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Hugo Bouteiller, Vincent Pelletier, Sylvain Le Tonquesse, Bruno Fontaine, [Takao Mori](https://orcid.org/0000-0003-2682-1846), Jean-François Halet, Régis Gautier, David Berthebaud, Franck Gascoin

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[Advancing very high temperature thermoelectric performance of Yb<sub>4</sub>Sb<sub>3</sub> through dual-substitutions: a combined experimental and theoretical study](https://mdr.nims.go.jp/datasets/18c3b12d-3496-49b3-bdb7-d95e154c75a5)

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Advancing very high temperature thermoelectric performance of Yb4Sb3 through dual-substitutions: a combined experimental and theoretical study© 2024 The Author(s). Published by the Royal Society of Chemistry Mater. Adv., 2024, 5, 1217–1225 |  1217Cite this: Mater. Adv., 2024,5, 1217Advancing very high temperature thermoelectricperformance of Yb4Sb3 through dual-substitutions: a combined experimental andtheoretical studyHugo Bouteiller, *ab Vincent Pelletier, c Sylvain Le Tonquesse, abBruno Fontaine,cd Takao Mori, ef Jean-François Halet, bc Régis Gautier, *cDavid Berthebaud *bg and Franck Gascoin aThis article reports and discusses the synthesis and the transport properties of the binary rare-earthantimonide Yb4Sb3 and some of its substituted derivatives. Specifically, co-substitution of La on the Ybsite and Bi on the Sb site was attempted to further improve its thermoelectric properties. The solubilitylimit of the LaxYb4�xSb2.8Bi0.2 solid solution was established to be x = 0.3. Subsequent synthesis ofx = 0.1, 0.2, and 0.3 compositions at a larger scale enabled their transport property evaluation and thecomparison with Yb4Sb3. The Seebeck coefficient of the substituted compounds was found to be similarto the pristine material from 373 to 1273 K, while an increase in resistivity was observed. Detailed DFTcalculations confirmed that the Seebeck coefficient may not be significantly improved by Lasubstitutions and explained the p-type conducting behavior at high temperatures of the titlecompounds. The thermal conductivity of La0.2Yb3.8Sb2.8Bi0.2 was found to be reduced by about 30%compared to that of the binary Yb4Sb3. The figure of merit zT of the parent Yb4Sb3 compound reaches0.5 at 1273 K. While dual substitutions have not permitted a significant improvement in the figure ofmerit mostly due to a resistivity increase, this study provides a stepping stone for further optimization.IntroductionIn response to the escalating global demand for energy, effectiveutilization of waste heat through thermoelectric energy conversionhas garnered substantial attention.1–3 Industries such as steel millsor power plants operating at very high temperatures, typicallyabove 800 K, dissipate significant amounts of heat that could beconverted into electricity by thermoelectric generators.4,5 Theconversion efficiency of such modules mostly depends on theperformance of the integrated thermoelectric components, whichis evaluated by the adimensional figure of merit zT = S2T/(rk), Sbeing the Seebeck coefficient, T the absolute temperature, r theresistivity and k the thermal conductivity of the material, respec-tively. Currently, viable solutions within the realm of very hightemperatures remain rather constrained, owing to the scarcity ofmaterials presenting suitable transport properties above 800 K.6–9Both n- and p-type SiGe have been used for decades as the mainsolution by NASA,10 especially for radio-isotope thermoelectric gen-erators (RTGs),11 complemented by the Zintl phase Yb14MnSb11which serves as a p-type alternative.12 Recent investigations havehighlighted the potential candidacy of Yb21Mn4Sb18 as well withinthis temperature range, exhibiting a zT value of 0.8 at 800 K.13Furthermore, Half-Heusler compounds have also emerged as pro-mising candidates for the development of high temperature ther-moelectric modules up to 1100 K.14 While the fabrication ofthermoelectric devices for power generation necessitates meticulousconsiderations encompassing low contact resistances and harmo-nious thermal expansion,15 the paramount factor governing netpower generation indisputably remains the figure of merit exhibitedby both n-type and p-type constituents.16 Therefore, the pursue ofnovel materials showcasing optimal transport properties in the veryhigh temperature range (800–1300 K) is much needed and stand asthe focus of this work.a Laboratoire