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High Seebeck Coefficient and Unusually Low Thermal Conductivity Near Ambient Temperatures in Layered Compound Yb2–xEuxCdSb2
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  • Joya A. Cooley
    Joya A. Cooley
    Department of Chemistry, University of California, One Shields Avenue, Davis, California 95616, United States
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  • Phichit Promkhan
    Phichit Promkhan
    Department of Chemistry, University of California, One Shields Avenue, Davis, California 95616, United States
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  • Shruba Gangopadhyay
    Shruba Gangopadhyay
    Department of Chemistry, University of California, One Shields Avenue, Davis, California 95616, United States
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  • Davide Donadio
    Davide Donadio
    Department of Chemistry, University of California, One Shields Avenue, Davis, California 95616, United States
    IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain
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    Orcidhttp://orcid.org/0000-0002-2150-4182
  • Warren E. Pickett
    Warren E. Pickett
    Department of Physics, University of California, One Shields Avenue, Davis, California 95616, United States
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  • Brenden R. Ortiz
    Brenden R. Ortiz
    Department of Physics, Colorado School of Mines, Golden, Colorado 80401, United States
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  • Eric S. Toberer
    Eric S. Toberer
    Department of Physics, Colorado School of Mines, Golden, Colorado 80401, United States
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  • Susan M. Kauzlarich*
    Susan M. Kauzlarich
    Department of Chemistry, University of California, One Shields Avenue, Davis, California 95616, United States
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    Orcidhttp://orcid.org/0000-0002-3627-237X
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Chemistry of Materials

Cite this: Chem. Mater. 2018, 30, 2, 484–493
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https://doi.org/10.1021/acs.chemmater.7b04517
Published December 18, 2017

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Abstract

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Zintl phases are promising thermoelectric materials because they are composed of both ionic and covalent bonding, which can be independently tuned. An efficient thermoelectric material would have regions of the structure composed of a high-mobility compound semiconductor that provides the “electron–crystal” electronic structure, interwoven (on the atomic scale) with a phonon transport inhibiting structure to act as the “phonon–glass”. The phonon–glass region would benefit from disorder and therefore would be ideal to house dopants without disrupting the electron–crystal region. The solid solution of the Zintl phase, Yb2–xEuxCdSb2, presents such an optimal structure, and here we characterize its thermoelectric properties above room temperature. Thermoelectric property measurements from 348 to 523 K show high Seebeck values (maximum of ∼269 μV/K at 523 K) with exceptionally low thermal conductivity (minimum ∼0.26 W/m K at 473 K) measured via laser flash analysis. Speed of sound data provide additional support for the low thermal conductivity. Density functional theory (DFT) was employed to determine the electronic structure and transport properties of Yb2CdSb2 and YbEuCdSb2. Lanthanide compounds display an f-band well below (∼2 eV) the gap. This energy separation implies that f-orbitals are a silent player in thermoelectric properties; however, we find that some hybridization extends to the bottom of the gap and somewhat renormalizes hole carrier properties. Changes in the carrier concentration related to the introduction of Eu lead to higher resistivity. A zT of ∼0.67 at 523 K is demonstrated for Yb1.6Eu0.4CdSb2 due to its high Seebeck, moderate electrical resistivity, and very low thermal conductivity.

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Introduction

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Thermoelectric (TE) generators can transform thermal energy into electrical energy. This thermal energy can come from a wide variety of sources such as vehicle exhaust systems (1) and solar radiation. (2) These devices work using the Seebeck effect in two dissimilar materials. Ideally, an n-type (electron conduction) semiconductor and p-type (hole conduction) semiconductor are joined electrically in series and thermally in parallel across a temperature gradient. In a semiconductor, carriers diffuse from the hot side of the gradient to the cold side and, since the carriers are charged, allow for a voltage difference to develop. When a load is connected across the two materials, electricity can flow. The maximum efficiency is governed in part by a dimensionless figure of merit, zT (= S2T/ρκ). It follows that, in order to achieve high efficiency, it is necessary to have a high Seebeck coefficient (S), low electrical resistivity (ρ), and low thermal conductivity (κ). Slack (3) suggested that the ideal thermoelectric material would be a “phonon–glass, electron–crystal” (PGEC), in which the material conducts heat poorly, as in an amorphous glass, but can conduct electronic charge very well, as in a crystalline material.
In general, semiconductors provide a suitable combination of high thermopower and reasonably low electrical resistivity to make suitable PGEC materials, if their structures can be suitably tuned to yield low thermal conductivity. Zintl phases, (4) a subset of intermetallic phases combining ionic and covalent bonding, have been targeted as viable TE materials as they often intrinsically exhibit PGEC properties since they readily form valence precise semiconductors. Zintl phases have been studied at temperatures far above room temperature, up to ∼1250 K, for TE power generation applications, and show great promise. (5−13) Yb14MnSb11 (5) and variants thereof (14) illustrate well the PGEC concept, with a lattice thermal conductivity reaching as low as 0.16 W/m K combined with an electrical resistivity of less than 1.0 mΩ cm in Yb14MgBi11. (15) PGEC behavior has also been seen in other Zintl phases such as coinage-metal-stuffed Eu9Cd4Sb9, (9) a derivative of Mg3+δSb2, Mg3.2Sb1.5Bi0.49Te0.01, (16) and clathrate Ba8Ga16Ge30. (17)
Despite this progress, there is still considerable room for growth with respect to applications at lower temperatures, where there are a significant number of technologies that would benefit from the additional energy recovery from heat, for example, solar thermoelectric generators (STEGs). STEGs are an emerging technology that, much like photovoltaics, harvest energy from the sun to create electricity, but use concentrated thermal energy the sun provides rather than radiation. (18) With a zT = 1 and hot and cold sides of temperatures 220 and 20 °C, respectively, STEGs can reach 8.6% efficiency. (2) Thus, high zTs in this temperature range are of great consequence, and more study to find thermoelectrically competitive materials in this temperature range is worthwhile.
Discovery of materials with high zT involves some intuition (19) and appropriate choice of structure. (20) Semiconductors with large Seebeck coefficients at high temperature can be difficult to identify, thereby focusing research on low thermal conductivity materials. One method of enhancing zT involves striving for very low inherent κ in a material and working to further lower the lattice thermal conductivity (κlatt). So-called complex structures have been linked to having low κlatt because their large unit cells, use of heavy elements, and complex bonding schemes allow for significant phonon scattering, thus acting as a “phonon glass”. Some of these complex structures include clathrates and skutterudites, (21) as well as Zintl phases such as Yb14MnSb11, (5) coinage-metal-stuffed Eu9Cd4Sb9, (9) Ca5Al2Sb6, (11) and nanostructured materials. (22,23) Despite this apparent requirement of complex structure types, phases with relatively simple layered structures have demonstrated favorable thermoelectric properties: often the layered structure plays a role in the compound’s PGEC properties. For example, NaCo2O4 contains CoO2 layers, responsible for electronic conduction, while the disordered Na layer acts as a phonon scattering mechanism, allowing for κ of ∼0.5 W/m K at relatively low temperatures. (24) Bi2Te3, a state-of-the-art TE material that is in commercial use today, is a layered compound whose low thermal conductivity of near ∼0.7 W/m K resembles that of a glass and contributes to its high figure of merit near room temperature. (25) Layered Zintl phases have also garnered attention: the AM2Pn2 (A = Ca, Sr, Eu Yb; M = Zn, Cd; Pn = As, Sb) family of compounds, in the CaAl2Si2 structure type, has yielded a wealth of structures with low κ and high S, often resulting in impressive zT values. (26,27)
Herein, we have investigated the layered solid-solution Yb2–xEuxCdSb2 (Figure 1) as a potential thermoelectric material for near room temperature applications as motivated by the promising S and ρ reported for the single crystals. (28,29) Yb2–xEuxCdSb2 crystallizes in the polar space group of Cmc21. The structure is almost like that of Ca2CdSb2 except for a small distortion that destroys the center of inversion. The lack of an inversion center, which splits degeneracies compared to the higher-symmetry structure, should translate into a more complex phonon spectrum and phonon–phonon interaction and thereby lower the thermal conductivity and increase the figure of merit. Compared to Ca- or Ba-based compounds the noncentrosymmetric space group is unique to this combination of Yb and Eu. (28) The layered structure and zigzag bonding of the anionic substructure are reminiscent of SnSe, (30,31) a phase exhibiting significant anharmonicity yielding low thermal conductivity. Therefore, one might expect anharmonicity to play a role in this structure type as well. There are two crystallographic sites in this structure for the rare earth cations, providing an additional degree of freedom. Not only does site substitution provide an alloy scattering mechanism to reduce thermal conductivity, but site preferences for the two cations provide additional complexity that can tune properties. In this solid-solution phase, we are substituting Eu for Yb, and Eu preferentially substitutes on the interlayer (Yb1) site, shown in Figure 1. Eu will add additional f-bands to the band structure and, more importantly, may provide Eu–Sb bonding, as is the case in the coinage-metal-stuffed Eu9Cd4Sb9 complexes, (9) to also affect the gap or placement of the Fermi level. The structural features of Yb2CdSb2 combined with the high thermopower reported at room temperature (28) provide incentive to investigate Yb2–xEuxCdSb2 in order to confirm a high figure of merit phase based on the chemical intuition outlined above.

Figure 1

Figure 1. (a) Ball-and-stick depiction of the structures of Yb2–xEuxCdSb2 with one unit cell outlined. Yb, Eu, Cd, and Sb are shown as teal, pink, purple, and tan spheres, respectively. Coordination spheres of sites: (b) Yb1, interlayer, and (c) Yb2, intralayer.

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Experimental Section

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Synthesis

Bulk samples were synthesized through a combination of mechanical milling to pulverize elements to a homogeneous powder and spark plasma sintering (SPS) to simultaneously provide a phase pure sample and densify the powder into a pellet. Yb was filed to pieces using a metal rasp and combined stoichiometrically with cut Eu pieces, Cd shot, and Sb shot (sources: Eu metal, Stanford Materials, 99.99%; Yb pieces, Metall Rare Earth Limited, 99.99%; Cd shot, Alfa Aesar, 99.95%; and Sb shot, Alfa Aesar 99.9%). The elements were weighed according to the following stoichiometry: 2 – x Yb:x Eu:1 Cd:2 Sb (x = 0.3, 0.8, 1, and 1.1) to total reaction masses of 3–3.5 g. For each reaction, Yb, Cd, and Sb, and two tungsten carbide (WC) balls (diameter 8.0 mm) were loaded into a 5 cm3 stainless steel ball mill, capped via a Viton O-ring with WC disks held in place by Teflon caps. The milling container was heat-sealed in two poly bags to prevent oxidation in air and placed in an SPEX 8000 M for 1 h total in two 30 min milling duration increments. Between increments, the milling container was transferred to a drybox, and the inside and end-caps were scraped down with a metal spatula; Eu was added for the second ball-milling. The resultant powder was transferred to a drybox and ground via alumina mortar and pestle to remove any large agglomerates and sieved through a 100 mesh sieve. Approximately 2.5–3 g of powder was transferred to a 12.7 mm diameter high-density graphite die (from POCO) for densification via a Dr. Sinter SPS-2050 spark plasma sintering (SPS) system (Sumitomo, Tokyo, Japan). The die was transferred to the instrument chamber, which was evacuated (below ∼20 Pa) and filled with a partial pressure of Ar. The temperature was increased from room temperature to 500 °C in 15 min and then to 600 °C in 1 min (to prevent temperature overshoot), and it remained stable for 45 min. When the temperature reached ∼480 °C and compression began, the force was increased from 2 to 8 kN. Afterward, samples were cooled to room temperature with pressure released. Sample densities were larger than 90% of the theoretical density according to the Archimedes method.

Powder X-ray Diffraction

Ground powders of pelleted samples were loaded on a Bruker zero-background holder for powder X-ray diffraction (XRD). XRD data were collected by a Bruker D8 Advance diffractometer with Cu Kα radiation (λ = 1.54060 Å) with 2θ range 20–80° with a step size ∼0.02° and scan rate of 1 s per step. Refinements of unit cell parameters were performed with the program FullProf. (32)

Electron Microprobe Analysis

Pellet pieces from each sample were examined for phase composition by electron microprobe analysis (EMPA) using a Cameca SX-100 electron probe microanalyzer equipped with a wavelength-dispersive spectrometer with 15 kV accelerating potential and a 20 nA beam current. Small pellet pieces (∼1.5 mm × 1.5 mm × 1.5 mm) were coated in epoxy and polished for analysis. The polished samples were mounted on 25 mm metal rounds with carbon tape and coated with carbon for conductivity. Characteristic X-rays generated by samples were qualitatively analyzed by wavelength-dispersive spectroscopy to determine compositions of samples using X-ray intensities of Yb, Eu, Cd, Sb as compared to calibrated standards Yb14MnSb11, EuGa4, Cd (metal), Sb (metal). Elemental mapping was performed to qualify element homogeneity.

Thermoelectric Property Measurement

High-temperature thermal diffusivity (λ, shown in Table S3 of the Supporting Information) was measured between 348 and 523 K on 12.7 mm diameter circular pellets using a Netzsch Laser Flash Analysis (LFA) 457 instrument. Measured thermal diffusivity was used to calculate thermal conductivity using the equation κtot = λρCp, where ρ is the density and Cp is the heat capacity. The density was measured using the Archimedes method, and the heat capacity was estimated using the Dulong–Petit equation Cp = 3RN/FW (R = 8.3145 J/mol K, N = number of moles of atoms in the formula unit, FW = formula weight). Experimental heat capacity (Figure S3 in the Supporting Information) was measured with a Netzsch Thermal Analysis DSC 404 F3 with a TASC 414/4 controller using alumina pans placed in platinum pans and the platinum furnace from 313 to 523 K. The Netzsch software package automatically subtracted the data and referenced against the standard (sapphire) to calculate the heat capacity values. A Linseis LSR-3 instrument was used to measure Seebeck coefficient and electrical resistivity via a standard four-probe method from 348 to 523 K under a helium atmosphere each sample. Samples were cut into bars (∼12 mm × 2 mm × 2 mm) using a Buehler diamond saw and polished before measurement. The probe distance was 6 mm. The Seebeck coefficient, electrical resistivity, and thermal conductivity data were fit to fifth- or sixth-order polynomial functions to calculate zT values.

Computational Details

The present DFT-based electronic structure calculations were performed using the full-potential augmented plane-wave plus local orbital method as implemented in the WIEN2K code. (33−35) The generalized gradient approximation (GGA) as described by Perdew, Burke, and Ernzerhof (PBE) was used for the underlying semilocal exchange-correlation potential. (36) GGA+U calculations with fully localized limit are used for approximating local repulsion effects on localized atomic orbitals. In this method an on-site Hubbard repulsion U is included for the rare earth 4f-orbitals and Cd 4d-orbitals. The double counting correction approach proposed by Anisimov et al. (37) and Liechtenstein et al. (38) was chosen for these highly localized orbitals, and the value U = 8 eV and Hund’s exchange parameter J = 1 eV were chosen for f-orbitals in Yb and Eu. For Cd d-orbital we applied U = 3 eV. Although the Cd 4d-orbital shows minor participation near the valence edge, Flage-Larsen et al. (39) have shown that, in the case of YbZn2Sb2, applying an on-site U for Zn d states can lead to a more accurate description of electronic structure; therefore, the on-site U for Cd was employed. Also, to keep numerical consistency with magnetic YbEuCdSb2 we applied spin polarized calculations for both Yb2CdSb2, nonmagnetic (4f14 configuration), and YbEuCdSb2, magnetic (Eu2+, 4f7 configuration). The wave functions in the interstitial regions were expanded in plane-waves up to a cutoff of RmtKmax = 9 (Rmt is the smallest muffin tin radius of atoms, and Kmax is the maximum plane-wave vector) to achieve convergence for energy eigenvalues (especially the 4f-bands). Nonoverlapping atomic sphere radii, in a.u., were chosen as 2.5 for all the constituent atoms. Plane-waves with a kinetic energy cutoff of 500 eV are used as basis sets, and a 4 × 1 × 2 k-point grid in Brillouin zone is chosen as per the Monkhorst–Pack scheme. All the pseudopotentials were calibrated with respect to the density of states obtained from all-electron WIEN2K calculations, and for both cases the same Hubbard U was applied for all rare earth 4f-orbitals. Applied pseudopotentials have the following valence configurations: 5s2, 5p6, 4f14, 6s2 for Yb; 5s2, 5p6, 4f7, 6s2 for Eu; 4d10, 5s2 for Cd; and 5s2, 5p3 for Sb. The lattice structure relaxations are carefully performed so that the forces on atoms are smaller than 0.2 meV/Å, in which the conjugate gradient algorithm is utilized.
Starting from the experimental crystallographic coordinates, (29) the crystal lattice parameters were optimized, computing the energy versus volume curves of both compounds and fitting the Vinet equations of state. (40) The electronic transport properties (e.g., Seebeck coefficient and electrical conductivity) were calculated by solving the semiclassical Boltzmann transport equation assuming constant relaxation time approximation (CRTA) as implemented in the BoltzTrap package, (41) using band energies obtained from WIEN2K electronic structure calculation as input. A dense mesh of 31 × 8 × 16 k-points in the irreducible wedge of the Brillouin zone was used to obtain converged results.
Vibrational analysis and phonon dispersion curves were computed using the plane-wave pseudopotential approach, as implemented in the VASP package, (42) with projector-augmented-wave pseudopotentials. (43) GGA+U applied for frozen phonon calculations is based on the approach by Dudarev et al. as implemented in VASP. (44) Phonon dispersion curves, speed of sounds calculations, and phonon density of states are obtained using the supercell frozen phonon method and the phonopy code. (45)

Speed of Sound Measurements

Speed of sound measurements are performed using an Olympus 5072PR Pulser/Receiver system with a gain of 20 dB and a 5 kHz signal. Both longitudinal and shear measurements were made, using Olympus V112 (longitudinal) and Olympus V156 (shear) transducers and an Atten ADS 1102 oscilloscope.

Hall Measurements

Hall effect and resistivity measurements are performed using the Van der Pauw geometry on a home-built apparatus. (46) Measurements are conducted up to 523 K under dynamic vacuum (<10–4 Torr). Contacts are pressure-assisted nichrome wire.

