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[Illia Serhiienko](https://orcid.org/0000-0002-3072-9412), Michael Parzer, Fabian Garmroudi, [Andrei Novitskii](https://orcid.org/0000-0002-7304-806X), [Naohito Tsujii](https://orcid.org/0000-0002-6181-5911), Tarachand, Ernst Bauer, Yuri Grin, [Takao Mori](https://orcid.org/0000-0003-2682-1846)

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Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsJournal ofMaterials Chemistry APAPEROpen Access Article. Published on 14 April 2025. Downloaded on 5/24/2025 1:17:35 PM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article OnlineView Journal  | View IssuePivotal role of SbaResearch Center for Materials NanoarchiMaterials Science (NIMS), Tsukuba 305-004jpbGraduate School of Pure and Applied Scien8573, JapancInstitute of Solid State Physics, TU Wien, VdMax Planck Institute for Chemical Physics† Electronic supplementary informahttps://doi.org/10.1039/d5ta01437aCite this: J. Mater. Chem. A, 2025, 13,15268Received 20th February 2025Accepted 14th April 2025DOI: 10.1039/d5ta01437arsc.li/materials-a15268 | J. Mater. Chem. A, 2025, 13,vacancies in quaternary half-Heusler thermoelectrics†Illia Serhiienko, ab Michael Parzer, c Fabian Garmroudi, c Andrei Novitskii, aNaohito Tsujii, a Tarachand,a Ernst Bauer, c Yuri Grind and Takao Mori *abHalf-Heusler compounds are promising high-temperature thermoelectric materials due to their high figureof merit and excellent mechanical properties. The capability of the Heusler structure to accommodatea large variety of different elements allows for a vast phase space of substitutions and compositions. Thequaternary half-Heuslers (also known as “double half-Heuslers”) with XðY0:5Y00:5ÞZ stoichiometry havesparked particular interest as a route to lower the lattice thermal conductivity and enhancethermoelectric performance. Here, we unveil the pivotal role of intrinsic defects, namely Sb vacancies, innominally stoichiometric X(Ni0.5Fe0.5)Sb quaternary half-Heuslers, where X = Ti, Zr, Hf. Sb vacanciesnaturally occur during synthesis and can switch the conduction behavior from intrinsic n-type to p-type.To control the formation of Sb vacancies, we developed a sophisticated synthesis method, which weargue will be crucial for rational design of n- and p-type quaternary half-Heusler thermoelectrics.1 IntroductionThe rising global demand for energy, coupled with pressingenvironmental challenges, highlights the crucial need forsustainable and eco-friendly energy sources. Thermoelectric(TE) materials and devices are interesting for those purposes asthey realize direct conversion of heat into electricity via theSeebeck effect, which can be leveraged to enhance energy effi-ciency. From a material science perspective, the conversionefficiency of a TE device is determined by a dimensionless gureof merit, dened as zT = a2sT/k, with a being the Seebeckcoefficient, s the electrical conductivity, T the absolutetemperature, and k the thermal conductivity, including bothelectronic and lattice contributions (k = kel + klat).1 Due to thecorrelated and intertwined nature of these transport properties,enhancing zT poses an outstanding challenge.Among various semiconducting material families investi-gated over the past decades, half-Heusler phases, with thegeneral formula XYZ (F�43m space group), represent a largefamily of compounds with promising TE properties.2,3 Ingeneral, their crystal structure and chemical bonding stronglycorrelate with the valence electron count (VEC), whichtectonics (MANA), National Institute for4, Japan. E-mail: MORI.Takao@nims.go.ces, University of Tsukuba, Tsukuba 305-ienna A-1040, Austriaof Solids, Dresden 01187, Germanytion (ESI) available. See DOI:15268–15277determines electronic structure and stability. The Zintl–Klemmconcept helps rationalize the valence electron rule, consideringthat the most electropositive X element transfers its electrons tothe more electronegative Y and Z elements, forming d10 ands2p6 closed shell ions, making 18 valence electron half-Heuslercompounds particularly stable semiconductors.4 Altering thevalence electron count (VEC + 18) typically disrupts the semi-conducting ground state, causing the compounds to becomemetallic.5 Despite signicant advancements in 18-electronshalf-Heuslers,6,7 their high lattice thermal conductivity klatremains a major barrier to further improvements in their zT.To overcome these limitations, Anand et al. proposed that anincrease in structural complexity can be realized by combiningtwo half-Heusler compounds with VEC= 17 and 19 to obtain aneffective 18 valence electrons per formula unit, XðY0:5Y00:5ÞZ:8 Tovalidate this approach, they compared the widely studied half-Heusler compound TiCoSb (VEC = 18) with the valencebalanced quaternary half-Heusler alloy Ti(Fe0.5Ni0.5)Sb (VEC =(17 + 19)/2 = 18) derived from the two parent compoundsTiFeSb (VEC = 17) and TiNiSb (VEC = 19). A twofold reductionin klat was achieved for Ti(Fe0.5Ni0.5)Sb compared to TiCoSb dueto enhanced phonon scattering while a high Seebeck coefficientand semiconducting ground state were retained. Since then,such compounds have garnered signicant interest in thecommunity as they open a whole new phase space of