CRISMAT, ENSICAEN, UNICAEN, CNRS Normandie Univ. (UMR6508), Caen, Franceb CNRS–Saint-Gobain–NIMS, IRL 3629, Laboratory for Innovative Key Materialsand Structures (LINK), National Institute for Materials Science (NIMS), 305–0044,Tsukuba, Japanc Univ Rennes, CNRS, Ecole Nationale Supérieure de Chimie de Rennes, ISCR-UMR6226, F–35000, Rennes, Franced Saint-Cyr Coëtquidan Military Academy, CReC, F–56380, Guer, Francee Graduate School of Pure and Applied Sciences, University of Tsukuba, 305–8671,Tsukuba, Japanf National Institute for Materials Science (NIMS), WPI-MANA, University of Tsukuba,305–0044, Tsukuba, Japang Nantes Université, CNRS, Institut des Matériaux de Nantes Jean Rouxel, IMN,Nantes F–44000, FranceReceived 25th October 2023,Accepted 19th December 2023DOI: 10.1039/d3ma00903crsc.li/materials-advancesMaterialsAdvancesPAPEROpen Access Article. Published on 21 December 2023. Downloaded on 7/30/2024 2:03:42 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article OnlineView Journal  | View Issuehttps://orcid.org/0009-0004-2132-2962https://orcid.org/0000-0002-4289-1951https://orcid.org/0000-0002-1939-7816https://orcid.org/0000-0003-2682-1846https://orcid.org/0000-0002-2315-4200https://orcid.org/0000-0002-8104-4982https://orcid.org/0000-0002-2892-2125https://orcid.org/0000-0002-9791-1358http://crossmark.crossref.org/dialog/?doi=10.1039/d3ma00903c&domain=pdf&date_stamp=2023-12-28https://rsc.li/materials-advanceshttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d3ma00903chttps://pubs.rsc.org/en/journals/journal/MAhttps://pubs.rsc.org/en/journals/journal/MA?issueid=MA0050031218 |  Mater. Adv., 2024, 5, 1217–1225 © 2024 The Author(s). Published by the Royal Society of ChemistryLa3�xTe4 is a promising n-type material that exhibits a zTabove unity around 1300 K.17 This compound crystallizes in theTh3P4 structure type, wherein vacancies are accommodated onthe rare-earth sites. Rare-earth antimonides of typical formulaRE4Sb3 (RE = Yb, La, Sm, Ce) are presenting the anti-Th3P4crystal structure.18 In this cubic structural arrangement (spacegroup I%43d), rare-earth atoms occupy P sites (Wyckoff position16c) at the center of a distorted octahedron, while antimonyatoms occupy Th sites (12a), forming a bis-disphenoid environ-ment shaped by two interpenetrated Yb tetrahedra (Fig. 1). As itturns out, La4Sb3, Sm4Sb3 and Ce4Sb3 all exhibit n-type metallicconductive behavior with low Seebeck values in the 300–1300 Ktemperature range.19 Yb4Sb3, on the other hand, present a quitedifferent behavior: while the Seebeck coefficient is negative atroom temperature (around �20 mV K�1), it then increaseslinearly with temperature, reaching 70 mV K�1 at 1300 K accord-ing to previous studies.19,20 Meanwhile, the resistivity remainconsistently low, as expected for metallic conductive behavior,with values of about 1.2 mO cm at 1300 K,20 leading to a decentpower factor around 4 mW cm�1 K�2 at this temperature.21 Forthis reason, Yb4Sb3 was investigated for possible thermoelectricapplications at very high temperature as a p-type counterpart ofn-type La3�xTe4. An intriguing aspect of Yb4Sb3 is its p-typeconduction, dominated by hole carriers above 600 K. This isnotable since other rare-earth antimonides consistently exhibitn-type behavior across all temperatures. This peculiarity arisesfrom Yb’s mixed valency, switching between 2+ and 3+ oxida-tion states. However, magnetic studies have shown that theoxidation state of Yb atoms was predominantly 2+, not 3+.19This suggests, based on the Zintl formalism, that Yb atomsdonate only 8 electrons per formula unit to the anionic frame-work, which is comprised of Sb atoms able to accept 9 electronsoverall per formula unit. This electron deficiency might explainthe p-type conductive behavior in Yb4Sb3 above 600 K, but thisneeds to be confirmed by further theoretical investigations.Efforts to enhance transport properties have been pursuedthrough various strategies. Initially, substituting La for Yb wasexplored to lower the concentration of charge carriers, specificallyholes, present in Yb4Sb3 at high temperatures. This exchange ofYb2+/3+ atoms with La3+ atoms aimed to enhance the Seebeckcoefficient through the reduction of available holes. Several com-positions were investigated and it was shown that La0.5Yb3.5Sb3exhibited the best performance with an improvement of the powerfactor up to 10 mW cm�1 K�2 at 1300 K.19 Associated to asignificantly reduced thermal conductivity of 1.7 W m�1 K�1 