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Xinyi He, Shigeru Kimura, Takayoshi Katase, [Terumasa Tadano](https://orcid.org/0000-0002-8132-2161), [Satoru Matsuishi](https://orcid.org/0000-0001-8905-0255), Makoto Minohara, Hidenori Hiramatsu, Hiroshi Kumigashira, Hideo Hosono, Toshio Kamiya

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[Inverse‐Perovskite Ba<sub>3</sub><i>B</i>O (<i>B</i> = Si and Ge) as a High Performance Environmentally Benign Thermoelectric Material with Low Lattice Thermal Conductivity](https://mdr.nims.go.jp/datasets/dc29d4f8-df6b-4c9d-9ba1-eeb4bf54bec5)

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Inverse‐Perovskite Ba3BO (B = Si and Ge) as a High Performance Environmentally Benign Thermoelectric Material with Low Lattice Thermal ConductivityRESEARCH ARTICLEwww.advancedscience.comInverse-Perovskite Ba3BO (B = Si and Ge) as a HighPerformance Environmentally Benign ThermoelectricMaterial with Low Lattice Thermal ConductivityXinyi He, Shigeru Kimura, Takayoshi Katase,* Terumasa Tadano, Satoru Matsuishi,Makoto Minohara, Hidenori Hiramatsu, Hiroshi Kumigashira, Hideo Hosono,and Toshio Kamiya*High energy-conversion efficiency (ZT) of thermoelectric materials has beenachieved in heavy metal chalcogenides, but the use of toxic Pb or Te is anobstacle for wide applications of thermoelectricity. Here, high ZT isdemonstrated in toxic-element free Ba3BO (B = Si and Ge)with inverse-perovskite structure. The negatively charged B ion contributes tohole transport with long carrier life time, and their highly dispersive bandswith multiple valley degeneracy realize both high p-type electronicconductivity and high Seebeck coefficient, resulting in high power factor (PF).In addition, extremely low lattice thermal conductivities (𝜿lat)1.0–0.4 W m−1 K−1 at T = 300–600 K are observed in Ba3BO. Highly distortedO–Ba6 octahedral framework with weak ionic bonds between Ba with largemass and O provides low phonon velocities and strong phonon scattering inBa3BO. As a consequence of high PF and low 𝜿lat, Ba3SiO (Ba3GeO) exhibitsrather high ZT = 0.16–0.84 (0.35–0.65) at T = 300–623 K (300–523 K). Finally,based on first-principles carrier and phonon transport calculations, maximumZT is predicted to be 2.14 for Ba3SiO and 1.21 for Ba3GeO at T = 600 K byoptimizing hole concentration. Present results propose thatinverse-perovskites would be a new platform of environmentally-benignhigh-ZT thermoelectric materials.X. He, S. Kimura, T. Katase, S. Matsuishi, H. Hiramatsu, H. Hosono,T. KamiyaMDX Research Center for Element StrategyInternational Research Frontiers InitiativeTokyo Institute of Technology4259 Nagatsuta, Midori, Yokohama 226-8501, JapanE-mail: katase@mces.titech.ac.jp; kamiya.t.aa@m.titech.ac.jpThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/advs.202307058© 2023 The Authors. Advanced Science published by Wiley-VCH GmbH.This is an open access article under the terms of the Creative CommonsAttribution License, which permits use, distribution and reproduction inany medium, provided the original work is properly cited.DOI: 10.1002/advs.2023070581. IntroductionDue to the recently increasing energy crisis,there has been increasing attention to ther-moelectric technology for power generationusing waste heat energy.[1–3] The efficiencyof thermoelectric energy conversion is gov-erned by the dimensionless figure of merit(ZT), defined as ZT = S2·𝜎·T·𝜅–1, where T isthe absolute temperature, S is the Seebeckcoefficient, 𝜎 is the electronic conductivity,and 𝜅 is the thermal conductivity of thethermoelectric materials.[4–6] The productS2𝜎 is known as the power factor (PF),and the 𝜅 includes the contributions fromelectronic (𝜅ele) and lattice (𝜅 lat) heat con-duction. Therefore, high ZT thermoelectricmaterials should exhibit large S and high𝜎 to obtain high PF, as well as low 𝜅 tocreate a large temperature gradient. So far,the high ZT has been demonstrated mainlyin heavy metal chalcogenides, such asBi2Te3, PbTe, and GeTe,[7–9] which possesslow 𝜅 lat, but the use of toxic elements, suchas Pb and Te, is not preferred for wideapplications of thermoelectricity. ThereT. TadanoResearch Center for Magnetic and Spintronic MaterialsNational Institute for Materials Science1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, JapanS. Matsuishi, H. HosonoResearch Center for Materials NanoarchitectonicsNational Institute for Materials Science1-1 Namiki, Tsukuba, Ibaraki 305-0044, JapanM. MinoharaResearch Institute for Advanced Electronics and PhotonicsNational Institute of Advanced Industrial Science and TechnologyTsukuba, Ibaraki 305-8568, JapanH. HiramatsuLaboratory for Materials and StructuresInstitute of Innovative Research, Tokyo Institute of Technology4259 Nagatsuta, Midori, Yokohama 226-8501, JapanH. KumigashiraInstitute of Multidisciplinary Research for Advanced MaterialsTohoku UniversitySendai 980-8577, JapanAdv. Sci. 2024, 11, 2307058 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2307058 (1 of 14)http://www.advancedscience.commailto:katase@mces.titech.ac.jpmailto:kamiya.t.aa@m.titech.ac.jphttps://doi.org/10.1002/advs.202307058http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/http://crossmark.crossref.org/dialog/?doi=10.1002%2Fadvs.202307058&domain=pdf&date_stamp=2023-12-25www.advancedsciencenews.com www.advancedscience.comInverse-perovskite PerovskiteHighLightHeavylatLow latHeatHeatB4+�O2� bondShortO2��A2+ bondLongSoft framework of O�A6 octahedron(e.g. Ti�O)(e.g. O�Ba)Hard framework of B�O6 octahedronFigure 1. Schematic illustration of crystal structures and phonon transport in inverse-perovskite A3BO (left) and normal perovskite ABO3 (right). Thenormal perovskite structure of ABO3 (e.g., SrTiO3) is built with the hard framework of B−O6 octahedron with short B−O bonds, providing high-densitypacking structure of the light element O2− ions. In contrast, the inverse-perovskite structure of A3BO (e.g., Ba3BO (B = Si and Ge)) is constructedfrom the soft framework of O−A6 octahedron with long O−A bonds, providing the high-density packing structure of heavy A2+ ions. The lattice thermalconductivity (𝜅 lat) of normal perovskite ABO3 is usually high, while the largely contrasting structure characteristics are expected to lead the large reductionof 𝜅 lat in inverse-perovskite A3BO.are many efforts on the development of environmentally be-nign thermoelectric materials, such as oxides, silicides, andsulfides,[10–14] but further exploration of novel material systemsis demanded for improving the thermoelectric performance.We herein focus on inverse-perovskite oxides as potentialenvironmentally benign thermoelectric materials without toxicelements. The inverse-perovskite oxides are represented bychemical formula of A3BO with formal ion charges of A2+ (alka-line earth = Ca2+, Sr2+, Ba2+), B4– (the p-block 14 group = Si4−,Ge4−, Sn4−, Pb4−), and O2−.