potentiallyinteresting thermoelectric materials. The above-mentionedapproach has oen been referred to as “double half-Heuslers”in the literature. However, as Rogl et al. point out, thisdescription is not without problems from a structural chemistryperspective.16 Instead, in this work, we prefer to use the moregeneral and correct term - quaternary half-Heuslers. Despite theThis journal is © The Royal Society of Chemistry 2025http://crossmark.crossref.org/dialog/?doi=10.1039/d5ta01437a&domain=pdf&date_stamp=2025-05-17http://orcid.org/0000-0002-3072-9412http://orcid.org/0000-0003-3509-7474http://orcid.org/0000-0002-0088-1755http://orcid.org/0000-0002-7304-806Xhttp://orcid.org/0000-0002-6181-5911http://orcid.org/0000-0001-7376-5897http://orcid.org/0000-0003-2682-1846https://doi.org/10.1039/d5ta01437ahttp://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d5ta01437ahttps://pubs.rsc.org/en/journals/journal/TAhttps://pubs.rsc.org/en/journals/journal/TA?issueid=TA013020Paper Journal of Materials Chemistry AOpen Access Article. Published on 14 April 2025. Downloaded on 5/24/2025 1:17:35 PM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinegrowing interest, the properties of these systems, particularlythose reported for isovalent X(Fe0.5Ni0.5)Sb, where X representsTi, Zr, or Hf, vary dramatically (Fig. 1), hindering further prog-ress in enhancing zT. In their initial study, Anand et al. identi-ed Ti(Fe0.5Ni0.5)Sb as a p-type semiconductor with a z 300 mVK−1, whereas subsequent studies reported signicantly smallervalues (a z 120 mV K−1) and even a change of the conductiontype (from p- to n-type) for the samples with the same nominalcomposition8,9,12,14,17 (Fig. 1). Similar ambiguity with respect tothe conduction type exists in the Zr analogue Zr(Fe0.5Ni0.5)Sb.12,13Here, we unveil that the origin of this discrepancy can beunderstood by considering the pivotal role of point defects,such as vacancies and antisites, oen encountered in Heuslercompounds.18–20 Such defects can directly affect the chargecarrier concentration and carrier scattering,21,22 and theirformation is strongly inuenced by the synthesis conditions.19,23Arc melting is one of the most common synthesis routes forHeusler compounds. Precise control of stoichiometry, however,is a well-known key challenge. In Sb-containing half-Heuslersand quaternary half-Heuslers, for instance, arc meltingusually involves poorly controlled evaporation of Sb. Tocompensate for Sb losses, excess Sb (typically 2 to 10 wt%) maybe added prior to the melt synthesis. However, the chemicalcomposition is difficult to control precisely and inevitable smallcompositional differences, sometimes barely detectable byconventional analyses, can lead to fundamentally differenttransport properties.In this work, we developed a sophisticated synthesis route toenable a higher degree of control over the stoichiometry andelucidate the phase formation mechanism in detail. Conse-quently, we identify the key experimental knobs to systemati-cally tune the Sb vacancy formation in X(Fe0.5Ni0.5)Sb (X = Ti,Zr, or Hf), and nd that, following this careful synthesisprocedure, Ti(Fe0.5Ni0.5)Sb and Zr(Fe0.5Ni0.5)Sb exhibit intrinsicn-type conductivity. In contrast, the unavoidable formation ofSb vacancies in Hf(Fe0.5Ni0.5)Sb during phase formation makesit intrinsically p-type. These observations underscore theimportance of precise control over the synthesis conditions toFig. 1 Range of variations in the maximum Seebeck coefficient valuesamong X(Fe0.5Ni0.5)Sb compounds (X = Ti, Zr, or Hf) reportedpreviously8–15 and values obtained in this work (colored symbols).This journal is © The Royal Society of Chemistry 2025tailor the TE performance of quaternary half-Heuslers.Furthermore, we demonstrate that Ti(Fe0.5Ni0.5)Sb can beswitched from n- to p-type, merely by changing the annealingconditions. This peculiar ability to switch the conduction type isparticularly advantageous for the design of TE modules, as itenables the use of a single material for both p- and n-type legs,thereby mitigating device failures arising from mismatchedthermal expansion coefficients and other compatibilitychallenges.2 Results and discussion2.1 Phase formationTo minimize Sb losses and improve control over its stoichi-ometry during the synthesis of X(Fe0.5Ni0.5)Sb (X= Ti, Zr, or Hf),we initially synthesized the master alloys FeSb2 and X2Ni (X =Ti, Zr, or Hf) and used them as starting materials, as describedin detail in Section 4. To investigate the phase formationmechanism of X(Fe0.5Ni0.5)Sb, we employed differential scan-ning calorimetry (DSC), thermogravimetric analysis (TGA),powder X-ray diffraction (XRD), and energy-dispersive X-rayspectroscopy (EDX) on two different powder mixtures of FeSb2and X2Ni. The rst one represented a stoichiometric mixture ofFeSb2 and X2Ni powders (solid lines in Fig. 2), while the secondmixture represented X(Fe0.5Ni0.5)Sb (Fig. S1†), obtained viaa solid-state reaction between FeSb2 and X2Ni at 1273 K (dashedlines in Fig. 2).Upon heating the stoichiometrically mixed FeSb2 and X2Nimaster alloys, we observed two endothermic peaks in the DSCcurves for all samples (solid lines in Fig. 2). We attribute the rstpeak (”1st”, Fig. 2), observed in the range of 850–1000 K, to