids. For more details about their structural relationships, we refer to ref. 12 (and references therein). In recent studies,12–14 several new cubic, tetragonal, rhombohedral and monoclinic distorted variants of the Remeika prototype with a Pt–Ge framework were reported. In these structures, distortions occur exclusively in the Ge-framework, while M and Pt atoms remain in their original positions. In the M3T4X13 structures, twelve X atoms form icosahedra filled by one remaining X atom, T atoms reside in trigonal prisms formed by two neighboring [X12] icosahedra, and M atoms are encapsulated in cubooctahedra built by X atoms (see Fig. S3 in the ESI†). Owing to the variety of M, T, and X elements forming such compounds without major changes in the crystal structures, substitution by elements not only limited to the above mentioned groups should be possible.
In this study, we report the boride AlPd15B7 with a new type of structure, which is closely related to the Yb3Rh4Sn13 prototype. Physical property measurements reveal superconducting behavior of this new boride with Tc ≈ 2.9 K. The thermodynamic properties are compatible with an s-wave energy gap conventional superconductivity and moderate electron–phonon coupling.
Single crystals were selected from the stress-annealed crushed sample. Single crystal XRD data were collected on a Rigaku AFC7 diffraction system equipped with a Saturn 724+ CCD detector (Mo Kα radiation, λ = 0.71073 Å). Absorption correction was made using a multi-scan procedure. The crystal structure was solved by a direct phase determination method and refined by a full-matrix least-squares procedure within the program package WinCSD.16 Details of the single crystal XRD data collection are listed in Table 1.
| Composition | AlPd15B7 |
|---|---|
| Space group |
Ia d |
| Lattice parameters | |
| a (Å) | 16.4466(3) |
| V (Å3) | 4448.7(3) |
| Formula unit per cell, Z | 16 |
| Calculated density (g cm−3) | 10.14 |
| Diffraction system | Rigaku AFC7 |
| Radiation; λ (Å) | Mo Kα; 0.71073 Å |
| 2θmax (°) | 67.07 |
| Absorption coefficient (mm−1) | 23.07 |
| N(hkl)measured | 18 108 |
| N(hkl)unique | 730 |
| N(hkl)observed (Fhkl > 4σ(F)) | 718 |
| R int/Rσ | 0.053/0.037 |
| Refined parameters | 32 |
| R F/wRF2 | 0.058/0.064 |
| Extinction coefficient | 0.00026(2) |
| Residual electron density (e Å−3) | +1.1; −0.8 |
:
Pd atomic ratio of the studied phase from EDXS and its composition from WDXS were measured to be 0.9(1)
:
15.0(1) and Al4.6(2)Pd66.5(2)B28.9(1), respectively, in good accordance with the theoretical values (1
:
15 and Al4.35Pd65.22B30.43, respectively).
| Atom | Site | x | y | z | B iso/Beqa |
|---|---|---|---|---|---|
a
B
eq = 1/3[a*2a2B11 + b*2b2B22 + c*2c2B33 + 2aba*b*(cos γ)B12 + 2aca*c*(cos β)B13 + 2bcb*c*(cos α)B23].
|
|||||
| Al | 16a | 0 | 0 | 0 | 1.08(8) |
| Pd1 | 48g | 1/8 | 0.24484(6) | 0.00516(6) | 1.23(2) |
| Pd2 | 96h | 0.00090(6) | 0.14693(6) | 0.07718(6) | 0.99(2) |
| Pd3 | 96h | 0.10758(6) | 0.24514(6) | 0.33770(6) | 1.13(2) |
| B1 | 16b | 1/8 | 1/8 | 1/8 | 1.4(5) |
| B2 | 48f | 0.263(2) | 0 | 1/4 | 1.5(3) |
| B3 | 48g | 1/8 | 0.619(1) | 0.631(1) | 1.4(3) |
Details on single crystal XRD data collection for AlPd15B7 are listed in Table 1. Analysis of the reflection intensities and the extinction conditions confirm the appearance of the superstructure, indicating centrosymmetry and only one possible space group Ia
d. Positions of the heavy Pd and Al atoms and the light B atoms were acquired by a direct phase determination procedure and from difference Fourier maps, respectively. Anisotropic displacement parameters for all the Al and Pd atoms were refined. Final atomic coordinates and anisotropic atomic displacement parameters are listed in Tables 2 and 3, respectively. Moreover, diffraction data were also collected for single crystals selected from powders of the as-cast sample without stress annealing, and reveal the same structure solution result and only larger residual values due to broadening of the reflections. The acquired composition is in good agreement with the compositions from the EDXS and WDXS analysis.