at1300 K, La0.5Yb3.5Sb3 displayed a promising zT value of 0.75.19Furthermore, substituting a small amount of Sb by Bi also yieldpositive results. The Yb4Sb2.8Bi0.2 composition, for instance,shows an enhanced power factor of approximately 8 mW cm�1 K�2at 1300 K.20Building upon prior research efforts, the main objective ofthis study was to investigate the outcomes of a dual substitu-tion, involving the replacement of both La on Yb sites and Bi onSb sites. The aim was to potentially harness synergetic effects inorder to further enhance the thermoelectric properties of theparent material. The Bi substitution level was set at y = 0.2, guidedby the promising outcomes observed for the Yb4Sb2.8Bi0.2 compo-sition’s transport properties. Very recently, we used a similarstrategy with partial Bi substitution on Sb sites while a partialamount of Yb atoms were replaced by Ce atoms.22 Findings fromthis study demonstrated a significant enhancement in thethermoelectric properties of the Ce-substituted solid solution,motivating further exploration into the transport properties ofthe La-substituted solid solution.To explore the limits of solubility within the LaxYb4�xSb2.8Bi0.2solid solution, the La substitution level was progressively increasedfrom x = 0.1 to 1. Notably, the replacement of Sb with the larger-radius Bi may allow a broader solubility range in regard to thesubstitution of La for Yb, eventually leading to a reduction incharge carrier concentration by introducing a greater amount of Lainto the structure. Upon establishing the solubility limit, thesynthesis and preparation of homogeneous LaxYb4�xSb2.8Bi0.2compositions were undertaken to characterize their transportproperties. Additionally, a theoretical analysis was conducted toexplore the influence of both La and Bi substitution on theelectronic structure of Yb4Sb3 and better understand the transportproperties of the solid solution. We thus report in this article anunprecedented combined experimental and theoretical investiga-tion on this chemical system which shows great promise forthermoelectric applications in the very high temperature range.Experimental and theoreticalproceduresSynthesis and preparationYb4Sb3 and substituted LaxYb4�xSb3�yBiy compounds were synthe-sized in niobium tubes by mixing appropriate amounts of La(ingot, 99.8%), Yb (ingot, 99.8%), Sb (shots, 99.99%) and Bi (shots,99.999%) within an Ar-filled glovebox. To ensure an inert reactionenvironment, the niobium tubes were hermetically sealed underhigh-purity argon, using a custom arc furnace setup, before beingenclosed in fused silica tubes and further sealed to preventoxidation of the niobium containers. The solid solution studywas carried out using low quantities of reactants (500 mg).Fig. 1 Crystal structure of Yb4Sb3 and coordination polyhedra of Yb(yellow) and Sb (purple) atoms.Paper Materials AdvancesOpen Access Article. Published on 21 December 2023. Downloaded on 7/30/2024 2:03:42 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d3ma00903c© 2024 The Author(s). Published by the Royal Society of Chemistry Mater. Adv., 2024, 5, 1217–1225 |  1219These samples were heated at 1000 1C during 96 h with heatingand cooling ramps of 16 h. Subsequently, Nb containers wereopened under argon atmosphere, powders were finely ground,sealed back in new Nb capsules and annealed at 1000 1C forthree weeks. Samples aimed at the measurement of the trans-port properties were shaped from a higher quantity of powder(5 g), heated at 1050 1C, over an 8-day dwell period featuring10-hour ramps, followed by an annealing at 1000 1C for another8 days. X-ray diffraction measurements were carried out usingan X’Pert Pro MRD (Panalytical) (Cu-Ka1 and Cu-Ka2 radiations)and a D8 Advance Vario1 (Bruker) apparatus (Cu-Ka1 radiationl = 1.540598 Å). Structure refinements were performed using theFullprof suite.23 Samples were densified by Spark Plasma Sinter-ing using Dr Sinter Lab Jr’s SPS-322Lx with +10 mm graphitedies. Uniaxial pressure of 50 MPa was applied with a tempera-ture dwell of 1200 1C kept for 10 minutes during a one-hour run,yielding pellets of relative densities beyond 95%. Densifiedsamples were annealed in either Ta or Mo foils at 1000 1C for24 hours to ensure chemical stability and homogeneity. Com-position and microstructure were assessed by scanning electronmicroscopy coupled with energy-dispersive X-ray spectroscopy.Seebeck coefficient and resistivity were measured from 373 to1273 K on 3 � 3 � 