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Ryuta Yurishima, [Yoshiki Takagiwa](https://orcid.org/0000-0003-4508-1708), [Ayako Ikeda](https://orcid.org/0000-0002-1705-9004), Teruyuki Ikeda

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[Microstructure Optimization of Thermoelectric τ1-Al2Fe3Si3 via Graded Temperature Heat Treatments](https://mdr.nims.go.jp/datasets/76fd580d-0537-4681-a616-1a2dd3534e30)

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Microstructure Optimization of Thermoelectric 1-Al2Fe3Si3 via Graded Temperature Heat TreatmentsCitation: Yurishima, R.; Takagiwa, Y.;Ikeda, A.; Ikeda, T. MicrostructureOptimization of Thermoelectricτ1-Al2Fe3Si3 via Graded TemperatureHeat Treatments. Materials 2024, 17,5899. https://doi.org/10.3390/ma17235899Academic Editor: Andres SoteloReceived: 5 November 2024Revised: 22 November 2024Accepted: 26 November 2024Published: 2 December 2024Copyright: © 2024 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).CommunicationMicrostructure Optimization of Thermoelectric τ1-Al2Fe3Si3 viaGraded Temperature Heat TreatmentsRyuta Yurishima 1, Yoshiki Takagiwa 2,† , Ayako Ikeda 3 and Teruyuki Ikeda 1,*1 Graduate School of Science and Engineering, Ibaraki University, 4-12-1 Nakanarusawa,Hitachi 316-8511, Japan2 Thermoelectric Materials Group, National Institute for Materials Science, 1-2-1 Sengen,Tsukuba 305-0047, Japan3 Research Center for Structural Materials, National Institute for Materials Science, 1-2-1 Sengen,Tsukuba 305-0047, Japan; ikeda.ayako@nims.go.jp* Correspondence: teruyuki.ikeda.hy@vc.ibaraki.ac.jp; Tel.: +81-294-38-5066† Current address: Hitachi Research Laboratory, Hitachi, Ltd., Ohmika-cho 7-1-1, Hitachi 319-1292, Japan.Abstract: To investigate the relationship between microstructure, chemical composition, and ther-moelectric properties, we have applied graded temperature heat treatments to recently developedτ1-Al2Fe3Si3-based thermoelectric (FAST) materials formed by a peritectic reaction. We investigatedmicrostructures, chemical compositions, and Seebeck coefficients as continuous functions of heattreatment temperature. The τ1 phase can become p- and n-type semiconductors without dopingby changing the Al/Si ratio. The Seebeck coefficient was maximized, exceeding |S| > 140 µVK−1for both p- and n-type materials, by heat treatment at 1173 K for 24 h through microstructural opti-mization. These results show that combining the graded temperature heat treatments and spatialmapping measurements of thermoelectric properties gives effective routes to determine the suitableheat treatment temperature for materials with multiphase microstructure.Keywords: graded temperature heat treatments; thermoelectric properties; microstructure; phasediagram1. IntroductionPhysical, mechanical, and thermoelectric properties depend on chemical compositionand microstructure [1]. Heat treatments can control microstructure; annealing at hightemperatures could remove compositional inhomogeneity due to segregation at the mi-crometer scale, which may occur in melt-solidified materials. While the heat treatmentconditions could be estimated by calculation if the diffusion coefficient is known, diffusioncoefficients are unknown in many cases. Therefore, based on a known phase diagram, ifavailable, a trial-and-error approach is often employed in various heat treatments suchas homogenizing chemical compositions, promoting phase transition, or controlling mi-crostructures. Exploring optimal heat treatment conditions is, in general, time-consumingand labor-intensive. In order to efficiently optimize heat conditions, taking a look at highthroughput techniques, there are some, but limited, studies found using graded tempera-ture heat treatments [2,3]. Ning et al. developed a graded temperature heat treatment toprepare a Ni base superalloy (FGH4096) with structural gradient [2]. Wei and Zhao used asimilar heat treatment to study the solid state precipitation in Fe-Cr-Mo steel over a widerange of temperatures [3].Recently, a new thermoelectric material, “FAST materials” (Fe-Al-Si Thermoelectricmaterials), has been developed [4,5]. It is a ubiquitous material based on the τ1–Al2Fe3Si3single phase [6]. The τ1 phase has such a wide compositional range that allows varia-tion in the Al and Si concentrations, xAl = 21.0–41.5 at.