[15–20] It crystallizes in the inverse-perovskite structure that has an inverted cation and anion sitesin comparison to the normal perovskite oxide ABO3 (A2+B4+O2−)such as SrTiO3 (Figure 1). In the normal perovskite structure,B4+ cation occupies the body-centered site of the pseudo-cubicunit cell and O2− anion occupies the face-centered sites, forminga B–O6 octahedron. A2+ cation occupies the vertex sites of theunit cell. On the other hand, in the inverse-perovskite structure,O2− anion occupies the body-centered site and the A2+ cationoccupies the face-centered sites, forming an O−A6 octahedron.B4− anion occupies the vertex sites. ZT of perovskite SrTiO3 isusually limited to ∼0.1 due to its high 𝜅 lat ≈10 W m−1 K−1 atroom temperature (RT),[21] originating from the hard frameworkof the Ti–O6 octahedra with the strong Ti–O bonds. In contrast,the inverse-perovskite structure is constructed from the softframework of the O–A6 octahedra because of the larger A2+ion than B4+ ion and the consequent longer O–A bonds. Fromanother point of view, normal perovskite SrTiO3 is formed bythe high-density packing structure of the light element O2− ions,while inverse-perovskite A3BO is formed by the high-densitypacking structure of heavier A2+ ions. These largely contrastingstructural characteristics let us expect a large reduction of 𝜅 latin inverse-perovskite A3BO. The most distinctive feature ofinverse-perovskite A3BO is that the B ion is negatively charged,which actively contributes to hole conduction; the localized O2p state forms valence band maximum (VBM) in conventionaloxides including normal perovskite oxides, while spatially spreadp orbital of large-size B4− anion (ion radius: > 2 Å of B4−, 1.4Å of O2−) forms VBM in inverse-perovskite oxide,[22] which canrealize high hole mobility and 𝜎. Our work is hence motivatedby the expectation that the inverse-perovskite oxide would be apotential candidate for high ZT thermoelectric materials.The A3BO with B = Sn and Pb adopts a high-symmetry cubicstructure (Pm-3m) and exhibits unique Dirac electronic struc-tures with high carrier mobility, being expected as a new classof topological crystalline insulators and superconductors.[22–26]However, their narrow bandgaps (theoretical bandgaps < 0.2eV) limit their thermoelectric properties because the compen-sation by the coexistence of electrons and holes leads to lowS, resulting in low PF at high temperatures.[27] On the otherhand, theoretical studies proposed that bandgap is sensitiveto structural distortion, which enhances the thermoelectricproperties of inverse-perovskite A3BO.[28–30] By replacing the Bsite with smaller Si and Ge ions, the cubic structure is distortedto an orthorhombic lattice in agreement with a smaller tolerancefactor (t = rB+rA21∕2(rO+rA)) of an inverse-perovskite structure, whererA, rB, rO are ionic radii for A, B, O ions.[28,31] The orthorhombicCa3SiO (Ca3GeO) with t = 0.937 (0.948) takes the space groupof Imma and increases the bandgap to 0.7–0.9 eV.[28,32] The ther-moelectric properties were experimentally measured for Ca3SiOand Ca3GeO bulk polycrystals, which show low 𝜅 lat = 1.0–1.9W m−1K−1 at RT but the obtained ZT are limited to less than 10−5because the properties were measured with cold-pressed bulkswith large amount of CaO impurity (24%–32% in the Ca3SiOsample and 8%–10% in the Ca3GeO sample).[33]Here, we synthesized high-purity bulk polycrystals of highlydistorted Ba3BO (B = Si and Ge) with t = 0.908 and 0.918, whichcrystalize in orthorhombic inverse-perovskite structures (spacegroup: Pnma) with the pronounced tilting and twisting of theO−Ba6 octahedra (Figure 2a). The theoretical bandgaps are 0.86eV for Ba3SiO and 0.80 eV for Ba3GeO. The undoped samplesshowed p-type degenerate conduction with hole concentrations≈4.8 × 1018 cm−3 for Ba3SiO and ≈6.2 × 1019 cm−3 for Ba3GeOat RT. The bulk samples exhibited low 𝜅 lat of 1.00 W m−1 K−1 forBa3SiO and 0.77 W m−1 K−1 for Ba3GeO, which are lower than1.7–2.0 W m−1 K−1 of Bi2Te3 and PbTe bulks at RT. Ba3SiO andAdv. Sci. 2024, 11, 2307058 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2307058 (2 of 14) 21983844, 2024, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202307058 by National Institute For, Wiley Online Library on [29/08/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.com�2�1�0.20E (eV)�0.200123Energy, E (eV)YTR YXSZ ��kUYXSZ ��k�4 �2 0 2DOS (states/eV/f.u.)E (eV)40250100100�4 �2 0 2DOS (states/eV/f.u.)E (eV)402501001002p OSi 3p3sBa 5d4p4sTotaled�2�10123Energy, E (eV)YXSZ ��kYTRUYXSZ ��k2p OGe 4p4sBa 5d4p4sTotalacabO(160o)2.733c abBa2Ba1Si(2.731   )158oBa OGeBa OSiE (eV)cb157o (158o)5.353(5.366   )2.720(2.703   )2.725(2.735   )158o(160o)(Ge)(5.357   )5.347Figure 2. Crystal structure and electronic structure analyses of inverse-perovskite Ba3BO (B = Si and Ge). a) Crystal structures of Ba3SiO (Ba3GeO) withspace group of Pnma. The top and the bottom panels are the side view of (101) plane and the top view of (010) plane, respectively. b,c) Electronic bandstructures and d,e) partial density of states for b,d) Ba3SiO and c,e) Ba3GeO. The right panels of (b,c) are enlarged views of valence band maximum.Ba3GeO bulks exhibited relatively high ZT = 0.16 and 0.35 at RT,respectively, and the ZT value increased up to 0.84 for Ba3SiObulk at T = 623 K and 0.65 for Ba3GeO bulk at T = 523 K. Wesystematically investigated the electronic and phonon transportproperties of Ba3BO by using first-principles calculations to clar-ify the underlying physical mechanisms for their low 𝜅 lat and thepotential of thermoelectric ZT.2. Results and Discussion2.1. Crystal Structure and Electronic Structure AnalysesThe bulk polycrystals of Ba3BO (B = Si and Ge) were synthesizedby high-temperature solid-state reactions of 2Ba + Si(Ge) +BaO→ Ba3SiO(Ba3GeO). From X-ray diffraction (XRD) measure-ments, a small amount of BaO impurity (7.3 mol%) is detectedfor the Ba3GeO bulk, and the weak unidentified diffraction peaksare observed for the Ba3SiO bulk (Figure S1, Supporting Infor-mation, and CCDC 2291770 and 2291771 are the supplementarycrystallographic data for this paper). Microstructure analysis bya field-emission scanning electron microscopy (FE-SEM) showsthat the bulks are composed of sintered grains with an averagegrain size of ≈10 μm with some pores (Figure S2, Supporting In-formation), resulting in the sintered density of 80–87%. Energydispersive X-ray spectroscopy (EDS) mapping confirms the uni-formity of the chemical composition of Ba, Si (Ge), and O overthe grain region. The orthorhombic lattice parameters estimatedby Rietveld analysis of XRD patterns are a = 7.581 Å, b = 10.706Å, c = 7.543 Å for Ba3SiO and a = 7.592 Å, b = 10.732 Å, c = 7.559Å for Ba3GeO. Lattice volume is expanded from 612.261 Å3 ofBa3SiO to 615.896 Å3 of Ba3GeO because of the slightly larger ionradius of 2.08 Å for Ge4− anion than 2.04 Å of Si4− anion.[31] Thepseudo-cubic lattice parameters of the orthorhombic unit cellfor Ba3SiO (Ba3GeO) are b/2 = 5.353 Å (5.366 Å) and√a2 + c2= 5.347 Å (5.357 Å), indicating the O−Ba6 octahedra are slightlyelongated along the b-axis (Figure 2a). The orthorhombic distor-tion splits the Ba sites to the non-equivalent Ba1 and Ba2 sites.The O−Ba6 octahedra are tilted and twisted around all three oc-tahedral axes, where the apical O−Ba2−O and basal O−Ba1−Obond angles for Ba3SiO (Ba3GeO) are 157o (158o) and 158o(160o), showing distinct deviations from 180o of the cubic lattice.Figure 2b-e summarizes electronic band structures and den-sity of states (DOSs) of Ba3BO calculated by the VASP[34,35] codewith Heyd–Scuseria–Ernzerhof (HSE) hybrid functional.