Article pubs.acs.org/cm
Coinage-Metal-Stuffed Eu9Cd4Sb9: Metallic Compounds with Anomalous Low Thermal Conductivities Nasrin Kazem,† Julia V. Zaikina,† Saneyuki Ohno,‡ G. Jeffrey Snyder,§ and Susan M. Kauzlarich*,† †
Department of Chemistry, University of California, One Shields Ave., Davis, California 95616, United States Materials Science, California Institute of Technology, 1200 E. California Boulevard, Pasadena, California 91125, United States § Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States ‡
S Supporting Information *
ABSTRACT: The synthesis and transport properties of the family of coinage metal-stuffed Zintl compounds, Eu 9 Cd 4−x CM 2+x−y □y Sb 9 (CM = coinage metal, □ = vacancies), is presented as a function of coinage metal substitution. Eu9Cd4−xCM2+x−y□ySb9 compounds are shown to be rare examples of metallic Zintl phases with low thermal conductivities. While the lattice thermal conductivity is low, which is attributed to the complex structure and presence of interstitials, the electronic contribution to thermal conductivity is also low. In these p-type compounds, the carriers transmit less heat than expected, based on the Wiedemann−Franz law and metallic conduction, κe = L0T/ρ. Density functional theory (DFT) calculations indicate that the Fermi level resides in a pseudogap, which is consistent with the metallic description of the properties. While the contribution from the interstitial CM states to the Fermi level is small, the interstitial CMs are required to tune the position of the Fermi level. Analysis of the topology of electron localization function (ELF) basins reveals the multicenter Eu−Cd(CM)−Sb interactions, as the Eu and Sb states have the largest contribution at the top of the valence band. Regardless of the success of the Zintl concept in the rationalization of the properties, the representation of the CM-stuffed Eu9Cd4Sb9 structure as Eu cations encapsulated into a polyanionic (Cd/Cu)Sb network is oversimplified and underestimates the importance of the Eu−Sb bonding interactions. These results provide motivation to search for more efficient thermoelectric materials among complex metallic structures that can offer less electronic thermal conductivity without deteriorating the electrical conductivity.
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INTRODUCTION The relatively limited choice of efficient thermoelectric (TE) materials has motivated many scientists to search for potential novel materials. TE materials can generate energy without harmful emissions and can be considered as one strategy to replace fossil-based fuels as a green source of energy, or at least to improve energy conservation through waste-heat harvesting. Although theoretical studies show no restriction for TE materials to attain the maximum efficiency given by the Carnot efficiency, enhancing the efficiency of thermoelectric materials has remained a practical challenge.1−4 This challenge has its roots in the antagonistic properties contributing to the thermoelectric figure of merit,
in TE technology. The most efficient solid-state thermoelectrics (high zT) are based on the materials with reduced lattice thermal conductivities, which is the only independent parameter not correlated to the electronic structure. One of the most successful strategies to manipulate lattice thermal conductivities is making solid solutions: creating disorder by providing atomic mass fluctuation in specific crystallographic sites. To date, the lattice thermal conductivity of thermoelectric materials is typically estimated indirectly by considering that the experimentally measured thermal conductivity is from charge carriers and lattice: κ = κe + κl The charge carrier contribution is estimated based on the Wiedemann−Franz law,
2
zT =
αT κρ
κe =
where α is the Seebeck coefficient, ρ the electrical resistivity, κ the thermal conductivity, and T the temperature. A material with a high figure of merit can convert a heat gradient into electricity more efficiently. Thus, to uncover more efficient TE materials, exploratory synthesis and discovery of as-yet unimagined compounds or tuning the properties of the already-known compounds are essential keys for advancements © XXXX American Chemical Society
LT ρ
(where ρ is the electrical resistivity, T the absolute temperature, and L the Lorenz number) and the remainder would be Received: September 27, 2015 Revised: October 12, 2015
A
DOI: 10.1021/acs.chemmater.5b03808 Chem. Mater. XXXX, XXX, XXX−XXX
Article