| Atom | B 11 | B 22 | B 33 | B 12 | B 13 | B 23 |
|---|---|---|---|---|---|---|
| Al | 1.1(1) | B 11 | B 11 | −0.06(15) | B 12 | B 12 |
| Pd1 | 1.09(5) | 1.31(4) | B 22 | −0.11(3) | B 12 | 0.12(4) |
| Pd2 | 0.93(4) | 1.09(4) | 0.96(4) | 0.01(2) | −0.02(2) | 0 |
| Pd3 | 1.26(4) | 1.08(4) | 1.06(4) | −0.09(3) | −0.02(3) | −0.14(3) |
n to Ia
d, due to the shift of the Pd atoms from some special positions. As one can see in Fig. 6 in ref. 13, the relationship between many derivatives of the primitive cubic Yb3Rh4Sn13-type of structure (e.g. La3Rh4Sn13 (I4132), Ca3Pt4+xGe13−y (I213),12 HT-Y3Pt4Ge13 (R3c),13 Yb3Pt4Ge13 (P42cm),12 and LT-Y3Pt4Ge13 (Cc)14) can be understood within a group–subgroup scheme. AlPd15B7 crystallizes with the space group Ia
d, which links the space groups Pm
n and I4132 via the indices of k4 (klassengleiche) and t2 (translationengleiche) symmetry reductions, respectively.
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| Fig. 2 (a) Crystal structure of AlPd15B7. For a better visualization, only a part of the structure in one unit cell is shown. [Al@Pd12] icosahedra – light gray; distorted [B@Pd6] trigonal prisms – dark gray; [B@Pd6] octahedra – blue. (b) group–subgroup relationship between the structures of Yb3Rh4Sn13 and AlPd15B7 (see text). For better visualization the coordinates for AlPd15B7 are not standardized, like those given in Table 2. | ||
The AlPd15B7 structure is shown in Fig. 2a, and interatomic distances are listed in Table S1 in the ESI.† In such a structural arrangement, similar to Al residing in [Ni12] icosahedra in the AlNi9B8 structure,19 each Al atom resides in a distorted [Pd12] icosahedron, consisting of 6Pd2 and 6Pd3 atoms, with the Al–Pd and Pd–Pd distances ranging from 2.730 Å to 2.752 Å, and from 2.714 Å to 2.955 Å, respectively. The empty spaces between the icosahedra are occupied by the Pd1, B1, B2 and B3 atoms. Each [Al@Pd12] icosahedron interconnects with 14 neighboring [Al@Pd12] icosahedra via 8 distorted corner-sharing trigonal prisms and 6 distorted octahedra. The two sorts of corner-sharing [Pd6] trigonal prisms, formed by 6 Pd2 atoms or 2Pd2 and 4Pd3 atoms, are centered by the B1 or B3 atoms, respectively. In a [B1Pd6] trigonal prism, the Pd2–Pd2 distances are 2.850 Å and 2.942 Å, and the Pd–B distance is 2.217 Å; in a [B3Pd6] trigonal prism, the Pd–Pd distances are in the range of 2.885 Å to 2.955 Å, the Pd2–B3 distance is 2.139 Å, and the Pd3–B3 distances are 2.157 Å and 2.28 Å. Each [Pd6] octahedron, formed by 2Pd1, 2Pd2, and 2Pd3 atoms, is centered by a B2 atom, with Pd–Pd distances and Pd–B distances ranging from 2.714 Å to 3.5423 Å and from 2.08 Å to 2.252 Å, respectively. These kinds of metal–atom coordination of boron are commonly observed in borides.20,21 In Pd3B (Fe3C type of structure),22 B resides in trigonal prisms with Pd–B distances of 2.166 Å to 2.180 Å; in Pd2B (anti-CaCl2 type of structure),23 B centers Pd octahedra with Pd–B distances of 2.104 Å to 2.122 Å. In comparison with the sum of atomic radii of pure elements (rB = 0.83 Å, rAl = 1.43 Å, and rPd = 1.38 Å (ref. 24)), the Al–Pd distances are shorter than the sum of atomic radii of Al and Pd, the Pd–Pd distances obviously deviate from the two-fold atomic radius of Pd, and the shortest and longest Pd–B distances are 6% shorter and ∼3% longer than the sum of atomic radii of Pd and B, respectively. Coordination polyhedra of all the atoms in AlPd15B7 are shown in Fig. S4 in the ESI.†
The temperature dependence of the zero-field-cooled (zfc) and field-cooled (fc) magnetic susceptibility of AlPd15B7 in an external field of μ0H = 2 mT is given in Fig. 3, indicating a superconducting transition. The transition temperature was determined via a tangent to the steepest slope of χzfc(T), resulting in Tcmag = 2.78 K. Considering the demagnetization correction, the diamagnetic response in zfc is close to complete. The fc signal (Meißner effect) is much weaker, which is due to strong flux line pinning in the type-II superconductor (see below).