[36] Theconduction band minimum (CBM) and VBM located around theΓ point (left panels of Figure 2b,c), where the difference in the kvector between direct and indirect bandgap (Eg) is small, as in-dicated by the blue and the red arrows. The Eg are calculated tobe 0.86 eV for Ba3SiO and 0.80 eV for Ba3GeO, which are a littlelarger than the experimentally measured Eg of 0.62 eV and 0.58eV (See diffuse reflectance spectra in Figure S3, Supporting Infor-mation), due to the Eg overestimation by HSE hybrid functional.The atomic charges estimated by the Bader charge analysis areBa+1.153Si–2.02O−1.45 and Ba+1.143Ge–1.99O−1.45, confirming the an-ionic states of Si and Ge ions. The CBM is mainly contributed bythe Ba 5d state with only one single valley at the Γ point, while theVBM arises primarily from the Si 3p (Ge 4p) state (Figure 2d,e).Specifically, the valence bands around the Γ point are composedof one flat band and four highly dispersive bands nearly degener-ating within the 0.15 eV energy range below the Fermi level (rightAdv. Sci. 2024, 11, 2307058 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2307058 (3 of 14) 21983844, 2024, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202307058 by National Institute For, Wiley Online Library on [29/08/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comT (K)600500400300T (K)600500400300T (K)600500400300T (K)6005004002001000300(S/cm)6004002000S (�V/K)Ba3SiOa bf101104105103102Ba3GeOBa3SiOBa3GeO104103102101105 w [cm2 /(Vs)]Ba3SiO Ba3GeO10211020101910181017n (cm�3)102110201019101880060040020001017n (cm�3)Smeas.Scalc. (�V/K)Ba3GeO300 K600 KT =104103102101100calc. (S/cm)Ba3SiO300 K600 KT =dec w [cm2 /(Vs)]wScalc.calc. w,in-grainw,imp.w,opt.w w,totalw,opt.w,imp.w,in-grainw,totalFigure 3. Carrier transport properties of Ba3BO (B = Si and Ge). a,b) Temperature (T) dependences of a) electronic conductivity (𝜎) and b) Seebeckcoefficient (S) of Ba3BO bulks. c,d) Calculated electronic transport coefficients: c) 𝜎calc. and d) Scalc. as a function of carrier concentration (n) at T =300 K and 600 K. The solid lines are the polynominal fitting to the data points of 𝜎calc. vs n and Scalc. vs n. The measured S (Smeas.) of Ba3BO bulks areplotted in (d), and the dotted lines indicate the n estimated from the Smeas. in the Scalc. vs n relations. e,f) Weighted carrier mobility (μw) vs. T plotsfitted by 𝜇w,total(T) = exp( qEbkBT)𝜇w,in−grain(T), where μw,in − grain(T) is obtained by the Matthiessen’s rule, 𝜇−1w,in−grain = 𝜇−1w,imp. + 𝜇−1w,opt., for e) Ba3SiO bulkand f) Ba3SiO bulk. The red lines show the total mobility (μw,total) and the blue lines show the in-grain μw without GB scattering (μw,in-grain). The greenand the purple dotted lines show the ionized impurity scattering limited mobility (μw,imp.) and the optical phonon scattering limited mobility (μw,opt.),respectively.panels of Figure 2b,c). On the other hand, O 2p state located at adeeper energy level contributing little to carrier transport.2.2. Carrier Transport PropertiesFigure 3a,b shows the temperature (T) dependence of 𝜎 and S forBa3BO bulks. The Ba3GeO bulk exhibits higher 𝜎 = 151 S cm−1than 28 S cm−1 of Ba3SiO bulk at T ≃ 300 K (Figure 3a). Themetallic T dependence of 𝜎 is observed for the Ba3GeO bulk overthe whole T range. On the other hand, 𝜎 of Ba3SiO bulk showsmetallic T dependence at high T ≥ 510 K, while 𝜎 decreases atT < 500 K. Both the samples show positive S over the whole Trange (Figure 3b), indicating the majority carrier is hole. The S =+444 μV K−1 for Ba3SiO is larger than +255 μV K−1 for Ba3GeOat T ≃ 300 K. The S value linearly increases to +507 μV K−1 at T =Adv. Sci. 2024, 11, 2307058 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2307058 (4 of 14) 21983844, 2024, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202307058 by National Institute For, Wiley Online Library on [29/08/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comTable 1. Summary of experimentally measured and theoretically calculated carrier transport properties for Ba3BO (B = Si and Ge) at T = 300 K and 600K. m∗bandis the band effective mass and m∗DOS is the density of state effective mass, calculated by BoltzTraP2 code. n is the carrier concentration obtainedfrom the measured S in calculated Scalc. vs n relation (Figure 3d). 𝜎meas. is the experimentally measured electronic conductivity (Figure 3a). 𝜎calc. is thecalculated electronic conductivity obtained from the calculated 𝜎calc. vs n relation at the estimated n (Figure 3c). μ and μcalc. are the carrier mobilityobtained by μ = 𝜎meas./en and μcalc. = 𝜎calc./en. 𝜏e and 𝜏e,calc. are the carrier life time obtained by 𝜏e = m∗band𝜇∕e and 𝜏e,calc. = m∗band𝜇calc.∕e.m∗bandm∗DOS T [K] n [cm−3] 𝜎meas. [S cm−1] 𝜎calc. [S cm−1] μ [cm2 V−1 s−1] μcalc. [cm2 V−1 s−1] 𝜏e [fs] 𝜏e,calc.[fs]Ba3SiO 0.85m0 2.46m0 300 4.8×1018 28 89 36.4 115.7 17.6 55.9600 5.0×1018 37 28 46.6 35.0 22.5 16.9Ba3GeO 0.72m0 2.24m0 300 6.2×1019 151 195 15.2 19.6 6.2 8.0600 2.7×1019 21 35 4.8 8.1 2.0 3.3630 K for Ba3SiO and +372 μV K−1 at T = 624 K for Ba3GeO withincreasing T. Note that Hall effect measurement was difficult toperform because these samples are sensitive to air and sampledegradation occurs during the transfer to the measurement sys-tem.We then calculated the carrier lifetime (𝜏e) and obtained thecarrier concentration (n) dependences of 𝜎calc. and Scalc. at T =300 K and 600 K (Figure 3c,d) by density functional perturba-tion theory (DFPT)[37] as implemented in Quantum ESPRESSOpackage[38,39] and PERTURBO code.[40] It is seen that 𝜎calc. in-creases while Scalc. decreases with n as usually observed due tothe well-known competitive relationship. The 𝜎calc. of Ba3SiO isnearly one order of magnitude higher than that of Ba3GeO, whichoriginates from the smaller 𝜏e in Ba3GeO due to strong electron–phonon scattering (Figure S4, Supporting Information). Here,we need to compare 𝜎calc. and the measured 𝜎 but 𝜎calc. is a func-tion of n. We, therefore, first estimated experimental n from themeasured S (Smeas.) using the calculated Scalc. vs n relation as a ref-erence. We estimated n to be ≈4.8 × 1018 cm−3 (≈5.0 × 1018 cm−3)for the Ba3SiO bulk and ≈6.2 × 1019 cm−3 (≈2.7 × 1019 cm−3) forthe Ba3GeO bulk at T = 300 K (600 K) as shown by the yellowcircles in Figure 3d, indicating that the n of Ba3SiO is one orderof magnitude lower than that of Ba3GeO. The n exhibits a weakT dependence for both the Ba3SiO and the Ba3GeO bulks, indi-cating degenerate hole conduction, which is supported by X-rayphoto-emission spectroscopy spectra near the VBM (Figure S5,Supporting Information) because the Fermi level locates 0.1 eVbelow the VBM. We finally estimated 𝜎calc. at the estimated n asthe crossing points of the solid and dotted lines in Figure 3c.Table 1 compares the experimentally measured and theoret-ically calculated carrier transport properties of Ba3BO. Prior toexplaining the detailed results, we like to summarize that the ex-perimentally obtained results are consistent with the calculatedones both at T = 300 K and 600 K for Ba3GeO while three timesdifferences are found at T = 300 K for Ba3SiO. For Ba3GeO, the𝜎calc. (n at 300 K) = 195 S cm−1 and 𝜎calc. (n at 600 K) = 35 S cm−1are almost consistent with the measured 𝜎 (𝜎meas.) = 151 S cm−1at 300 K and 21 S cm−1 at 600 K, respectively. Accordingly, carriermobility μ = 𝜎meas./en and 𝜏e = m∗band𝜇∕e (m∗band is band effectivemass) in Table 1 show similar consistency. On the other hand,for Ba3SiO, although the 𝜎calc. (n at 600 K) = 28 S cm−1 is con-sistent with 𝜎meas. = 37 S cm−1 at T = 600 K, but 𝜎calc. (n at 300K) = 89 S cm−1 is three-times higher than 𝜎meas. = 28 S cm−1at T = 300 K. Accordingly, the estimated μ = 46.6 cm2 V−1 s−1is consistent with μcalc. = 35.0 cm2 V−1 s−1 at T = 600 K, whilethey show three-times difference (μ = 36.4 cm2 V−1 s−1 and μcalc.