theinitial formation of the half-Heusler phase (space group F�43m),as conrmed by the XRD (Fig. S1†). However, EDX analysisreveals that the majority of the grains within the powder parti-cles exhibit noticeable deviations in the Fe/Ni ratio, and thesample contains secondary phases such as XFe0.5Sb andXNi0.5Sb (Fig. S1†). The second endothermic peak (“2nd”, Fig. 2)at the range of 1150–1250 K indicates the reaction betweenternary intermediates formed in the rst step and results insingle-phase X(Fe0.5Ni0.5)Sb quaternary half-Heusler, as veriedby XRD and EDX analysis of the master alloy mixture annealedat 1273 K for 5 days (Fig. S1†). Overall, according to the DSC/TGA, XRD, and EDX results, the complete quaternary half-Heusler phase formation mechanism can be proposed asfollows (see Fig. S1† for more details):X2Niþ FeSb2 ����!T . 1100 KXFe0:5�dNi0:5�dSbþXFe0:5SbþXNi0:5Sb ����!T . 1250 KXFe0:5Ni0:5Sb:According to our data, the minimum temperature requiredfor the formation of the pristine half-Heusler phase must be atmore than 1250 K, e.g., 1273 K (Fig. 2). However, at thistemperature, all samples exhibited mass loss, which was mostpronounced in Hf(Fe0.5Ni0.5)Sb (z0.4 wt%). EDX analysis, inturn, revealed that a thin metallic layer formed on the walls ofthe quartz tube during the solid-state reaction between FeSb2J. Mater. Chem. A, 2025, 13, 15268–15277 | 15269http://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d5ta01437aFig. 2 Differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) results for X(Fe0.5Ni0.5)Sb with X representing (a) Ti, (b) Zr,and (c) Hf. The upper panels show amass loss, while the lower panels display heat flow during heating of a stoichiometric mixture of X2Ni (X= Ti,Zr, Hf) and FeSb2 (solid curves) and same mixture after solid-state reaction at 1273 K (dashed curves). The “1st” (z1000 K) and “2nd” (z1250 K)exothermic peaks correspond to sequential phase formation reactions, while the “dec.” peak at higher temperatures indicates the decompo-sition. Note that decomposition of Zr(Fe0.5Ni0.5)Sb happens at noticeably lower temperature (z1350 K) compared to that of Ti(Fe0.5Ni0.5)Sb andHf(Fe0.5Ni0.5)Sb (z1550 K). Vertical dashed lines represent the temperature at which all the bulk samples were synthesized, sinter and annealedafter SPS.Journal of Materials Chemistry A PaperOpen Access Article. Published on 14 April 2025. Downloaded on 5/24/2025 1:17:35 PM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlineand X2Ni at 1273 K corresponds to pure Sb. This conrms thatSb loss is unavoidable even during solid-state reaction andappears to be the main reason for the variations in the reportedSeebeck coefficient values and conduction behavior ofX(Fe0.5Ni0.5)Sb (X = Ti, Zr, Hf) quaternary half-Heuslercompounds (Fig. 1). For example, signicant Sb loss inHf(Fe0.5Ni0.5)Sb inevitably results in p-type conductionbehavior, while the smaller Sb loss in Ti(Fe0.5Ni0.5)Sb andZr(Fe0.5Ni0.5)Sb allows it to retain n-type conduction as will beshown later. Moreover, since Sb loss increases with tempera-ture, it should, in principle, be possible to switch the conduc-tion type of X(Fe0.5Ni0.5)Sb (X = Ti, Zr) by annealing attemperatures above 1273 K, e.g., 1373 K. However, the decom-position of Zr(Fe0.5Ni0.5)Sb occurs at a much lower temperature(z1350 K) compared to that of Ti(Fe0.5Ni0.5)Sb and Hf(Fe0.5-Ni0.5)Sb (z1550 K). This hinders the possibility of switchingZr(Fe0.5Ni0.5)Sb from n- to p-type solely by processing condi-tions, unlike in the case of Ti(Fe0.5Ni0.5)Sb.Investigations of decomposition of X(Fe0.5Ni0.5)Sb samplesaer solid-state reaction at 1273 K (as indicated by dashed linesin Fig. 2) revealed that the Hf- and Zr-based compounds exhibitminimal mass loss and decomposition temperature remain thesame. In contrast, Ti(Fe0.5Ni0.5)Sb shows additional Sb lossbeginning above 1250 K, reaching approximately 0.4 wt% at1573 K. This feature opens the possibility for additional controlover the Sb content in Ti-based quaternary half-Heuslers,which, in turn, allows tuning of the conduction type from n-to p-type, as demonstrated and discussed below.2.2 Microstructure and elemental compositionThe relative density of all samples exceeds 97% of the theoret-ical density. The average grain sizes for the X(Fe0.5Ni0.5)Sbsamples are approximately 13.1 mm (X = Ti), 9.4 mm (X = Zr),and 8.7 mm (X = Hf), respectively (Fig. 3b–d). Additional15270 | J. Mater. Chem. A, 2025, 13, 15268–15277annealing of Ti(Fe0.5Ni0.5)Sb at 1373 K (Fig. 3a) did not result insignicant changes of the grain size.The interquartile range obtained by EDX for all constitutingelements of X(Fe0.5Ni0.5)Sb consistently aligns with the nominalstoichiometry (Fig. 3, right panel). However, as expected,a slight Sb deciency was observed in all compositions exceptfor Zr(Fe0.5Ni0.5)Sb. To precisely determine the average chem-ical composition, we performed ICP-OES analysis, whichconrmed the EDX ndings by revealing an actual Sb deciencyof approximately 0.3–0.4 at% in Ti(Fe0.5Ni0.5)Sb and Zr(Fe0.5-Ni0.5)Sb and z0.9 at% in Hf(Fe0.5Ni0.5)Sb and annealedTi(Fe0.5Ni0.5)Sb (Fig. 3 and Table S2†).Additionally, the comparison of EDX spectra reveals distin-guishable variation in the Ka line intensities for Fe and Ni acrossdifferent