Chemistry of Materials attributed to the lattice contribution. Lorenz numbers of 2.44 × 10−8 V2 K−2 and 1.45 × 10−8 V2 K−2, which are used for metals and semiconductors, respectively, are typically considered to be constants and are robust numbers for a wide variety of compounds. However, an incorrect decision about the Lorenz number can result in the wrong interpretation of heat transfer in the materials, which can hamper lattice thermal conductivity reduction strategies for TE efficiency enhancement.5,6 Compounds with complex crystal structures are one of the best candidates in the search for better materials for TE applications, as they can provide low thermal conductivity, which is essential for highly efficient TE materials. There are many examples of Zintl phases with exceptionally low thermal conductivities, such as Yb14MnSb11,7 Eu11Cd6Sb12−xAsx,8 Eu11Cd6−xZnxSb12,9 and Ca5Al2Sb6.10 These compounds may also provide separate mechanisms for the transport of electrons and phonons leading to the ideal properties of phonon-glass electron-crystal (PGEC) which, when coupled with high thermopower, provide a desired set of properties for efficient TE materials. The superior performance of the p-type complex Zintl phase Yb14MnSb11 over the long-term state-of-the-art SiGe alloys11,12 is an excellent example of how structural complexity contributes to highly efficient TE materials.7 Other examples of Zintl phases include Yb1−xEuxCd2Sb2,13 and Ba0.08La0.05Yb0.04Co4Sb12 skutterudites14 and clathrates15 with high zT values. A fairly large group of interstitially stabilized Ca9Mn4Bi9 (9−4−9) family of compounds, A9TM4+xPn9 (A = Ca, Sr, Yb, Eu; TM = transition metal = Zn, Cd, Mn; and Pn = Sb or Bi), has been characterized to date.16−18 The chemical formulas range from stoichiometric to nonstoichiometric compounds, with x = 0 and x ≠ 0, respectively. These compounds crystallize in the orthorhombic space group Pbam (No. 55) and are all related to the Ca9Mn4Bi9 structure type.16,19,20 The generic stoichiometric compound can be considered as being composed of 9 A2+, 4 TM2+, and 9 Pn3− components (assuming the complete charge transfer from A and TM atoms to antimony). This electron counting indicates that the stoichiometric compounds are one electron deficient/ formula, as only 26 electrons are provided by the electropositive elements whereas 27 electrons are needed by the electronegative pnicogen, 9 Pn3−. Therefore, the interstitially stabilized compounds are valence-precise when one additional electron is provided. These electron-precise complex compounds with their flexibility for tunable properties by adjusting both the element and the extent of the occupation at the interstitial site are ideal candidates for thermoelectric applications. Yb9Mn4.2Sb9 is the first member of this family that has been studied for TE applications.21 The deviation from the valence-precise 9−4.5−9 composition makes Yb9Mn4.2Sb9 an electrically conductive material which, along with the very low thermal conductivity, as a result of the high level of disorder in this structure (κl < 0.4 W m K−1), makes it a promising compound for thermoelectric applications (zT = 0.7 at 950 K). These studies were continued by Ohno et al.,22 who examined the effect of substituting Zn on both the Mn and the interstitial sites of Yb9Mn4.2−xZnxSb9. Zn substitution led to a reduction in the valence band mass resulting in high carrier mobility and, thus, very low Seebeck coefficient that, overall, decreased zT to ∼0.18 at ∼975 K. With the increased electrical conductivity, determining the Lorenz number (L)and, therefore, the electronic contribution to the thermal conductivitywas problematic and L was estimated by setting the minimum experimental lattice thermal conductivities to the
calculated theoretical minimum. This work shows the importance of the choice of the element for the interstitial position, which is the key role of the interstitial atom for electronic properties, and hints at the problems with calculating lattice thermal conductivity for complex structures with low electrical resistivity. The coinage metal-stuffed compounds, Eu9Cd4−xCM2+x−y□ySb9 CM = coinage metal: Cu, Ag and Au, □ = vacancy sites, are the only members of the 9−4−9 family with monovalent interstitial atoms.23 Here, we investigate how the transport properties change through the substitution of coinage metals in the Eu9Cd4−xCM2+x−y□ySb9 series. We show that Eu9Cd3.8Au1.2Sb9 is an excellent example of a phonon-glass electron-crystal (PGEC) material, providing low thermal conductivity in concert with extremely low electrical resistivity, which is a combination of properties that is essential for an ideal PGEC compound. We show that an unprecedentedly low Lorenz number is required to describe the electronic contribution of heat transfer in this family of compounds. A combination of electronic structure calculations and classical transport models provide insight into the experimentally observed t ran sp ort pro perties o f Eu9Cd4−xCM2+x−y□ySb9, following by a discussion of the correlation between interstitial atom identity and properties for TE applications.
