AlPd 15 B 7 : a new superconducting cage-compound with an anti-Yb 3 Rh 4 Sn 13 -type of structure †

A new intermetallic compound AlPd 15 B 7 was synthesized by arc-melting the stoichiometric mixture of the elements. Single crystal X-ray di ﬀ raction data of ternary metal-rich boride reveal a new type of structure with the space group Ia 3¯ d and the lattice parameter a = 16.4466(3) Å. It adopts a ﬁ lled anti -Yb 3 Rh 4 Sn 13 - 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 speci ﬁ c heat measurements reveal bulk superconductivity with a critical temperature T c ≈ 2.9 K. Electronic structure calculations show that Pd 4d and B 2p states dominate the density of states (DOS) at the Fermi level E F .


Introduction
6][7][8][9] The crystal structures of both Remeika M 3 T 4 X 13 phases and filled-skutterudites 10,11 are derivatives of the simple perovskite-type structure, and show similar arrays of cornersharing 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][13][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 M 3 T 4 X 13 structures, twelve X atoms form icosahedra filled by one remaining X atom, T atoms reside in trigonal prisms formed by two neighboring [X 12 ] 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 AlPd 15 B 7 with a new type of structure, which is closely related to the Yb 3 Rh 4 Sn 13 prototype.Physical property measurements reveal superconducting behavior of this new boride with T c ≈ 2.9 K.The thermodynamic properties are compatible with an s-wave energy gap conventional superconductivity and moderate electron-phonon coupling.

Sample preparation
The samples with a nominal composition of AlPd 15 B 7 were synthesized by arc-melting of aluminum (Chempur, 99.9999 mass%) and palladium (Chempur, 99.9 mass%) foils and crystalline boron powder (Alfa Aesar, 99.999 mass%).The obtained button was remelted several times to obtain a homogeneous sample.The weight loss during arc-melting was less than 0.1 mass%.All above operations were performed inside an argon-filled glove box ( p(O 2 /H 2 O) ≤ 1 ppm).A nearly single phase sample was obtained.The resulting sample is stable in air for long time.

Powder and single-crystal X-ray diffraction
Due to the ductility, stress annealing of ground powders was performed at 840 °C for 1.5 h to obtain powder diffraction patterns with sharper and better resolved diffraction peaks.Powder X-ray diffraction (XRD) data were collected on a † Electronic supplementary information (ESI) available.CCDC 1440657.For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/ c5dt04751j a Max-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Str.40, 01187 Dresden, Germany.E-mail: roman.gumeniuk@physik.tu-freiberg.deHUBER G670 imaging plate Guinier camera (Cu K α1 radiation, λ = 1.540598Å).Phase analysis and indexing were performed within the WinXPow program package. 15Lattice parameters were refined by least-squares fitting with LaB 6 internal standard correction within the program package WinCSD. 16ingle 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 K α 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. 16Details of the single crystal XRD data collection are listed in Table 1.

Metallography
A small piece of the as-cast AlPd 15 B 7 sample was embedded in a conductive resin and then subjected to a multistep grinding and polishing process to achieve a high-quality surface.The microstructure observations were performed on an optical microscope (Axioplan 2, Zeiss) as well as on a scanning electron microscope (JSM-7800F, JEOL).The chemical composition of the observed phase was analysed by means of energy dispersive X-ray spectroscopy (EDXS, Quantax 400 EDXS system, Silicon Drift Detector, Bruker) and wavelength dispersive X-ray spectroscopy (WDXS, SX 100, Cameca) using Al K α , Pd L α , and B K α signals with elemental Al and Pd 3 B as standards.The Al : 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 Al 4.6(2) Pd 66.5(2) B 28.9(1) , respectively, in good accordance with the theoretical values (1 : 15 and Al 4.35 Pd 65.22 B 30.43 , respectively).

Physical properties
The magnetization data of a polycrystalline AlPd 15 B 7 sample were collected in external fields μ 0 H ranging from 2 mT to 7 T and temperatures between 1.8 K and 400 K on a SQUID magnetometer (MPMS-XL7, Quantum Design).The electrical resistivity was measured using a four-point ac method between 1.8 K and 320 K (PPMS, Quantum Design) on a small bar (1 mm × 1 mm × 6.5 mm).The heat capacity was measured by means of a relaxation-type calorimeter on a PPMS in external fields μ 0 H up to 0.5 T between 0.35 and 320 K.

Electronic structure calculations
The scalar-relativistic band-structure of AlPd 15 B 7 was calculated within the local-density approximation (LDA) of density functional theory (DFT) using the full-potential local-orbital FPLO code (version 9.01-35). 17The calculation was performed by employing the exchange-correlation potential of Perdew and Wang 18 and using the experimental structural data from Table 2.The first Brillouin zone was sampled by a mesh of 12 × 12 × 12 (1728) k points.