RESULTS/DISCUSSION

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Powder X-ray Diffraction and Sample Purity

The Yb2CdSb2 structure type crystallizes in the noncentrosymmetric space group Cmc21 and has been well-described by previous publications. (28,29) Ball-milling of elements followed by spark plasma sintering (SPS) resulted in samples with densities greater than 90% of theoretical values. Figure 2 shows the powder X-ray diffraction (PXRD) patterns of ground pellets of Yb2–xEuxCdSb2 (x = 0, 0.36, 0.85, 1.13, and 1.18, determined from EMPA provided below) compared to the calculated pattern for Yb2CdSb2 (top). Black asterisks indicate small impurity peaks arising from impurity phases, one of which disappears as Eu content increases (∼25°) that could not be indexed to this structure type. This peak does match to a peak from the calculated pattern of YbCd2Sb2, which has also been found in a highly defected form by electron microprobe analysis (Yb1.06(4)Cd1.93(2)Sb2.00(3)); however, there are too few peaks visible to unequivocally assign this phase as the impurity by PXRD. Since one impurity (∼29°) is a consistent impurity for the series, we expect this study will provide insight into the intrinsic properties of the system. (47) Samples show a gradual left-shift in peak position with increasing x as unit cell parameters increase, consistent with Eu being incorporated into the structure primarily in the Yb1 six-coordinate site (Figure 1b) as Eu2+ has a larger ionic radius than Yb2+ (1.14 and 1.03 Å, respectively (48)). Single crystal X-ray diffraction refinement results from Yb2–xEuxCdSb2 indicate that Eu2+ prefers the Yb1 site, consistent with these results. (28,29) The Yb1 site, with its greater average bond distance of 3.338 Å, accommodates the larger Eu2+ more easily than the Yb2 site with its average bond distance of 3.168 Å. Lattice parameters extracted from whole-pattern fitting show increasing unit cell volume with increasing Eu concentration as expected, in good agreement with lattice parameters reported from single crystal X-ray diffraction results (Supporting Information). (28,29) No further Rietveld analysis was employed due to significant peak broadening, likely from strain stemming from the ball-milling process as well as the high force applied by the SPS process.

Figure 2

Figure 2. Powder X-ray diffraction (PXRD) patterns for synthesized samples, Yb2–xEuxCdSb2. Black asterisks indicate an impurity unable to be indexed by PXRD. Whole-pattern fitting for x = 0, 0.36, 0.85, 1.13, and 1.18 revealed unit cell volumes of 581, 586, 600, 607, and 610 Å3, respectively.

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EMPA was used to verify stoichiometry and qualify the element homogeneity (EMPA images can be found in the Supporting Information). The average compositions of samples as determined by wavelength-dispersive spectroscopy (WDS) are shown in Table 1. These results indicate that the Yb2–xEuxCdSb2 phase was formed in each case. Results are also in relatively good agreement with the preparative amounts of Eu and Yb and show, within error, that the total cation count is near 2 in all samples. The samples of x = 1, 1.1 show cation totals with large standard deviations which can be attributed to inhomogeneity due to grain boundaries. The experimental value of x is employed to identify samples throughout.
Table 1. Sample Compositions of Yb2–xEuxCdSb2 As Determined by Electron Microprobe Analysis (EMPA)
preparative Eu amountexptl Eu amountsample composition (as determined by EMPA)total cation count (Eu + Yb)
00Yb1.99(3)Cd1.02(3)Sb1.99(1)1.99(3)
0.30.36Yb1.58(2)Eu0.36(1)Cd1.03(3)Sb2.017(7)1.94(2)
0.80.85Yb1.18(6)Eu0.85(3)Cd0.98(1)Sb1.98(3)2.03(3)
11.13Yb0.98(7)Eu1.13(7)Cd0.89(11)Sb1.99(4)2.11(10)
1.11.18Yb0.87(4)Eu1.18(3)Cd0.93(6)Sb2.01(1)2.05(6)

Electronic Structure

Yb2CdSb2 is a valence precise compound that can be described by the Zintl formalism. In a simple Zintl picture, Yb2+ donates two electrons to the more electronegative atoms, as confirmed by magnetic measurements. (28) The [CdSb2]4– layers can be considered as composed of Cd2+ and Sb3–; thus, [Yb2+]2[Cd2+][Sb3–]2 is considered to be a charge balanced, (49) narrow-gap semiconductor. Given the inclusion of d- and f-block metals, the definition of Zintl phases has expanded, and in this case, Cd acts as a metalloid bonding with Sb. Density functional theory (DFT) calculations were employed to provide insight into the electronic structure, electronic transport and vibrational properties of these materials.

a. Crystal Structure

Electronic structure calculations were performed for two stoichiometric configurations of Yb2–xEuxCdSb2 with x = 0 and 1. Consistent with experimental structural analysis, the calculations support the preference of Eu substitution in the Yb1 site. In fact, the electronic structure would not converge when Eu substitutes on the Yb2 sites, without Eu occupying the Yb1 sites. Conversely, the system for x = 1.25 (that is, all Yb1 sites plus one Yb2 site out of four are substituted with Eu) converges and is stable. Theoretical lattice parameters are in good agreement with experiments (see Table S1 in the Supporting Information). In particular, the calculated volume of Yb2CdSb2 (586 Å3) is within 1.6% of the experimental estimate (577 Å3). For x = 1 Eu substitution induces a significant volume expansion due to the larger radius of Eu2+ (calculated 620 Å3; experimental 607 Å3). Further substantial volume expansion occurs for x = 1.25 (641 Å3). The lack of such drastic volume expansion in experiments indicates that for x > 1 the Eu atoms are not being incorporated on the Yb sites as a solid solution. The additional Eu may simply be present at the grain boundary. Electronic structure and electronic transport property calculations were performed using fully optimized crystal structures.

b. Electronic Structure

Spin polarized density functional theory calculations show that Yb2CdSb2 is nonmagnetic, as expected due to the presence of closed shell Yb2+ (4f14), whereas the magnetic moment of YbEuCdSb2 stems from the Eu 4f-orbitals. (28) Eu2+ in the crystal retains its atomic magnetic moment (6.94 μB in the atomic sphere) of 7 unpaired electrons, suggesting that 4f-orbitals are inert and participate neither in chemical bonding nor in the Fermi level states involved in charge transport. We show below that this picture is oversimplified.
The band structure of Yb2CdSb2 is shown in Figure 3a, and both spin-up (—) and spin-down (---) bands of Yb2–xEuxCdSb2 (x = 1) are shown in Figure 3b. The valence band maximum occurs at the Γ point while the conduction band minimum occurs at the Y symmetry point, yielding an indirect band gap (92 meV) in Yb2CdSb2. This finding of a gap differs from the report of Xia and Bobev [ref (29)], who used the augmented spherical wave method that applies spherical averages to potential and density within the atom sphere. Also not applied in ref (29) were the on-site repulsive interactions on Yb. The distinction results in our obtaining a band gap, and in placing the Yb 4f levels at −1.9 eV in our calculaion, whereas their result had the center of the Yb 4f-bands centered at −0.2 eV, leading to strong hybridization with the conduction bands up to the hole chemical potential at the higher hole concentrations.

Figure 3

Figure 3. Band structure of Yb2–xEuxCdSb2 with valence (---) and conduction (—) bands indicated (a) for x = 0, and (b) for combined spin majority (—) and spin minority (---) bands for x = 1. Panel a shows flat bands at −1.9 eV from Yb 4f states whereas panel b shows flat bands around −1.9 eV arising from Yb 4f complemented with Eu 4f-bands at −2.6 eV. Panel c presents an enlargement of the x = 0 band in panel a near the band gap.

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The calculated band gap opens slightly to 111 meV for YbEuCdSb2. While band gaps calculated with DFT may be underestimated, the opening of the gap with increasing Eu concentration is consistent with the literature and experimental results presented below. Band gaps calculated from maximum Seebeck coefficient (Eg = 2eSmaxTmax) in YbCd2Sb2 and EuCd2Sb2 (50) and with band structure calculations for YbMg2Bi2 and EuMg2Bi2 provide a similar trend. (51) In both compounds the flat lanthanide f-bands within the band structure can be clearly identified. In Yb2CdSb2 the valence band edge contains one roughly isotropic band, with a second band lying around 150 meV higher binding energy. An enlarged view is provided in Figure 3c. The valence band edge is very similar for both compounds, but the spin-down channel in Figure 3b reveals an exchange splitting of 0.5 eV reflecting the exchange coupling between Eu 4f- and 5d-orbitals. The half filled 4f-orbitals provide an additional magnetic scattering mechanism when Eu is substituted into Yb2CdSb2.
The projected density of states (PDOS, Figure 4) for both x = 0 and x = 1 shows that the main character of the valence band is dictated by Sb 5p states, with Sb p, Cd p, and Yb f-orbitals contributing at higher hole binding energy. In both compounds, Sb 5p, Cd 5p, lanthanide 5d electrons are the majority participants in covalent bonding in the valence band (see more details in Figure S8 in the Supporting Information). While the band structure (Figure 3) might suggest little interaction of the f-orbitals, the PDOS reveals Yb f character rising rapidly a few tenths of an eV below the gap. In the x = 1 compound the f-bands of Eu, which lie −2.6 eV below the gap, push the Yb f character near the gap to higher energy, thus accentuating the f character of holes doped into the valence band. Such doping-induced changes in the PDOS are small enough not to produce major changes in hole mobility, but dictate the different trends in the Seebeck coefficient computed for pure and Eu-doped Yb2CdSb2.

Figure 4

Figure 4. Orbital-projected density of states plot using the DFT+U functional for Yb2–xEuxCdSb2. (a) Participating atomic orbitals near the valence edge are shown for x = 0. (b) All participating orbitals near the valence edge are shown for x = 1. The majority spin channel is shown for x = 1 in these plots. Additional detailed PDOS plots are provided in the Supporting Information.

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Electronic Transport Properties

On the basis of Zintl valence-counting rules and consistent with the DFT-calculated band structure calculations, stoichiometric Yb2–-xEuxCdSb2 compounds are expected to show semiconducting behavior. The electrical resistivities (Figure 5a) of x = 0, 0.36 and x = 0.85 samples are small and show metallic temperature dependences, as in degenerate semiconductors, while x = 1.13 and x = 1.18 show higher resistivity, consistent with both the widening of the band gap and the lowered carrier concentrations. The transition from degenerate to nondegenerate behavior seen in electrical resistivity is reflected in Seebeck measurements, as it would be expected that metallic systems have lower Seebeck coefficients. S(T, x) increases monotonically with Eu concentration, correlating with the system becoming less metallic. Hole concentrations at 323 K (Table 2) are in the range of ∼1019 due to intrinsic and compositional defects. Increasing Eu concentration causes the hole concentration to decrease, possibly because there are more defects on Yb sites, as has been seen in other cases of Eu substitution for Yb. (52,53) This is consistent with the cation totals seen in the composition (Table 1). According to the Nagle electronegativity scale, (54) Yb is more electronegative than Eu which has been suggested to influence carrier concentration because of incomplete electron donation from the cation. (53) The 373 K mobility data (Table 2) show high values for x = 0, 0.36 and 0.85, not often seen in Zintl phases, and values sharply decrease for x = 1.13 and x = 1.18. Additional Hall data are provided in the Supporting Information.

Figure 5

Figure 5. Temperature dependent (a) electrical resistivity and (b) Seebeck coefficient on polycrystalline samples of Yb2–xEuxCdSb2. The calculated Seebeck coefficients (open symbols) use experimental carrier (hole) concentration from Table 2. For x = 1 the carrier concentration is obtained by interpolating between the experimental carrier concentrations at x = 0.85 and x = 1.13. Experimental data points are shown as filled symbols and fits as solid lines.

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Table 2. Carrier (Hole) Concentration and Mobility Data for Each Sample Composition, Yb2–xEuxCdSb2, at 323 K
Eu conc (x)carrier conc (n) (cm–3)mobility (cm2/(V s))
04.53 × 101970.30
0.363.56 × 101972.18
0.858.96 × 101895.93
1.135.37 × 101824.55
1.181.41 × 101917.51
The x = 0.36 phase shows the highest carrier concentration. From this, we can propose that Yb vacancies are the major source for charge carriers (total cation stoichiometry is less than 2, Table 1), and substituting the Yb site with other alio- and isovalent cations can be a useful tool for band engineered thermoelectrics. The high mobility for the samples with x < 1 makes these phases attractive for further optimization. The nonmonotonous mobility is one of the key subjects of interest of further investigation.
Experimental temperature dependent Seebeck coefficients are shown in Figure 5b (filled symbols). All are positive in the entire range, indicative of holes as the dominant charge carriers. Consistent with previous studies on single crystal samples, the Seebeck is large in all samples. The Seebeck coefficient increases with Eu concentration, reaching a maximum value of ∼270 μV/K for the x = 1.18 phase at 523 K. Each sample shows nearly linear temperature dependence, typical of heavily doped semiconductors. Additionally, theoretically computed Seebeck coefficients are plotted in Figure 5b (open symbols) for x = 0, 0.85, and 1. To compare to experiments, which are performed on polycrystalline samples, S is defined as 1/3 of the trace of the anisotropic Seebeck tensor of a single crystal. For these calculations, the experimentally determined carrier concentrations (Table 2) were used, and for the x = 1 compound the carrier concentration was interpolated from the experimental data at x = 0.85 and 1.13. To compute the Seebeck coefficient of Yb1.15Eu0.85CdSb2 the band structure of YbEuCdSb2 was employed. Theory and experiments for this system exhibit excellent agreement, which suggests all electron-based DFT+U level of calculations and the semiclassical Boltzmann transport equation in CRTA can provide a faithful prediction of Seebeck coefficients for the Yb2–xEuxCdSb2 (2-1-2) Zintl family.
The effect of carrier concentration (n) on the calculated Seebeck coefficients is shown in Figure 6, which reveals that Yb2CdSb2 exhibits a crossover in its temperature dependence, at n ∼ 7 × 1019 cm–3. Below this value, the Seebeck coefficient decreases with increasing temperature, while at larger n the Seebeck coefficients become proportional to the temperature. This is the fingerprint of a transition from a nondegenerate to a degenerate semiconductor. For YbEuCdSb2S(T) is proportional to the temperature irrespective of carrier concentration. All experimental samples follow the trend of YbEuCdSb2 shown in Figure 6, so even the smallest amount of Eu substituted into the structure leads to S(T) that trends according to YbEuCdSb2 (Yb2–xEuxCdSb2, x = 1 model). From the calculation of the electrical transport coefficients of Yb2CdSb2 and YbEuCdSb2 in CRTA we can infer the ratio between the electrical resistivity (ρ) of the two systems at the same n, without making any assumption on the carrier lifetime. Since ρ is inversely proportional to the effective mass (m*) we can also estimate the change in m* upon Eu doping. We also calculated valence band effective mass m* from the second derivative of the band dispersion curve along the Γ-Y, Γ-SM, and Γ-S directions (Figure 3a–c). Since both Yb2–xEuxCdSb2 (x = 0, 1) exhibit multivalley band dispersion along three different band directions, we calculated the average (geometric mean) m* along these three directions. The results are m* = 0.33 and 0.36 for the x = 0 and 1 phases, respectively. Such a small difference in m* suggests that the changes observed in the transport coefficients as a function of Eu concentration are dictated by the carrier concentration.

Figure 6

Figure 6. Dependence of the calculated Seebeck coefficients on carriers (holes) concentration for Yb2–xEuxCdSb11 (x = 0, 1). For x = 0 configuration, a temperature dependent crossover is observed near 7 × 101 9 cm–3.

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The small changes in hole mobility, which stem from the valence band edge being relatively insensitive to Eu alloying, suggest that codoping with other elements to achieve a disordered Zintl phase might be used to engineer a higher Seebeck and possibly better zT, as observed for Ca doping in (Eu0.5Yb0.5)1–xCaxMg2Bi2. (51)

Thermal Transport Properties

The total thermal conductivity, shown in Figure 7, is calculated from the thermal diffusivity (D). The DFT-calculated heat capacity of Yb2CdSb2 (Supporting Information) yields a value of 0.17 J/g K, in good agreement with values predicted by the Dulong–Petit model as well as experimentally measured Cp. The calculated thermal conductivity is extremely low and comparable to other systems with anomalously low κT such as coinage-metal-stuffed Eu9Cd4Sb9 (9) and Yb2Mn4.2Sb9. (55) The total thermal conductivity (κT) is a combination of lattice (κL) and electronic (κe) contributions. κe can be estimated using the Wiedemann–Franz relation (κe = LT/ρ). Here, L was calculated using eq 2, (56) assuming a single parabolic band (SPB) model and primarily acoustic phonon scattering. L values are shown in the Supporting Information.
(1)

Figure 7

Figure 7. Total and lattice thermal conductivity of Yb2–xEuxCdSb2. Total thermal conductivity is shown as solid symbols, and lattice thermal conductivity is shown as open symbols.

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In all systems, κe is small, and subtracting it from κT yields κL (Supportng Information), the main contributor to κT. Cahill et al. (57) proposed an empirical expression for the theoretical minimum for κL as
(2)
where kB is the Boltzmann constant, V is the average volume per atom, and νT and νL are the transverse and longitudinal speeds of sound, respectively. kmin values are calculated for each composition and shown compared to κL, and in each composition, κL falls below its theoretical minimum. In a physical description, κL cannot be lower than κmin, and it can be inferred that the SPB model is inadequate or there are scattering mechanisms other than acoustic phonon scattering that are present (e.g., ionized impurity scattering) that yield unphysical values of L. Regardless, κT is extremely low at these near ambient temperatures, comparable to or lower than other materials (55,58,59) at high temperatures where κT should be at its lowest, which makes this a promising system for thermoelectric applications.
Such low κT values are not necessarily expected in such a simple structure. Similarly, PbTe, a simple rocksalt structure with no nanoinclusions, complex unit cell, or “rattler” atoms, yielded an inexplicably low κT (∼2 W/m K). This was attributed to avoided crossing in the phonon band structure and softening of certain branches generating soft lattice behavior. (60) To elucidate the possible origin of the low thermal conductivity of these compounds, the phonon band structure for x = 0 was calculated and is shown in Figure 8. The unit cell of Yb2CdSb2 contains 20 atoms, yielding 3 acoustic and 57 optical branches. The acoustic modes are confined to low frequency, below 2 THz (∼8.3 meV), with low group velocities over the whole Brillouin zone. Optical branches start as low as 0.7 THz (∼2.9 meV) and intersect with acoustic branches providing a large density of 3-phonon scattering channels. The optical bands have very low group velocities, thus contributing very little to the overall thermal conductivity. These features work in tandem to lower the lattice thermal conductivity of the compound, as has been seen in other Cd-based Zintl compounds, especially in the antimonides. (61)

Figure 8

Figure 8. Phonon dispersion of Yb2–xEuxCdSb2x = 0 by frozen phonon approximation. All optical bands are very flat in nature.

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The lattice thermal conductivity can be expressed in the following equation:
(3)
where νs is the phonon group velocity, cs is the speed of sound, and lph is the phonon mean free path. According to eq 3, thermal conductivity is proportional to the speed of sound in the material. The computed longitudinal group velocity for Yb2CdSb2 along three different crystallographic axes (a, b, and c) provides speeds of sound along different axis values: 3520 m/s (a), 2644 m/s (b), 2671 m/s (c). With the average value of above three velocities, 2900 m/s as longitudinal speed of sound is obtained. The transverse (shear) phonon mode yields 1878 m/s (a), 2163 m/s (b), 2105 m/s (c), and 2048 m/s as an average. These values are in good agreement with the experimental values (Figure 9) and support the decreasing thermal conductivity with increasing Eu incorporation as this would increase point scattering throughout the system.