= 115.7 cm2 V−1 s−1) at 300 K. We here need to recognize thatthe calculated results reflect the transport properties of the idealsingle crystal while the experimental ones include carrier scatter-ing by defects and grain boundaries (GB), giving the significantdiscrepancy at lower temperatures.To separate the single-crystalline-like carrier transport incrystalline grains and the effect of GBs, we employ the Setomodel,[42] 𝜇(T) = exp( qEbkBT)𝜇in−grain(T), where μin − grain(T) is thein-grain carrier mobility and the GB contribution is expressedas exp( qEbkBT) (Eb is the GB barrier height and kB is the Boltzmannconstant). As we could not perform Hall effect measure-ments, we estimate μ(T) as weighted mobility from 𝜎 and S by𝜇w = 3h3𝜎8𝜋e(2mekBT)3∕2 [exp[ |S|kB∕e−2]1+exp[−5( |S|kB∕e−1)]+3𝜋2|S|kB∕e1+exp[5( |S|kB∕e−1)]], where me is thefree electron mass.[41] The μw is related to the drift mobility μ by𝜇w ≈ 𝜇(m∗DOSme)3∕2, where m∗DOS is density of state effective mass.The μw of Ba3SiO bulk exhibits a negative T coefficient at T ≥ 440K, while it decreases with a decrease of T at low T region ≤ 440 K(the black circles in Figure 3e). The μw of Ba3GeO bulk increaseswith a decrease of T in a wide range of T ≥ 327 K but it levels offat T < 327 K (the black circles in Figure 3f). Then, μw,in − grain(T) ismodeled by Matthiessen’s rule, 𝜇−1w,in−grain = 𝜇−1w,imp. + 𝜇−1w,opt.. Theimpurity scattering mobility is expressed as 𝜇−1w,imp. = A (tempera-ture independent) in the degenerate regime. The optical phononscattering mobility is expressed as 𝜇−1w,opt. = 1∕ (B(exp( ℏ𝜔0kT) − 1))(B is a constant), where ℏ𝜔0 is the longitudinal optical phononenergy. These parameters are obtained by least-squares fitting ofthe total mobility 𝜇w,total(T) = exp( qEbkBT)𝜇w,in−grain(T) to the exper-imental μw(T). In Figure 3e,f, the solid red line shows the μw,totalproviding good agreement with experimental μw over a wide Trange. At high T region, the μw,in-grain (blue lines) is dominatedby optical phonon scattering (the purple dotted lines), wherethe ℏ𝜔0 values were optimized to be 260 meV for Ba3SiO and210 meV for Ba3GeO. The μw,in-grain increases and approachesthe μw,imp. (green dotted lines), when T is reduced to ≈300 K.The μw,in-grain is higher than μw,total especially at lower T range forBa3SiO bulk, indicating that the carrier transport is limited byGB scattering. The μw,in-grain is 3.2 times higher than μw,total at T≃ 300 K, which is consistent with the μcalc./μ = 3.2 obtained inTable 1. For Ba3GeO, the μw,in-grain is nearly the same with μw,totalin a wide range of T ≥ 327 K but the difference becomes a littlelarger at T < 327 K. The μw,in-grain is 1.3 times higher than μw,totalAdv. Sci. 2024, 11, 2307058 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2307058 (5 of 14) 21983844, 2024, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202307058 by National Institute For, Wiley Online Library on [29/08/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comat T ≃ 300 K, in consistence with the μcalc./μ = 1.3. The Eb isestimated to be 28 meV for Ba3SiO while Eb = 8 meV is muchsmaller for Ba3GeO. The higher density carriers in Ba3GeObulk may screen the GB background charges and reduce the GBbarrier heights. Although the Ba3BO bulks have a relatively poorpolycrystalline nature with low sintered densities 80–87% andthe carrier transport of Ba3SiO bulk is limited by GB scattering atlow T region, the mobility analysis suggests that Ba3BO possesspotentially high carrier mobility.Next, effective masses m* are estimated as m* de-termines S in the simple free electron model by S =kBe( 32ln m∗DOS + ln 2( 2𝜋kBTh2)32 + r + 2 − ln n), where m∗DOS is thedensity-of-states effective mass at VBM. Here the band effectivemasses (m∗band= Ne2 𝜏e𝜎) at VBM are calculated to be slightlylarge at 0.85m0 for Ba3SiO and 0.72m0 for Ba3GeO (Table 1).However, the calculated carrier lifetime (𝜏e,calc.) is long at 55.9 fsfor Ba3SiO and 8.0 fs for Ba3GeO, resulting in the relatively highμcalc. of 115.7 and 19.6 cm2 V−1 s−1 at T = 300 K, respectively.The dispersive bands at VBM with relatively small m∗band andlong 𝜏e contribute to high μ (= e𝜏em∗band) and 𝜎 (= μne). However, thelifetime calculations were performed at the rigid band scheme(no ion dynamics) and polaron effect is not considered but itcan reduce the real μ. On the other hand, m∗DOS are calculated tobe 2.46m0 for Ba3SiO and 2.24m0 for Ba3GeO. The large m∗DOSoriginates from the high valence band degeneracy as explainedfor Figure 2b,c, which contributes to the large S. Therefore, thenegatively-charged B ion contributes to hole transport with longcarrier life time, and the dispersive valence bands (small m∗band)with the high valley degeneracy (large mDOS*) are suitable forrealizing high PF (= S2𝜎).2.3. Thermal Transport PropertiesNext we discuss thermal transport properties by separating elec-tronic and lattice contributions. Figure 4a summarizes the T de-pendence of total 𝜅 (𝜅 total) and electronic 𝜅 (𝜅ele) of Ba3SiO andBa3GeO bulks. The 𝜅ele is calculated by Wiedemann-Franz lawas 𝜅ele = LT𝜎, where L is the Lorenz number calculated fromL = ( kBe)2((r+ 72)Fr+5∕2(𝜂)(r+ 32)Fr+ 12(𝜂)− [(r+ 52)Fr+3∕2(𝜂)(r+ 32)Fr+1∕2(𝜂)]2). Here, the reduced Fermienergy 𝜂 is obtained based on the free carrier model using themeasured S as S = kBe((r+ 52)Fr+3∕2(𝜂)(r+ 32)Fr+1∕2(𝜂)− 𝜂) with the Fermi integraldefined as Fn(𝜂) =∞∫0𝜒n1+e𝜒−𝜂d𝜒 , where 𝛾 = −1/2 is the scatteringfactor.[43] The Ba3SiO and Ba3GeO bulks showed low 𝜅 total of 1.02W m−1K−1 for Ba3SiO and 0.84 W m−1K−1 for Ba3GeO at T = 300K. The 𝜅 total values of Ba3SiO and Ba3GeO bulks decrease to 0.69W m−1K−1 and 0.43 W m−1K−1 as the T rises to 623 K. The esti-mated 𝜅ele was less than 0.1 W m−1K−1, where the maximum 𝜅elewas 0.04 W m−1K−1 at T = 523 K for Ba3SiO and 0.07 W m−1K−1at T = 300 K for Ba3GeO, indicating the small electronic contri-bution to 𝜅 total. Then, the lattice 𝜅 (𝜅 lat) is extracted by subtractingthe electronic contribution from the 𝜅 total, i.e. 𝜅 lat = 𝜅 total – 𝜅ele.The T dependences of 𝜅 lat are summarized in Figure 4b, wherethose of the normal perovskite SrTiO3 bulk[44] as well as represen-tative chalcogenides of Bi2Te3 and PbTe bulks[45–47] are superim-posed for comparison. The 𝜅 lat decreases from 1.00 W m−1 K−1at T = 300 K to 0.66 W m−1 K−1 at T = 623 K for Ba3SiO andit decreases from 0.77 W m−1 K−1 at RT to 0.41 W m−1 K−1 atT = 623 K for Ba3GeO. The 𝜅 lat at T = 300 K is much lowerthan 8.2 W m−1 K−1 of SrTiO3 bulk[44] and also even lower than≈1.7 W m−1 K−1 of Bi2Te3 bulk[45] and ≈2.0 W m−1 K−1 of PbTebulk,[47] while it is comparable to 𝜅 lat of state-of-the-art chalco-genide thermoelectric materials, such as 0.7 W m−1K−1 of SnSebulk,[48] 0.6 W m−1K−1 of Cu2Se bulk,[49] and 0.6–0.8 W m−1K−1of GeTe bulk.