Crystal structure determination
As shown in Fig. 1 and Fig. S1 (in the ESI †), the XRD patterns of the ground powders of an as-cast AlPd 15 B 7 sample with and without stress-annealing reveal no difference between them besides peaks broadening in the latter one.As revealed by Fig. S2 in the ESI, † the content of impurities in the as-cast sample is less than 1 vol%.The strong reflections could be indexed in a simple cubic unit cell with lattice parameter a = 8.2233(2) Å.However, as one can see as an example in the inset of Fig. 1, there are still many reflections that could not be indexed in this unit cell, revealing the appearance of a superstructure.Taking these reflections into account, a body centered cubic unit cell with lattice parameter a = 16.4466(3)Å is obtained.Subsequently, single crystals were selected for XRD experiments.
Details on single crystal XRD data collection for AlPd 15 B 7 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 Ia3 ˉd.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, respect-  ively.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.

Physical properties
The magnetic susceptibility of AlPd 15 B 7 in an external field of μ 0 H = 7 T is shown in the inset of Fig. 3, revealing that it is a diamagnet with an extrapolated value of χ 0 = −2.0× 10 −4 emu mol −1 at T = 0.The slight upturn towards low temperature is probably due to minor paramagnetic impurities or point defects.
The temperature dependence of the zero-field-cooled (zfc) and field-cooled (fc) magnetic susceptibility of AlPd 15 B 7 in an external field of μ 0 H = 2 mT is given in Fig. 3 As shown in Fig. 4, the electrical resistivity of AlPd 15 B 7 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 ρ 0 + A FL T 2 with a residual resistivity ρ 0 = 0.20(1) μΩ m from impurity scattering, and the cross section of quasiparticle-quasiparticle scattering A FL = 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 res c = 2.89 K.The specific heat c p /T vs. T for AlPd 15 B 7 in the temperature range 0.35-4.0K and in various magnetic fields is shown in   5a.For zero-field, a sizable sharp step-like anomaly confirms the bulk nature of the superconductivity.The normalstate specific heat (Fig. 5b) can be described by c p,n (T ) = γ tot T + βT 3 + δT 5 in the temperature range 0.5-5 K, where γ tot is the Sommerfeld coefficient of the electronic heat capacity, and βT 3 + δT 5 are the first terms of the harmonic lattice approximation for the phonon contribution.The resulting parameters are γ tot = 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 Θ D (0) = 319 K, and δ = 2.86(6) × 10 −5 mol −1 K −6 .
The electronic contribution c el (T, H) below T c can be analyzed by subtracting the lattice terms βT 3 + δT 5 .Fig. 5c shows Δc p = c el -γ tot T which is well described by the BCS theory (for weak electron-phonon coupling) in the whole temperature range.The resulting parameters are the jump Δc p /T c = 37.5 mJ mol −1 K −2 , the transition midpoint T cal c = 2.796 K, and the width of the transition of 0.026 T c .The ratio Δc p /(γ tot T c ) of 1.32 is somewhat lower than the value 1.43 from the BCS theory.At the lowest temperatures (in the range 0. The resulting parameters for zero field are γ 0 = 2.17 mJ mol −1 K −2 and the energy gap ratio Δ/k B T c = 1.08.The non-zero γ 0 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 γ n = γ tot − γ 0 .The corrected value for the jump Δc p /(γ n T c ) = 1.44 reproduces even better the weak-coupling BCS value 1.43.However, the energy gap ratio Δ/k B T c observed at the lowest temperatures is much smaller than expected from BCS theory (Δ/k B T c = 1.76).It is therefore possible that AlPd 15 B 7 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 fitted Sommerfeld parameters γ(H) − γ 0 , 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 AlPd 15 B 7 .The upper critical field values were estimated from the midpoints of superconducting transition in c p (T, μ 0 H), as shown in Fig. 5d.It is obvious that T c (μ 0 H) varies almost linearly with μ 0 H.This most simple extrapolation results in μ 0 H c2 (0) ≈ 500(100) mT.