Figure 9

Figure 9. Shear and longitudinal speeds of sound for each sample. Speed of sound data are tabulated in Table S2 of the Supporting Information.

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Additionally, as aforementioned, Eu preferentially substitutes on the interlayer site between polyanionic sheets. As the Eu concentration surpasses unity in x = 1.13 and 1.18, Eu is also found on the intralayer site (28) and stretches out the accordion-like polyanionic units. This yields disorder and strain in the lattice, further lowering thermal conductivity as can be seen by the discontinuity in κT between x = 0.85 and x = 1.13. Experimentally determined speeds of sound (Figure 9) support this conclusion as these values are comparable to other materials with low thermal conductivity, (9,55) decreasing with increasing Eu concentration. Speed of sound values suddenly make a dramatic drop at x = 1.13, further supporting the idea that the additional Eu on the intralayer site significantly affects the lattice. Thus, it can be concluded that the site specific substitution, alloy scattering, and lack of center of symmetry in this structure type lead to the low sound velocity and significant phonon–phonon scattering that are the origins of the extremely low κL.

Figure of Merit

The figure of merit of Yb2–xEuxCdSb2 (x = 0, 0.36, 0.85, 1.13, 1.18) is shown in Figure 10 as a function of temperature. All zT curves increase with temperature to 523 K with decreasing zT as Eu concentration increases. The reduction of zT is due to the large increase in electrical resistivity rendered upon having concentrations of Eu equal to or greater than that of Yb in the structure. The x = 0.36 composition of Yb2–xEuxCdSb2 shows near optimal carrier concentration and good mobility making it the best in this series for moderate to low-temperature applications, as the zT curve for x = 0.36 is slightly greater than that of TAGS, a well-known moderate temperature thermoelectric material. (62) Overall, x = 0.36 reaches a maximum zT of ∼0.7 at 523 K, an excellent temperature range for waste heat recovery such as in the case of midtemperature STEGs. However, the thermal conductivity is not the lowest for this composition, suggesting that further tuning of the 2-1-2 family can lead to increased efficiency.

Figure 10

Figure 10. Calculated figure of merit of Yb2–xEuxCdSb2.

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Conclusion

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In this paper we have described a promising thermoelectric structure type, Yb2–xEuxCdSb2, with favorable thermoelectric properties. Band structure calculations reveal the compounds to be indirect band gap semiconductors with a band gap that increases with Eu concentration. Though their band centers lie well below the gap, the f-orbitals of Yb influence somewhat the values of the Seebeck coefficients through hybridization in states just below the gap, contributing to the high Seebeck coefficients observed in these compounds. Complexities in the phonon dispersion along with point defect scattering from Eu substitution allow for very low thermal conductivity. This paired with low electrical resistivity in Yb1.7Eu0.3CdSb2 results in high zT of ∼0.7 at 523 K. These results represent an initial set of measurements that guide our understanding of how to optimize this system further. The very low thermal conductivity of the series is optimized, as the lattice contribution (the major contribution to thermal conductivity) is at or below the theoretical minimum, and further efforts to improve zT can be focused on improving electrical transport properties either through controlling carrier concentration (e.g., aliovalent doping), as zT could likely be greater with higher carrier concentration, or through enhancing thermopower (e.g., band engineering). Further efforts of substituting on the rare earth sites of Yb2–xEuxCdSb2 with nonmagnetic group I or group II materials may provide a higher Seebeck coefficient and increase zT further.

Supporting Information

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.7b04517.

  • Comparison of single crystal and powder X-ray diffraction unit cell parameters, electron microprobe analysis elemental mapping images, heat capacity data, mobility and carrier concentration data, Lorenz numbers, lattice thermal conductivity with minumum values, k-path, additional projected density of states plots, Seebeck versus chemical potential, optimized DFT lattice parameters, speed of sound, thermal diffusivity, and optimized Cartesian coordinates (PDF)

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Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Author
  • Authors
    • Joya A. Cooley - Department of Chemistry, University of California, One Shields Avenue, Davis, California 95616, United States
    • Phichit Promkhan - Department of Chemistry, University of California, One Shields Avenue, Davis, California 95616, United States
    • Shruba Gangopadhyay - Department of Chemistry, University of California, One Shields Avenue, Davis, California 95616, United States
    • Davide Donadio - Department of Chemistry, University of California, One Shields Avenue, Davis, California 95616, United States;  IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain;  Orcidhttp://orcid.org/0000-0002-2150-4182
    • Warren E. Pickett - Department of Physics, University of California, One Shields Avenue, Davis, California 95616, United States
    • Brenden R. Ortiz - Department of Physics, Colorado School of Mines, Golden, Colorado 80401, United States
    • Eric S. Toberer - Department of Physics, Colorado School of Mines, Golden, Colorado 80401, United States
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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We thank Nicholas Botto for microprobe analysis, GAANN (J.A.C.), and NSF DMR-1405973, -1709382, and NSF CAREER award DMR-1555340 for funding. W.E.P. was supported by DOE NNSA Grant DE-NA0002908. The National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, as well as an in-house computational cluster at the University of California Davis are gratefully acknowledged.