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EXPERIMENTAL SECTION Synthesis. Eu9Cd4−xCM2+x−y□ySb9 (CM is coinage metal; CM = Cu, Ag and Au) compounds were synthesized by means of a Sn flux reaction, according to the literature.23 In brief, the elements were loaded with the molar ratio of Eu:Cd:CM:Sb:Sn = 9:3.5:1.5:9:23, scaled for 5 g of Sn, in an alumina crucible inside an argon-filled drybox and sealed under vacuum in a fused silica tube. The reaction vessel was heated at 100 °C/h to 500 °C, allowed to dwell for 6 h before continued heating at 100 °C/h to 950 °C, and then allowed to dwell for 96 h. The reaction vessel was cooled from 950 °C to 600 °C at a rate of 5 °C/h. Then, the flux was separated by quickly transferring the reaction vessel from the furnace to a centrifuge where the reaction vessel was inverted and spun for 2−3 min at 6500 rpm. The reaction vessels were opened in a N2-filled glovebox equipped with an optical microscope and at a moisture level of 95% of the crystallographic density. The purity of the samples after SPS was verified by PXRD. Electron Microprobe Analysis (EMPA). The cut pressed pellets were enclosed in epoxy and polished to provide flat surfaces for analysis. The polished samples were mounted on 25 mm metal rounds using adhesive carbon tape and were carbon-coated to make their surface conductive. Microprobe analysis was performed by using an electron probe microanalyzer (Cameca, Model SX-100) with wavelength-dispersive spectrometers. Back-scattered electrons were used for imaging the surfaces of the samples, characteristic X-rays generated by the samples were analyzed by wavelength-dispersive spectroscopy to determine the compositions of samples, and element mapping was accomplished to assess the spatial distribution of elements in the samples. X-ray intensities of Cd, Cu, Ag, Au, Sb, and Sn were compared with the calibrated standards of elemental form and for Eu with the EuPO3 reference for quantitative analysis. At least 15 different points with a spot size of 1 μm were analyzed for each sample. Quantum-Chemical Calculations. Calculations of band structure and density of states (DOS) for four different structural models of Eu9Cd3.7Cu1.5Sb9 were performed with the tight-binding−linear muffin-tin orbitals−atomic sphere approximation TB-LMTO-ASA program package.25 The experimentally determined unit-cell dimensions and atomic coordinates for Eu9Cd3.7Cu1.5Sb9 were used.23 Four ordered models with different Cd/Cu ratios were constructed, three of them (models i, ii, and iii) in space group Pbam (No. 55) corresponding to the actual symmetry of the structure. To construct model iv, the structure was transformed into space group Pmc21 (No. 26) (see Figure S1 in the Supporting Information). The radial scalar-relativistic Dirac equation was solved to obtain the partial waves. Interstitial empty spheres were added to fill the interstitial space. The calculation was made for a grid of 4 × 8 × 18 κ-points with 150 κ-points in the irreducible Brillouin zone for models i, ii, and iii and for the grid of 9 × 4 × 2 κ-points with 30 κ-points in the irreducible Brillouin zone for model iv. Integration over the Brillouin zone was made using the tetrahedron method.26 The basis set contained Eu (6s, 6p, 5d), Sb (5s, 5p), Cd (5s, 5p, 4d), and Cu (4s, 4p, 3d) with Eu(6p), Sb(5d, 4f), Cd(4f) functions being downfolded, while 4f electrons of Eu were treated as core electrons. The band structure was also calculated for Ag and Au analogues using model iv (space group Pmc2 1 ) and experimentally determined unit-cell dimensions and atomic coordinates for compositions Eu 9 Cd 3.8 Ag 1.4 Sb 9 and Eu9Cd3.8Au1.2Sb9.23 Ag (5s, 5p, 4d) and Au (6s, 6p, 5d) orbitals were used as a basis set with Ag(4f) and Au(5f) functions downfolded. The electron localization function (ELF, η)27−29 was calculated with modules implemented within the TBLMTO-ASA program package and was evaluated on an adequately fine mesh of 0.06 Å. The topology of ELF and basins, which are bounded by zero flux surfaces in the ELF gradient field, was analyzed using the program Basin implemented into DGrid 4.6.30 The ParaView program was used for visualization of the ELF isosurfaces and basins.31 Heat Capacity Measurements. A Netzsch STA 409 thermal analysis cell equipped with a TASC 414/2 controller and a PU 1.851.01 power unit was used to measure the specific
