Article pubs.acs.org/cm
Phosphide−Tetrahedrite Ag6Ge10P12: Thermoelectric Performance of a Long-Forgotten Silver-Cluster Compound Jürgen Nuss,* Ulrich Wedig, Wenjie Xie,† Petar Yordanov, Jan Bruin, Ralph Hübner,‡ Anke Weidenkaff,† and Hidenori Takagi‡,§ Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany S Supporting Information *
ABSTRACT: The air-stable phosphide, Ag6Ge10P12, was synthesized from its elements in gram amounts. As its structure is closely related to high-performance thermoelectric tetrahedrites (Ag6□Ge4Ge6P12 ≡ Cu6SSb4Cu6S12), we studied temperature dependent single-crystal X-ray diffraction experiments, quantum chemical calculations, and thermoelectric transport properties of spark plasma sintered and pristine, single crystalline samples, in order to give a comprehensive picture of its thermoelectric performance and its origin. The semiconducting character of this material is reflected in band structure calculations. Measurements of the thermal diffusivity exhibit a very low thermal conductivity, κ < 1 W m−1 K−1, which is close to a phonon glass-like behavior, and has its origin in a strong local bonding asymmetry, induced by strong bonding of the phosphorus−germanium (Ge4+) covalent framework and weak bonding of lone-pair electrons (Ge2+). This chemical bond hierarchy creates a pronounced anisotropic behavior of the silver atoms leading to low-frequency vibrations and thermal damping. Combining this with a moderate electrical resistivity (ρ ∼ 15 mΩ cm) and a high Seebeck coefficient (S ∼ 380 μV K−1) results in a remarkably high figure of merit (zT) of about 0.6 at 700 K. These results demonstrate that Ag6Ge10P12 is one of the best thermoelectric phosphides and a promising new platform for the future development of thermoelectrics.
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INTRODUCTION Chalcogenides are important materials for thermoelectric applications. In particular in the Tetrahedrites, named after the mineral Cu12Sb4S13, the dimensionless thermoelectric figure of merit reaches zT ∼ 1 by tuning the composition.1−5 In the case of the pnictides, the neighboring group in the periodic table, the Skutterudites,6−9 and Zintl phases derived from Yb14MnSb1110,11 are further prominent examples with outstanding thermoelectric properties. The phosphides, being famous in Zintl chemistry,12,13 can show complex crystal structures, disorder, or multiple bonding types; accordingly these materials can fulfill a lot of the criteria for good thermoelectrics. Nevertheless, thermoelectric properties of such phosphides are still not heavily studied. A reason is that a lot of these phosphides are extremely sensitive to air, which makes them less suitable for applications. In addition, using materials containing light elements is usually not advisible because the strong covalent bonds present in such materials is expected to lead to high thermal conductivity and therefore to insufficient thermoelectric performance. Nonetheless, there are phosphides which are stable in air or even in hydrochloric acid, and in spite of containing light elements, they can exhibit remarkably low thermal conductivity for various reasons.14−18 Some of the examples are CuGe4P3,14 YbCuZnP2,15 Eu3Ga2P4,16 Ba8Au16P30,17 or LaCu1+xP2.18 Out© 2017 American Chemical Society
standing materials are YbCuZnP2 and Ba8Au16P30. In the latter case the metallic clathrate exhibits an unprecedentedly low lattice thermal conductivity (0.18 W m−1 K−1),17 and in the former, YbCuZnP2 has a figure of merit of zT ∼ 0.6, being the first phosphide reported that has potential as a thermoelectric material.15 The ternary transition metal phosphide, Ag6Ge10P12, was already discovered by von Schnering et al. in 1976.19−21 The silver-cluster compound has a stability similar to that of corresponding chalcogenides. It contains subvalent silver according to the formal charge [Ag6]4+, and it is a diamagnetic semiconductor, showing vibrational anharmonicity and anisotropic lattice distortion.19−29 The structure is closely related to that of the Tetrahedrites,25 which are prominent thermoelectric materials.1−5 Thus, it is worthwhile to study the thermoelectric potential of Ag6Ge10P12. The thermoelectric properties, or the physical properties in general, are coded into the structure of the compound, and therefore in the detailed arrangement of the constituent atoms. In view of this, and the rather complicated bonding properties in Ag6Ge10P12,25 a more precise structure analysis combined with state of the art quantum-chemical Received: June 15, 2017 Revised: July 25, 2017 Published: July 26, 2017 6956
DOI: 10.1021/acs.chemmater.7b02474 Chem. Mater. 2017, 29, 6956−6965
Article
Chemistry of Materials