% and xSi = 41.5–21.0 at.%, withMaterials 2024, 17, 5899. https://doi.org/10.3390/ma17235899 https://www.mdpi.com/journal/materialshttps://doi.org/10.3390/ma17235899https://doi.org/10.3390/ma17235899https://creativecommons.org/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://www.mdpi.com/journal/materialshttps://www.mdpi.comhttps://orcid.org/0000-0003-4508-1708https://orcid.org/0000-0002-1705-9004https://orcid.org/0000-0001-7076-6958https://doi.org/10.3390/ma17235899https://www.mdpi.com/journal/materialshttps://www.mdpi.com/article/10.3390/ma17235899?type=check_update&version=1Materials 2024, 17, 5899 2 of 9a limited range of the Fe concentration (xFe: 37.5–38.5 at.%) [6]. One can control the car-rier conduction behavior of FAST materials from p- to n-type depending on the Al/Siratio [7,8], and the maximum power factor S2σ is ~880 µWm−1K−2 [9]. For its abundance,environmentally friendly characteristics, and excellent thermoelectric properties, FASTis a promising material that would be utilized as autonomous power supplies for IoTdevices in an advanced information society [10]. In order to realize such widespread use ofthis material, optimization of material properties is desired from various points of view,including microstructure control; the heat treatment condition for FAST materials has notbeen refined.The τ1 phase is formed by a peritectic reaction between the FeSi and liquid phases [6],and hence an ordinary solidification processing results in the peritectic microstructure.Therefore, to prepare material with τ1 single phase, it is necessary to carry out heat treat-ments. To optimize heat treatment conditions, we conducted graded temperature heattreatments to evaluate thermoelectric performance and microstructure as continuous func-tions of heat treatment temperature.2. Materials and Methods2.1. Sample PreparationIngots of FAST materials with the nominal compositions of Fe38Al22+xSi40-x (x = 0 andx = 2.2 for n- and p-type, respectively) were synthesized using an induction heating furnace(NEV- SM04N; Nissin Giken Co., Iruma, Japan) under an argon atmosphere. After crushingthe ingots, gas atomization produced a powder sample. Powder with a particle size ofless than 45 µm was sintered in a graphite die with a diameter of 15 mm by spark plasmasintering method (LABOX-110MC; SinterLand, Inc., Nagaoka, Japan) at 1193 K under auniaxial pressure of 57 MPa and an argon atmosphere. After grinding the sample surfaceto remove surface impurities, the sample was cut into a rod shape with a 6 mm diameterand a 10 mm height using an electric discharge machine. Microstructures after sinteringwere observed by a scanning electron microscope (SEM) equipped with an electron-probemicroanalyzer with wavelength dispersive X-ray spectroscopy (EPMA; EPMA-8050G;Shimadzu Corp., Kyoto, Japan).2.2. Heat Treatments Under Temperature GradationSamples thus prepared were subject to heat treatments in a temperature gradation.A schematic view of the graded temperature furnace is shown in Figure 1a, and thetemperature distribution in the furnace measured with an R-type thermocouple is shownin Figure 1b. Samples were heat treated in a graphite container under Ar gas for 24 h.The temperature gradation was formed between the heated part by an infrared lamp andthe cooled part by water-cooling. Eight samples were stacked vertically in the graphitecontainer and set in the graded temperature region from ~873 K to 1323 K. Heat treatmenttemperature was estimated using the distance from the cap of the furnace comparedwith the temperature distribution shown in Figure 1b. The preciseness in measuring thedistance is estimated to be ±1 mm, which correspond to the preciseness of temperatureof ±5 K based on the temperature distribution. The accuracy of the temperatures thusmeasured was checked using the solvus in the Ni-Al system; a rod sample with the Ni-14at.%Al composition was subject to a graded temperature heat treatment, and the solvustemperature determined from the position of the boundary between the regions whereprecipitates are observed and not observed was 1097 K, which is in good agreement withthat in the reported Al-Ni phase diagram [11], 1098 K.After the heat treatment, the samples were water-cooled to freeze stable phases underheat treatment temperatures by dropping them into water.Materials 2024, 17, 5899 3 of 9Materials 2024, 17, x FOR PEER REVIEW 3 of 9    Figure 1. Schematic view of the furnace used for graded temperature heat treatments (a) and its temperature distribution (b). 