grains of each sample (Fig. 3 right panel, Fig. S2†).Although the peaks of the Gaussian distribution for Fe and Nialign well with the nominal values, the tails of the distributionsexceed 1 at% for all investigated compounds. This suggests thatvariations in the Fe/Ni ratio between the grains cannot becompletely ruled out.2.3 Crystal structureAll obtained samples crystallize in the face-centered cubicMgAgAs-type half-Heusler crystal structure with the F�43m spacegroup. No secondary phases were detected (Fig. 4a). The latticeparameter a strongly depends on the X element (X = Ti, Zr orHf) at 4a site; a increases when Ti is replaced by Zr, most likelydue to a larger atomic radius of Zr (160 pm) compared to that ofTi (147 pm) (Fig. 4b). However, replacing Zr (160 pm) with Hf(159 pm) results in a decrease of a, a trend that cannot beexplained solely by atomic size differences. Interestingly,a similar trend has also been observed in other XCoSb (X = Ti,Zr or Hf) half-Heuslers.24This journal is © The Royal Society of Chemistry 2025http://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d5ta01437aFig. 3 SEM micrographs captured in electron channeling contrastmode and corresponding box plots of elemental composition distri-bution across different grains estimated from EDX of (a) annealedTi(Fe0.5Ni0.5)Sb and (b)–(d) X(Fe0.5Ni0.5)Sb (X = Ti, Zr, and Hf) samples,respectively. The upper parts of box plots demonstrate Fe and Nidistribution across different grains. Average element compositionobtained from ICP-OES and EDX displayed under each SEM image andbox plot, respectively.Paper Journal of Materials Chemistry AOpen Access Article. Published on 14 April 2025. Downloaded on 5/24/2025 1:17:35 PM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article OnlineQuaternary half-Heuslers XðY0:5Y00:5ÞZ are commonlycompared with their ternary analogs XYZ with the same VEC =18.8,9,29 In the case of X(Fe0.5Ni0.5)Sb, both the crystal and elec-tronic structures are expected to resemble those of XCoSb.8However, a comparison of the lattice parameter of X(Fe0.5Ni0.5)Sb with values reported in the literature for XCoSb revealsThis journal is © The Royal Society of Chemistry 2025signicant differences.24,25 The substitution of Co by an equia-tomic mixture of Fe and Ni at the Y-site does not yield similarlattice parameter values to XCoSb, as the majority of reporteda values are noticeably lower. This, instead, may be caused bydifferences in chemical bonding30 as it has been shown thatcovalent interactions in T’TE-type compounds contributesignicantly more to the total energy of the system thanCoulomb interactions for details see ref. 31. Further analysisreveals that the lattice parameter (Fig. 4b) of Ti(Fe0.5Ni0.5)Sb (a= 5.91146(3) Å) lies between those of TiFeSb (a= 5.9480 Å)27 andTiNiSb (a = 5.8903 Å).28 This additionally supports thehypothesis that the investigated quaternary half-Heuslers aremore likely a solid solution of the two ternary half-Heuslers32rather than a distinct new phase.8Renement of the crystal structures for Ti(Fe0.5Ni0.5)Sb andZr(Fe0.5Ni0.5)Sb with different site occupancy, based on powderX-ray diffraction data, indicates that the smallest R-factor isobtained when the atomic sites 4aX, 4bY, and 4cZ are modeled asfully occupied (Table S3†). However, renements for Hf(Fe0.5-Ni0.5)Sb reveal increased displacement parameter values for theSb position, highlighting the probability of reduced Sb occu-pancy at this site aligning with EDX/ICP-OES ndings. There-fore, the site occupancy factor (SOF) for Sb was rened to be0.96. This approach resulted in lower R-factor values andphysically reasonable atomic displacement parameter values(Table S3†), indicating that under controlled synthesis condi-tions, Sb vacancies in X(Fe0.5Ni0.5)Sb compounds can be mini-mized. Nonetheless, the Hf-based quaternary half-Heuslercompound inherently forms with Sb deciency.The comparison of diffraction patterns reveals clear differ-ences between Ti(Fe0.5Ni0.5)Sb and annealed Ti(Fe0.5Ni0.5)Sb(Fig. 4c). For the annealed sample, the peak positions shiedtoward lower diffraction angles, indicating an increase of thelattice parameter (from 5.91146(3) Å to 5.91657(2) Å) and thecorresponding intensity ratio (I331 + I222)/I440 compared to thenon-annealed sample. Rietveld renement, in turn, yieldeda SOF = 0.95 for annealed Ti(Fe0.5Ni0.5)Sb, revealing Sb vacancyin this sample. This conrms the feasibility of ne-tuning thestoichiometry, conduction type, and maximum Seebeck coeffi-cient value in Ti(Fe0.5Ni0.5)Sb solely through careful control ofsynthesis parameters.Summarizing, the consistency between the EDX and ICP-OES-derived chemical compositions and the site occupanciesrened through Rietveld analysis revealed that X(Fe0.5Ni0.5)Sb(X = Ti, Zr, or Hf) quaternary half-Heuslers naturally tend toform Sb vacancies during synthesis or annealing processes.However, our developed synthesis route provides a means tominimize vacancy formation, allowing for a more precisecontrol over the thermoelectric transport properties.2.4 Transport propertiesIn previously published data, Ti(Fe0.5Ni0.5)Sb was reported asa p-type semiconductor with amax values ranging from 120 to300 mV K−1.8,9 Later, the same composition was reported as