10 mm samples by a ZEM5 apparatus(ULVAC) and thermal conductivity measurements were per-formed with a LFA467 HT HyperFlash (Netzsch) under N2 flux,employing Ø10 mm graphite-coated cylinders of up to 2 mmthickness.CalculationsAll density functional theory (DFT) calculations were performedusing the VASP software version 6.2.0.24–26 and the Perdew,Burke and Ernzerhof (PBE) exchange–correlation functional.27Structural optimizations and average properties were performedwith a cut-off energy of 350 eV and a 7 � 7 � 7 k-points gridsampled by the Monkhorst–Pack method.28 The band structurewas computed with the same cut-off energy using 15 k-pointsper symmetry line.Electronic transport coefficients were calculated within theBoltzmann Transport Equation. A constant relaxation time t for theelectrons was assumed as well as a rigid band structure,29,30 asimplemented in the BoltzTrap2 code.31 A 11 � 11 � 11 k-point gridwas used to compute the band derivatives for transport calculations.Results and discussionSynthesis of the binary Yb4Sb3 compoundThe pristine compound Yb4Sb3 was first synthesized. Theobtained powder X-ray diffraction pattern was refined by theLe Bail method (Rp = 2.78; Rwp = 3.88), yielding a cell parametera = 9.3324(1) Å (Fig. 2), which closely aligns with other pre-viously reported values.18 Very low intensity reflections of Yb2O3were also indexed and attributed to the slightly oxidized Ybstarting reagent. Subsequently, partial substitutions of La forYb and Bi for Sb were carried out.Study of the LaxYb4�xSb2.8Bi0.2 solid solutionInvestigation of the LaxYb4�xSb2.8Bi0.2 solid solution was initiatedprimarily to identify single-phase compounds for subsequenttransport property measurements. Based on the findings fromthe previously explored LaxYb4�xSb3 solid solution, where thesolubility limit was determined to be x = 0.5,19 it was of interestto investigate the potential influence of partial Sb substitution withthe larger-radius Bi atoms. Given the larger atomic radius of Bi(1.60 Å) compared with that of Sb (1.45 Å), the conjecture was thatthis substitution could open up greater possibilities for La atomsubstitution on the Yb site. To test this hypothesis, the quantity ofLa was varied from x = 0 to 1, while maintaining a Bi stoichiometryof 0.2 on the Sb site, in line with prior studies.20,21The results sketched in Fig. 3 indicate that starting from thenominal composition La0.6Yb3.4Sb2.8Bi0.2, the presence of LaSb isdetected in the bulk. This is due to the pronounced incorporationof La, resulting in a biphasic domain under the specific synthesistemperature and pressure conditions. This assumption is sup-ported by the correlation which is observed: higher La amountcorresponds to an elevated intensity of LaSb reflections (Fig. 3).In the case of La0.4Yb3.6Sb2.8Bi0.2, despite the absence of the LaSbphase, some reflections exhibit distortion, implying that thesubstitution level is still somewhat excessive, hindering completeintegration of La and Bi atoms within the parent structure.However, compositions with x r 0.3 display no LaSb impuritiesand exhibit undistorted peaks, signifying successful substitutionof La and Bi for Yb and Sb, respectively, in the structure. Thissolubility limit is slightly lower than that observed in the Ce-inserted CexYb4�xSb2.8Bi0.2 solid solution (x = 0.5),22 mainlyowing to the higher atomic radius of La atoms (1.95 Å) comparedwith Ce atoms (1.85 Å). The refined cell parameters are displayedin Fig. 4. Based on this investigation, compositions with x = 0.1,0.2, and 0.3 have been selected for further synthesis at largerscales, targeting subsequent transport property measurements.Fig. 2 Le Bail refinement of the X-ray diffraction pattern of Yb4Sb3synthesized in niobium containers. Low intensity peaks could be indexedas Yb2O3 impurity. The experimental data are plotted in red symbols, thecalculated pattern is drawn with a black line, the difference with a blue line,and the Bragg positions with green vertical ticks.Materials Advances PaperOpen Access Article. Published on 21 December 2023. Downloaded on 7/30/2024 2:03:42 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d3ma00903c1220 |  Mater. Adv., 2024, 5, 1217–1225 © 2024 The Author(s). Published by the Royal Society of ChemistryScanning electron microscopySamples of Yb4Sb3 and LaxYb4�xSb2.8Bi0.2 (x = 0.1, 0.2 and 0.3) werecharacterized by SEM on densified samples. Homogeneous densi-fied materials were observed, the illustrative