[7]2.4. Origin of Low Lattice Thermal Conductivity inInverse-PerovskiteWe compared the phonon transport properties of Ba3BO with thenormal perovskite SrTiO3 to discern the distinguishing charac-teristics of inverse perovskites. First, we performed the simplephonon gas model analysis using 𝜅lat =13Cv ⋅ vs ⋅ lph = 13Cv ⋅ v2s ⋅𝜏ph, where Cv is the specific heat per volume, vs is the sound ve-locity, lph is the phonon mean free path, and 𝜏ph is the phonon life-time (Table S1, Supporting Information). The vs, measured by ul-trasonic pulse echo method at RT, are 2317 m s−1 (1981 m s−1) forBa3SiO (Ba3GeO), which is less than a half of 5241 m s−1 for thenormal perovskite SrTiO3. In addition, the estimated 𝜏ph of 0.16ps (0.16 ps) for Ba3SiO (Ba3GeO) is a half of 0.32 ps of SrTiO3. Thesmaller vs and lower 𝜏ph lead to the shorter lph (= vs𝜏ph) of 0.38 nm(0.32 nm) for Ba3SiO (Ba3GeO) than 1.70 nm for SrTiO3, result-ing in the low 𝜅 lat. The bulk modulus was calculated to be 92.8GPa (80.0 GPa) and the Debye temperature was 220 K (187 K)for Ba3SiO (Ba3GeO). The estimated Grüneisen parameter wasrelatively large at 1.3–1.4, which is comparable to low 𝜅 lat ther-moelectric materials such as Bi2Te3 and PbTe,[50] Therefore, boththe low sound velocity and the strong phonon scattering are re-sponsible for the intrinsically low 𝜅 lat in Ba3BO.To further elucidate the underlying mechanism responsiblefor the low 𝜅 lat in Ba3BO, we conducted first-principles anhar-monic lattice dynamics (ALD) calculations based on the den-sity functional theory (DFT), as implemented in the ALAMODEcode.[52,53] Figure 4c,d compares the anharmonic phonon disper-sions (left panels) and the partial phonon DOSs projected on eachelement (right panels) for Ba3BO and SrTiO3 models at T= 300 K.Ba3BO exhibits flatter phonon bands and all phonon bands onlyexist at a low frequency below 9 THz (left panel of Figure 4c). Thephonon DOSs of the Ba3SiO reveal that the vibrations of Ba atomspredominantly contribute to the lower frequency phonon bandswith the cut-off frequency ≈4.3 THz, while the Si and O atomsprimarily contribute to higher frequency phonon branches (rightpanel of Figure 4c). For Ba3GeO, the phonon bands of heavier Geion shift to lower frequency and have interaction with the phononbands of Ba ion. On the other hand, SrTiO3 exhibits largely dis-persive phonon bands even at higher frequencies (left panel ofFigure 4d), with extensive dispersion at high frequencies of 4–14THz, originating from the cooperative Ti and O atomic vibration(right panel of Figure 4d). The dispersion is considerably largerthan observed in the low-frequency phonon bands primarily at-tributed to Sr atomic vibrations at frequencies below ≈4.3 THz.We then calculated 𝜅 lat by solving the Peierls–Boltzmann trans-port equation (PBTE) within the relaxation time approximation.The calculated 𝜅 lat (averaged along a,b,c-axes) as a function of TAdv. Sci. 2024, 11, 2307058 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2307058 (6 of 14) 21983844, 2024, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202307058 by National Institute For, Wiley Online Library on [29/08/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.com0 5 10 0 2 4SrOTi0 5 10DOSBaOSic151050Frequency (THz)� YTRUY� XSZkd151050Frequency (THz)� MR� MXk0 5 10 152310Frequency (THz)1.00.50lat spectra (W/mK/THz)feT (K)300 400 500 600T (K)300 600 900b00.51.0 (W/mK)10�1100101lat (W/mK)Ba3GeOBa3SiOSrTiO310410310210110210110010�1ph (ps)0 5 10 15Frequency (THz)v ph (m/s)BaOGeBa3SiO Ba3GeOBa3GeOBa3SiOSrTiO3(states/THz/f.u.)DOS(states/THz/f.u.)Ba3GeOBa3SiOBa3GeOBa3SiOSrTiO3total SrTiO3PbTeBi2Te3lat, calc.aBa3GeOBa3SiOele0101Cumulative    lat,  / Total    latFigure 4. Phonon transport properties of Ba3BO (B = Si and Ge). a) Temperature (T) dependences of total thermal conductivity (𝜅total) and electronicthermal conductivity (𝜅ele) for Ba3BO bulks. b) T dependence of lattice thermal conductivity (𝜅 lat) for Ba3BO bulks, compared with the reported 𝜅 lat ofnormal perovskite SrTiO3 bulk[44] as well as PbTe and Bi2Te3 bulks.[45–47] Calculated 𝜅 lat of Ba3BO and SrTiO3 models are also shown by the solid lines.c,d) Anharmonic phonon dispersions (left panel) and partial phonon density of states (DOSs) projected on each element (right panel) for c) Ba3BO andd) SrTiO3 at T = 300 K obtained by the self-consistent phonon (SCPH) approximation. e) Comparison of 𝜅 lat spectra for Ba3BO (top panel) and SrTiO3(bottom panel) at T = 300 K. Frequency-dependent cumulative 𝜅 lat normalized by total 𝜅 lat is also shown for each panel. f) Phonon group velocity, 𝜈ph(top panel), and phonon lifetime, 𝜏 ph (bottom panel) in terms of the phonon frequency.Adv. Sci. 2024, 11, 2307058 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2307058 (7 of 14) 21983844, 2024, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202307058 by National Institute For, Wiley Online Library on [29/08/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comfor Ba3BO and SrTiO3 are compared in Figure 4b. The calculated𝜅 lat of Ba3SiO (Ba3GeO) are 1.21 W m−1 K−1 (0.86 W m−1 K−1)and that of SrTiO3 is 8.46 W m−1 K−1 at T = 300 K, in consistencewith the experimentally measured values. Figure 4e comparesthe 𝜅 lat spectra at T = 300 K with respect to phonon frequencyfor Ba3BO and SrTiO3 models. The frequency-dependent cumu-lative 𝜅 lat normalized by total 𝜅 lat are also shown in the panels.For Ba3BO, the 𝜅 lat spectra peak at ≈1 THz and phonons in thelow-frequency region below ≈4.3 THz contribute mostly to 𝜅 lat.The acoustic and optical modes are hybridized when the q point isfar from the Γ point, making it difficult to distinguish the acous-tic and optical contributions clearly. However, if we consider acut-off frequency for acoustic phonons, at which the acoustic andoptical branches cross (Figure 4c), at ≈1.4 THz for Ba3BO, thecontribution of low-frequency acoustic phonons to 𝜅 lat is ≈55%.The low-frequency acoustic phonons and mid-frequency opticalphonons within 4.3 THz contribute to the ≈91% of total 𝜅 lat, indi-cating that heat conduction primarily arises from the vibrationalmotion of Ba atoms (also Ge atoms in Ba3GeO). In contrast, forSrTiO3, the low-frequency acoustic phonons and mid-frequencyoptical phonons within 4.3 THz contribute to only the ≈31% oftotal 𝜅 lat, i.e., not only the low-frequency Sr atom vibrations butalso high-frequency phonons associated with Ti and O atomic vi-brations contribute greatly to heat conduction.Figure 4f compares the phonon group velocity, 𝜈 ph (top panel)and phonon lifetime, 𝜏ph (bottom panel) in terms of the phononfrequency. Ba3BO exhibit much lower 𝜈 ph than SrTiO3 across allfrequency ranges, primarily due to the presence of flat phononband branches (left panel of Figure 4c). On the other hand, 𝜏ph isalmost similar at low frequency (<3.5 THz) for both Ba3BO andSrTiO3, but the value of Ba3BO becomes smaller at higher fre-quency region (3.5–5 THz). For SrTiO3, the 𝜏ph becomes smallerat high frequency (>6 THz), but 𝜈 ph is still large, reflecting thewidely spread optical phonon bands. Therefore, the large 𝜈ph forphonons associated