sample was determined with a differential scanning calorimeter, DSC (DSC 404, Netzsch, Selb, Germany), in the temperature range 350− 750 K at a heating rate of 10 K min−1. Physical Properties. Transport properties and heat capacity at low temperatures were measured with a Physical Property Measurement System using the thermal transport and resistivity options (PPMS, Quantum Design, San Diego, CA). The electrical resistivity was measured on bars (3.0 × 3.0 × 10.0 mm3) in the temperature range of 1.8−300 K. In addition, the Hall effect was measured on square plates (3.0 × 3.0 × 0.2 mm3) at room temperature in magnetic fields up to ±6 T. To investigate the thermoelectric properties at high temperatures (300−710 K), the samples were cut into discs (Ø = 12 mm, l ∼ 2.0 mm) and bars (3.0 × 3.0 × 10.0 mm3). The Seebeck coefficient S and electrical resistivity ρ were measured simultaneously using a static DC method (ZEM-3, ULVAC Technologies, Methuen, MA). The thermal conductivity κ was calculated using the relation κ = Cp × α × d, where Cp denotes the specific heat capacity, α the thermal diffusivity, and d the density. The values of α were measured by means of the laser flash method (LFA 457 microFlash system, Netzsch, Selb, Germany), the density was measured with a helium pycnometer (AccuPyc-II-1340, Micromertics, Norcross, GA), and the heat capacity was estimated by the Dulong-Petit law. Quantum-Chemical Calculations. Density functional calculations were performed with the CRYSTAL14 program package,35 using atom-centered Gaussian basis functions. The atomic cores were represented by pseudopotentials, approximating 28 core electrons of silver,36 the [Ar]-core of germanium,37 and the [Ne]-core of phosphorus.37 For the valence space, 19 electrons of Ag, 4 electrons of Ge, and 5 electrons of P, the corresponding basis sets of at least double-ζ quality including polarization functions were modified to meet the numerical peculiarities of the CRYSTAL14 code. Band structure, density of states, electron densities, and localized Wannier functions38 were computed with the crystal structure measured at room temperature (see Supporting Information). For the frequenciy calculations, the atomic positions and the lattice constant were optimized according to the procedure in CRYSTAL14, keeping the given crystal symmetry. The frequencies at the Γ-point in harmonic approximation are evaluated by numerically differentiating the analytical gradients of the energy with respect to the nuclear displacements.39,40 The splitting between traverse and longitudinal optical modes was obtained with the high frequency dielectric tensor computed with the coupled perturbed Kohn−Sham (CPHF) module41−43 of CRYSTAL14. The phonon density of states was determined via a supercell approach including a Fourier interpolation scheme. Ionic contributions were considered by applying the approach of Wang et al.44 Details of the computational parameters are given in the Supporting Information. The PBEsol45 GGA (generalized gradient approximation) functional was used to calculate the exchange and correlation terms in the Kohn−Sham equations. Band gaps computed with GGA functionals tend to be too small compared to experimental values. In order to check this effect, a single-point calculation was performed with the short-range-separated hybrid functional HSEsol.46 The computational effort with HSEsol increases by a factor of 5 compared to PBEsol, becoming problematic for the supercell calculations. Although the band gap computed with HSEsol agrees better with the experimental results, the interpretation of the results does not change, and PBEsol data will be discussed throughout in this article. The atomic charges were evaluated by a topological analysis of the electron density according to the QTAIM approach47 with the critic2 program.48,49 The atomic basins were determined from a 200 × 200 × 200 grid of data points of the valence electron density, augmented by core densities. Within the basins, the net charges were obtained by the integration of the valence electron density. Structural data, together with volumetric data, were visualized with VESTA.50
calculations should also help to resolve the bonding picture for this material.
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EXPERIMENTAL SECTION
Synthesis. Ag6Ge10P12 was synthesized in ∼5 g batches from stoichiometric amounts of silver and germanium, and the phosphorus was used with an excess of about 3−5% (Ag 99.99%, Sigma-Aldrich, Steinheim, Germany; Ge 99.999%, Alfa Aesar, Karlsruhe, Germany; P 99.999% ultrapure, amorphous red lumps, electronic grade, Hoechst AG, Knapsack, Germany). The elements were mixed in a drybox (MBraun, Garching, Germany) in an argon atmosphere (