an n-type semiconductor with amax = −200 mV K−1.11,17 Literaturedata for Zr(Fe0.5Ni0.5)Sb vary from amax −15 to 85 mV K−1.12,13 InJ. Mater. Chem. A, 2025, 13, 15268–15277 | 15271http://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d5ta01437aFig. 4 (a) Rietveld refinements of X-ray powder diffraction patterns of annealed Ti(Fe0.5Ni0.5)Sb and X(Fe0.5Ni0.5)Sb (X = Ti, Zr, Hf) samples,respectively. Positions of Bragg's reflections for the reference half-Heusler phase (F�43m space group) are indicated by black ticks at the bottom.Experimental data, simulated patterns, and the difference profiles are shown (black, blue, and green, respectively). Corresponding R-factorsvalues of the refinement can be found in the ESI (Table S3†). (b) Calculated lattice parameters for annealed Ti(Fe0.5Ni0.5)Sb and X(Fe0.5Ni0.5)Sb (X=Ti, Zr, Hf), compared with reference values for other Sb-based half-Heusler compounds reported in the literature.24–28 (c) Comparison of relativeintensities in the XRD patterns of Ti(Fe0.5Ni0.5)Sb (red) and annealed Ti(Fe0.5Ni0.5)Sb (black) samples, highlighting changes attributed to Sb vacancyformation, as evidenced by the shift in lattice parameter a and variations in peak intensity ratios for (331), (222), and (400) reflections.Journal of Materials Chemistry A PaperOpen Access Article. Published on 14 April 2025. Downloaded on 5/24/2025 1:17:35 PM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlineour study, the Ti(Fe0.5Ni0.5)Sb and Zr(Fe0.5Ni0.5)Sb samples wereidentied as non-degenerate n-type semiconductors, with amaxreaching up to −350 mV K−1 and −200 mV K−1, respectively(Fig. 5a). To understand these observed deviations, one mustconsider the synthesis procedures. In several studies wereviewed, arc melting was used to prepare X(Fe0.5Ni0.5)Sbsamples.8,11,12,17 Liu et al. used ball-milling9 to synthesizeTi(Fe0.5Ni0.5)Sb. Both methods inevitably induce defects, due touncontrollable Sb evaporation during arc melting and struc-tural disorder from long-term ball-milling, which complicatesinvestigations of their intrinsic properties. In the case ofZr(Fe0.5Ni0.5)Sb, uncontrollable synthesis conditions during arcmelting inevitably lead to partial decomposition of the desiredphase and, as a consequence, only modest a values.12,13Hf(Fe0.5Ni0.5)Sb and annealed Ti(Fe0.5Ni0.5)Sb samples, withthe highest concentration of Sb vacancies, are identied as non-15272 | J. Mater. Chem. A, 2025, 13, 15268–15277degenerate p-type semiconductors, with amax of 300 mV K−1 and250 mV K−1, respectively. From a VEC perspective, deciency ofSb decreases the VEC compared to the nominal 18 electrons perunit cell in the pristine material, lowering EF towards thevalence band. The most pronounced realization of this conceptis observed in the Ti(Fe0.5Ni0.5)Sb sample without annealing,which demonstrates n-type behavior as the chemical composi-tion closely approximates the nominal one. Formation of Sbvacancies during annealing reduces the VEC, leading to p-typeconduction behavior in annealed Ti(Fe0.5Ni0.5)Sb. On theother hand, the formation of Hf(Fe0.5Ni0.5)Sb inherently comesalong with the formation of Sb vacancies that determine itsconduction type. This intrinsic doping mechanism is also re-ected in the electrical conductivity (Fig. 5b), which increases byabout one to two orders of magnitude in the samples, for whichsubstantial formation of Sb vacancies was identied. The effectThis journal is © The Royal Society of Chemistry 2025http://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d5ta01437aFig. 5 Temperature dependence of (a) Seebeck coefficient a, (b)electrical conductivity s, and (c) lattice thermal conductivity klat ofX(Fe0.5Ni0.5)Sb samples (X = Ti, Zr, and Hf) and the annealed Ti(Fe0.5-Ni0.5)Sb sample, respectively. Both samples, annealed Ti(Fe0.5Ni0.5)Sband Hf(Fe0.5Ni0.5)Sb, with evident Sb vacancies demonstrate p-typeconductivity. Solid lines represent the fitting by the modified Debye-Callaway model,33 dashed line represent klat of Ti(Fe0.5Ni0.5)Sbsynthesized via arcmelting from.8 The inset in (c) shows klat(T) in a log–log scale, highlighting the reduction in klat of Ti(Fe0.5Ni0.5)Sb afterannealing at 1373 K due to induced Sb vacancy formation.This journal is © The Royal Society of Chemistry 2025Paper Journal of Materials Chemistry AOpen Access Article. Published on 14 April 2025. Downloaded on 5/24/2025 1:17:35 PM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlineon the thermal conductivity (Fig. 5c), however, is much moresubtle (compare Ti(Fe0.5Ni0.5)Sb versus annealed Ti(Fe0.5Ni0.5)Sb), suggesting that the effect of the Sb vacancies is especiallydramatic with respect to the electronic transport properties.To assess whether the sizeable differences in thetemperature-dependent Seebeck coefficient between Zr- and Ti/Hf-based compounds can be accounted for by differences in theelectronic structure, we performed density functional theorycalculations of the ground state electronic structure. Theunfolded band structures along with the atom-projected partialand total densities of states are plotted in Fig. 6. It can be seenthat all compounds share a similar semiconducting groundFig. 