not only with Sr atomic vibration but alsowith Ti and O atomic vibrations provides a large contribution tohigh 𝜅 lat in SrTiO3. The 𝜏ph of Ba3BO becomes further smallerin the higher frequency region. The low 𝜅 lat of Ba3BO predom-inantly originates from the low 𝜈ph for phonons associated withBa atomic vibration, and the phonons associated with Si and Oatomic vibrations have a negligible contribution to 𝜅 lat due to thevery short 𝜏ph. Ba3BO shows more phonon bands than SrTiO3(left panel of Figure 4c), because it has the local structure dis-tortion with lower crystalline symmetry, resulting in the splittingof degenerated phonon bands. These broad frequency shifts en-hance the phonon-phonon scattering probability that leads to alarge 𝜏ph reduction in Ba3BO. The inverse and the normal per-ovskite structures are constructed from the network of O−Ba6and Ti−O6 octahedra. Then, the bonding energies of O−Ba inBa3BO and Ti−O in SrTiO3 as a measure of bonding strengthswere estimated through the chemical bonding analysis using thecrystal orbital Hamilton population (COHP)[53] performed by theLOBSTER code.[54] For the Ba3BO case, the −iCOHP values (theintegrated −COHP up to the Fermi level, corresponding to thebond strength) averaged for O−Ba bonds are as small as 0.276 eVper bond for Ba3SiO and 0.283 eV per bond for Ba3GeO, indicat-ing ionic interaction between the Ba atom and O atom in O−Ba6octahedra of the Ba3BO. On the other hand, the Ti−O bonds ofSrTiO3 have more than 10 times larger −iCOHP values of 3.48eV per bond, originating from the strong covalent interaction be-tween the Ti atom and the O atom in SrTiO3 lattice. The inverse-perovskite Ba3BO has a similar crystal structure to the perovskiteSrTiO3, but the ionic nature of the O−Ba bond softens the oc-tahedra framework and thus the contribution of high-frequencyoptical phonons is negligible for heat transport in Ba3BO. Notethat the related phenomenon of low 𝜅 lat and strong phonon scat-tering is observed in layered BaAgSb with weakly ionic bondedBa atoms.[55]2.5. Thermoelectric PropertiesFigure 5a,b summarizes the T dependences of PF (= S2𝜎) andZT (= S2𝜎T/𝜅) of the Ba3BO bulks. The calculated PF (PFcalc. =S2𝜎 calc.) and ZT (ZTcalc. = S2𝜎calc.T/𝜅calc.) are also superimposedin the panel. The PF of Ba3SiO and Ba3GeO bulks are limitedto 5.5 and 9.8 μW cm−1 K−2 at T ≃ 300 K, respectively, becauseof GB scattering (Figure 5a), but, as a consequence of their low𝜅, Ba3SiO and Ba3GeO show relatively high ZT = 0.16 and 0.35at T ≃ 300 K, respectively (Figure 5b). On the other hand, theypotentially show higher PFcalc. = 17.3 and 12.4 μW cm−1 K−2 byeliminating GB scattering, and ZTcalc. would be increased up to0.44 and 0.40 for Ba3SiO and Ba3GeO, respectively. The PF ofBa3SiO largely increases to 11.6 μW cm−1 K−2 when T increasesto 464 K, and then decreases to 9.0 μW cm−1 K−2 at high T = 630K. The ZT value increases continuously up to 0.84 at T = 623K, which is slightly higher than ZTcalc. = 0.65 at T = 600 K dueto higher 𝜎 than 𝜎calc. On the other hand, Ba3GeO exhibits themaximum PF = 10.8 μW cm−1 K−2 at low T = 327 K, and thePF decreases continuously down to 5.9 μW cm−1 K−2 at T = 523K, where the maximum ZT = 0.65 was obtained. The ZTcalc. ofBa3GeO increases continuously up to 0.74 at T = 600 K, but thePF and ZT suddenly decrease at T ≥ 548 K due to the decrease of𝜎 (Figure 3a) and the increase of 𝜅 (Figure 4a). We speculate thatthese 𝜎 and 𝜅 changes of Ba3GeO would originate from the tran-sition to higher symmetric inverse-perovskite structure at high Tbecause it has slightly high tolerance factor = 0.918. The high Tcrystal-structure characterization is necessary for this conclusion.Note that we tried hole doping to obtain optimum ZT by potas-sium ion (K+) substitution for Ba3SiO. The 𝜎 is increased byK doping and the two-orders of magnitude increase of carrierconcentration is observed in (Ba2.6K0.4)SiO. However, a consid-erably large amount of K dopant is necessary to increase the car-rier concentration and also carrier mobility is largely suppressedby such heavy K doping. Therefore, further exploration of ef-ficient acceptor dopants is necessary to optimize their ZT. In-stead, we estimate the maximum ZT of Ba3BO with optimizedn theoretically. We here calculate PFcalc. and ZTcalc. as a func-tion of n (Figure 5c,d). The PFcalc. vs n and ZTcalc. vs n plotshave maxima with respect to n, and the maximum values (maxPFcalc. and max ZTcalc.) are obtained at optimal n (nopt.) as indi-cated by the arrows in Figure 5c,d. The nopt. are estimated to be4.0 (8.1) × 1019 cm−3 and 1.6 (1.6) × 1020 cm−3 for Ba3SiO andBa3GeO at T = 300(600) K. Table 2 summarizes the theoreticalthermoelectric properties of Ba3BO with nopt. at T = 300 and 600K. The max ZTcalc. of Ba3SiO is predicted to be 0.98 and 2.14 atT = 300 and 600 K, respectively, where the max PFcalc. are muchincreased to 48.0 and 28.9 μW cm−1 K−2 by tuning n to nopt.. TheAdv. Sci. 2024, 11, 2307058 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2307058 (8 of 14) 21983844, 2024, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202307058 by National Institute For, Wiley Online Library on [29/08/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.com012ZTcalc.10211020101910181017n (cm�3)102110201019101860402001017n (cm�3)PFcalc. [�W/(cmK2)]dcT (K)600500400300a 1.00.50ZTbT (K)600500400300150510PF [�W/(cmK2)]Ba3SiO300 K600 KT =Ba3GeO300 K600 KT =Max ZTcalc.Max PFcalc.PFcalc. ZTcalc.Ba3GeOBa3SiOZTcalc.Ba3GeOBa3SiOPFcalc.PFcalc. (Ba3SiO)(Ba3GeO)at nexp. at nexp.at nopt.at nopt.Figure 5. Thermoelectric properties of Ba3BO (B = Si and Ge). a,b) Temperature (T) dependences of a) power factor (PF) and b) dimensionlessfigure of merit (ZT) of Ba3BO bulks. c,d) Carrier concentration (n) dependences of c) calculated PF (PFcalc. = S2𝜎calc.) and d) calculated ZT (ZTcalc.= S2𝜎calc.T/𝜅calc.) at T = 300 K and 600 K. The arrows indicate the maximum PFcalc. and ZTcalc. at the optimal n (nopt.). The yellow circles in a-d indicatethe PFcalc. and ZTcalc. obtained from the experimental n (nexp.) estimated in Figure 3d.max ZTcalc. of Ba3GeO are predicted to be 0.43 and 1.21 at T =300 K and 600 K, respectively, where the max PFcalc. is increasedto 15.8 and 11.2 μW cm−1 K−2. The higher ZT of Ba3SiO com-pared with Ba3GeO accounts for its higher PF. Figure 6 comparesthe present maximum predictions for Ba3SiO and Ba3GeO withstate-of-the-art thermoelectric materials. The max ZTcalc. value ofBa3SiO is much higher than those of eco-friendly thermoelec-tric materials[56–82] as seen in Figure 6a. Although higher ZT hasbeen reported for the thermoelectric materials with heavy toxicelements of Pb, Te, Se, and Sb,[49,83–136] the max ZTcalc. value ofBa3SiO is comparable in the same temperature range (Figure 6b).For fair discussion, we like to note that these predictions are ofideal single crystals so the real maximum values would be re-duced a bit by the impurity doping and consequent electron scat-tering. The present results, nonetheless, demonstrate the poten-tial of inverse-perovskite Ba3BO as a high-performance environ-mentally benign thermoelectric material that can be alternative tocurrently practical ones composed of heavy and toxic elements.Table 2. Summary of