case for x = 0.3composition being displayed in Fig. 5. The examination of samplesurfaces in secondary electrons mode revealed minimal porosity,the slight contrast observed being attributed to the polishing stepof the assessed sample. Energy-dispersive spectroscopy analysesconfirmed these findings and show great compositional homo-geneity, consistent with the expected compositions.Transport propertiesThe transport properties of the investigated compounds areshown in Fig. 6. Diligent efforts were directed toward achievingclear and reproducible results. Nonetheless, several difficultieswere encountered during the measurements of the electricaltransport properties. In addition to the inherent complexitiesassociated with maintaining robust electrical contacts with theelevated temperature range, a substantial tendency of the samplesto oxidize was observed. Despite the utilization of a high-purityhelium partial pressure atmosphere during measurements, it isplausible that a thin oxide layer may have formed between themeasurement probes and the sample surface as temperaturesescalated. This occurrence is in line with a recent research workdemonstrating the rapid surface oxidation of the relatedYb14MnSb11 compound around 700 K,32 and was also pointed outin our recent study on the CexYb4�xSb2.8Bi0.2 solid solution.22Although these factors contributed to certain limitations in achiev-ing precise measurements, in particular for the La0.3Yb3.7Sb2.8Bi0.2composition which will not be presented here, the measurements ofthe binary Yb4Sb3 and LaxYb4�xSb2.8Bi0.2 (x = 0.1 and 0.2) com-pounds were reasonably successful and allowed us to gain valuableinsights into the influence of the present dual substitution on thetransport properties.The Seebeck coefficient of all compositions maintains itspositive trend above 500 K, consistent with previous studies,Fig. 3 X-Ray diffraction patterns of Yb4Sb3 and the solid solution LaxYb4�xSb2.8Bi0.2 (0 r x r 1). The solubility limit occurs for x = 0.3 as diffraction peaksare significantly distorted for higher La substitution. LaSb impurity is observed for x Z 0.6.Fig. 4 Cell parameter a of the LaxYb4�xSb2.8Bi0.2 versus amount of La (x =0.1, 0.2 and 0.3) solid solution refined by the Le Bail refinement method.The cell parameter increases linearly with La content, following a classicalVegard law.Fig. 5 Electron Dispersive X-ray Spectroscopy characterization of theLa0.3Yb3.7Sb2.8Bi0.2 compound. The presence of all elements was con-firmed with a good homogeneity.Paper Materials AdvancesOpen Access Article. Published on 21 December 2023. Downloaded on 7/30/2024 2:03:42 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d3ma00903c© 2024 The Author(s). Published by the Royal Society of Chemistry Mater. Adv., 2024, 5, 1217–1225 |  1221indicating a conductive behavior dominated by holes at elevatedtemperatures. It can be noted that Yb4Sb3 presents a higherSeebeck coefficient at 1273 K compared to previous reports(100 mV K�1 versus 65 mV K�1),19,20 leading to improved thermo-electric performance. This difference is probably due to thedistinct synthesis and shaping routes that might significantlyinfluence the transport properties. Indeed, the co-substitutionof Yb by La and Sb by Bi have a relatively modest effect on theSeebeck values. However, a noteworthy enhancement wasobserved in the case of La0.2Yb3.8Sb2.8Bi0.2 with values around110 mV K�1 at 1273 K, possibly stemming from a reduction inhole concentration due to the substantial Yb substitutionamount with La atoms (see theoretical section below).The resistivity trends confirm the characteristic metallicconductive behavior, with values increasing as temperature rises,ranging from 0.3 to 1.1 mO cm between 373 and 1273 K for thebinary compound Yb4Sb3. Substituted compounds exhibit analo-gous conductive behavior, yet with higher resistivity values com-pared to the parent Yb4Sb3 compound, spanning from 0.8 to2.2 mO cm between 373 and 1273 K for the x = 0.2 composition.This observation is consistent with the anticipated reduction inhole concentration due to La substitution at the Yb site. As thecharge carrier concentration could not be measured in thistemperature range, this point was assessed via theoretical calcula-tions (vide infra). That being said, the evolution of the electronictransport properties is similar to that encountered in comparablesystems such as Yb21Mn4Sb18 where the substitution of Yb for Nadid not change much the Seebeck coefficient while the resistivitywas significantly modified.13Thermal conductivities measurements are displayed inFig. 