As shown in Fig. 4, the electrical resistivity of AlPd15B7 increases with increasing temperature in the range of 3.0–320 K, revealing a metallic behavior of this compound. For 4 K < T < 40 K, it can be fitted to ρ0 + AFLT2 with a residual resistivity ρ0 = 0.20(1) μΩ m from impurity scattering, and the cross section of quasiparticle–quasiparticle scattering AFL = 3.96(3) × 10−5 μΩ m K−2. The room-temperature resistivity ρ(300 K) is 0.68 μΩ m, and the residual resistivity ratio RRR = 3.4 indicates moderate quality of the investigated polycrystalline sample. As revealed by the inset of Fig. 4, a sharp superconducting transition can be observed, and the resistivity drops to zero at T
resc = 2.89 K.
The specific heat cp/T vs. T for AlPd15B7 in the temperature range 0.35–4.0 K and in various magnetic fields is shown in Fig. 5a. For zero-field, a sizable sharp step-like anomaly confirms the bulk nature of the superconductivity. The normal-state specific heat (Fig. 5b) can be described by cp,n(T) = γtotT + βT3 + δT5 in the temperature range 0.5–5 K, where γtot is the Sommerfeld coefficient of the electronic heat capacity, and βT3 + δT5 are the first terms of the harmonic lattice approximation for the phonon contribution. The resulting parameters are γtot = 28.3(1) mJ mol−1 K−2 and β = 1.38(2) mJ mol−1 K−4, which corresponds to an initial Debye temperature ΘD(0) = 319 K, and δ = 2.86(6) × 10−5 mol−1 K−6.
The electronic contribution cel(T, H) below Tc can be analyzed by subtracting the lattice terms βT3 + δT5. Fig. 5c shows Δcp = cel – γtotT which is well described by the BCS theory (for weak electron–phonon coupling) in the whole temperature range. The resulting parameters are the jump Δcp/Tc = 37.5 mJ mol−1 K−2, the transition midpoint Tcalc = 2.796 K, and the width of the transition of 0.026 Tc. The ratio Δcp/(γtotTc) of 1.32 is somewhat lower than the value 1.43 from the BCS theory. At the lowest temperatures (in the range 0.35–0.70 K) cel(T) is well fitted by
(as shown in Fig S5a in the ESI†). Such exponential behavior is expected for an s-wave superconductor without nodes of the gap, as in the BCS theory. The resulting parameters for zero field are γ0 = 2.17 mJ mol−1 K−2 and the energy gap ratio Δ/kBTc = 1.08. The non-zero γ0 is probably due to the presence of a non-superconducting metallic impurity phase. We may thus correct the normal state electronic specific heat coefficient by γn = γtot − γ0. The corrected value for the jump Δcp/(γnTc) = 1.44 reproduces even better the weak-coupling BCS value 1.43. However, the energy gap ratio Δ/kBTc observed at the lowest temperatures is much smaller than expected from BCS theory (Δ/kBTc = 1.76). It is therefore possible that AlPd15B7 needs to be described within a two-gap model. The resolution of the present specific heat data, due to the small available mass for the study, is insufficient for a more sophisticated analysis.
The DFT calculations reveal a DOS at the Fermi level N(EF) = 7.9 states eV−1 f.u.−1 (see below), converting to a “bare” Sommerfeld coefficient of the electronic specific heat γbare = 18.6 mJ mol−1 K−2. The electron–phonon coupling parameter λ in the relation γN = (1 + λ) γbare is calculated to be 0.40. λ can also be estimated from the McMillan formula ln(1.45Tc/ΘD) = −1.04 (1 + λ)/[λ − μ*(1 + 0.62λ)]. Assuming the common value μ* = 0.15, λ results as 0.58, which is somewhat larger than the above value.
The fitted Sommerfeld parameters γ(H) − γ0, extrapolated to T = 0, were plotted against the fields (Fig. S5b in the ESI†), showing a linear relationship with the magnetic fields. This also indicates a typical s-wave gap for AlPd15B7. The upper critical field values were estimated from the midpoints of superconducting transition in cp(T, μ0H), as shown in Fig. 5d. It is obvious that Tc(μ0H) varies almost linearly with μ0H. This most simple extrapolation results in μ0Hc2(0) ≈ 500(100) mT.
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| Fig. 6 (a) Total and atom resolved electronic density of states (DOS) for AlPd15B7. Orbital resolved DOS for (b) palladium and (c) boron atoms. | ||
Magnetic susceptibility, electrical resistivity, and specific heat measurements show a superconducting transition of AlPd15B7 at a Tc of about 2.9 K. The specific heat measurements reveal AlPd15B7 to be a conventional s-wave superconductor with weak electron–phonon coupling according to the BCS theory. Electronic structure calculations by DFT reveal that the DOS at EF is dominated by d states.
AlPd15B7 is the first boride with a crystal structure comprising the framework of the Remeika Yb3Rh4Sn13 prototype but being decorated by completely different types of elements. The occurrence of this new type of structure suggests that the constituting elements in the Remeika structure framework could be extended to a variety of elements in future investigations.
Footnote |
| † Electronic supplementary information (ESI) available. CCDC 1440657. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c5dt04751j |
| This journal is © The Royal Society of Chemistry 2016 |