theoretical thermoelectric properties for Ba3BO (B = Si and Ge) with optimal n (nopt.) at T = 300 K and 600 K.T [K] nopt. [cm−3] 𝜎calc. [S cm−1] Scalc. [μV K−1] PFcalc. [μW cm−1 K−2] 𝜅calc. [W m−1 K−1] 𝜅ele,calc. [W m−1 K−1] 𝜅 lat,calc. [W m−1 K−1] ZTcalc.Ba3SiO300 4.0×1019 726.7 +257 48.0 1.46 0.25 1.21 0.98600 8.1×1019 411.2 +265 28.9 0.81 0.21 0.60 2.14Ba3GeO300 1.6×1020 503.5 +177 15.8 0.86 0.25 0.86 0.43600 1.6×1020 197.2 +238 11.2 0.43 0.13 0.43 1.21Adv. Sci. 2024, 11, 2307058 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2307058 (9 of 14) 21983844, 2024, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202307058 by National Institute For, Wiley Online Library on [29/08/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comSilicideOxideMaximum ZT321130011009007005003000T (K)PbCh (Ch = S,Se,Te)SnTeBiCuOSeFeNbSb, NbTaSbCu2Ch (Ch = Se,Te)SnSeGeTeAgSeTe2Cu12Sb4S13Bi0.5Sb1.5Se3321130011009007005003000T (K)Sulfidea bBa3GeOBa3SiOMaximum ZTBa3SiOBa3GeOFigure 6. Comparison of maximum ZT as a function of temperature (T) for Ba3BO (B = Si and Ge) with respect to a) eco-friendly thermoelectricmaterials including sulfides (Cu2S,[56–59] SnS,[60] Cu0.1TiS2,[61] (Cu,Fe)S2,[62] Cu7Sn3S10,[63] Cu5FeS4,[64] Cu26Ta2Sn5.5S32,[65] Cu2ZnSnS4[66]),silicides (Si0.8Ge0.2,[67] Mg2Si,[68–70] Mg2(Si,Sn),[71] MnSi1.75,[72] CrSi2,[73] 𝛽-FeSi2,[74] Sr0.92Y0.08Si2[75]), oxides (Sr0.9La0.1Ti0.9Nb0.1O3,[76]Sr0.93La0.07Ti0.93Nb0.07O3,[77] Sr0.775La0.15□0.075TiO3−𝛿 ,[78] Zn0.96Al0.02Ga0.02O,[79] Na1.7Co2O4,[80] Ca2.8Ag0.05Lu0.15Co4O9+𝛿 ,[81]Ca2.95Tb0.05Co4O9Bi0.25[82]), and b) state-of-the-art thermoelectric materials with heavy (toxic) elements: Bi0.5Sb1.5Se3,[83–86] AgSeTe2,[87,88]GeTe,[89–96] SnSe,[97–104] SnTe,[105–112] PbCh (Ch = S, Se, Te),[113–121] Cu2Ch (Ch = Se, Te),[49,122–129] Half Heusler FeNbSb and FeTaSb,[130–132]BiCuOSe,[133,134] Tetrahedrite Cu12Sb4S13.[135,136] Green, purple, and orange symbols in (a) indicate maximum ZT values for sulfide, silicide, and oxidethermoelectric materials, respectively.3. ConclusionIn summary, we demonstrated the high ZT in bulk polycrystalsof the p-type inverse-perovskite Ba3BO (B = Si and Ge) withouttoxic elements. The valence band around the Fermi level arisesfrom the p state of the negatively charged B anion with largeion size, and the hole transport with long carrier life time andtheir highly dispersive bands with multiple valley degeneracy re-alize both high 𝜎 and high S, simultaneously. In addition, thebulks exhibited low 𝜅 lat of 1.00 W m−1 K−1 for Ba3SiO and 0.77W m−1 K−1 for Ba3GeO at RT, which is significantly lower than 8.2W m−1 K−1 of normal perovskite SrTiO3 bulk,[44] and even lowerthan 1.7−2.0 W m−1 K−1 of Bi2Te3 and PbTe bulks.[45–47] The low𝜅 lat of Ba3BO originates from the low 𝜈ph for phonons associatedwith Ba atomic vibration, and the phonons associated with Si andO atomic vibrations have a negligible contribution to 𝜅 lat due tothe very short 𝜏ph. The crystal structure of Ba3BO is constructedfrom the highly distorted O−Ba6 octahedra framework with weakO−Ba ionic bonds, which provides extremely low 𝜈ph and strongphonon scattering. As a consequence of high PF and low 𝜅 lat, theBa3SiO and Ba3GeO exhibited rather high ZT of 0.16 and 0.35 atRT, respectively. The ZT value increased continuously up to 0.84at T = 623 K for Ba3SiO and 0.65 at T = 523 K for Ba3GeO. Inaddition, based on first-principles carrier and phonon transportcalculations, we predicted that a higher ZT could be obtained byoptimizing hole concentration in Ba3BO. Specifically, the max-imum ZT potentially increases to 2.14 for Ba3SiO and 1.21 forBa3GeO at T = 600 K. The present results indicate that inverse-perovskites would be a new platform of environmentally benignhigh ZT thermoelectric materials.4. Experimental SectionBulk Synthesis: The Ba3SiO and Ba3GeO bulk polycrystals were syn-thesized by solid-state reactions of a stoichiometric mixture of Ba, Si orGe, and BaO via a reaction of 2Ba + Si(Ge) +BaO → Ba3SiO(Ba3GeO).First, fresh Ba metal (purity 99.99%, Sigma–Aldrich) was finely cut intosmall pieces of grains.[137] The Ba grain, Si (purity 99.9%, Kojundo Chem-ical Lab.) or Ge powders (purity 99.9%, Kanto Chemical), and BaO pow-der (purity 99.9%, Kanto Chemical) were mixed and then pressed into 10-mmϕ pellet. The obtained pellet was wrapped in Ta foil and then sealed inan Ar-filled stainless tube. The sealed stainless tube was heated at an op-timized temperature of 750 °C for 10 h for Ba3SiO and 700 °C for 10 h forBa3GeO. The product was reground and densified to 10-mmϕ pellet again,and then it was wrapped in Ta foil and then sealed in an Ar-filled stainlesstube. The sealed stainless tube was heated again at 900 °C for 10 h forBa3SiO and 700 °C for 10 h for Ba3GeO. The bulk densities are 4.30 g cm−3for Ba3SiO and 4.35 g cm−3 for Ba3GeO. The sintered densities are esti-mated to be 87.0% and 80.4%, respectively. The chemical compositions ofthe bulk samples measured with EDS are Ba3.2SiO1.6 and Ba3.3GeO1.5. Thedeviation from the stoichiometric composition would come from the coex-istence of impurity phases, such as BaO, and the oxidation during sampletransfer to measurement chamber. All the synthesis processes were per-formed in a glovebox with a dry inert Ar gas (the dew point < −100 °C, theoxygen concentration < 1 ppm).Crystal Structure Analysis: Crystalline phases were determined by XRDwith the Bragg−Brentano geometry with a Cu K𝛼 radiation source at RT.The lattice parameters were determined by the Pawley method using theTOPAS ver. 4.2 program (Karlsruhe, Germany: Bruker AXS GmbH). Ri-etveld analysis, where the fundamental parameter (FP) method was em-ployed, was performed for crystal structure refinement. The microstruc-ture of the bulks was evaluated using a field-emission scanning elec-tron microscopy (FE-SEM; JSM-7600F, JEOL) equipped with an energy-dispersive spectrometer (EDS). The electronic structures were character-ized by X-ray photoemission spectroscopy (XPS) performed at the undu-lator beamline BL-2A of the Photon Factory, High Energy Accelerators Re-search Organization (KEK). The binding energy was calibrated with theFermi level of an evaporated reference Au film. Diffuse reflectance (R)spectra were measured at RT with a spectrophotometer in the wavelength(𝜆) range of 200−2400 nm. The obtained R spectra were converted usingthe Kubelka−Munk function (1−R)2/(2R) = 𝛼/Sf, where 𝛼 and Sf denotethe optical absorption coefficient and the scattering factor, respectively, toobtain the quasi-optical absorption spectra.Electronic and Thermal Properties: 𝜎 and S were simultaneously mea-sured by the four-probe method (ZEM-3, ADVANCE RIKO, Inc.) under aHe atmosphere. The 𝜅 was obtained from 𝜅 = D·C·𝜌, where the thermaldiffusivity (D) along the out-of-plane direction in the bulk was measuredAdv. Sci. 2024, 11, 2307058 © 2023 The Authors. Advanced Science published by Wiley-VCH GmbH2307058 (10 of 14) 21983844, 2024, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202307058 by National Institute For, Wiley Online Library on [29/08/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.comwww.advancedsciencenews.com www.advancedscience.comin an Ar atmosphere by a laser flash diffusivity method (LFA 457, NET-ZSCH) and the heat capacity (C) was measured by differential scanningcalorimetry (DSCvesta, Rigaku Corp.), and the sample density (𝜌) was de-termined by the dimensions and mass of the samples. The sound velocity(vs) is obtained by vs = ( 13[ 2v3t+ 1v3l])−1∕3, where vt and vl are the trans-verse and longitudinal sound velocities measured by ultrasonic pulse-echo method (1077DATA, KARL DEUTSCH) at RT. A detail of the phonongas model analysis is described in the caption of Table S1 (SupportingInformation).Density Functional Theory Calculation: The electronic structure calcu-lations were performed for Ba3BO models by DFT conducted using theprojector augmented wave (PAW) method as implemented in the VASPcode.