6 Unfolded electronic band structure and corresponding totaland partial density of states (DOS) for X(Fe0.5Ni0.5)Sb samples, with Xrepresenting (a) Ti, (b) Zr, and (c) Hf, respectively. The horizontaldashed lines indicate the Fermi level EF, formation of Sb vacancies tuneEF from the conduction band to the valence band.J. Mater. Chem. A, 2025, 13, 15268–15277 | 15273http://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d5ta01437aJournal of Materials Chemistry A PaperOpen Access Article. Published on 14 April 2025. Downloaded on 5/24/2025 1:17:35 PM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinestate with a band gap ranging from 0.8–0.9 eV. Thus, the mostobvious explanation for the change in thermoelectric propertiesis the variation of the Fermi level caused by the differentconcentration of defects. The shi of the stoichiometry and VECdue to the formation of Sb vacancies pushes the Fermi levelfrom the conduction band bottom towards the valence bandtop, thus changing the conduction type from n-type to p-type.All measured X(Fe0.5Ni0.5)Sb samples exhibit a semi-conducting temperature dependence of s (Fig. 5b), i.e., theelectrical conductivity increases with temperature. Similar tothe Seebeck coefficient, a clear difference is observed betweennon-defective n-type (Ti- and Zr-based) samples and p-type (Hf-based and annealed Ti-based) samples with Sb vacancies. Sinceonly the p-type samples demonstrate an enhancement in s, itsuggests that the presence of Sb vacancies increases hole chargecarrier concentration, thereby improving s at low to mid-rangetemperatures. At higher temperatures, where bipolar conduc-tion becomes signicant, both electrons and holes contribute tocharge transport, resulting in similar s values across allsamples. The unusual low-temperature behavior of s will bediscussed in Chapter 2.5.The lattice thermal conductivity klat (Fig. 5c) is a dominantpart of total thermal conductivity in all investigated samplessince the ke contribution accounts for less than 3% owing torelatively low s values. The Debye–Callaway model modied bySlack33 reveals that for X(Fe0.5Ni0.5)Sb materials (where X = Ti,Zr, or Hf), normal scattering dominates in the low-temperatureregion which is responsible for observed klat peak. At elevatedtemperatures, Umklapp, point defect, and phonon-electronscattering processes become dominant due to their high crys-tallinity, as evidenced in the crystal structure section and alsoconsistent with a recently published study for other half-Heusler materials.34–36 The Hf(Fe0.5Ni0.5)Sb and annealedTi(Fe0.5Ni0.5)Sb samples demonstrate noticeably higher contri-bution from point defect scattering additionally revealing thepresence of Sb vacancies (Table S4†).2.5 Features of low-temperature transportAt low temperatures, a(T) and s(T) decrease rapidly, clearlyindicating a changing scattering mechanism. Notably, attemptsto model the electrical transport using diffusive charge trans-port (e.g., the two-band model) failed to accurately describe thelow-temperature behavior (Fig. S3†).37 Among the potentialmechanisms considered, the Kondo effect, Mott's variablerange hopping (VRH), and the phonon drag effect emerge as themost plausible phenomena commonly observed in half-Heuslercompounds.35,38Magnetic eld-dependent measurements of s and a revealedno eld dependence, ruling out the Kondo effect (see Fig. S4†).Fitting revealed that ln(1/s) proportional to T−0.2 suggestsscattering mechanism similar to VRH (T−0.25).39 However, theVRH model failed to explain Seebeck coefficient behavior, as itpredicts a = 0 at 8 K, which is physically inappropriate.Furthermore, crystal structure analyses revealed that all ob-tained compounds are well-crystallized and lack signicantatomic disorder, making the presence of VRH unlikely. On the15274 | J. Mater. Chem. A, 2025, 13, 15268–15277other hand, the peak in lattice thermal conductivity (Fig. 5c)occurs in the temperature range where s and a exhibita noticeable change in slope. This observation suggests that thetemperature dependence of s and a may be inuenced by thephonon drag effect, where the mean free paths of phononsbecome comparable to charge carriers, introducing an addi-tional scatteringmechanism below 50 K. In the case of annealedTi(Fe0.5Ni0.5)Sb, most likely that the Sb vacancies shi the Fermilevel into the valence band noticeably increasing holesconcentration (as can be noted from relatively high s) minimizethe impact of electron scattering on long-wavelength phononresulting in weak s and a temperature dependence. A moredetailed discussion of the phonon drag effect is provided in theESI.