References

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    The Zintl phase Sr5Al2Sb6 has a large, complex unit cell and is composed of relatively earth-abundant and non-toxic elements, making it an attractive candidate for thermoelec. applications. The structure of Sr5Al2Sb6 is characterized by infinite oscillating chains of AlSb4 tetrahedra. It is distinct from the structure type of the previously studied Ca5M2Sb6 compds. (M = Al, Ga, or In), all of which were shown to have promising thermoelec. performance. The lattice thermal cond. of Sr5Al2Sb6 (≈0.55 W mK-1 at 1000 K) was found to be lower than that of the related Ca5M2Sb6 compds. due to its larger unit cell (54 atoms per primitive cell). D. functional theory predicts a relatively large band gap in Sr5Al2Sb6, in agreement with the exptl. detd. band gap of Eg ≈0.5 eV. High temp. electronic transport measurements reveal high resistivity and high Seebeck coeffs. in Sr5Al2Sb6, consistent with the large band gap and valence-precise structure. Doping with Zn2+ on the Al3+ site was attempted, but did not lead to the expected increase in carrier concn. The low lattice thermal cond. and large band gap in Sr5Al2Sb6 suggest that, if the carrier concn. can be increased, thermoelec. performance comparable to that of Ca5Al2Sb6 could be achieved in this system.
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  13. 13
    Shuai, J.; Mao, J.; Song, S.; Zhang, Q.; Chen, G.; Ren, Z. Recent Progress and Future Challenges on Thermoelectric Zintl Materials. Materials Today Physics 2017, 1, 74– 95,  DOI: 10.1016/j.mtphys.2017.06.003
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  14. 14
    Hu, Y.; Bux, S. K.; Grebenkemper, J. H.; Kauzlarich, S. M. The Effect of Light Rare Earth Element Substitution in Yb14MnSb11 on Thermoelectric Properties. J. Mater. Chem. C 2015, 3 (40), 10566– 10573,  DOI: 10.1039/C5TC02326B
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    14
    The effect of light rare earth element substitution in Yb14MnSb11 on thermoelectric properties
    Hu, Yufei; Bux, Sabah K.; Grebenkemper, Jason H.; Kauzlarich, Susan M.
    Journal of Materials Chemistry C: Materials for Optical and Electronic Devices (2015), 3 (40), 10566-10573CODEN: JMCCCX; ISSN:2050-7534. (Royal Society of Chemistry)
    After the discovery of Yb14MnSb11 as an outstanding p-type thermoelec. material for high temps. (≥900 K), site substitution of other elements has been proven to be an effective method to further optimize the thermoelec. properties. Yb14-xRExMnSb11 (RE = Pr and Sm, 0 < x < 0.55) compds. were prepd. by powder metallurgy to study their thermoelec. properties. According to powder X-ray diffraction, these samples are iso-structural with Yb14MnSb11 and when >5% RE is used in the synthesis the presence of (Yb,RE)4Sb3 is apparent after synthesis. After consolidation and measurement, (Yb,RE)Sb and (Yb,RE)11Sb10 appear in the powder X-ray diffraction patterns. Electron microprobe anal. results show that consolidated pellets have small (Yb,RE)Sb domains and that the max. amt. of RE in Yb14-xRExMnSb11 is x = 0.55, however, (Yb,RE)11Sb10 cannot be distinguished by electron microprobe anal. By replacing Yb2+ with RE3+, one extra electron is introduced into Yb14MnSb11 and the carrier concn. is adjusted. Thermoelec. performance from room temp. to 1275 K was evaluated through transport and thermal cond. measurements. The measurement shows that Seebeck coeffs. initially increase and then remain stable and that elec. resistivity increases with increasing substitution. Thermal cond. is slightly reduced. Substitution of Pr and Sm leads to enhanced zT. Yb13.82Pr0.18Mn1.01Sb10.99 has the best max. zT value of ∼1.2 at 1275 K, while Yb13.80Sm0.19Mn1.00Sb11.02 has its max. zT of ∼1.0 at 1275 K, ∼45% and ∼30% higher resp., than Yb14MnSb11 prepd. in the same manner.
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  15. 15
    Hu, Y.; Kauzlarich, S. M. Yb14MgBi11: Structure, Thermoelectric Properties and the Effect of the Structure on Low Lattice Thermal Conductivity. Dalton Trans. 2017, 46 (12), 3996– 4003,  DOI: 10.1039/C7DT00183E
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    15
    Yb14MgBi11: structure, thermoelectric properties and the effect of the structure on low lattice thermal conductivity
    Hu, Yufei; Kauzlarich, Susan M.
    Dalton Transactions (2017), 46 (12), 3996-4003CODEN: DTARAF; ISSN:1477-9226. (Royal Society of Chemistry)
    Zintl phases Yb14MnSb11 and Yb14MgSb11, which share the same complex structure type, have been demonstrated as the best p-type thermoelec. materials for the high temp. region (800-1200 K). A new iso-structural compd., Yb14MgBi11, was synthesized in order to investigate the structure and thermoelec. properties of the Bi analogs. Yb14MgBi11 crystallizes in the Ca14AlSb11 structure-type with the space group I41/acd [a = 16.974(2) Å, c = 22.399(4) Å, V = 6454(2) Å3, R1/wR2 = 0.0238/0.0475]. The structure follows the previous description of this structure type and the trend obsd. in previous analogs. Thermoelec. properties of Yb14MgBi11 are measured together with Yb14MnBi11 and both compds. are metallic. Compared to Yb14MgSb11, Yb14MgBi11 has a higher carrier concn. with a similar mobility and effective mass. The lattice thermal cond. of Yb14MgBi11 is extremely low, which is as low as 0.16-0.36 W(mK)-1. The zT values of Yb14MgBi11 and Yb14MnBi11 reach 0.2 at 875 K.
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  16. 16
    Tamaki, H.; Sato, H. K.; Kanno, T. Isotropic Conduction Network and Defect Chemistry in Mg3+δSb2-Based Layered Zintl Compounds with High Thermoelectric Performance. Adv. Mater. 2016, 28 (46), 10182– 10187,  DOI: 10.1002/adma.201603955
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    Isotropic Conduction Network and Defect Chemistry in Mg3+δSb2-Based Layered Zintl Compounds with High Thermoelectric Performance
    Tamaki, Hiromasa; Sato, Hiroki K.; Kanno, Tsutomu
    Advanced Materials (Weinheim, Germany) (2016), 28 (46), 10182-10187CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
    The authors revealed a high ZT value ≈1.5 of the layered Zintl phase n-Mg3Sb2 was realized by defect chem. approach and introducing Sb/Bi disorder. The present discovery in the low-cost and earth-abundant material bridges the gap to practical application in thermoelecs. The defect chem. approach by incorporating an extraordinarily large amt. of excess cations will lead to new materials discovery in a wide variety of thermoelec. Zintl phases with stable intrinsic defects. The isotropic thermoelec. transport in Mg3Sb2-based material, which originates from its heterogeneous structure, provides a new and effective strategy to develop practical thermoelec. materials for waste heat recovery.
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  17. 17
    Saramat, A.; Svensson, G.; Palmqvist, A. E. C.; Stiewe, C.; Mueller, E.; Platzek, D.; Williams, S. G. K.; Rowe, D. M.; Bryan, J. D.; Stucky, G. D. Large Thermoelectric Figure of Merit at High Temperature in Czochralski-Grown Clathrate Ba8Ga16Ge30. J. Appl. Phys. 2006, 99 (2), 023708,  DOI: 10.1063/1.2163979
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    17
    Large thermoelectric figure of merit at high temperature in Czochralski-grown clathrate Ba8Ga16Ge30
    Saramat, A.; Svensson, G.; Palmqvist, A. E. C.; Stiewe, C.; Mueller, E.; Platzek, D.; Williams, S. G. K.; Rowe, D. M.; Bryan, J. D.; Stucky, G. D.
    Journal of Applied Physics (2006), 99 (2), 023708/1-023708/5CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)
    The Czochralski method was used to grow a 46-mm-long crystal of the Ba8Ga16Ge30 clathrate, which was cut into disks that were evaluated for thermoelec. performance. The Seebeck coeff. and elec. and thermal conductivities all showed evidence of a transition from extrinsic to intrinsic behavior in the range of 600-900 K. The corresponding figure of merit (ZT) was found to be a record high of 1.35 at 900 K and with an extrapolated max. of 1.63 at 1100 K. This makes the Ba8Ga16Ge30 clathrate an exceptionally strong candidate for medium and high-temp. thermoelec. applications.
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    Sundarraj, P.; Maity, D.; Roy, S. S.; Taylor, R. A. Recent Advances in Thermoelectric Materials and Solar Thermoelectric Generators - A Critical Review. RSC Adv. 2014, 4 (87), 46860– 46874,  DOI: 10.1039/C4RA05322B
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    Recent advances in thermoelectric materials and solar thermoelectric generators - a critical review
    Sundarraj, Pradeepkumar; Maity, Dipak; Roy, Susanta Sinha; Taylor, Robert A.
    RSC Advances (2014), 4 (87), 46860-46874CODEN: RSCACL; ISSN:2046-2069. (Royal Society of Chemistry)
    A review. Due to the fact that much of the world's best solar resources are inversely correlated with population centers, significant motivation exists for developing technol. which can deliver reliable and autonomous conversion of sunlight into electricity. Thermoelec. generators are gaining incremental ground in this area since they do not require moving parts and work well in remote locations. Thermoelec. materials have been extensively used in space satellites, automobiles, and, more recently, in solar thermal applications as power generators, known as solar thermoelec. generators (STEG). STEG systems are gaining significant interest in both concd. and non-concd. systems and have been employed in hybrid configurations with solar thermal and photovoltaic systems. In this article, the key developments in the field of thermoelec. materials and on-going research work on STEG design conducted by various researchers to date are critically reviewed. Finally, we highlight the strategic research directions being undertaken to make highly efficient thermoelec. materials for developing a cost-effective STEG system, which could serve to bring this technol. towards com. readiness.
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  19. 19
    Zeier, W. G.; Zevalkink, A.; Gibbs, Z. M.; Hautier, G.; Kanatzidis, M. G.; Snyder, G. J. Thinking Like a Chemist: Intuition in Thermoelectric Materials. Angew. Chem., Int. Ed. 2016, 55 (24), 6826– 6841,  DOI: 10.1002/anie.201508381
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    Thinking like a chemist: intuition in thermoelectric materials
    Zeier, Wolfgang G.; Zevalkink, Alex; Gibbs, Zachary M.; Hautier, Geoffroy; Kanatzidis, Mercouri G.; Snyder, G. Jeffrey
    Angewandte Chemie, International Edition (2016), 55 (24), 6826-6841CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    A review. The coupled transport properties required to create an efficient thermoelec. material necessitates a thorough understanding of the relation between the chem. and physics in a solid. The authors approach thermoelec. material design using the chem. intuition provided by MO diagrams, tight binding theory, and a classic understanding of bond strength. Concepts such as electronegativity, band width, orbital overlap, bond energy, and bond length are used to explain trends in electronic properties such as the magnitude and temp. dependence of band gap, carrier effective mass, and band degeneracy and convergence. The lattice thermal cond. is discussed in relation to the crystal structure and bond strength, with emphasis on the importance of bond length. The authors provide an overview of how symmetry and bonding strength affect electron and phonon transport in solids, and how altering these properties may be used in strategies to improve thermoelec. performance.
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  20. 20
    Liu, W.; Hu, J.; Zhang, S.; Deng, M.; Han, C.-G.; Liu, Y. New Trends, Strategies and Opportunities in Thermoelectric Materials: A Perspective. Materials Today Physics 2017, 1, 50– 60,  DOI: 10.1016/j.mtphys.2017.06.001
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    Kleinke, H. New Bulk Materials for Thermoelectric Power Generation: Clathrates and Complex Antimonides. Chem. Mater. 2010, 22 (3), 604– 611,  DOI: 10.1021/cm901591d
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    New bulk Materials for Thermoelectric Power Generation: Clathrates and Complex Antimonides
    Kleinke, Holger
    Chemistry of Materials (2010), 22 (3), 604-611CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
    A review. Thermoelec. power generation is foreseen to play a much larger role in the near future, considering the need for alternative energies because of declining natural resources as well as the increasing efficiency of thermoelec. materials. The latter is a consequence of the discoveries of new materials as well as of improvements of established materials by, for example, nanostructuring or band structure engineering. Within this review, two major classes of high-temp. thermoelecs. are presented: clathrates formed by silicides and germanides, and complex antimonides including but not limited to the filled skutterudites. The clathrates and the skutterudites are cage compds. that exhibit low thermal cond., reportedly related to the rattling effect of the guest atoms, whereas the other antimonides achieve low thermal cond. via defects or simply via the high complexity of their crystal structures.
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    Kanatzidis, M. G. Advances in Thermoelectrics: From Single Phases to Hierarchical Nanostructures and Back. MRS Bull. 2015, 40 (08), 687– 695,  DOI: 10.1557/mrs.2015.173
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    Minnich, A. J.; Dresselhaus, M. S.; Ren, Z. F.; Chen, G. Bulk Nanostructured Thermoelectric Materials: Current Research and Future Prospects. Energy Environ. Sci. 2009, 2 (5), 466– 479,  DOI: 10.1039/b822664b
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    Bulk nanostructured thermoelectric materials: current research and future prospects
    Minnich, A. J.; Dresselhaus, M. S.; Ren, Z. F.; Chen, G.
    Energy & Environmental Science (2009), 2 (5), 466-479CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
    A review. Thermoelecs. have long been recognized as a potentially transformative energy conversion technol. due to their ability to convert heat directly into electricity. Despite this potential, thermoelec. devices are not in common use because of their low efficiency, and today they are only used in niche markets where reliability and simplicity are more important than performance. However, the ability to create nanostructured thermoelec. materials has led to remarkable progress in enhancing thermoelec. properties, making it plausible that thermoelecs. could start being used in new settings in the near future. Of the various types of nanostructured materials, bulk nanostructured materials have shown the most promise for com. use because, unlike many other nanostructured materials, they can be fabricated in large quantities and in a form that is compatible with existing thermoelec. device configurations. The first generation of these materials is currently being developed for commercialization, but creating the second generation will require a fundamental understanding of carrier transport in these complex materials which is presently lacking. In this review we introduce the principles and present status of bulk nanostructured materials, then describe some of the unanswered questions about carrier transport and how current research is addressing these questions. Finally, we discuss several research directions which could lead to the next generation of bulk nanostructured materials.
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    Takahata, K.; Iguchi, Y.; Tanaka, D.; Itoh, T.; Terasaki, I. Low Thermal Conductivity of the Layered Oxide (Na,Ca)Co2O4}: Another Example of a Phonon Glass and an Electron Crystal. Phys. Rev. B: Condens. Matter Mater. Phys. 2000, 61 (19), 12551– 12555,  DOI: 10.1103/PhysRevB.61.12551
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    Goldsmid, H. J. The Thermal Conductivity of Bismuth Telluride. Proc. Phys. Soc., London, Sect. B 1956, 69 (2), 203,  DOI: 10.1088/0370-1301/69/2/310
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    Toberer, E. S.; May, A. F.; Melot, B. C.; Flage-Larsen, E.; Snyder, G. J. Electronic Structure and Transport in Thermoelectric Compounds AZn2Sb2 (A = Sr, Ca, Yb, Eu). Dalton Trans. 2010, 39 (4), 1046– 1054,  DOI: 10.1039/B914172C
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    26
    Electronic structure and transport in thermoelectric compounds AZn2Sb2 (A = Sr, Ca, Yb, Eu)
    Toberer, Eric S.; May, Andrew F.; Melot, Brent C.; Flage-Larsen, Espen; Snyder, G. Jeffrey
    Dalton Transactions (2010), 39 (4), 1046-1054CODEN: DTARAF; ISSN:1477-9226. (Royal Society of Chemistry)
    The AZn2Sb2 (P3m1, A = Ca, Sr, Eu, Yb) class of Zintl compds. has shown high thermoelec. efficiency (zT∼ 1) and is an appealing system for the development of Zintl structure-property relationships. High temp. transport measurements have previously been conducted for all known compns. except for SrZn2Sb2; here we characterize polycryst. SrZn2Sb2 to 723 K and review the transport behavior of the other compds. in this class. Consistent with the known AZn2Sb2 compds., SrZn2Sb2 is found to be a hole-doped semiconductor with a thermal band gap ∼0.27 eV. The Seebeck coeffs. of the AZn2Sb2 compds. are found to be described by similar effective mass (m* ∼ 0.6 me). Electronic structure calcns. reveal similar m* is due to antimony p states at the valence band edge which are largely unaffected by the choice of A-site species. However, the choice of A-site element has a dramatic effect on the hole mobility, with the room temp. mobility of the rare earth-based compns. approx. double that found for Ca and Sr on the A site. This difference in mobility is examd. in the context of electronic structure calcns.
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    Zhang, H.; Baitinger, M.; Tang, M.-B.; Man, Z.-Y.; Chen, H.-H.; Yang, X.-X.; Liu, Y.; Chen, L.; Grin, Y.; Zhao, J.-T. Thermoelectric properties of Eu(Zn1-xCdx)2Sb2. Dalton Trans. 2010, 39 (4), 1101– 1104,  DOI: 10.1039/B916346H
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    Thermoelectric properties of Eu(Zn1-xCdx)2Sb2
    Zhang, Hui; Baitinger, Michael; Tang, Mei-Bo; Man, Zhen-Yong; Chen, Hao-Hong; Yang, Xin-Xin; Liu, Yi; Chen, Ling; Grin, Yuri; Zhao, Jing-Tai
    Dalton Transactions (2010), 39 (4), 1101-1104CODEN: DTARAF; ISSN:1477-9226. (Royal Society of Chemistry)
    The thermoelec. performance of EuZn2Sb2 and EuCd2Sb2 was optimized by mixed occupation of the transition metal position. Samples in the solid soln. Eu(Zn1-xCdx)2Sb2 with the CaAl2Si2-type crystal structure (space group Pm1) were prepd. from the elements for compns. with x = 0, 0.1, 0.3, 0.5, and 1. The thermoelec. properties were investigated after densification of the products by spark plasma sintering (SPS). The samples show low elec. resistivity, high thermopower and a low lattice thermocond. The highest ZT value of 1.06 at 650 K is obtained for x = 0.1.
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  28. 28
    Saparov, B.; Saito, M.; Bobev, S. Syntheses, and Crystal and Electronic Structures of the New Zintl Phases Na2ACdSb2 and K2ACdSb2 (A = Ca, Sr, Ba, Eu, Yb): Structural Relationship with Yb2CdSb2 and the Solid Solutions Sr2–xAxCdSb2, Ba2–xAxCdSb2 and Eu2–xYbxCdSb2. J. Solid State Chem. 2011, 184 (2), 432– 440,  DOI: 10.1016/j.jssc.2010.12.015
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    Syntheses, and crystal and electronic structures of the new Zintl phases Na2ACdSb2 and K2ACdSb2 (A = Ca, Sr, Ba, Eu, Yb): Structural relationship with Yb2CdSb2 and the solid solutions Sr2-xAxCdSb2, Ba2-xAxCdSb2 and Eu2-xYbxCdSb2
    Saparov, Bayrammurad; Saito, Maia; Bobev, Svilen
    Journal of Solid State Chemistry (2011), 184 (2), 432-440CODEN: JSSCBI; ISSN:0022-4596. (Elsevier B.V.)
    Presented are the details of the syntheses, crystal and electronic structures of a new family of Zintl phases Na2ACdSb2 and K2ACdSb2 (A = Ca, Sr, Ba, Eu, Yb), as well as the solid solns. Sr2-xAxCdSb2, Ba2-xAxCdSb2 and Eu2-xYbxCdSb2. The structures of Na2ACdSb2 and K2ACdSb2 (A = Ca, Sr, Ba, Eu, Yb) are of a new type with the noncentrosym. space group Pmc21, Pearson symbol oP12, with a 4.684(1)-4.788(1); b 9.099(3)-9.117(2); c 7.837(1)-8.057(2) Å for the Na2ACdSb2 series, and a 4.6637(9)-5.0368(8); b = 9.100(2)-9.8183(15); and c 7.7954(15) -8.4924(13) Å for K2ACdSb2, resp. The solid solns. Sr2-xAxCdSb2, Ba2-xAxCdSb2 and Eu2-xYbxCdSb2 (x ≈ 1) are isostructural and isoelectronic to the recently reported Yb2CdSb2 (space group Cmc21, Pearson symbol cP20). All discussed structures are based upon CdSb24- polyanionic layers, similar to the ones obsd. in Yb2CdSb2, with various alkali- and/or alk.-earth cations coordinated to them. Magnetic susceptibility and Seebeck coeff. measurements on selected Eu2-xYbxCdSb2 samples, taken at low temps. up to 300 K, are also reported.
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    Xia, S.-q.; Bobev, S. Cation–Anion Interactions as Structure Directing Factors: Structure and Bonding of Ca2CdSb2 and Yb2CdSb2. J. Am. Chem. Soc. 2007, 129 (13), 4049– 4057,  DOI: 10.1021/ja069261k
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    29
    Cation-Anion Interactions as Structure Directing Factors: Structure and Bonding of Ca2CdSb2 and Yb2CdSb2
    Xia, Sheng-Qing; Bobev, Svilen
    Journal of the American Chemical Society (2007), 129 (13), 4049-4057CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Two new transition-metal-contg. Zintl phases, Ca2CdSb2 and Yb2CdSb2, were synthesized by flux reactions, and their structures were detd. by single-crystal x-ray diffraction. Yb2CdSb2 crystallizes in the noncentrosym. orthorhombic space group Cmc21, Z = 4. Ca2CdSb2 crystallizes in the centrosym. orthorhombic space group Pnma, Z = 4. Despite the similarity in their chem. formulas and unit cell parameters, the structures of Yb2CdSb2 and Ca2CdSb2 are subtly different: Ca2CdSb2 has a layered structure built up of infinite layers of CdSb4 tetrahedra connected through corner-sharing. These layers are stacked in an alternating AA-1AA-1 sequence along the direction of the longest crystallog. axis (A denotes a layer; A-1 stands for its inversion symmetry equiv.), with Ca2+ cations filling the space between them. The structure of Yb2CdSb2 features the very same [CdSb2]4- layers of CdSb4 tetrahedra, which because of the lack of inversion symmetry are stacked in an AAAA-type fashion and are sepd. by Yb2+ cations. Electronic band structure calcns. performed using the TB-LMTO-ASA method show a small band gap at the Fermi level for Ca2CdSb2, whereas the gap closes for Yb2CdSb2. These results suggest narrow gap semiconducting and poorly metallic behavior, resp., and are confirmed by resistivity and magnetic susceptibility measurements. The structural relation between these new layered structure types and some known structures with three-dimensional four-connected nets are discussed as well.