Electronic structure
The total and partial (atomic and orbital resolved) density of states (DOS) for AlPd 15 B 7 are shown in Fig. 6(a-c).Similar to the electronic structures of the M 3 Pt 4 Ge 13 compounds, 12,13 the Fermi level E F for AlPd 15 B 7 is located close to a dip in the DOS.Thus, the system is a metal with 7.9 states eV −1 f.u.−1 at E F .This DOS is mostly due to the contributions of the Pd 4d (∼71%) and the B 2p (∼25%) states.The broad valence band (∼7 eV) in the electronic structure of AlPd 15 B 7 is dominated by Pd 4d states (Fig. 6b) with sizeable B 2p contributions (Fig. 6c) at lower energies (between −7 eV and −3.5 eV).Furthermore, the lowest lying separate band (between −11 eV and −7.5 eV) is mainly formed by B 2s and Pd 4d states.All this is related to the covalent bonding in the Pd-B framework.Al contributions to the valence band are negligibly small.Interestingly, a narrow separate band (∼0.3 eV) centered at −7.1 eV is mostly due to 4d states of Pd2 and Pd3 as well as Al 3s.Obviously, it reflects covalent interaction of Al and Pd atoms within the [Al@Pd 12 ] icosahedra (Fig. 2).The electronic band structure of AlPd 15 B 7 is reminiscent of the electronic structures of such Pdrich borides as Pd 3 B and SrPd 4 B. 25 They also possess a broad valence band dominated by Pd 4d and B 2p states followed by a separate low energy band due to the mixing of B 2s and Pd 4d states.The differences are that for AlPd 15 B 7 a larger DOS at E F as well as an additional narrow band at −7.1 eV are observed.

Conclusions
We gratefully acknowledge Prof. Yu.Grin's interest and steady support.A new ternary boride AlPd 15 B 7 , with a filled anti-Yb 3 Rh 4 Sn 13 -type structure, has been synthesized by arcmelting mixtures of elements, and its crystal structure was determined from the single-crystal X-ray diffraction data.In this structure, the Al atoms reside in the [Pd 12 ] icosahedra, and each icosahedron interconnects with 14 neighboring [Pd 12 ] icosahedra, forming 8 corner-sharing trigonal prisms and 6 octahedra, which are all filled by the B atoms.In comparison, the corresponding octahedra are empty in the Yb 3 Rh 4 Sn 13 -type structure.
Magnetic susceptibility, electrical resistivity, and specific heat measurements show a superconducting transition of AlPd 15 B 7 at a T c of about 2.9 K.The specific heat measurements reveal AlPd 15 B 7 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 E F is dominated by d states.
AlPd 15 B 7 is the first boride with a crystal structure comprising the framework of the Remeika Yb 3 Rh 4 Sn 13 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.

AlPd 15 B
7 crystallizes with a new type of structure, which can be regarded as a filled anti-Yb 3 Rh 4 Sn 13 structure.The crystal structures of AlPd 15 B 7 and Yb 3 Rh 4 Sn 13 are shown in Fig. 2a and Fig. S3 in the ESI, † respectively.The group-subgroup relationship between them is shown in Fig. 2b.The crystallographic positions for 3Yb, 4Rh and 13Sn atoms in the Yb 3 Rh 4 Sn 13 structure 1 are now occupied by 3Pd, 4B, and 1Al + 12Pd atoms in the AlPd 15 B 7 structure, respectively.The octahedra formed by Yb and Sn atoms are empty in the Yb 3 Rh 4 Sn 13 -type structure, whereas the corresponding octahedra solely formed by Pd atoms are filled by additional B atoms in the AlPd 15 B 7 structure.The transformation between these two types of structures can be described as: M 3 T 4 X 12 X 1A3 ÀÀÀÀÀÀ!anti-type T 3 X 4 T 12 M 1A3 ÀÀÀÀÀÀ!A filled by X T 3 X 4 T 12 M 1 X 3 !M 1 T 15 X 7 where M, T, and X are Yb, Rh, and Sn in Yb 3 Rh 4 Sn 13 , and Al, Pd and B in AlPd 15 B 7 .Different from Yb 3 Rh 4 Sn 13 , the lattice parameters of AlPd 15 B 7 are doubled and the space group changes from Pm3 ˉn to Ia3 ˉd, 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 Yb 3 Rh 4 Sn 13 -type of structure (e.g.La 3 Rh 4 Sn 13 (I4 1 32), Ca 3 Pt 4+x Ge 13−y (I2 1 3),

Fig. 1
Fig. 1 Experimental (black circles) and calculated (red line) powder XRD patterns of an as-cast AlPd 15 B 7 sample after grinding and subsequent stress-annealing at 840 °C for 1.5 h.Peak positions of AlPd 15 B 7 are given by black ticks; the difference plot is shown as a black line in the bottom.The inset shows the 2θ-range from 45.8°to 52°, where the reflections corresponding to the superstructure are marked by asterisks (see text).