†3 ConclusionsSummarizing, we revealed that the phase formation process ofquaternary half-Heusler follows two stages, ultimately leadingto the formation of single-phase half-Heusler compounds. Wefound that Ti- and Hf-based quaternary half-Heuslers areparticularly sensitive to synthesis temperatures and annealingabove 1250 K, which promotes the formation of Sb vacancies.The Zr-based compounds hardly form any vacancies butdecompose around 1340 K. Experimentally and theoretically, ithas been established that non-defective X(Fe0.5Ni0.5)Sb mate-rials are non-degenerate n-type semiconductors. However, thepresence of Sb vacancies in Ti- and Hf-based materials inducesa transition to non-degenerate p-type conduction behavior. Ourwork resolves the ambiguity of literature reports on theconduction type of the compounds and highlights the impor-tance of preventing Sb vacancy formation for rational design ofn-type quaternary half-Heusler thermoelectrics.4 Materials and methods4.1 SynthesisAs starting materials, we used a Ti rod (99.99 mass%), Zr rod(99.99 mass%), Hf ingot (99.9 mass%, with 1.2 at% of Zr), Feingot (99.995 mass%), Ni ingot (99.99 mass%), and Sb shot(99.999 mass%), all produced by Rare Metallic Co. (Japan). Dueto the signicant difference in the melting points of theelements, master alloys FeSb2 and X2Ni (X = Ti, Zr, or Hf) wereinitially synthesized and used as precursors. FeSb2 wasprepared by the melting of Fe and Sb in an evacuated carbon-coated quartz ampule for 24 h at 1323 K. The obtainedproduct was ground into ne powder inside a glovebox, cold-pressed, and subsequently sealed in a quartz ampoule fora second annealing step at 873 K for 7 days, followed byquenching in cold water. The master alloy X2Ni was prepared byarcmelting under an Ar atmosphere, followed by hand-crushinginside a glovebox.X2Ni and FeSb2 master alloys were weighed according to thestoichiometric ratio and subsequently mixed in a stainless-steeljar in a shaker mill (8000D Mixer/Mill, SPEX SamplePrep, USA)with a powder/ball ratio of 2 : 1 for 30 minutes. Aerward, theresulting powder was cold-pressed, sealed in a quartz tube, andThis journal is © The Royal Society of Chemistry 2025http://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d5ta01437aPaper Journal of Materials Chemistry AOpen Access Article. Published on 14 April 2025. Downloaded on 5/24/2025 1:17:35 PM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlineannealed for 5 days at 1273 K, followed by quenching in coldwater. The powder, aer solid-state reaction, was densied byspark plasma sintering (Dr Sinter-1080, Fuji-SPS, Japan) ina B10 mm graphite die under uniaxial pressure of 50 MPa at1273 K for 10 min, under Ar atmosphere, with a heating rate of100 K min−1. Finally, to homogenize chemical composition andremove residual stress, all fabricated specimens were annealedfor three days at 1273 K under vacuum and quenched. Todemonstrate the switchability of the Ti(Fe0.5Ni0.5)Sb samplefrom n- to p-type, the obtained bulk sample was additionallyannealed for three days at 1373 K following the same procedure.This synthesis approach enables precise control over thechemical composition and provides detailed insight into thephase formation process, a level of control unattainable withother methods such as arc melting or mechanical alloying.4.2 Materials characterizationFor phase identication, powder X-ray diffraction (XRD) usinga q/2q Bragg–Brentano diffractometer (SmartLab3, RigakuCorporation, Japan) was used. The measurements covered anangular range from 10° to 130° with a CuKa1 radiation source (l= 1.54056 Å), a step width of 0.02°, and a scan speed of 1°per min. For data evaluation and crystal structure renement,the program package WinCSD was employed.40The microstructure and elemental composition of the ob-tained samples were investigated by scanning electron micros-copy and energy-dispersive X-ray spectroscopy (EDX) using anultra-high resolution HRSEM (SU8230 Hitachi, Japan) equip-ped with an EDX detector (X-MaxN Horiba, Japan). The EDXspectra were collected with an acceleration voltage of 25 keV,reaching 5 × 106 counts per spectrum. Electron ChannelingContrast Imaging (ECCI) with a photo-diode BSE detector wasapplied to enhance grain structure representation. This methodnot only identies variations in the local average atomicnumber but also discerns differences in grain orientation.41Precise average elemental composition was determined byinductively coupled plasma-optical emission spectrometry (ICP-OES) using a 5800 ICP-OES spectrometer (Agilent, USA).Approximately 10 mg of the crushed bulk sample was decom-posed in a 100 mL PFA beaker using 10 mL of aqua regia and 1–3mL of HF by heating. The cooled residue was ltered (type 5C),and the ltrate was diluted to 250 mL with Milli-Q water. Theresidue and lter paper were ashed in an alumina crucible,fused with 0.25 g Na2CO3 and 0.75 g Na2O2, and the cooled meltwas dissolved in Milli-Q water and 10 mL of HCl (1 : 1), thendiluted to 100 mL. The ltrate was analyzed by radial viewingand emission intensity ratio method (20 mg L−1 Mn:257.610 nm, on-line addition), while the residue solution wasmeasured by axial viewing and emission intensity method.Thermogravimetric analysis (TGA) and differential scanningcalorimetry (DSC) were performed using a simultaneous ther-mogravimetry analyzer (449 F1 Jupiter Netzsch, Germany). Thephase formation mechanism was investigated using ∼0.1 g ofa stoichiometric mixture of FeSb2 and X2Ni (X = Ti, Zr, Hf)master alloys (dashed curves in Fig. 2) placed in Al2O3 cruciblesunder a 6N argon stream, with a heating rate of 10 Kmin−1 fromThis journal is © The Royal Society of Chemistry 2025400 K to 1573 K. To conrm the thermal stability of the samples,mixtures of FeSb2 and X2Ni aer solid-state reaction at 1273 K(solid curves in Fig. 2) were also subjected to the DSC-TGAanalysis in the same conditions.4.3 Transport properties measurementsTemperature dependencies of the