6c. Yb4Sb3 and La0.1Yb3.9Sb2.8Bi0.2 exhibit analogous beha-vior, maintaining a relatively constant value of 3.20 W m�1 K�1up to 600 K, followed by a gradual decrease with temperature to2.65 W m�1 K�1 at 1273 K for both compounds. The substitutedLa0.2Yb3.8Sb2.8Bi0.2 compound shows lower values, rangingfrom 2.3 W m�1 K�1 at lower temperatures down to about1.9 W m�1 K�1 at 1173 K. This is in agreement with valuesalready reported for LaxYb4�xSb3 where thermal conductivitiesof substituted compounds were decreased by the local massfluctuation on the Yb site, contributing to enhanced phononscattering in substituted compounds.33 While not being pro-nounced for the La0.1Yb3.9Sb2.8Bi0.2 composition, the phenom-enon seems accentuated in the La0.2Yb3.8Sb2.8Bi0.2 compound,although it doesn’t entirely account for the significant reductionin thermal conductivity observed in this particular case. Thesubstantial increase in resistivity also plays an important roleaccording to the Wiedemann–Franz law in diminishing theelectronic contribution to thermal conductivity. This might thusexplain why the thermal conductivity experiences a notablereduction (about 30%) in the case of the x = 0.2 composition,although this effect seems limited for La0.1Yb3.9Sb2.8Bi0.2 as itsthermal conductivity was measured to be similar to that of theparent material within a relatively large uncertainty range.The thermoelectric figure of merit zT of the investigatedcompounds demonstrates a reasonable performance at elevatedtemperatures (Fig. 6d). Yb4Sb3 achieves a zT value of approxi-mately 0.5 at 1273 K, representing a notable outcome for thepristine compound. The substituted La0.1Yb3.9Sb2.8Bi0.2 andFig. 6 Thermoelectric properties of Yb4Sb3 and LaxYb4�xSb2.8Bi0.2 (x = 0.1 and 0.2) solid solution. (a) Seebeck coefficient, (b) resistivity, (c) thermalconductivity, and (d) figure of merit zT.Materials Advances PaperOpen Access Article. Published on 21 December 2023. Downloaded on 7/30/2024 2:03:42 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d3ma00903c1222 |  Mater. Adv., 2024, 5, 1217–1225 © 2024 The Author(s). Published by the Royal Society of ChemistryLa0.2Yb3.8Sb2.8Bi0.2 compounds exhibit zT values of 0.32 and 0.38at 1273 K, respectively, although slightly lower than that of thepure Yb4Sb3 compound. The difference can be attributed primar-ily to higher resistivities associated with weakly affected Seebeckcoefficients in the substituted compounds. The relatively lowerthermal conductivity measured for the x = 0.2 composition, whilenot fully compensated with the rise in resistivity, leaves room forfurther optimization within this family of compounds.Theoretical insightThe electronic properties of Yb4Sb3 were previously theoreticallystudied using first-principles calculations. V. N. Antonov et al.carried out local spin density approximation (LSD) + U DFTcalculations to study the heavy fermion Yb4As3 compound aswell as several isostructural ytterbium pnictides includingYb4Sb3.34 They demonstrated that the width and position ofthe pnictide p band when going through the pnictogen group ofthe Periodic Table leads to a transition into a semiconductingbehavior towards the light pnictogen element with a charge-transfer gap between the Yb 4f states and the pnictide p band.They also showed that this leads to an increasing carrierconcentration and hence an increasing metallic charactertowards the heavy pnictogen element. M. Shirakawa et al. com-pared their de Haas-van Alphen (dHvA) measurements with localdensity approximation (LDA) band structure calculations.35Further combined experimental and theoretical studies wereconducted in order to better understand the dHvA effect in thiscompound.36 These studies showed that six bands are involvedin the Fermi surfaces. They also computed total and atom-projected density of states (DOS) and showed that the top ofthe valence band is mainly centered on Yb-4f and Sb-5p levelswhereas the bottom of the conduction band is dominated by Yb-5d levels.We ourselves first performed DFT geometry optimization ofthe cell parameters and atomic positions of the binary com-pound Yb4Sb3. As often observed in the literature, the volumeof the PBE-DFT optimized unit cell is slightly larger (lessthan 2%) than the one obtained from X-ray diffraction studies(824.8 Å3 vs. 810.1 Å3). Optimized Yb–Sb bond