Fig. 2
Fig. 2 (a) Crystal structure of AlPd 15 B 7 .For a better visualization, only a part of the structure in one unit cell is shown.[Al@Pd 12 ] icosahedralight gray; distorted [B@Pd 6 ] trigonal prismsdark gray; [B@Pd 6 ] octahedrablue.(b) group-subgroup relationship between the structures of Yb 3 Rh 4 Sn 13 and AlPd 15 B 7 (see text).For better visualization the coordinates for AlPd 15 B 7 are not standardized, like those given in Table2.
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 (r B = 0.83 Å, r Al = 1.43 Å, and r Pd = 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 AlPd 15 B 7 are shown in Fig. S4 in the ESI.† , indicating a superconducting transition.The transition temperature was determined via a tangent to the steepest slope of χ zfc (T ), resulting in T c mag = 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).

Fig. 3 Fig. 4
Fig. 3 Magnetic susceptibility for AlPd 15 B 7 in a field μ 0 H = 2 mT measured during warming after zero-field cooling (zfc) and during field cooling (fc).The inset shows the magnetic susceptibility in a field μ 0 H = 7 T.

Fig.
Fig.5a.For zero-field, a sizable sharp step-like anomaly confirms the bulk nature of the superconductivity.The normalstate specific heat (Fig.5b) can be described by c p,n (T ) = γ tot T + βT 3 + δT 5 in the temperature range 0.5-5 K, where γ tot is the Sommerfeld coefficient of the electronic heat capacity, and βT 3 + δT 5 are the first terms of the harmonic lattice approximation for the phonon contribution.The resulting parameters are γ tot = 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 Θ D (0) = 319 K, and δ = 2.86(6) × 10 −5 mol −1 K −6 .The electronic contribution c el (T, H) below T c can be analyzed by subtracting the lattice terms βT 3 + δT5 .Fig.5cshows Δc p = c el -γ tot T which is well described by the BCS theory (for weak electron-phonon coupling) in the whole temperature range.The resulting parameters are the jump Δc p /T c = 37.5 mJ mol −1 K −2 , the transition midpoint T cal c = 2.796 K, and the width of the transition of 0.026 T c .The ratio Δc p /(γ tot T c ) of 1.32 is somewhat lower than the value 1.43 from the BCS theory.At the lowest temperatures (in the range 0.35-0.70K) c el (T ) is well Fig.5a.For zero-field, a sizable sharp step-like anomaly confirms the bulk nature of the superconductivity.The normalstate specific heat (Fig.5b) can be described by c p,n (T ) = γ tot T + βT 3 + δT 5 in the temperature range 0.5-5 K, where γ tot is the Sommerfeld coefficient of the electronic heat capacity, and βT 3 + δT 5 are the first terms of the harmonic lattice approximation for the phonon contribution.The resulting parameters are γ tot = 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 Θ D (0) = 319 K, and δ = 2.86(6) × 10 −5 mol −1 K −6 .The electronic contribution c el (T, H) below T c can be analyzed by subtracting the lattice terms βT 3 + δT5 .Fig.5cshows Δc p = c el -γ tot T which is well described by the BCS theory (for weak electron-phonon coupling) in the whole temperature range.The resulting parameters are the jump Δc p /T c = 37.5 mJ mol −1 K −2 , the transition midpoint T cal c = 2.796 K, and the width of the transition of 0.026 T c .The ratio Δc p /(γ tot T c ) of 1.32 is somewhat lower than the value 1.43 from the BCS theory.At the lowest temperatures (in the range 0.35-0.70K) c el (T ) is well fitted by c el ¼ γ 0 T þ γT c Ae ÀΔð0Þ kBT (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 γ 0 = 2.17 mJ mol −1 K −2 and the energy gap ratio Δ/k B T c = 1.08.The non-zero γ 0 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 γ n = γ tot − γ 0 .The corrected value for the jump Δc p /(γ n T c ) = 1.44 reproduces even better the weak-coupling BCS value 1.43.However, the energy gap ratio Δ/k B T c observed at the lowest temperatures is much smaller

Fig. 5
Fig. 5 (a) Molar specific heat c p /T of AlPd 15 B 7 in various magnetic fields; (b) the low-temperature normal-state c p (T ) for AlPd 15 B 7 together with the fit to c p = γ tot T + βT 3 + δT 5 ; (c) fitting of the difference specific heat Δc p = c el -γ tot T based upon the BSC theory; (d) upper critical field μ 0 H c2 of AlPd 15 B 7 vs.T derived from the midpoints of the superconducting transitions in c p (T, H).

Fig. 6
Fig. 6 (a) Total and atom resolved electronic density of states (DOS) for AlPd 15 B 7 .Orbital resolved DOS for (b) palladium and (c) boron atoms.

Table 1
Crystallographic data for AlPd 15 B 7