electrical conductivity s andthe Seebeck coefficient a were simultaneously measured alongthe radial direction perpendicular to the pressure direction inthe SPS of bar-shaped samples with dimensions of 10 mm ×3 mm × 1.5 mm by the four-probe method in the commercialset-up ZEM 3 (Advance-Riko, Japan). The temperature depen-dence of total thermal conductivity k was calculated using theformula k = c × Cp × d, where c is the thermal diffusivitydetermined from thermal diffusivity measurements by a laserashmethod (LFA 457MicroFlash, Netzsch, Germany), Cp is thespecic heat capacity estimated using the comparison methodwith a standard sample (pyroceram-9606), and d is the bulkdensity determined using the Archimedes method. To mini-mize errors from the emissivity and reectivity of thematerial toinfrared radiation, the samples were covered with a thin layer ofgraphite. The lattice thermal conductivity (klat) was calculatedthrough klat = k − ke, where ke = sLT according to the Wiede-mann–Franz law, with the Lorenz number derived from themeasured Seebeck coefficient values.42Low-temperature s, a, and k were measured using a physicalproperty measurement system (PPMS, Quantum Design, USA)from 10 to 300 K under a magnetic eld of 7 T and without eld.The magnetic eld, electric current, and temperature gradientwere all parallel to each other. Magnetization measurementswere performed from 2 to 300 K using a superconductingquantum interference device magnetometer (MPMS, QuantumDesign, USA).4.4 Electronic structure calculationsThe supercell DFT calculations for the quaternary half-Heuslercompounds were performed using the Vienna ab initio simu-lation package (VASP).43–48 To incorporate the partial substitu-tion of Fe and Ni atoms at the 4c site, 2 × 2 × 2 supercellscontaining 24 atoms were constructed. The calculations wereperformed using the Perdew–Burke–Enzerhof generalizedgradient approximation (GGA-PBE) exchange-correlationfunctional.49The crystal structures were relaxed in terms of total volumesand individual atomic positions, which is crucial for accom-modating possible local distortions caused by the Fe and Nisubstitution at the 4c site. For structural relaxation, a grid witha k-point spacing of 0.08 Å−1 was employed to sample the Bril-louin zone. A ner k-point mesh with a spacing of 0.04 Å−1 wasused for the self-consistent calculations of the electronicstructure to minimize uctuations in the density of states. Thepartial occupancies for each orbital were determined using thetetrahedron method with Bloch corrections. The optimal energycutoff for the plane-wave basis set was determined throughconvergence tests on several supercells to be 450 eV.J. Mater. Chem. A, 2025, 13, 15268–15277 | 15275http://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d5ta01437aJournal of Materials Chemistry A PaperOpen Access Article. Published on 14 April 2025. Downloaded on 5/24/2025 1:17:35 PM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article OnlineTo obtain the band structures of the respective supercells,the band structures were unfolded using the b4vasp tool.50–52b4vasp utilizes robust algorithms in unfolding the band struc-ture, effectively mapping the complex bands from the supercellback to the simpler Brillouin zone of the primitive cell. In therepresentation of the unfolded band structure, the colorgradient depicts the spectral wave function A(k, E), whichdescribes the probability density of nding an electron witha particular crystal momentum k and energy E. The method-ology follows the principles outlined in ref. 50 and 52.Data availabilityThe data that support the ndings of this study are availablefrom the corresponding author upon request.Conflicts of interestThere are no conicts to declare.AcknowledgementsJST Mirai JPMJMI19A1 and JST SPRING JPMJSP2124 supportedthis work. Yu. G. acknowledges National Institute for MaterialsScience (NIMS, Japan) for nancial support. The authors wouldlike to acknowledge NIMS Nanofabrication Facility (NIMS,Japan) for SEM analysis and Material Analysis Station (NIMS,Japan) for the XRD and ICP-OES analysis. I.S. thanks Jean-François Halet (University of Rennes) and Cédric Bourges(University of Limoges) for fruitful and stimulating discussions.References1 A. F. Ioffe, Semiconductor Thermoelements, and ThermoelectricCooling, Infosearch, London, 1957.2 C. Felser and A. Hirohata, Heusler Alloys: Properties, Growth,Applications, Springer International Publishing, 2015.3 W. Li, S. Ghosh, N. Liu and B. Poudel, Joule, 2024, 8, 1274–1311.4 W. G. Zeier, J. Schmitt, G. Hautier, U. Aydemir, Z. M. Gibbs,C. Felser and G. J. Snyder, Nat. Rev. Mater., 2016, 1, 1–10.5 T. Graf, C. Felser and S. S. Parkin, Prog. Solid State Chem.,2011, 39, 1–50.6 M. Schwall and B. Balke, Phys. Chem. Chem. Phys., 2013, 15,1868–1872.7 H. Zhu, R. He, J. Mao, Q. 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A, 2025, 13, 15268–15277 | 15277https://doi.org/10.48550/arXiv.2409.06261https://github.com/QuantumMaterialsModelling/bands4vasphttps://github.com/QuantumMaterialsModelling/bands4vasphttp://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a Pivotal role of Sb vacancies in quaternary half-Heusler thermoelectricsElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta01437a