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  30. 30
    Serrano-Sánchez, F.; Gharsallah, M.; Nemes, N. M.; Mompean, F. J.; Martínez, J. L.; Alonso, J. A. Record Seebeck Coefficient and Extremely Low Thermal Conductivity in Nanostructured SnSe. Appl. Phys. Lett. 2015, 106 (8), 083902,  DOI: 10.1063/1.4913260
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    Zhao, L.-D.; Lo, S.-H.; Zhang, Y.; Sun, H.; Tan, G.; Uher, C.; Wolverton, C.; Dravid, V. P.; Kanatzidis, M. G. Ultralow Thermal Conductivity and High Thermoelectric Figure of Merit in SnSe Crystals. Nature 2014, 508 (7496), 373– 377,  DOI: 10.1038/nature13184
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    Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals
    Zhao, Li-Dong; Lo, Shih-Han; Zhang, Yongsheng; Sun, Hui; Tan, Gangjian; Uher, Ctirad; Wolverton, C.; Dravid, Vinayak P.; Kanatzidis, Mercouri G.
    Nature (London, United Kingdom) (2014), 508 (7496), 373-377CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
    The thermoelec. effect enables direct and reversible conversion between thermal and elec. energy, and provides a viable route for power generation from waste heat. The efficiency of thermoelec. materials is dictated by the dimensionless figure of merit, ZT (where Z is the figure of merit and T is abs. temp.), which governs the Carnot efficiency for heat conversion. Enhancements above the generally high threshold value of 2.5 have important implications for com. deployment, esp. for compds. free of Pb and Te. Here we report an unprecedented ZT of 2.6 ± 0.3 at 923 K, realized in SnSe single crystals measured along the b axis of the room-temp. orthorhombic unit cell. This material also shows a high ZT of 2.3 ± 0.3 along the c axis but a significantly reduced ZT of 0.8 ± 0.2 along the a axis. We attribute the remarkably high ZT along the b axis to the intrinsically ultralow lattice thermal cond. in SnSe. The layered structure of SnSe derives from a distorted rock-salt structure, and features anomalously high Grueneisen parameters, which reflect the anharmonic and anisotropic bonding. We attribute the exceptionally low lattice thermal cond. (0.23 ± 0.03 W m-1 K-1 at 973 K) in SnSe to the anharmonicity. These findings highlight alternative strategies to nanostructuring for achieving high thermoelec. performance.
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    Rodríguez-Carvajal, J. Recent Advances in Magnetic Structure Determination by Neutron Powder Diffraction. Phys. B 1993, 192 (1–2), 55– 69,  DOI: 10.1016/0921-4526(93)90108-I
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    Recent advances in magnetic structure determination by neutron powder diffraction
    Rodriguez-Carvajal, Juan
    Physica B: Condensed Matter (Amsterdam, Netherlands) (1993), 192 (1-2), 55-69CODEN: PHYBE3; ISSN:0921-4526.
    A review with 30 refs. Some recent improvements in the anal. of magnetic neutron powder diffraction data are discussed. After an introduction to the subject, the main formulas governing the anal. of the Bragg magnetic scattering are summarized and shortly discussed. Next, the method of profile fitting without a structural model to get precise integrated intensities and refine the propagation vector(s) of the magnetic structure is discussed. The simulated annealing approach for magnetic structure detn. is briefly discussed and, finally, some features of the program FullProf concerning the magnetic structure refinement are presented and discussed. The different themes are illustrated with simple examples.
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    Blaha, P.; Schwarz, K.; Sorantin, P.; Trickey, S. B. Full-Potential, Linearized Augmented Plane-Wave Programs for Crystalline Systems. Comput. Phys. Commun. 1990, 59 (2), 399– 415,  DOI: 10.1016/0010-4655(90)90187-6
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    Full-potential, linearized augmented plane wave programs for crystalline systems
    Blaha, P.; Schwarz, K.; Sorantin, P.; Trickey, S. B.
    Computer Physics Communications (1990), 59 (2), 399-415CODEN: CPHCBZ; ISSN:0010-4655.
    In solids, linearized augmented plane waves (LAPW's) were proven to be an effective basis for the soln. of the Kohn-Sham equations, the main calculational task in the local spin d. approxn. (LSDA) to d. functional theory. The WIEN package uses LAPW's to calc. the LSDA total energy, spin densities, Kohn-Sham eigenvalues, and the elec. field gradients at nuclear sits for a broad variety of space groups. Options include retention or omission of non-muffin-tin contributions (hence WIEN is a full-potential or F-LAPW code) and relativistic corrections (full treatment for core states, scalar-relativistic for valence states).
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    Madsen, G. K. H.; Blaha, P.; Schwarz, K.; Sjostedt, E.; Nordstrom, L. Efficient Linearization of the Augmented Plane-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 64 (19), 195134,  DOI: 10.1103/PhysRevB.64.195134
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    Efficient linearization of the augmented plane-wave method
    Madsen, Georg K. H.; Blaha, Peter; Schwarz, Karlheinz; Sjostedt, Elisabeth; Nordstrom, Lars
    Physical Review B: Condensed Matter and Materials Physics (2001), 64 (19), 195134/1-195134/9CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    We present a detailed anal. of the APW+lo basis set for band-structure calcns. This basis set consists of energy independent augmented plane-wave (APW) functions. The linearization is introduced through local orbitals evaluated at the same linearization energy as the APW functions. It is shown that results obtained with the APW+lo basis set converge much faster and often more systematically towards the final value. The APW+lo thereby allows accurate treatment of systems that were previously unaccessible to linearized APW. Furthermore, it is shown that APW+lo converges to the same total energy as LAPW provided the higher angular momenta l are linearized, either by adding extra local orbitals or treating them by LAPW. It is illustrated that the APW basis functions are much closer to the true form of the eigenfunctions than the LAPW basis functions. This is esp. true for basis functions that have a strong energy dependence inside the sphere.
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    Schwarz, K.; Blaha, P.; Madsen, G. K. H. Electronic Structure Calculations of Solids Using the WIEN2k Package for Material Sciences. Comput. Phys. Commun. 2002, 147 (1–2), 71– 76,  DOI: 10.1016/S0010-4655(02)00206-0
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    Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77 (18), 3865– 3868,  DOI: 10.1103/PhysRevLett.77.3865
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    Generalized gradient approximation made simple
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    Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
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    Anisimov, V. I.; Solovyev, I. V.; Korotin, M. A.; Czyzyk, M. T.; Sawatzky, G. A. Density-Functional Theory and Nio Photoemission Spectra. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 48 (23), 16929– 16934,  DOI: 10.1103/PhysRevB.48.16929
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    Density-functional theory and NiO photoemission spectra
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    The generalization of the local-d.-approxn. method for the systems with strong Coulomb correlations is proposed, which restores the discontinuity in the one-electron potential as in the exact d. functional. The method is based on the model-Hamiltonian approach and allows the authors to take into account the nonsphericity of the Coulomb and exchange interactions. The calcn. scheme could be regarded as a first-principle method due to the absence of adjustable parameters. The method was applied to the calcn. of the photoemission (x-ray photoemission spectroscopy) and bremsstrahlung isochromat spectra of NiO.
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    Liechtenstein, A. I.; Anisimov, V. I.; Zaanen, J. Density-Functional Theory and Strong-Interactions - Orbital Ordering in Mott-Hubbard Insulators. Phys. Rev. B: Condens. Matter Mater. Phys. 1995, 52 (8), R5467– R5470,  DOI: 10.1103/PhysRevB.52.R5467
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    Density-functional theory and strong interactions: orbital ordering in Mott-Hubbard insulators
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    Physical Review B: Condensed Matter (1995), 52 (8), R5467-R5470CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    Evidence is presented that within the d.-functional theory orbital polarization has to be treated on an equal footing with spin polarization and charge d. for strongly interacting electron systems. Using a basis-set independent generalization of the LDA + U functional, we show that electronic orbital ordering is a necessary condition to obtain the correct crystal structure and parameters of the exchange interaction for the Mott-Hubbard insulator KCuF3.
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    Flage-Larsen, E.; Diplas, S.; Prytz, O.; Toberer, E. S.; May, A. F. Valence Band Study of Thermoelectric Zintl-phase SrZn2Sb2 and YbZn2Sb2: X-ray Photoelectron Spectroscopy and Density Functional Theory. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81 (20), 205204,  DOI: 10.1103/PhysRevB.81.205204
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    Vinet, P.; Rose, J. H.; Ferrante, J.; Smith, J. R. Universal Features of the Equation of State of Solids. J. Phys.: Condens. Matter 1989, 1 (1941), 1941,  DOI: 10.1088/0953-8984/1/11/002
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    Universal features of the equation of state of solids
    Vinet, Pascal; Rose, James H.; Ferrante, John; Smith, John R.
    Journal of Physics: Condensed Matter (1989), 1 (11), 1941-63CODEN: JCOMEL; ISSN:0953-8984.
    A study of the energetics of solids leads to the conclusion that the equation of state for all classes of solids in compression can be expressed in terms of a universal function. The form of this universal function is detd. by scaling exptl. compression data for measured isotherms of a wide variety of solids. The equation of state is thus known (in the absence of phase transitions), if zero-pressure vol. and isothermal compression and its pressure deriv. are known. The discovery described in this paper has two immediate consequences: first, despite the well known differences in the microscopic energies of the various classes of solids, there is a single equation of state for all classes in compression; and second, a new method is provided for analyzing measured isotherms and extrapolating high-pressure data from low-pressure (e.g. acoustic) data.
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    Madsen, G. K. H.; Singh, D. J. BoltzTraP. A Code for Calculating Band-Structure Dependent Quantities. Comput. Phys. Commun. 2006, 175 (1), 67– 71,  DOI: 10.1016/j.cpc.2006.03.007
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    BoltzTraP. A code for calculating band-structure dependent quantities
    Madsen, Georg K. H.; Singh, David J.
    Computer Physics Communications (2006), 175 (1), 67-71CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
    A program for calcg. the semi-classic transport coeffs. is described. It is based on a smoothed Fourier interpolation of the bands. From this anal. representation we calc. the derivs. necessary for the transport distributions. The method is compared to earlier calcns., which in principle should be exact within Boltzmann theory, and a very convincing agreement is found.
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    Kresse, G.; Furthmuller, J. Efficient Iterative Schemes for ab initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54 (16), 11169– 11186,  DOI: 10.1103/PhysRevB.54.11169
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    Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
    Kresse, G.; Furthmueller, J.
    Physical Review B: Condensed Matter (1996), 54 (16), 11169-11186CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    The authors present an efficient scheme for calcg. the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrixes will be discussed. This approach is stable, reliable, and minimizes the no. of order Natoms3 operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special "metric" and a special "preconditioning" optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calcns. It will be shown that the no. of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order Natoms2 scaling is found for systems contg. up to 1000 electrons. If we take into account that the no. of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. They have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.
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    Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59 (3), 1758– 1775,  DOI: 10.1103/PhysRevB.59.1758
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    From ultrasoft pseudopotentials to the projector augmented-wave method
    Kresse, G.; Joubert, D.
    Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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    Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P. Electron-Energy-Loss Spectra and the Structural Stability of Nickel Oxide: An LSDA+U Study. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 57 (3), 1505– 1509,  DOI: 10.1103/PhysRevB.57.1505
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    Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study
    Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P.
    Physical Review B: Condensed Matter and Materials Physics (1998), 57 (3), 1505-1509CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    By taking better account of electron correlations in the 3d shell of metal ions in Ni oxide it is possible to improve the description of both electron energy loss spectra and parameters characterizing the structural stability of the material compared with local spin d. functional theory.
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    Togo, A.; Tanaka, I. First Principles Phonon Calculations in Materials Science. Scr. Mater. 2015, 108, 1– 5,  DOI: 10.1016/j.scriptamat.2015.07.021
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    First principles phonon calculations in materials science
    Togo, Atsushi; Tanaka, Isao
    Scripta Materialia (2015), 108 (), 1-5CODEN: SCMAF7; ISSN:1359-6462. (Elsevier Ltd.)
    Phonon plays essential roles in dynamical behaviors and thermal properties, which are central topics in fundamental issues of materials science. The importance of first principles phonon calcns. cannot be overly emphasized. Phonopy is an open source code for such calcns. launched by the present authors, which has been world-widely used. Here we demonstrate phonon properties with fundamental equations and show examples how the phonon calcns. are applied in materials science.
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    Borup, K. A.; de Boor, J.; Wang, H.; Drymiotis, F.; Gascoin, F.; Shi, X.; Chen, L.; Fedorov, M. I.; Muller, E.; Iversen, B. B.; Snyder, G. J. Measuring Thermoelectric Transport Properties of Materials. Energy Environ. Sci. 2015, 8 (2), 423– 435,  DOI: 10.1039/C4EE01320D
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    Measuring thermoelectric transport properties of materials
    Borup, Kasper A.; de Boor, Johannes; Wang, Heng; Drymiotis, Fivos; Gascoin, Franck; Shi, Xun; Chen, Lidong; Fedorov, Mikhail I.; Muller, Eckhard; Iversen, Bo B.; Snyder, G. Jeffrey
    Energy & Environmental Science (2015), 8 (2), 423-435CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
    In this review we discuss considerations regarding the common techniques used for measuring thermoelec. transport properties necessary for calcg. the thermoelec. figure of merit, zT. Advice for improving the data quality in Seebeck coeff., elec. resistivity, and thermal cond. (from flash diffusivity and heat capacity) measurements are given together with methods for identifying possible erroneous data. Measurement of the Hall coeff. and calcn. of the charge carrier concn. and mobility is also included due to its importance for understanding materials. It is not intended to be a complete record or comparison of all the different techniques employed in thermoelecs. Rather, by providing an overview of common techniques and their inherent difficulties it is an aid to new researchers or students in the field. The focus is mainly on high temp. measurements but low temp. techniques are also briefly discussed.
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    Ohno, S.; Aydemir, U.; Amsler, M.; Pöhls, J.-H.; Chanakian, S.; Zevalkink, A.; White, M. A.; Bux, S. K.; Wolverton, C.; Snyder, G. J. Achieving zT > 1 in Inexpensive Zintl Phase Ca9Zn4+xSb9 by Phase Boundary Mapping. Adv. Funct. Mater. 2017, 27 (20), 1606361,  DOI: 10.1002/adfm.201606361
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    Jia, Y. Q. Crystal Radii and Effective Ionic Radii of the Rare Earth Ions. J. Solid State Chem. 1991, 95 (1), 184– 187,  DOI: 10.1016/0022-4596(91)90388-X
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    Crystal radii and effective ionic radii of the rare earth ions
    Jia, Y. Q.
    Journal of Solid State Chemistry (1991), 95 (1), 184-7CODEN: JSSCBI; ISSN:0022-4596.
    There exist some relations between the crystal radii of the rare earth ions, the 4f electron no., and the coordination no. On the basis of these relations, 2 empirical formulas are proposed to calc. the unknown crystal radii of the rare earth ions from the known crystal radii of the trivalent rare earth ions. The crystal radii and effective ionic radii of all the rare earth ions (trivalent and divalent) with different coordination no. (N = 6-12) were evaluated. The calcd. results are very satisfactory, and for most of examples the relative error is <1.0%.
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    Chemistry, Structure, and Bonding of Zintl Phases and Ions; VCH: New York, 1996.
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    Zhang, H.; Fang, L.; Tang, M.-B.; Man, Z. Y.; Chen, H. H.; Yang, X. X.; Baitinger, M.; Grin, Y.; Zhao, J.-T. Thermoelectric Properties of YbxEu1–xCd2Sb2. J. Chem. Phys. 2010, 133 (19), 194701,  DOI: 10.1063/1.3501370
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    Shuai, J.; Geng, H.; Lan, Y.; Zhu, Z.; Wang, C.; Liu, Z.; Bao, J.; Chu, C.-W.; Sui, J.; Ren, Z. Higher thermoelectric performance of Zintl phases (Eu0.5Yb0.5)1–xCaxMg2Bi2 by band engineering and strain fluctuation. Proc. Natl. Acad. Sci. U. S. A. 2016, 113 (29), E4125– E4132,  DOI: 10.1073/pnas.1608794113
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    Shuai, J.; Wang, Y.; Liu, Z.; Kim, H. S.; Mao, J.; Sui, J.; Ren, Z. Enhancement of Thermoelectric Performance of Phase Pure Zintl Compounds Ca1–xYbxZn2Sb2, Ca1–xEuxZn2Sb2, and Eu1–xYbxZn2Sb2 by Mechanical Alloying and Hot Pressing. Nano Energy 2016, 25, 136– 144,  DOI: 10.1016/j.nanoen.2016.04.023
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    Enhancement of thermoelectric performance of phase pure Zintl compounds Ca1-xYbxZn2Sb2, Ca1-xEuxZn2Sb2, and Eu1-xYbxZn2Sb2 by mechanical alloying and hot pressing
    Shuai, Jing; Wang, Yumei; Liu, Zihang; Kim, Hee Seok; Mao, Jun; Sui, Jiehe; Ren, Zhifeng
    Nano Energy (2016), 25 (), 136-144CODEN: NEANCA; ISSN:2211-2855. (Elsevier Ltd.)
    It has been previously shown that Zintl compds. Ca1-xYbxZn2Sb2 and EuZn2Sb2 could be good candidates as thermoelec. materials. However, the conventional synthesis process via melting-solidification-annealing introduces impurities and vacancies, resulting in abnormal high carrier concn. and ultimately low thermoelec. properties. Here we report the enhanced thermoelec. performance of Ca1-xYbxZn2Sb2 (x=0, 0.25, 0.5, 0.75, and 1) prepd. by ball milling and hot pressing. XRD confirms the samples are pure Zintl phase within its limit. Other compds. EuZn2Sb2, Eu0.5Yb0.5Zn2Sb2, and Eu0.5Ca0.5Zn2Sb2 are also prepd. by ball milling and hot pressing to further understand them. The obsd. changes in effective mass appear to be one of the reasons for the big difference of carrier mobility in Ca and rare earth (Yb, Eu) alloyed compds. The defects caused by alloying are the dominant phonon scattering source in these materials. The highest figure of merit of ∼0.9 is achieved in Ca0.25Yb0.75Zn2Sb2, ∼50% higher than the best reported ZT in similar materials prepd. by melting-solidification-annealing method.
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    Pomrehn, G. S.; Zevalkink, A.; Zeier, W. G.; van de Walle, A.; Snyder, G. J. Defect-Controlled Electronic Properties in AZn2Sb2 Zintl Phases. Angew. Chem. 2014, 126 (13), 3490– 3494,  DOI: 10.1002/ange.201311125
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    Atomic polarizability and electronegativity
    Nagle, Jeffrey K.
    Journal of the American Chemical Society (1990), 112 (12), 4741-7CODEN: JACSAT; ISSN:0002-7863.
    A close relationship between at. polarizability and electronegativity is demonstrated. It is shown how at. polarizability can be used in conjunction with the no. of s and p valence electrons to derive electronegativities interpreted as either valence electron densities or the electrostatic force exerted on valence electrons. This leads to a new set of electronegativities for every element in the periodic table that can be easily calcd. and understood. Such values are in substantially better agreement with traditional Pauling values than those derived as the av. of ionization energy and electron affinity. Traditional or chem. electronegativities are more closely related to the d. functional definition of hardness than to the corresponding definition of electronegativity. This approach offers promise to ongoing theor. efforts to delineate the role of electronegativity in chem. bonding.
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    Bux, S. K.; Zevalkink, A.; Janka, O.; Uhl, D.; Kauzlarich, S.; Snyder, J. G.; Fleurial, J.-P. Glass-Like Lattice Thermal Conductivity and High Thermoelectric Efficiency in Yb9Mn4.2Sb9. J. Mater. Chem. A 2014, 2 (1), 215– 220,  DOI: 10.1039/C3TA14021K
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    Glass-like lattice thermal conductivity and high thermoelectric efficiency in Yb9Mn4.2Sb9
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Cite this: Chem. Mater. 2018, 30, 2, 484–493
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  • Abstract