[34,35] Ba [5d6s6p], Si [3s3p], Ge [4s4p], and O [2s2p] orbitals were in-cluded as valence states. The variable-cell structure relaxations were per-formed by the generalized gradient approximation (GGA) Perdew–Burke–Ernzerhof (PBE) functional[138] with a plane wave cut-off energy of 550eV, a Γ-centered k-mesh with the k-spacing of 0.2 Å−1, as well as theconvergence criteria of 10−6 eV for the energy and 0.01 eV Å−1 for theforce. The relaxed lattice parameters are a = 7.762 Å, b = 10.844 Å, c= 7.569 Å for Ba3SiO and a = 7.761 Å, b = 10.888 Å, c = 7.608 Å forBa3GeO, in consistence with the experimentally obtained values within3% differences. The electronic band structures and DOSs were obtainedby the HSE hybrid functional.[36] The carrier effective masses were calcu-lated by BoltzTraP2 code.[139] The carrier transport properties of Ba3BOwere calculated by using DFT and DFPT as implemented in the Quan-tum ESPRESSO package.[38,39] The GBRV ultrasoft pseudopotentials[140]were employed with the kinetic energy cutoff of 40 Ry (320 Ry) for wave-functions (charge density). The k-mesh density of 6×4×6 was used for theDFT calculations, and the 2×2×2 q points were used for the phonon andelectron-phonon calculations within DFPT. To compute the transport co-efficients using dense k and q grids, the maximally localized Wannier func-tions (MLWFs) were constructed from the isolated 12 Kohn–Sham statesbelow the VBM. The Wannierization was performed using the Wannier90code,[141] where the Si (Ge) p orbitals were used as initial projections andthe outer energy window of [−2.0, 0] eV relative to the VBM. The n, S, 𝜅ele,𝜎, and 𝜏e values at T = 300 K and 600 K were calculated using the PER-TURBO code.[41] The electron–phonon coupling coefficients were interpo-lated to the dense 120×80×120 k and q points and then used to solve theBoltzmann transport equation within the relaxation time approximation(RTA). The carrier lifetimes were computed from the imaginary part of theFan–Migdal self-energy, where the summation over the q points was per-formed by randomly sampling 106 q points from a uniform distribution. Itwas confirmed that the transport coefficients reached converged with theabove parameters.The phonon transport calculations for Ba3BO were performed usingthe ALAMODE code.[51,52] A 2×2×2 supercell (160 atoms) was usedfor the calculation of harmonic interatomic force constants (IFCs) andthe anharmonic IFCs. The harmonic IFCs were determined by the finite-displacement approach[142,143] and the anharmonic IFCs up to sixth-order were estimated by the compressive sensing lattice dynamics. Thetemperature-induced renormalized harmonic IFCs at T = 300 K were com-puted using the self-consistent phonon (SCPH) theory,[52] and were em-ployed in the subsequent phonon transport calculations. All allowed in-teractions were included for the harmonic IFCs, the third-order IFCs in-side the cutoff radii of 12 bohr, and fourth-, fifth-, and sixth-order IFCsinside the cutoff radii of 8 bohr. The DFT calculations to obtain the forcewere performed using the GGA-PBE functional with a plane-wave energycutoff of 400 eV, a Γ-centered 2×2×1 k-mesh and an energy convergencecriterion of 10−8 eV. 𝜅 lat was calculated by solving the Peierls–Boltzmanntransport equation under the RTA with a 7×7×5 q point mesh, which pro-vides sufficient accuracy confirmed by the convergence tests (Figure S6,Supporting Information). The non-analytic correction was included to thedynamical matrix by the mixed-space approach,[144] in which the Born ef-fective charges of constituent elements and the dielectric constants wereobtained by DFPT.[37]CCDC 2291770 and 2291771 contain the supplementary crystallo-graphic data for this paper. These data can be obtained free of chargefrom The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif .Supporting InformationSupporting Information is available from the Wiley Online Library or fromthe author.AcknowledgementsThe authors thank Mr. Tatsuya Cho (Tokyo Institute of Technology, Japan)for supporting initial experiment and valuable discussion. This work wassupported by MEXT Program: Data Creation and Utilization Type Mate-rial Research and Development Project Grant Number JPMXP1122683430.Ta.K. was supported by Japan Society for the Promotion of Science (JSPS)through Grants-in-Aid for Scientific Research (B) (Grant No. JP22H01766),Scientific Research (S) (Grant No. JP22H04964), and Challenging Re-search (Exploratory) (Grant No. JP22K18881). T.T. was supported by JSPSthrough Grant-in-Aid for Scientific Research (C) (Grant No. JP21K03424).H.Hi. was supported by JSPS through Grants-in-Aid for Scientific Research(A) (Grant Nos. JP20H00302 and JP21H04612). The numerical calcu-lations were carried out on the TSUBAME3.0 supercomputer at TokyoInstitute of Technology supported by the MEXT Project of the TokyoTech Academy for Convergence of Materials and Informatics (TAC-MI).The crystal structures in Figures 1 and 2a were drawn using the VESTAcode.[145]Conflict of InterestThe authors declare no conflict of interest.Data Availability StatementThe data that support the findings of this study are available from the cor-responding author upon reasonable request.Keywordselectronic transport, material design, phonon scattering, semiconductor,thermoelectric materialReceived: September 25, 2023Revised: November 19, 2023Published online: December 25, 2023[1] F. J. Disalvo, Science 1999, 285, 703.[2] L. E. Bell, Science 2008, 321, 1457.[3] Q. H. Zhang, X. Y. Huang, S. Q. Bai, X. Shi, C. Uher, L. D. Chen, Adv.Eng. Mater. 2016, 18, 194.[4] G. J. Snyder, E. S. Toberer, Nat. Mater. 2008, 7, 105.[5] J. He, T. M. 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Advanced Science published by Wiley-VCH GmbH2307058 (14 of 14) 21983844, 2024, 10, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/advs.202307058 by National Institute For, Wiley Online Library on [29/08/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advancedscience.com Inverse-Perovskite Ba3BO (B Si and Ge) as a High Performance Environmentally Benign Thermoelectric Material with Low Lattice Thermal Conductivity 1. Introduction 2. Results and Discussion 2.1. Crystal Structure and Electronic Structure Analyses 2.2. Carrier Transport Properties 2.3. Thermal Transport Properties 2.4. Origin of Low Lattice Thermal Conductivity in Inverse-Perovskite 2.5. Thermoelectric Properties 3. Conclusion 4. Experimental Section Supporting Information Acknowledgements Conflict of Interest Data Availability Statement Keywords