distances com-pare very well with the X-ray measured ones: 3.14 Å vs. 3.12 Åand 3.36 Å vs. 3.32 Å. The spin-polarized band structure ofYb4Sb3 is sketched in Fig. 7. It compares quite well with theLDA ones previously reported in the literature. Small differ-ences between up and down band structures suggest weak spin-polarization. This band structure strongly differs from the onereported for the isostructural La4Sb3 compound: while theFermi level crosses the top of the valence band in Yb4Sb3, itis located in the bottom of the conduction band in La4Sb3.37This agrees with the lowest electronic transfer from the metalatoms towards the antimonide network in the case of theytterbium compound, resulting in a formal Yb(II) oxidationstate and p-type character of the compound. This is at theorigin of the difference in the transport behavior of Yb4Sb3 withregard to other RE4Sb3 compounds where RE is a trivalent rare-earth atom.19 A full theoretical analysis of the electronicstructure of both compounds will be further discussed in anupcoming study. The band structure of Yb4Sb3 shows that thebands located in the vicinity of the Fermi level are rather flat inthe N - P and H - N directions and more dispersive along theG - N and P - G - H symmetry lines. Such a situationencourages higher Seebeck coefficient as well as good electro-nic conductivity. Electronic transport properties of the binarywere simulated using a semi-classical approach assuming theconstant relaxation time approximation. Fig. 8 displays thecomputed thermopower of Yb4Sb3 at 300 and 1300 K as afunction of the chemical potential m. It is noteworthy to men-tion that the Seebeck coefficient is computed to be negative formB 0 eV. Even if the band structure suggests that several bandsare involved in the conduction, this shows that electronsdominate the conduction at low temperature as observedexperimentally. At higher temperature, holes dominate theconduction as expected from the previously published DOS34and the band structure sketched in Fig. 7.As massively exemplified in the literature, the thermopowercan be tuned with the variation of the carrier concentration.This can be achieved in particular via doping. In order to assessthe effect of doping Yb4Sb3 with La and Bi, two model com-pounds were computed: La0.25Yb3.75Sb3 and Yb4Sb2.75Bi0.25.Since Z equals 4 in the crystal structure of the binary com-pound, the computed models were obtained from the substitu-tion of one Yb atom out of 16 by one La in the case ofLa0.25Yb3.75Sb3, and of one Sb atom out of 12 by one Bi forFig. 7 PBE-DFT spin-up (blue dotted lines) and spin-down (orange solidlines) band structures of Yb4Sb3.Paper Materials AdvancesOpen Access Article. Published on 21 December 2023. Downloaded on 7/30/2024 2:03:42 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d3ma00903c© 2024 The Author(s). Published by the Royal Society of Chemistry Mater. Adv., 2024, 5, 1217–1225 |  1223Yb4Sb2.75Bi0.25. Cell parameters and atomic positions wererelaxed without any symmetry constraints. The DFT-optimizedvolumes of La0.25Yb3.75Sb3 and Yb4Sb2.75Bi0.25 are larger thanthe optimized one of Yb4Sb3 by ca. 4%. Such an increase isconsistent with the larger size of La and Bi compared to Yb andSb, respectively.Total and atom-projected DOS are sketched in Fig. 9. It isobvious that La and Bi substitutions have different impacts onthe electronic structure. Bi substitution hardly modifies theelectronic structure of Yb4Sb3; this is consistent with theisovalent character of both pnictogens. Therefore, assumingsimilar carrier concentrations, the electronic transport proper-ties of Bi-doped Yb4Sb3 are not expected to change significantlyas shown in Fig. 8 for the Seebeck coefficient. Indeed, aspreviously observed experimentally,21 the Bi-doped Yb4Sb3compound only exhibits a slightly enhanced thermopowerirrespective of the chemical potential. On the other hand, thesubstitution of one Yb(II) atom by one La(III) atom alters muchmore the electronic structure and the computed electronictransport properties. One can note that spin polarizationdecreases in the La-doped model compound whereas it hardlychanges in the Bi-doped model compound. The additionalelectrons brought by the lanthanum atoms contribute to fillthe valence band in La0.25Yb3.75Sb3, making the compound lesselectron conductive. This also favours a p-type conduction andexplains why the Seebeck coefficient turns positive at the Fermilevel at both simulated temperatures. The