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    Figure 1

    Figure 1. (a) Ball-and-stick depiction of the structures of Yb2–xEuxCdSb2 with one unit cell outlined. Yb, Eu, Cd, and Sb are shown as teal, pink, purple, and tan spheres, respectively. Coordination spheres of sites: (b) Yb1, interlayer, and (c) Yb2, intralayer.

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    Figure 2

    Figure 2. Powder X-ray diffraction (PXRD) patterns for synthesized samples, Yb2–xEuxCdSb2. Black asterisks indicate an impurity unable to be indexed by PXRD. Whole-pattern fitting for x = 0, 0.36, 0.85, 1.13, and 1.18 revealed unit cell volumes of 581, 586, 600, 607, and 610 Å3, respectively.

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    Figure 3

    Figure 3. Band structure of Yb2–xEuxCdSb2 with valence (---) and conduction (—) bands indicated (a) for x = 0, and (b) for combined spin majority (—) and spin minority (---) bands for x = 1. Panel a shows flat bands at −1.9 eV from Yb 4f states whereas panel b shows flat bands around −1.9 eV arising from Yb 4f complemented with Eu 4f-bands at −2.6 eV. Panel c presents an enlargement of the x = 0 band in panel a near the band gap.

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    Figure 4

    Figure 4. Orbital-projected density of states plot using the DFT+U functional for Yb2–xEuxCdSb2. (a) Participating atomic orbitals near the valence edge are shown for x = 0. (b) All participating orbitals near the valence edge are shown for x = 1. The majority spin channel is shown for x = 1 in these plots. Additional detailed PDOS plots are provided in the Supporting Information.

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    Figure 5

    Figure 5. Temperature dependent (a) electrical resistivity and (b) Seebeck coefficient on polycrystalline samples of Yb2–xEuxCdSb2. The calculated Seebeck coefficients (open symbols) use experimental carrier (hole) concentration from Table 2. For x = 1 the carrier concentration is obtained by interpolating between the experimental carrier concentrations at x = 0.85 and x = 1.13. Experimental data points are shown as filled symbols and fits as solid lines.

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    Figure 6

    Figure 6. Dependence of the calculated Seebeck coefficients on carriers (holes) concentration for Yb2–xEuxCdSb11 (x = 0, 1). For x = 0 configuration, a temperature dependent crossover is observed near 7 × 101 9 cm–3.

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    Figure 7

    Figure 7. Total and lattice thermal conductivity of Yb2–xEuxCdSb2. Total thermal conductivity is shown as solid symbols, and lattice thermal conductivity is shown as open symbols.

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    Figure 8

    Figure 8. Phonon dispersion of Yb2–xEuxCdSb2x = 0 by frozen phonon approximation. All optical bands are very flat in nature.

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    Figure 9

    Figure 9. Shear and longitudinal speeds of sound for each sample. Speed of sound data are tabulated in Table S2 of the Supporting Information.

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    Figure 10

    Figure 10. Calculated figure of merit of Yb2–xEuxCdSb2.