heat (heat capacity, Cp) of Eu9Cd4−xCM2+x−y□ySb9 (CM = Au) compound. It was determined quantitatively using the DSC method by subtracting a baseline from the heat flow curve by setting up three runs. During the first run, only the baseline with empty pans placed in the platinum furnace were measured in the temperature range of 350−600 K. In the next step, a sapphire disk as a reference was added in the sample pan and the same measurements were carried out. Then, the reference was replaced by the sample for running the same measurement. A Netzsch software package automatically subtracted the data and referenced them against the standard to calculate the heatcapacity values. Transport Properties Measurements. High-temperature resistivity (ρ) data are measured to 775 K by using the van der Pauw technique. Hall effect measurements are taken in a 2 T magnetic field using pressed niobium contacts. Seebeck data are obtained using chromel−Nb thermocouples and by oscillating the temperature gradient ±10 K. For measurements at each temperature, the temperature gradient is oscillated about a fixed average temperature, the resulting voltage response to the temperature gradient reveals a linear relationship with the slope yielding the Seebeck coefficient (ΔV = α ΔT). Thermal diffusivity data were collected using a Netzsch LFA 457 system. Thermal conductivities are calculated from the equation κ = CpdD
in which Cp is the Dulong−Petit heat capacity (Cp = 3RN/M, where R is the gas constant, N the number of atoms per formula unit, and M the molar mass), d the geometric density, and D the measured thermal diffusivity from flash diffusivity measurements given in the Supporting Information. Both the longitudinal and transverse speeds of sound are measured at room temperature by collecting reflected sound waves from the bottom of the sample after applying a sound wave from the top.
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RESULTS AND DISCUSSION Structure Description. The structure and magnetic properties of the series of compounds Eu9Cd4−xCM2+x−y□ySb9 (CM = coinage metal = Cu, Ag, Au; □ = vacancy sites) have been described.23 Therefore, only the main features of the Eu9Cd4−xCM2+x−y□ySb9 structures are highlighted here. The structure of Eu9Cd4−xCM2+x−y□ySb9 is closely related to the Ca9Mn4Bi9 structure type (Pearson code oP44) or, more generally, A9TM4Pn9 (9−4−9) (A = Ca, Sr, Ba, Eu, Yb; TM = transition metal, Pn = pnicogen), but contains an additional interstitial TM3 position (4g Wyckoff site). The interstitially stabilized structure contains 13 crystallography unique positions comprised of 5 A, 5 Pn, and 3 TM sites. Full occupancy at the interstitial position, TM3, would provide a composition of the hypothetical formula A9TM6Pn9. In the case of Eu9Cd4−xCM2+x−y□ySb9 compounds, TM2 and TM3 positions are occupied exclusively by 100% Cd and ∼50% by CM, respectively. The TM1 site splits in two sites, Cd1 and CM1, providing a different coordination of CM1 (trigonal planar) and Cd1 (tetrahedral) atoms introducing additional disorder.23 This trigonal planar site is a similar motif to that observed for Cu12Sb4S13 tetrahedrite identified as the origin of the low thermal conductivity in this system.32 The occupancy factor of the split CM1 site is dependent on the identity of CM, ranging from ∼15% for the Cu analogue to 95% compactness). The temperature dependency of the electrical resistivity for the Eu9Cd4−xTM2+x−y□ySb9 samples is shown in Figure 3a. All of the samples exhibit low resistivity (ρ), which linearly increases with increasing temperature (dρ/dT > 0, with the increase rate being