thermopower iscomputed lower than that of the parent compound, regardlessof the chemical potential. Assuming a rigid band model, theextra electron provided by La implies an increase in the Fermilevel that crosses mainly dispersive bands in the G - N andP - G - H directions (see Fig. 7), which is consistent with aSeebeck coefficient reduction.ConclusionsThis study delved into and discussed the potential thermoelectricapplications of Yb4Sb3 and related substituted compounds up to1300 K. By simultaneously substituting Yb with La and Sb with Bi,we aimed to enhance their performance through the optimiza-tion of their figure of merit zT. Exploration of the solubility limitof the LaxYb4�xSb2.8Bi0.2 solid solution revealed a maximumvalue of x = 0.3, beyond which complete substitutions were notobtained. Subsequent syntheses of Yb4Sb3 and LaxYb4�xSb2.8Bi0.2Fig. 8 Seebeck coefficient as a function of the chemical potential mcomputed at the PBE-DFT level for Yb4Sb3 (red), La0.25Yb3.75Sb3 (green),and Yb4Sb2.75Bi0.25 (blue), at 300 K (solid line) and 1300 K (dashed line).Fig. 9 PBE-DFT total and atom projected DOS computed for La0.25Yb3.75Sb3 (left) and Yb4Sb2.75Bi0.25 (right).Materials Advances PaperOpen Access Article. Published on 21 December 2023. Downloaded on 7/30/2024 2:03:42 AM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d3ma00903c1224 |  Mater. Adv., 2024, 5, 1217–1225 © 2024 The Author(s). Published by the Royal Society of Chemistry(x = 0.1, 0.2 and 0.3) on a larger scale followed by high-temperature transport properties measurements brought substan-tial new insights. As expected for materials exhibiting metallicconductive behavior, resistivity showcases a temperature-dependent increase while remaining in a desirable range. TheSeebeck coefficients were hardly affected by the co-substitutionwith values reaching 110 mV K�1 at 1273 K for x = 0.2. First-principles calculations helped in understanding the electronictransport properties of Yb4Sb3, especially the n-type to p-typetransition at high temperature. These calculations also confirmedthat Bi-substitution left electronic transport properties unaffected,while La substitution did not enhance the Seebeck coefficient butrather increased resistivity. Furthermore, this investigationunveiled a promising zT of 0.5 for Yb4Sb3 at 1300 K, which isthe highest maximum zT value reported so far for the parentcompound, confirming its thermoelectric potential in high-temperature scenarios. While both experimental and theoreticalresults have shown that the dual substitutions did not yield asubstantial enhancement of zT for the LaxYb4�xSb2.8Bi0.2 (x = 0.1and 0.2) solid solution, the study lays a foundation for furtheroptimization. Future directions should involve the exploration ofalternative substitutions, innovative nano-structuring, or defectengineering to potentially achieve elevated zT values.Author contributionsH. Bouteiller: conceptualization, data curation, formal analysis,investigation, methodology, validation, visualization, writing –original draft, writing – review & editing. V. Pelletier: software,data curation, formal analysis, investigation, validation, visua-lization, writing – review & editing. S. Le Tonquesse: concep-tualization, data curation, formal analysis, investigation,validation, visualization, writing – review & editing. B. Fontaine:software, data curation, formal analysis, investigation, super-vision. T. Mori: funding acquisition, resources, supervision,writing – review & editing. J.-F. Halet: formal analysis, investi-gation, software, supervision, project administration, writing –review & editing. R. Gautier: conceptualization, data curation,formal analysis, investigation, methodology, software, super-vision, validation, visualization, project administration,writing – review & editing. D. Berthebaud: conceptualization,formal analysis, investigation, methodology, project adminis-tration, resources, supervision, writing – review & editing.F. Gascoin: conceptualization, formal analysis, funding acqui-sition, investigation, methodology, project administration,resources, supervision, writing – review & editing.Conflicts of interestThere are no conflicts to declare.AcknowledgementsThe authors are grateful to the Agence Nationale de la Recherche(ANR – Project HIGHTHERM – Ref ANR-18-CE05-0037) and theJapan Society for the Promotion of Science (JSPS – PE21708) forfinancial support. 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