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      Yb14MnSb11. New high efficiency thermoelectric material for power generation
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      Chemistry of Materials (2006), 18 (7), 1873-1877CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
      Thermoelec. materials provide a key soln. to energy problems through the conversion of heat into elec. energy. We report that the complex Zintl compd., Yb14MnSb11, breaks a 2-decade stagnation in high-temp. (>900 K), p-type materials development for thermoelec. power generation. This material achieves quadrupled efficiency and virtually doubled figure of merit over the current state-of-the-art, SiGe, thus earmarking it superior for thermoelec. applications in segmented devices. Yb14MnSb11 represents the 1st complex Zintl phase with substantially higher figure of merit and efficiency than any other competing materials, opening a new class of thermoelec. compds. with remarkable chem. and phys. properties.
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      Guo, K.; Cao, Q.; Zhao, J. Zintl Phase Compounds AM2Sb2 (A = Ca, Sr, Ba, Eu, Yb; M = Zn, Cd) and Their Substitution Variants: A Class of Potential Thermoelectric Materials. J. Rare Earths 2013, 31 (11), 1029– 1038,  DOI: 10.1016/S1002-0721(12)60398-6
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      Zintl phase compounds AM2Sb2 (A=Ca, Sr, Ba, Eu, Yb; M=Zn, Cd) and their substitution variants: a class of potential thermoelectric materials
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      A review. Zintl phase compds. AM2Sb2 (A=Ca, Sr, Ba, Eu, Yb; M=Zn, Cd) is a new class of promising thermoelecs. owing to their intrinsic features in electronic and crystal structure, such as a small or even disappeared band-gap, large d.-of-states at the Fermi level, covalently bonded network of M-Sb, as well as the layered stacking by cations A2+ and anionic slabs (M2Sb2)2-. In addn., the rich solid-state chem. of Zintl phase allows structural modification and chem. substitution to adjust the fundamental transport parameters (carrier concn., mobility, effective mass, electronic and lattice thermal cond.) for improving the thermoelec. performance. In the present review, the recent advances in synthesis and thermoelec. characterization of title compds. AM2Sb2 were presented, and the effects of alloying or substitution for sites A, M and Sb on the elec. and thermal transport were emphasized. The structural disorder yielded by the incorporation of multiple ions significantly increased the thermoelec. figure of merit mainly resulted from the redn. of thermal cond. without disrupting the carrier transport region in substance. Therefore, alloying or substitution has been a feasible and common route utilized to enhance thermoelec. properties in these Zintl phase compds., esp. for YbZn0.4Cd1.6Sb2 (ZT700 K=1.26), EuZn1.8Cd0.2Sb2 (ZT650 K=1.06), and YbCd1.85Mn0.15Sb2 (ZT650 K=1.14).
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      Kazem, N.; Xie, W.; Ohno, S.; Zevalkink, A.; Miller, G. J.; Snyder, G. J.; Kauzlarich, S. M. High-Temperature Thermoelectric Properties of the Solid–Solution Zintl Phase Eu11Cd6Sb12–xAsx (x < 3). Chem. Mater. 2014, 26 (3), 1393– 1403,  DOI: 10.1021/cm403345a
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      Chemistry of Materials (2015), 27 (21), 7508-7519CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
      The synthesis and transport properties of the family of coinage metal-stuffed Zintl compds., Eu9Cd4-xCM2+x-y.box.ySb9 (CM = coinage metal, .box. = vacancies), is presented as a function of coinage metal substitution. Eu9Cd4-xCM2+x-y.box.ySb9 compds. are rare examples of metallic Zintl phases with low thermal conductivities. While the lattice thermal cond. is low, which is attributed to the complex structure and presence of interstitials, the electronic contribution to thermal cond. is also low. In these p-type compds., the carriers transmit less heat than expected, based on the Wiedemann-Franz law and metallic conduction, κe = L0T/ρ. D. functional theory (DFT) calcns. indicate that the Fermi level resides in a pseudo-gap, 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. Anal. of the topol. 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 thermoelec. materials among complex metallic structures that can offer less electronic thermal cond. without deteriorating the elec. cond.
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      Toberer, E. S.; Zevalkink, A.; Crisosto, N.; Snyder, G. J. The Zintl Compound Ca5Al2Sb6 for Low-Cost Thermoelectric Power Generation. Adv. Funct. Mater. 2010, 20 (24), 4375– 4380,  DOI: 10.1002/adfm.201000970
      11
      The Zintl compound Ca5Al2Sb6 for low-cost thermoelectric power generation
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      Advanced Functional Materials (2010), 20 (24), 4375-4380CODEN: AFMDC6; ISSN:1616-301X. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Understanding transport in Zintl compds. is important due to their unusual chem., structural complexity, and potential for good thermoelec. performance. Resistivity measurements indicate that undoped Ca5Al2Sb6 is a charge-balanced semiconductor with a bandgap of 0.5 eV, consistent with Zintl-Klemm charge counting rules. Substituting divalent Ca with monovalent Na leads to the formation of free holes, and a transition from insulating to metallic electronic behavior is obsd. Seebeck measurements yield a hole mass of ∼2me, consistent with a structure contg. both ionic and covalent bonding. The structural complexity of Zintl compds. is implicated in their unusually low thermal cond. values. Indeed, Ca5Al2Sb6 possesses an extremely low lattice thermal cond. (0.6 W mK-1 at 850 K), which approaches the min. thermal cond. limit at high temp. A single parabolic band model is developed and predicts that Ca4.75Na0.25Al2Sb6 possesses a near-optimal carrier concn. for thermoelec. power generation. A max. zT > 0.6 is obtained at 1000 K. Beyond thermoelec. applications, the semiconductor Ca5Al2Sb6 possesses a 1D covalent structure which should be amenable to interesting magnetic interactions when appropriately doped.
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      Zevalkink, A.; Takagiwa, Y.; Kitahara, K.; Kimura, K.; Snyder, G. J. Thermoelectric properties and electronic structure of the Zintl phase Sr5Al2Sb6. Dalton Transactions 2014, 43 (12), 4720– 4725,  DOI: 10.1039/c3dt53487a
      12
      Thermoelectric properties and electronic structure of the Zintl phase Sr5Al2Sb6
      Zevalkink, Alex; Takagiwa, Yoshiki; Kitahara, Koichi; Kimura, Kaoru; Snyder, G. Jeffrey
      Dalton Transactions (2014), 43 (12), 4720-4725CODEN: DTARAF; ISSN:1477-9226. (Royal Society of Chemistry)
      The Zintl phase Sr5Al2Sb6 has a large, complex unit cell and is composed of relatively earth-abundant and non-toxic elements, making it an attractive candidate for thermoelec. applications. The structure of Sr5Al2Sb6 is characterized by infinite oscillating chains of AlSb4 tetrahedra. It is distinct from the structure type of the previously studied Ca5M2Sb6 compds. (M = Al, Ga, or In), all of which were shown to have promising thermoelec. performance. The lattice thermal cond. of Sr5Al2Sb6 (≈0.55 W mK-1 at 1000 K) was found to be lower than that of the related Ca5M2Sb6 compds. due to its larger unit cell (54 atoms per primitive cell). D. functional theory predicts a relatively large band gap in Sr5Al2Sb6, in agreement with the exptl. detd. band gap of Eg ≈0.5 eV. High temp. electronic transport measurements reveal high resistivity and high Seebeck coeffs. in Sr5Al2Sb6, consistent with the large band gap and valence-precise structure. Doping with Zn2+ on the Al3+ site was attempted, but did not lead to the expected increase in carrier concn. The low lattice thermal cond. and large band gap in Sr5Al2Sb6 suggest that, if the carrier concn. can be increased, thermoelec. performance comparable to that of Ca5Al2Sb6 could be achieved in this system.
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      Shuai, J.; Mao, J.; Song, S.; Zhang, Q.; Chen, G.; Ren, Z. Recent Progress and Future Challenges on Thermoelectric Zintl Materials. Materials Today Physics 2017, 1, 74– 95,  DOI: 10.1016/j.mtphys.2017.06.003
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      Hu, Y.; Bux, S. K.; Grebenkemper, J. H.; Kauzlarich, S. M. The Effect of Light Rare Earth Element Substitution in Yb14MnSb11 on Thermoelectric Properties. J. Mater. Chem. C 2015, 3 (40), 10566– 10573,  DOI: 10.1039/C5TC02326B
      14
      The effect of light rare earth element substitution in Yb14MnSb11 on thermoelectric properties
      Hu, Yufei; Bux, Sabah K.; Grebenkemper, Jason H.; Kauzlarich, Susan M.
      Journal of Materials Chemistry C: Materials for Optical and Electronic Devices (2015), 3 (40), 10566-10573CODEN: JMCCCX; ISSN:2050-7534. (Royal Society of Chemistry)
      After the discovery of Yb14MnSb11 as an outstanding p-type thermoelec. material for high temps. (≥900 K), site substitution of other elements has been proven to be an effective method to further optimize the thermoelec. properties. Yb14-xRExMnSb11 (RE = Pr and Sm, 0 < x < 0.55) compds. were prepd. by powder metallurgy to study their thermoelec. properties. According to powder X-ray diffraction, these samples are iso-structural with Yb14MnSb11 and when >5% RE is used in the synthesis the presence of (Yb,RE)4Sb3 is apparent after synthesis. After consolidation and measurement, (Yb,RE)Sb and (Yb,RE)11Sb10 appear in the powder X-ray diffraction patterns. Electron microprobe anal. results show that consolidated pellets have small (Yb,RE)Sb domains and that the max. amt. of RE in Yb14-xRExMnSb11 is x = 0.55, however, (Yb,RE)11Sb10 cannot be distinguished by electron microprobe anal. By replacing Yb2+ with RE3+, one extra electron is introduced into Yb14MnSb11 and the carrier concn. is adjusted. Thermoelec. performance from room temp. to 1275 K was evaluated through transport and thermal cond. measurements. The measurement shows that Seebeck coeffs. initially increase and then remain stable and that elec. resistivity increases with increasing substitution. Thermal cond. is slightly reduced. Substitution of Pr and Sm leads to enhanced zT. Yb13.82Pr0.18Mn1.01Sb10.99 has the best max. zT value of ∼1.2 at 1275 K, while Yb13.80Sm0.19Mn1.00Sb11.02 has its max. zT of ∼1.0 at 1275 K, ∼45% and ∼30% higher resp., than Yb14MnSb11 prepd. in the same manner.
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    15. 15
      Hu, Y.; Kauzlarich, S. M. Yb14MgBi11: Structure, Thermoelectric Properties and the Effect of the Structure on Low Lattice Thermal Conductivity. Dalton Trans. 2017, 46 (12), 3996– 4003,  DOI: 10.1039/C7DT00183E
      15
      Yb14MgBi11: structure, thermoelectric properties and the effect of the structure on low lattice thermal conductivity
      Hu, Yufei; Kauzlarich, Susan M.
      Dalton Transactions (2017), 46 (12), 3996-4003CODEN: DTARAF; ISSN:1477-9226. (Royal Society of Chemistry)
      Zintl phases Yb14MnSb11 and Yb14MgSb11, which share the same complex structure type, have been demonstrated as the best p-type thermoelec. materials for the high temp. region (800-1200 K). A new iso-structural compd., Yb14MgBi11, was synthesized in order to investigate the structure and thermoelec. properties of the Bi analogs. Yb14MgBi11 crystallizes in the Ca14AlSb11 structure-type with the space group I41/acd [a = 16.974(2) Å, c = 22.399(4) Å, V = 6454(2) Å3, R1/wR2 = 0.0238/0.0475]. The structure follows the previous description of this structure type and the trend obsd. in previous analogs. Thermoelec. properties of Yb14MgBi11 are measured together with Yb14MnBi11 and both compds. are metallic. Compared to Yb14MgSb11, Yb14MgBi11 has a higher carrier concn. with a similar mobility and effective mass. The lattice thermal cond. of Yb14MgBi11 is extremely low, which is as low as 0.16-0.36 W(mK)-1. The zT values of Yb14MgBi11 and Yb14MnBi11 reach 0.2 at 875 K.
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    16. 16
      Tamaki, H.; Sato, H. K.; Kanno, T. Isotropic Conduction Network and Defect Chemistry in Mg3+δSb2-Based Layered Zintl Compounds with High Thermoelectric Performance. Adv. Mater. 2016, 28 (46), 10182– 10187,  DOI: 10.1002/adma.201603955
      16
      Isotropic Conduction Network and Defect Chemistry in Mg3+δSb2-Based Layered Zintl Compounds with High Thermoelectric Performance
      Tamaki, Hiromasa; Sato, Hiroki K.; Kanno, Tsutomu
      Advanced Materials (Weinheim, Germany) (2016), 28 (46), 10182-10187CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
      The authors revealed a high ZT value ≈1.5 of the layered Zintl phase n-Mg3Sb2 was realized by defect chem. approach and introducing Sb/Bi disorder. The present discovery in the low-cost and earth-abundant material bridges the gap to practical application in thermoelecs. The defect chem. approach by incorporating an extraordinarily large amt. of excess cations will lead to new materials discovery in a wide variety of thermoelec. Zintl phases with stable intrinsic defects. The isotropic thermoelec. transport in Mg3Sb2-based material, which originates from its heterogeneous structure, provides a new and effective strategy to develop practical thermoelec. materials for waste heat recovery.
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    17. 17
      Saramat, A.; Svensson, G.; Palmqvist, A. E. C.; Stiewe, C.; Mueller, E.; Platzek, D.; Williams, S. G. K.; Rowe, D. M.; Bryan, J. D.; Stucky, G. D. Large Thermoelectric Figure of Merit at High Temperature in Czochralski-Grown Clathrate Ba8Ga16Ge30. J. Appl. Phys. 2006, 99 (2), 023708,  DOI: 10.1063/1.2163979
      17
      Large thermoelectric figure of merit at high temperature in Czochralski-grown clathrate Ba8Ga16Ge30
      Saramat, A.; Svensson, G.; Palmqvist, A. E. C.; Stiewe, C.; Mueller, E.; Platzek, D.; Williams, S. G. K.; Rowe, D. M.; Bryan, J. D.; Stucky, G. D.
      Journal of Applied Physics (2006), 99 (2), 023708/1-023708/5CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)
      The Czochralski method was used to grow a 46-mm-long crystal of the Ba8Ga16Ge30 clathrate, which was cut into disks that were evaluated for thermoelec. performance. The Seebeck coeff. and elec. and thermal conductivities all showed evidence of a transition from extrinsic to intrinsic behavior in the range of 600-900 K. The corresponding figure of merit (ZT) was found to be a record high of 1.35 at 900 K and with an extrapolated max. of 1.63 at 1100 K. This makes the Ba8Ga16Ge30 clathrate an exceptionally strong candidate for medium and high-temp. thermoelec. applications.
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    18. 18
      Sundarraj, P.; Maity, D.; Roy, S. S.; Taylor, R. A. Recent Advances in Thermoelectric Materials and Solar Thermoelectric Generators - A Critical Review. RSC Adv. 2014, 4 (87), 46860– 46874,  DOI: 10.1039/C4RA05322B
      18
      Recent advances in thermoelectric materials and solar thermoelectric generators - a critical review
      Sundarraj, Pradeepkumar; Maity, Dipak; Roy, Susanta Sinha; Taylor, Robert A.
      RSC Advances (2014), 4 (87), 46860-46874CODEN: RSCACL; ISSN:2046-2069. (Royal Society of Chemistry)
      A review. Due to the fact that much of the world's best solar resources are inversely correlated with population centers, significant motivation exists for developing technol. which can deliver reliable and autonomous conversion of sunlight into electricity. Thermoelec. generators are gaining incremental ground in this area since they do not require moving parts and work well in remote locations. Thermoelec. materials have been extensively used in space satellites, automobiles, and, more recently, in solar thermal applications as power generators, known as solar thermoelec. generators (STEG). STEG systems are gaining significant interest in both concd. and non-concd. systems and have been employed in hybrid configurations with solar thermal and photovoltaic systems. In this article, the key developments in the field of thermoelec. materials and on-going research work on STEG design conducted by various researchers to date are critically reviewed. Finally, we highlight the strategic research directions being undertaken to make highly efficient thermoelec. materials for developing a cost-effective STEG system, which could serve to bring this technol. towards com. readiness.
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    19. 19
      Zeier, W. G.; Zevalkink, A.; Gibbs, Z. M.; Hautier, G.; Kanatzidis, M. G.; Snyder, G. J. Thinking Like a Chemist: Intuition in Thermoelectric Materials. Angew. Chem., Int. Ed. 2016, 55 (24), 6826– 6841,  DOI: 10.1002/anie.201508381
      19
      Thinking like a chemist: intuition in thermoelectric materials
      Zeier, Wolfgang G.; Zevalkink, Alex; Gibbs, Zachary M.; Hautier, Geoffroy; Kanatzidis, Mercouri G.; Snyder, G. Jeffrey
      Angewandte Chemie, International Edition (2016), 55 (24), 6826-6841CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      A review. The coupled transport properties required to create an efficient thermoelec. material necessitates a thorough understanding of the relation between the chem. and physics in a solid. The authors approach thermoelec. material design using the chem. intuition provided by MO diagrams, tight binding theory, and a classic understanding of bond strength. Concepts such as electronegativity, band width, orbital overlap, bond energy, and bond length are used to explain trends in electronic properties such as the magnitude and temp. dependence of band gap, carrier effective mass, and band degeneracy and convergence. The lattice thermal cond. is discussed in relation to the crystal structure and bond strength, with emphasis on the importance of bond length. The authors provide an overview of how symmetry and bonding strength affect electron and phonon transport in solids, and how altering these properties may be used in strategies to improve thermoelec. performance.
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    20. 20
      Liu, W.; Hu, J.; Zhang, S.; Deng, M.; Han, C.-G.; Liu, Y. New Trends, Strategies and Opportunities in Thermoelectric Materials: A Perspective. Materials Today Physics 2017, 1, 50– 60,  DOI: 10.1016/j.mtphys.2017.06.001
      There is no corresponding record for this reference.
    21. 21
      Kleinke, H. New Bulk Materials for Thermoelectric Power Generation: Clathrates and Complex Antimonides. Chem. Mater. 2010, 22 (3), 604– 611,  DOI: 10.1021/cm901591d
      21
      New bulk Materials for Thermoelectric Power Generation: Clathrates and Complex Antimonides
      Kleinke, Holger
      Chemistry of Materials (2010), 22 (3), 604-611CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
      A review. Thermoelec. power generation is foreseen to play a much larger role in the near future, considering the need for alternative energies because of declining natural resources as well as the increasing efficiency of thermoelec. materials. The latter is a consequence of the discoveries of new materials as well as of improvements of established materials by, for example, nanostructuring or band structure engineering. Within this review, two major classes of high-temp. thermoelecs. are presented: clathrates formed by silicides and germanides, and complex antimonides including but not limited to the filled skutterudites. The clathrates and the skutterudites are cage compds. that exhibit low thermal cond., reportedly related to the rattling effect of the guest atoms, whereas the other antimonides achieve low thermal cond. via defects or simply via the high complexity of their crystal structures.
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    22. 22
      Kanatzidis, M. G. Advances in Thermoelectrics: From Single Phases to Hierarchical Nanostructures and Back. MRS Bull. 2015, 40 (08), 687– 695,  DOI: 10.1557/mrs.2015.173
      There is no corresponding record for this reference.
    23. 23
      Minnich, A. J.; Dresselhaus, M. S.; Ren, Z. F.; Chen, G. Bulk Nanostructured Thermoelectric Materials: Current Research and Future Prospects. Energy Environ. Sci. 2009, 2 (5), 466– 479,  DOI: 10.1039/b822664b
      23
      Bulk nanostructured thermoelectric materials: current research and future prospects
      Minnich, A. J.; Dresselhaus, M. S.; Ren, Z. F.; Chen, G.
      Energy & Environmental Science (2009), 2 (5), 466-479CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
      A review. Thermoelecs. have long been recognized as a potentially transformative energy conversion technol. due to their ability to convert heat directly into electricity. Despite this potential, thermoelec. devices are not in common use because of their low efficiency, and today they are only used in niche markets where reliability and simplicity are more important than performance. However, the ability to create nanostructured thermoelec. materials has led to remarkable progress in enhancing thermoelec. properties, making it plausible that thermoelecs. could start being used in new settings in the near future. Of the various types of nanostructured materials, bulk nanostructured materials have shown the most promise for com. use because, unlike many other nanostructured materials, they can be fabricated in large quantities and in a form that is compatible with existing thermoelec. device configurations. The first generation of these materials is currently being developed for commercialization, but creating the second generation will require a fundamental understanding of carrier transport in these complex materials which is presently lacking. In this review we introduce the principles and present status of bulk nanostructured materials, then describe some of the unanswered questions about carrier transport and how current research is addressing these questions. Finally, we discuss several research directions which could lead to the next generation of bulk nanostructured materials.
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    24. 24
      Takahata, K.; Iguchi, Y.; Tanaka, D.; Itoh, T.; Terasaki, I. Low Thermal Conductivity of the Layered Oxide (Na,Ca)Co2O4}: Another Example of a Phonon Glass and an Electron Crystal. Phys. Rev. B: Condens. Matter Mater. Phys. 2000, 61 (19), 12551– 12555,  DOI: 10.1103/PhysRevB.61.12551
      There is no corresponding record for this reference.
    25. 25
      Goldsmid, H. J. The Thermal Conductivity of Bismuth Telluride. Proc. Phys. Soc., London, Sect. B 1956, 69 (2), 203,  DOI: 10.1088/0370-1301/69/2/310
      There is no corresponding record for this reference.
    26. 26
      Toberer, E. S.; May, A. F.; Melot, B. C.; Flage-Larsen, E.; Snyder, G. J. Electronic Structure and Transport in Thermoelectric Compounds AZn2Sb2 (A = Sr, Ca, Yb, Eu). Dalton Trans. 2010, 39 (4), 1046– 1054,  DOI: 10.1039/B914172C
      26
      Electronic structure and transport in thermoelectric compounds AZn2Sb2 (A = Sr, Ca, Yb, Eu)
      Toberer, Eric S.; May, Andrew F.; Melot, Brent C.; Flage-Larsen, Espen; Snyder, G. Jeffrey
      Dalton Transactions (2010), 39 (4), 1046-1054CODEN: DTARAF; ISSN:1477-9226. (Royal Society of Chemistry)
      The AZn2Sb2 (P3m1, A = Ca, Sr, Eu, Yb) class of Zintl compds. has shown high thermoelec. efficiency (zT∼ 1) and is an appealing system for the development of Zintl structure-property relationships. High temp. transport measurements have previously been conducted for all known compns. except for SrZn2Sb2; here we characterize polycryst. SrZn2Sb2 to 723 K and review the transport behavior of the other compds. in this class. Consistent with the known AZn2Sb2 compds., SrZn2Sb2 is found to be a hole-doped semiconductor with a thermal band gap ∼0.27 eV. The Seebeck coeffs. of the AZn2Sb2 compds. are found to be described by similar effective mass (m* ∼ 0.6 me). Electronic structure calcns. reveal similar m* is due to antimony p states at the valence band edge which are largely unaffected by the choice of A-site species. However, the choice of A-site element has a dramatic effect on the hole mobility, with the room temp. mobility of the rare earth-based compns. approx. double that found for Ca and Sr on the A site. This difference in mobility is examd. in the context of electronic structure calcns.
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    27. 27
      Zhang, H.; Baitinger, M.; Tang, M.-B.; Man, Z.-Y.; Chen, H.-H.; Yang, X.-X.; Liu, Y.; Chen, L.; Grin, Y.; Zhao, J.-T. Thermoelectric properties of Eu(Zn1-xCdx)2Sb2. Dalton Trans. 2010, 39 (4), 1101– 1104,  DOI: 10.1039/B916346H
      27
      Thermoelectric properties of Eu(Zn1-xCdx)2Sb2
      Zhang, Hui; Baitinger, Michael; Tang, Mei-Bo; Man, Zhen-Yong; Chen, Hao-Hong; Yang, Xin-Xin; Liu, Yi; Chen, Ling; Grin, Yuri; Zhao, Jing-Tai
      Dalton Transactions (2010), 39 (4), 1101-1104CODEN: DTARAF; ISSN:1477-9226. (Royal Society of Chemistry)
      The thermoelec. performance of EuZn2Sb2 and EuCd2Sb2 was optimized by mixed occupation of the transition metal position. Samples in the solid soln. Eu(Zn1-xCdx)2Sb2 with the CaAl2Si2-type crystal structure (space group Pm1) were prepd. from the elements for compns. with x = 0, 0.1, 0.3, 0.5, and 1. The thermoelec. properties were investigated after densification of the products by spark plasma sintering (SPS). The samples show low elec. resistivity, high thermopower and a low lattice thermocond. The highest ZT value of 1.06 at 650 K is obtained for x = 0.1.
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    28. 28
      Saparov, B.; Saito, M.; Bobev, S. Syntheses, and Crystal and Electronic Structures of the New Zintl Phases Na2ACdSb2 and K2ACdSb2 (A = Ca, Sr, Ba, Eu, Yb): Structural Relationship with Yb2CdSb2 and the Solid Solutions Sr2–xAxCdSb2, Ba2–xAxCdSb2 and Eu2–xYbxCdSb2. J. Solid State Chem. 2011, 184 (2), 432– 440,  DOI: 10.1016/j.jssc.2010.12.015
      28
      Syntheses, and crystal and electronic structures of the new Zintl phases Na2ACdSb2 and K2ACdSb2 (A = Ca, Sr, Ba, Eu, Yb): Structural relationship with Yb2CdSb2 and the solid solutions Sr2-xAxCdSb2, Ba2-xAxCdSb2 and Eu2-xYbxCdSb2
      Saparov, Bayrammurad; Saito, Maia; Bobev, Svilen
      Journal of Solid State Chemistry (2011), 184 (2), 432-440CODEN: JSSCBI; ISSN:0022-4596. (Elsevier B.V.)
      Presented are the details of the syntheses, crystal and electronic structures of a new family of Zintl phases Na2ACdSb2 and K2ACdSb2 (A = Ca, Sr, Ba, Eu, Yb), as well as the solid solns. Sr2-xAxCdSb2, Ba2-xAxCdSb2 and Eu2-xYbxCdSb2. The structures of Na2ACdSb2 and K2ACdSb2 (A = Ca, Sr, Ba, Eu, Yb) are of a new type with the noncentrosym. space group Pmc21, Pearson symbol oP12, with a 4.684(1)-4.788(1); b 9.099(3)-9.117(2); c 7.837(1)-8.057(2) Å for the Na2ACdSb2 series, and a 4.6637(9)-5.0368(8); b = 9.100(2)-9.8183(15); and c 7.7954(15) -8.4924(13) Å for K2ACdSb2, resp. The solid solns. Sr2-xAxCdSb2, Ba2-xAxCdSb2 and Eu2-xYbxCdSb2 (x ≈ 1) are isostructural and isoelectronic to the recently reported Yb2CdSb2 (space group Cmc21, Pearson symbol cP20). All discussed structures are based upon CdSb24- polyanionic layers, similar to the ones obsd. in Yb2CdSb2, with various alkali- and/or alk.-earth cations coordinated to them. Magnetic susceptibility and Seebeck coeff. measurements on selected Eu2-xYbxCdSb2 samples, taken at low temps. up to 300 K, are also reported.
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    29. 29
      Xia, S.-q.; Bobev, S. Cation–Anion Interactions as Structure Directing Factors: Structure and Bonding of Ca2CdSb2 and Yb2CdSb2. J. Am. Chem. Soc. 2007, 129 (13), 4049– 4057,  DOI: 10.1021/ja069261k
      29
      Cation-Anion Interactions as Structure Directing Factors: Structure and Bonding of Ca2CdSb2 and Yb2CdSb2
      Xia, Sheng-Qing; Bobev, Svilen
      Journal of the American Chemical Society (2007), 129 (13), 4049-4057CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Two new transition-metal-contg. Zintl phases, Ca2CdSb2 and Yb2CdSb2, were synthesized by flux reactions, and their structures were detd. by single-crystal x-ray diffraction. Yb2CdSb2 crystallizes in the noncentrosym. orthorhombic space group Cmc21, Z = 4. Ca2CdSb2 crystallizes in the centrosym. orthorhombic space group Pnma, Z = 4. Despite the similarity in their chem. formulas and unit cell parameters, the structures of Yb2CdSb2 and Ca2CdSb2 are subtly different: Ca2CdSb2 has a layered structure built up of infinite layers of CdSb4 tetrahedra connected through corner-sharing. These layers are stacked in an alternating AA-1AA-1 sequence along the direction of the longest crystallog. axis (A denotes a layer; A-1 stands for its inversion symmetry equiv.), with Ca2+ cations filling the space between them. The structure of Yb2CdSb2 features the very same [CdSb2]4- layers of CdSb4 tetrahedra, which because of the lack of inversion symmetry are stacked in an AAAA-type fashion and are sepd. by Yb2+ cations. Electronic band structure calcns. performed using the TB-LMTO-ASA method show a small band gap at the Fermi level for Ca2CdSb2, whereas the gap closes for Yb2CdSb2. These results suggest narrow gap semiconducting and poorly metallic behavior, resp., and are confirmed by resistivity and magnetic susceptibility measurements. The structural relation between these new layered structure types and some known structures with three-dimensional four-connected nets are discussed as well.
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    30. 30
      Serrano-Sánchez, F.; Gharsallah, M.; Nemes, N. M.; Mompean, F. J.; Martínez, J. L.; Alonso, J. A. Record Seebeck Coefficient and Extremely Low Thermal Conductivity in Nanostructured SnSe. Appl. Phys. Lett. 2015, 106 (8), 083902,  DOI: 10.1063/1.4913260
      There is no corresponding record for this reference.
    31. 31
      Zhao, L.-D.; Lo, S.-H.; Zhang, Y.; Sun, H.; Tan, G.; Uher, C.; Wolverton, C.; Dravid, V. P.; Kanatzidis, M. G. Ultralow Thermal Conductivity and High Thermoelectric Figure of Merit in SnSe Crystals. Nature 2014, 508 (7496), 373– 377,  DOI: 10.1038/nature13184
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      Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals
      Zhao, Li-Dong; Lo, Shih-Han; Zhang, Yongsheng; Sun, Hui; Tan, Gangjian; Uher, Ctirad; Wolverton, C.; Dravid, Vinayak P.; Kanatzidis, Mercouri G.
      Nature (London, United Kingdom) (2014), 508 (7496), 373-377CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      The thermoelec. effect enables direct and reversible conversion between thermal and elec. energy, and provides a viable route for power generation from waste heat. The efficiency of thermoelec. materials is dictated by the dimensionless figure of merit, ZT (where Z is the figure of merit and T is abs. temp.), which governs the Carnot efficiency for heat conversion. Enhancements above the generally high threshold value of 2.5 have important implications for com. deployment, esp. for compds. free of Pb and Te. Here we report an unprecedented ZT of 2.6 ± 0.3 at 923 K, realized in SnSe single crystals measured along the b axis of the room-temp. orthorhombic unit cell. This material also shows a high ZT of 2.3 ± 0.3 along the c axis but a significantly reduced ZT of 0.8 ± 0.2 along the a axis. We attribute the remarkably high ZT along the b axis to the intrinsically ultralow lattice thermal cond. in SnSe. The layered structure of SnSe derives from a distorted rock-salt structure, and features anomalously high Grueneisen parameters, which reflect the anharmonic and anisotropic bonding. We attribute the exceptionally low lattice thermal cond. (0.23 ± 0.03 W m-1 K-1 at 973 K) in SnSe to the anharmonicity. These findings highlight alternative strategies to nanostructuring for achieving high thermoelec. performance.
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    32. 32
      Rodríguez-Carvajal, J. Recent Advances in Magnetic Structure Determination by Neutron Powder Diffraction. Phys. B 1993, 192 (1–2), 55– 69,  DOI: 10.1016/0921-4526(93)90108-I
      32
      Recent advances in magnetic structure determination by neutron powder diffraction
      Rodriguez-Carvajal, Juan
      Physica B: Condensed Matter (Amsterdam, Netherlands) (1993), 192 (1-2), 55-69CODEN: PHYBE3; ISSN:0921-4526.
      A review with 30 refs. Some recent improvements in the anal. of magnetic neutron powder diffraction data are discussed. After an introduction to the subject, the main formulas governing the anal. of the Bragg magnetic scattering are summarized and shortly discussed. Next, the method of profile fitting without a structural model to get precise integrated intensities and refine the propagation vector(s) of the magnetic structure is discussed. The simulated annealing approach for magnetic structure detn. is briefly discussed and, finally, some features of the program FullProf concerning the magnetic structure refinement are presented and discussed. The different themes are illustrated with simple examples.
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    33. 33
      Blaha, P.; Schwarz, K.; Sorantin, P.; Trickey, S. B. Full-Potential, Linearized Augmented Plane-Wave Programs for Crystalline Systems. Comput. Phys. Commun. 1990, 59 (2), 399– 415,  DOI: 10.1016/0010-4655(90)90187-6
      33
      Full-potential, linearized augmented plane wave programs for crystalline systems
      Blaha, P.; Schwarz, K.; Sorantin, P.; Trickey, S. B.
      Computer Physics Communications (1990), 59 (2), 399-415CODEN: CPHCBZ; ISSN:0010-4655.
      In solids, linearized augmented plane waves (LAPW's) were proven to be an effective basis for the soln. of the Kohn-Sham equations, the main calculational task in the local spin d. approxn. (LSDA) to d. functional theory. The WIEN package uses LAPW's to calc. the LSDA total energy, spin densities, Kohn-Sham eigenvalues, and the elec. field gradients at nuclear sits for a broad variety of space groups. Options include retention or omission of non-muffin-tin contributions (hence WIEN is a full-potential or F-LAPW code) and relativistic corrections (full treatment for core states, scalar-relativistic for valence states).
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    34. 34
      Madsen, G. K. H.; Blaha, P.; Schwarz, K.; Sjostedt, E.; Nordstrom, L. Efficient Linearization of the Augmented Plane-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 64 (19), 195134,  DOI: 10.1103/PhysRevB.64.195134
      34
      Efficient linearization of the augmented plane-wave method
      Madsen, Georg K. H.; Blaha, Peter; Schwarz, Karlheinz; Sjostedt, Elisabeth; Nordstrom, Lars
      Physical Review B: Condensed Matter and Materials Physics (2001), 64 (19), 195134/1-195134/9CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      We present a detailed anal. of the APW+lo basis set for band-structure calcns. This basis set consists of energy independent augmented plane-wave (APW) functions. The linearization is introduced through local orbitals evaluated at the same linearization energy as the APW functions. It is shown that results obtained with the APW+lo basis set converge much faster and often more systematically towards the final value. The APW+lo thereby allows accurate treatment of systems that were previously unaccessible to linearized APW. Furthermore, it is shown that APW+lo converges to the same total energy as LAPW provided the higher angular momenta l are linearized, either by adding extra local orbitals or treating them by LAPW. It is illustrated that the APW basis functions are much closer to the true form of the eigenfunctions than the LAPW basis functions. This is esp. true for basis functions that have a strong energy dependence inside the sphere.
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    35. 35
      Schwarz, K.; Blaha, P.; Madsen, G. K. H. Electronic Structure Calculations of Solids Using the WIEN2k Package for Material Sciences. Comput. Phys. Commun. 2002, 147 (1–2), 71– 76,  DOI: 10.1016/S0010-4655(02)00206-0
      There is no corresponding record for this reference.
    36. 36
      Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77 (18), 3865– 3868,  DOI: 10.1103/PhysRevLett.77.3865
      36
      Generalized gradient approximation made simple
      Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
      Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
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    37. 37
      Anisimov, V. I.; Solovyev, I. V.; Korotin, M. A.; Czyzyk, M. T.; Sawatzky, G. A. Density-Functional Theory and Nio Photoemission Spectra. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 48 (23), 16929– 16934,  DOI: 10.1103/PhysRevB.48.16929
      37
      Density-functional theory and NiO photoemission spectra
      Anisimov, V. I.; Solovyev, I. V.; Korotin, M. A.; Czyzyk, M. T.; Sawatzky, G. A.
      Physical Review B: Condensed Matter and Materials Physics (1993), 48 (23), 16929-34CODEN: PRBMDO; ISSN:0163-1829.
      The generalization of the local-d.-approxn. method for the systems with strong Coulomb correlations is proposed, which restores the discontinuity in the one-electron potential as in the exact d. functional. The method is based on the model-Hamiltonian approach and allows the authors to take into account the nonsphericity of the Coulomb and exchange interactions. The calcn. scheme could be regarded as a first-principle method due to the absence of adjustable parameters. The method was applied to the calcn. of the photoemission (x-ray photoemission spectroscopy) and bremsstrahlung isochromat spectra of NiO.
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    38. 38
      Liechtenstein, A. I.; Anisimov, V. I.; Zaanen, J. Density-Functional Theory and Strong-Interactions - Orbital Ordering in Mott-Hubbard Insulators. Phys. Rev. B: Condens. Matter Mater. Phys. 1995, 52 (8), R5467– R5470,  DOI: 10.1103/PhysRevB.52.R5467
      38
      Density-functional theory and strong interactions: orbital ordering in Mott-Hubbard insulators
      Liechtenstein, A. I.; Anisimov, V. I.; Zaanen, J.
      Physical Review B: Condensed Matter (1995), 52 (8), R5467-R5470CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      Evidence is presented that within the d.-functional theory orbital polarization has to be treated on an equal footing with spin polarization and charge d. for strongly interacting electron systems. Using a basis-set independent generalization of the LDA + U functional, we show that electronic orbital ordering is a necessary condition to obtain the correct crystal structure and parameters of the exchange interaction for the Mott-Hubbard insulator KCuF3.
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    39. 39
      Flage-Larsen, E.; Diplas, S.; Prytz, O.; Toberer, E. S.; May, A. F. Valence Band Study of Thermoelectric Zintl-phase SrZn2Sb2 and YbZn2Sb2: X-ray Photoelectron Spectroscopy and Density Functional Theory. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81 (20), 205204,  DOI: 10.1103/PhysRevB.81.205204
      There is no corresponding record for this reference.
    40. 40
      Vinet, P.; Rose, J. H.; Ferrante, J.; Smith, J. R. Universal Features of the Equation of State of Solids. J. Phys.: Condens. Matter 1989, 1 (1941), 1941,  DOI: 10.1088/0953-8984/1/11/002
      40
      Universal features of the equation of state of solids
      Vinet, Pascal; Rose, James H.; Ferrante, John; Smith, John R.
      Journal of Physics: Condensed Matter (1989), 1 (11), 1941-63CODEN: JCOMEL; ISSN:0953-8984.
      A study of the energetics of solids leads to the conclusion that the equation of state for all classes of solids in compression can be expressed in terms of a universal function. The form of this universal function is detd. by scaling exptl. compression data for measured isotherms of a wide variety of solids. The equation of state is thus known (in the absence of phase transitions), if zero-pressure vol. and isothermal compression and its pressure deriv. are known. The discovery described in this paper has two immediate consequences: first, despite the well known differences in the microscopic energies of the various classes of solids, there is a single equation of state for all classes in compression; and second, a new method is provided for analyzing measured isotherms and extrapolating high-pressure data from low-pressure (e.g. acoustic) data.
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    41. 41
      Madsen, G. K. H.; Singh, D. J. BoltzTraP. A Code for Calculating Band-Structure Dependent Quantities. Comput. Phys. Commun. 2006, 175 (1), 67– 71,  DOI: 10.1016/j.cpc.2006.03.007
      41
      BoltzTraP. A code for calculating band-structure dependent quantities
      Madsen, Georg K. H.; Singh, David J.
      Computer Physics Communications (2006), 175 (1), 67-71CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
      A program for calcg. the semi-classic transport coeffs. is described. It is based on a smoothed Fourier interpolation of the bands. From this anal. representation we calc. the derivs. necessary for the transport distributions. The method is compared to earlier calcns., which in principle should be exact within Boltzmann theory, and a very convincing agreement is found.
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    42. 42
      Kresse, G.; Furthmuller, J. Efficient Iterative Schemes for ab initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54 (16), 11169– 11186,  DOI: 10.1103/PhysRevB.54.11169
      42
      Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
      Kresse, G.; Furthmueller, J.
      Physical Review B: Condensed Matter (1996), 54 (16), 11169-11186CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      The authors present an efficient scheme for calcg. the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrixes will be discussed. This approach is stable, reliable, and minimizes the no. of order Natoms3 operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special "metric" and a special "preconditioning" optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calcns. It will be shown that the no. of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order Natoms2 scaling is found for systems contg. up to 1000 electrons. If we take into account that the no. of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. They have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.
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    43. 43
      Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59 (3), 1758– 1775,  DOI: 10.1103/PhysRevB.59.1758
      43
      From ultrasoft pseudopotentials to the projector augmented-wave method
      Kresse, G.; Joubert, D.
      Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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    44. 44
      Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P. Electron-Energy-Loss Spectra and the Structural Stability of Nickel Oxide: An LSDA+U Study. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 57 (3), 1505– 1509,  DOI: 10.1103/PhysRevB.57.1505
      44
      Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study
      Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P.
      Physical Review B: Condensed Matter and Materials Physics (1998), 57 (3), 1505-1509CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      By taking better account of electron correlations in the 3d shell of metal ions in Ni oxide it is possible to improve the description of both electron energy loss spectra and parameters characterizing the structural stability of the material compared with local spin d. functional theory.
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    45. 45
      Togo, A.; Tanaka, I. First Principles Phonon Calculations in Materials Science. Scr. Mater. 2015, 108, 1– 5,  DOI: 10.1016/j.scriptamat.2015.07.021
      45
      First principles phonon calculations in materials science
      Togo, Atsushi; Tanaka, Isao
      Scripta Materialia (2015), 108 (), 1-5CODEN: SCMAF7; ISSN:1359-6462. (Elsevier Ltd.)
      Phonon plays essential roles in dynamical behaviors and thermal properties, which are central topics in fundamental issues of materials science. The importance of first principles phonon calcns. cannot be overly emphasized. Phonopy is an open source code for such calcns. launched by the present authors, which has been world-widely used. Here we demonstrate phonon properties with fundamental equations and show examples how the phonon calcns. are applied in materials science.
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    46. 46
      Borup, K. A.; de Boor, J.; Wang, H.; Drymiotis, F.; Gascoin, F.; Shi, X.; Chen, L.; Fedorov, M. I.; Muller, E.; Iversen, B. B.; Snyder, G. J. Measuring Thermoelectric Transport Properties of Materials. Energy Environ. Sci. 2015, 8 (2), 423– 435,  DOI: 10.1039/C4EE01320D
      46
      Measuring thermoelectric transport properties of materials
      Borup, Kasper A.; de Boor, Johannes; Wang, Heng; Drymiotis, Fivos; Gascoin, Franck; Shi, Xun; Chen, Lidong; Fedorov, Mikhail I.; Muller, Eckhard; Iversen, Bo B.; Snyder, G. Jeffrey
      Energy & Environmental Science (2015), 8 (2), 423-435CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
      In this review we discuss considerations regarding the common techniques used for measuring thermoelec. transport properties necessary for calcg. the thermoelec. figure of merit, zT. Advice for improving the data quality in Seebeck coeff., elec. resistivity, and thermal cond. (from flash diffusivity and heat capacity) measurements are given together with methods for identifying possible erroneous data. Measurement of the Hall coeff. and calcn. of the charge carrier concn. and mobility is also included due to its importance for understanding materials. It is not intended to be a complete record or comparison of all the different techniques employed in thermoelecs. Rather, by providing an overview of common techniques and their inherent difficulties it is an aid to new researchers or students in the field. The focus is mainly on high temp. measurements but low temp. techniques are also briefly discussed.
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    47. 47
      Ohno, S.; Aydemir, U.; Amsler, M.; Pöhls, J.-H.; Chanakian, S.; Zevalkink, A.; White, M. A.; Bux, S. K.; Wolverton, C.; Snyder, G. J. Achieving zT > 1 in Inexpensive Zintl Phase Ca9Zn4+xSb9 by Phase Boundary Mapping. Adv. Funct. Mater. 2017, 27 (20), 1606361,  DOI: 10.1002/adfm.201606361
      There is no corresponding record for this reference.
    48. 48
      Jia, Y. Q. Crystal Radii and Effective Ionic Radii of the Rare Earth Ions. J. Solid State Chem. 1991, 95 (1), 184– 187,  DOI: 10.1016/0022-4596(91)90388-X
      48
      Crystal radii and effective ionic radii of the rare earth ions
      Jia, Y. Q.
      Journal of Solid State Chemistry (1991), 95 (1), 184-7CODEN: JSSCBI; ISSN:0022-4596.
      There exist some relations between the crystal radii of the rare earth ions, the 4f electron no., and the coordination no. On the basis of these relations, 2 empirical formulas are proposed to calc. the unknown crystal radii of the rare earth ions from the known crystal radii of the trivalent rare earth ions. The crystal radii and effective ionic radii of all the rare earth ions (trivalent and divalent) with different coordination no. (N = 6-12) were evaluated. The calcd. results are very satisfactory, and for most of examples the relative error is <1.0%.
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    49. 49
      Chemistry, Structure, and Bonding of Zintl Phases and Ions; VCH: New York, 1996.
      There is no corresponding record for this reference.
    50. 50
      Zhang, H.; Fang, L.; Tang, M.-B.; Man, Z. Y.; Chen, H. H.; Yang, X. X.; Baitinger, M.; Grin, Y.; Zhao, J.-T. Thermoelectric Properties of YbxEu1–xCd2Sb2. J. Chem. Phys. 2010, 133 (19), 194701,  DOI: 10.1063/1.3501370
      There is no corresponding record for this reference.
    51. 51
      Shuai, J.; Geng, H.; Lan, Y.; Zhu, Z.; Wang, C.; Liu, Z.; Bao, J.; Chu, C.-W.; Sui, J.; Ren, Z. Higher thermoelectric performance of Zintl phases (Eu0.5Yb0.5)1–xCaxMg2Bi2 by band engineering and strain fluctuation. Proc. Natl. Acad. Sci. U. S. A. 2016, 113 (29), E4125– E4132,  DOI: 10.1073/pnas.1608794113
      There is no corresponding record for this reference.
    52. 52
      Shuai, J.; Wang, Y.; Liu, Z.; Kim, H. S.; Mao, J.; Sui, J.; Ren, Z. Enhancement of Thermoelectric Performance of Phase Pure Zintl Compounds Ca1–xYbxZn2Sb2, Ca1–xEuxZn2Sb2, and Eu1–xYbxZn2Sb2 by Mechanical Alloying and Hot Pressing. Nano Energy 2016, 25, 136– 144,  DOI: 10.1016/j.nanoen.2016.04.023
      52
      Enhancement of thermoelectric performance of phase pure Zintl compounds Ca1-xYbxZn2Sb2, Ca1-xEuxZn2Sb2, and Eu1-xYbxZn2Sb2 by mechanical alloying and hot pressing
      Shuai, Jing; Wang, Yumei; Liu, Zihang; Kim, Hee Seok; Mao, Jun; Sui, Jiehe; Ren, Zhifeng
      Nano Energy (2016), 25 (), 136-144CODEN: NEANCA; ISSN:2211-2855. (Elsevier Ltd.)
      It has been previously shown that Zintl compds. Ca1-xYbxZn2Sb2 and EuZn2Sb2 could be good candidates as thermoelec. materials. However, the conventional synthesis process via melting-solidification-annealing introduces impurities and vacancies, resulting in abnormal high carrier concn. and ultimately low thermoelec. properties. Here we report the enhanced thermoelec. performance of Ca1-xYbxZn2Sb2 (x=0, 0.25, 0.5, 0.75, and 1) prepd. by ball milling and hot pressing. XRD confirms the samples are pure Zintl phase within its limit. Other compds. EuZn2Sb2, Eu0.5Yb0.5Zn2Sb2, and Eu0.5Ca0.5Zn2Sb2 are also prepd. by ball milling and hot pressing to further understand them. The obsd. changes in effective mass appear to be one of the reasons for the big difference of carrier mobility in Ca and rare earth (Yb, Eu) alloyed compds. The defects caused by alloying are the dominant phonon scattering source in these materials. The highest figure of merit of ∼0.9 is achieved in Ca0.25Yb0.75Zn2Sb2, ∼50% higher than the best reported ZT in similar materials prepd. by melting-solidification-annealing method.
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    53. 53
      Pomrehn, G. S.; Zevalkink, A.; Zeier, W. G.; van de Walle, A.; Snyder, G. J. Defect-Controlled Electronic Properties in AZn2Sb2 Zintl Phases. Angew. Chem. 2014, 126 (13), 3490– 3494,  DOI: 10.1002/ange.201311125
      There is no corresponding record for this reference.
    54. 54
      Nagle, J. K. Atomic Polarizability and Electronegativity. J. Am. Chem. Soc. 1990, 112 (12), 4741– 4747,  DOI: 10.1021/ja00168a019
      54
      Atomic polarizability and electronegativity
      Nagle, Jeffrey K.
      Journal of the American Chemical Society (1990), 112 (12), 4741-7CODEN: JACSAT; ISSN:0002-7863.
      A close relationship between at. polarizability and electronegativity is demonstrated. It is shown how at. polarizability can be used in conjunction with the no. of s and p valence electrons to derive electronegativities interpreted as either valence electron densities or the electrostatic force exerted on valence electrons. This leads to a new set of electronegativities for every element in the periodic table that can be easily calcd. and understood. Such values are in substantially better agreement with traditional Pauling values than those derived as the av. of ionization energy and electron affinity. Traditional or chem. electronegativities are more closely related to the d. functional definition of hardness than to the corresponding definition of electronegativity. This approach offers promise to ongoing theor. efforts to delineate the role of electronegativity in chem. bonding.
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    55. 55
      Bux, S. K.; Zevalkink, A.; Janka, O.; Uhl, D.; Kauzlarich, S.; Snyder, J. G.; Fleurial, J.-P. Glass-Like Lattice Thermal Conductivity and High Thermoelectric Efficiency in Yb9Mn4.2Sb9. J. Mater. Chem. A 2014, 2 (1), 215– 220,  DOI: 10.1039/C3TA14021K
      55
      Glass-like lattice thermal conductivity and high thermoelectric efficiency in Yb9Mn4.2Sb9
      Bux, Sabah K.; Zevalkink, Alexandra; Janka, Oliver; Uhl, David; Kauzlarich, Susan; Snyder, Jeffrey G.; Fleurial, Jean-Pierre
      Journal of Materials Chemistry A: Materials for Energy and Sustainability (2014), 2 (1), 215-220CODEN: JMCAET; ISSN:2050-7496. (Royal Society of Chemistry)
      Motivated by excellent thermoelec. performance in the well-known Yb-based Zintl compds. Yb14MnSb11 and YbZn2-xMnxSb2, this study investigates the thermoelec. properties of Yb9Mn4.2Sb9. Unlike most transition metal contg. Zintl phases, Yb9Mn4.2Sb9 contains a partially occupied Mn site and thus does not have a valence-precise stoichiometry. Samples were synthesized by direct ball milling of the elements, followed by hot pressing. Consistent with previous reports, x-ray diffraction and wavelength dispersive spectroscopy confirmed a narrow compn. range near Yb9Mn4.2Sb9. High temp. measurements of the electronic properties of Yb9Mn4.2Sb9 indicate that it is a degenerate p-type semiconductor with a band gap sufficiently large for high temp. thermoelec. applications. Hall measurements reveal that Yb9Mn4.2Sb9 has a high extrinsic carrier concn. (∼1020 h+ cm-3), which is due to the deviation from the theor. "Zintl compn." of Yb9Mn4.5Sb9. The measured carrier concn. coincides with the optimum concn. predicted using a single parabolic band model. Measurements of the thermal diffusivity and heat capacity reveal an extremely low, temp.-independent lattice thermal cond. in this compd. (κL < 0.4 W mK-1), which is due to both the large unit cell size (44 atoms per primitive cell) and substantial disorder on the Mn site. This favorable combination of optimized electronic properties and low lattice thermal cond. leads to a promising figure of merit at high temp. (zT = 0.7 at 950 K).
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    56. 56
      Kim, H.-S.; Gibbs, Z. M.; Tang, Y.; Wang, H.; Snyder, G. J. Characterization of Lorenz Number with Seebeck Coefficient Measurement. APL Mater. 2015, 3 (4), 041506,  DOI: 10.1063/1.4908244
      56
      Characterization of Lorenz number with Seebeck coefficient measurement
      Kim, Hyun-Sik; Gibbs, Zachary M.; Tang, Yinglu; Wang, Heng; Snyder, G. Jeffrey
      APL Materials (2015), 3 (4), 041506/1-041506/5CODEN: AMPADS; ISSN:2166-532X. (American Institute of Physics)
      In analyzing zT improvements due to lattice thermal cond. (κL) redn., elec. cond. (σ) and total thermal cond. (κTotal) are often used to est. the electronic component of the thermal cond. (κE) and in turn κL from κL = ∼ κTotal - LσT. The Wiedemann-Franz law, κE = LσT, where L is Lorenz no., is widely used to est. κE from σ measurements. It is a common practice to treat L as a universal factor with 2.44 × 10-8 WΩK-2 (degenerate limit). However, significant deviations from the degenerate limit (approx. 40% or more for Kane bands) are known to occur for non-degenerate semiconductors where L converges to 1.5 × 10-8 WΩK-2 for acoustic phonon scattering. The decrease in L is correlated with an increase in thermopower (abs. value of Seebeck coeff. (S)). Thus, a first order correction to the degenerate limit of L can be based on the measured thermopower, |S|, independent of temp. or doping. We propose the equation: L = 1.5 + exp[ - ((|S|)/116)] (where L is in 10-8 WΩK-2 and S in μV/K) as a satisfactory approxn. for L. This equation is accurate within 5% for single parabolic band/acoustic phonon scattering assumption and within 20% for PbSe, PbS, PbTe, Si0.8Ge0.2 where more complexity is introduced, such as non-parabolic Kane bands, multiple bands, and/or alternate scattering mechanisms. The use of this equation for L rather than a const. value (when detailed band structure and scattering mechanism is not known) will significantly improve the estn. of lattice thermal cond. (c) 2015 American Institute of Physics.
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    57. 57
      Cahill, D. G.; Watson, S. K.; Pohl, R. O. Lower limit to the thermal conductivity of disordered crystals. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 46 (10), 6131– 6140,  DOI: 10.1103/PhysRevB.46.6131
      57
      Lower limit to the thermal conductivity of disordered crystals
      Cahill, David G.; Watson, S. K.; Pohl, R. O.
      Physical Review B: Condensed Matter and Materials Physics (1992), 46 (10), 6131-40CODEN: PRBMDO; ISSN:0163-1829.
      Measurements of the thermal conductivities >30 K of mixed crystals with controlled disorder, (KBr)1-x(KCN)x, (NaCl)1-x(NaCN)x, Zr1-xYxO2-x/2, and Ba1-xLaxF2+x, support the idea of a lower limit to the thermal cond. of disordered solids. In each case, as x is increased, the data approach the calcd. min. cond. based on a model originally due to Einstein. The measurements support the claim that the lattice vibrations of these disordered crystals are essentially the same as those of an amorphous solid.
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    58. 58
      Zevalkink, A.; Zeier, W. G.; Pomrehn, G.; Schechtel, E.; Tremel, W.; Snyder, G. J. Thermoelectric Properties of Sr3GaSb3 - A Chain-Forming Zintl Compound. Energy Environ. Sci. 2012, 5 (10), 9121– 9128,  DOI: 10.1039/c2ee22378c
      58
      Thermoelectric properties of Sr3GaSb3 - a chain-forming Zintl compound
      Zevalkink, Alex; Zeier, Wolfgang G.; Pomrehn, Gregory; Schechtel, Eugen; Tremel, Wolfgang; Snyder, G. Jeffrey
      Energy & Environmental Science (2012), 5 (10), 9121-9128CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
      Inspired by the promising thermoelec. properties in the Zintl compds. Ca3AlSb3 and Ca5Al2Sb6, we investigate here the closely related compd. Sr3GaSb3. Although the crystal structure of Sr3GaSb3 contains infinite chains of corner-linked tetrahedra, in common with Ca3AlSb3 and Ca5Al2Sb6, it has twice as many atoms per unit cell (N = 56). This contributes to the exceptionally low lattice thermal cond. (κL = 0.45 W m-1 K-1 at 1000 K) obsd. in Sr3GaSb3 samples synthesized for this study by ball milling followed by hot pressing. High temp. transport measurements reveal that Sr3GaSb3 is a nondegenerate semiconductor (consistent with Zintl charge-counting conventions) with relatively high p-type electronic mobility (∼30 cm2 V-1 s-1 at 300 K). D. functional calcns. yield a band gap of ∼0.75 eV and predict a light valence band edge (∼0.5 me), in qual. agreement with expt. To rationally optimize the electronic transport properties of Sr3GaSb3 in accordance with a single band model, doping with Zn2+ on the Ga3+ site was used to increase the p-type carrier concn. In optimally hole-doped Sr3Ga1-xZnxSb3 (x = 0.0 to 0.1), we demonstrate a max. figure of merit of greater than 0.9 at 1000 K.
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    59. 59
      Zevalkink, A.; Toberer, E. S.; Zeier, W. G.; Flage-Larsen, E.; Snyder, G. J. Ca3AlSb3: An Inexpensive, Non-Toxic Thermoelectric Material for Waste Heat Recovery. Energy Environ. Sci. 2011, 4 (2), 510– 518,  DOI: 10.1039/C0EE00517G
      59
      Ca3AlSb3: an inexpensive, non-toxic thermoelectric material for waste heat recovery
      Zevalkink, Alex; Toberer, Eric S.; Zeier, Wolfgang G.; Espen, Flage-Larsen; Snyder, G. Jeffrey
      Energy & Environmental Science (2011), 4 (2), 510-518CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
      A review. Thermoelec. materials directly convert thermal energy into elec. energy, offering a promising solid-state soln. for waste heat recovery. For thermoelec. devices to make a significant impact on energy and the environment the major impediments are the efficiency, availability and toxicity of current thermoelec. materials. Typically, efficient thermoelec. materials contain heavy elements such as lead and Te that are toxic and not earth abundant. Many materials with unusual structures contg. abundant and benign elements are known, but remain unexplored for thermoelec. applications. The authors demonstrate, with the discovery of high thermoelec. efficiency in Ca3AlSb3, the use of elementary solid-state chem. and physics to guide the search and optimization of such materials.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXivF2msLs%253D&md5=0df53e87ba1b12c116568b15f6cc82da
    60. 60
      Delaire, O.; Ma, J.; Marty, K.; May, A. F.; McGuire, M. A.; Du, M. H.; Singh, D. J.; Podlesnyak, A.; Ehlers, G.; Lumsden, M. D.; Sales, B. C. Giant Anharmonic Phonon Scattering in PbTe. Nat. Mater. 2011, 10 (8), 614– 619,  DOI: 10.1038/nmat3035
      60
      Giant anharmonic phonon scattering in PbTe
      Delaire, O.; Ma, J.; Marty, K.; May, A. F.; McGuire, M. A.; Du, M-H.; Singh, D. J.; Podlesnyak, A.; Ehlers, G.; Lumsden, M. D.; Sales, B. C.
      Nature Materials (2011), 10 (8), 614-619CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
      Understanding the microscopic processes affecting the bulk thermal cond. is crucial to develop more efficient thermoelec. materials. PbTe is currently one of the leading thermoelec. materials, largely thanks to its low thermal cond. However, the origin of this low thermal cond. in a simple rocksalt structure has so far been elusive. Using a combination of inelastic neutron scattering measurements and first-principles computations of the phonons, we identify a strong anharmonic coupling between the ferroelec. transverse optic mode and the longitudinal acoustic modes in PbTe. This interaction extends over a large portion of reciprocal space, and directly affects the heat-carrying longitudinal acoustic phonons. The longitudinal acoustic-transverse optic anharmonic coupling is likely to play a central role in explaining the low thermal cond. of PbTe. The present results provide a microscopic picture of why many good thermoelec. materials are found near a lattice instability of the ferroelec. type.
      >> More from SciFinder ®
      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXmvFyqtbc%253D&md5=913e32dd8353503d51d4b5cdae420cb2
    61. 61
      Pandey, T.; Singh, A. K. High Thermopower and Ultra Low Thermal Conductivity in Cd-Based Zintl Phase Compounds. Phys. Chem. Chem. Phys. 2015, 17 (26), 16917– 16926,  DOI: 10.1039/C5CP02344K
      There is no corresponding record for this reference.
    62. 62

      NASA MMRTG Reference Data.

      There is no corresponding record for this reference.

  • Supporting Information

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    The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.7b04517.

    • Comparison of single crystal and powder X-ray diffraction unit cell parameters, electron microprobe analysis elemental mapping images, heat capacity data, mobility and carrier concentration data, Lorenz numbers, lattice thermal conductivity with minumum values, k-path, additional projected density of states plots, Seebeck versus chemical potential, optimized DFT lattice parameters, speed of sound, thermal diffusivity, and optimized Cartesian coordinates (PDF)


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