2.3. Characterization The samples were cut in the longitudinal direction, and the cut surfaces were pol-ished using abrasives of #320, #400, #600, followed by diamond slurries with particle sizes of 9 µm, 3 µm, and 0.05 µm, respectively. The microstructure was then observed, and the chemical compositions were determined using SEM and EPMA as functions of annealing temperature. Phase fractions were determined from the microstructural images. The See-beck coefficient was measured near room temperature as a function of the distance from the bottom edge. The sample was mounted on a temperature-controlled copper plate to provide uniform heat throughout the sample. The temperature difference was created be-tween a thermocouple with a small thermal mass located at a corner of the sample and a cold scan probe with a large thermal mass, which locally draws heat from the sample surface to create the local temperature difference ΔT. The procedure is similar to that de-scribed in [12,13]. In this work, the spatial resolution of the Seebeck coefficient measure-ments is ~150 µm, reflecting the wire diameter of the T-type thermocouple used in this work. At each distance from the top cap of the furnace, measurements were done for five different points and the five values were averaged. 3. Results and Discussion Compositions of the sintered samples measured by EPMA are Fe38.7±0.7Al23.6±0.5Si37.7±0.4 for p-FAST and Fe39.9±0.7Al21.8±2.2Si38.4±1.8 for n-FAST, where the error ranges correspond to the standard deviations of seven measured points. Three-phase microstructures with tens of micrometers size scales are observed in the as-sintered samples, as shown in Figure 2a,j. Since τ8 and FeSi phases cannot be in equilibrium with each other according to the equi-librium phase diagram [14], the three-phase state is thought to be in a non-equilibrium state reflecting the solidification microstructure after the solidification processing by gas atomization. Microstructures after the heat treatment are shown for various heat treatment tem-peratures in Figure 2b–i,k–r. The chemical compositions of phases observed in the micro-structures at respective temperatures are shown in Figure S1 together with the phase dia-gram [6]. Three-phase microstructures consisting of τ1, τ8, and FeSi are observed at tem-peratures up to 1033 K in both the p- and n-type samples, while the volume fraction of the τ8 phase decreases with increasing temperature. Above 1033 K, microstructures are com-posed of the τ1 and FeSi phases with a decreasing trend in the FeSi phase fraction. In ad-dition, there are precipitates at grain boundaries at 1273 K in the n-FAST sample, while this phase has not been identified. The phase fractions were evaluated using X-ray inten-sity maps for each element obtained by EPMA; results of analysis from the n-type sample at 993 K are shown as examples in Figure 3. Since the samples were prepared by sintering, significant fractions of voids were observed. The phase fractions were evaluated within solid regions. The cumulative phase fractions and Seebeck coefficients are shown in Figure 4. Absolute values of the Seebeck coefficients of both p- and n-types increase up to around Figure 1. Schematic view of the furnace used for graded temperature heat treatments (a) and itstemperature distribution (b).2.3. CharacterizationThe samples were cut in the longitudinal direction, and the cut surfaces were polishedusing abrasives of #320, #400, #600, followed by diamond slurries with particle sizes of9 µm, 3 µm, and 0.05 µm, respectively. The microstructure was then observed, and thechemical compositions were determined using SEM and EPMA as functions of annealingtemperature. Phase fractions were determined from the microstructural images. TheSeebeck coefficient was measured near room temperature as a function of the distancefrom the bottom edge. The sample was mounted on a temperature-controlled copperplate to provide uniform heat throughout the sample. The temperature difference wascreated between a thermocouple with a small thermal mass located at a corner of thesample and a cold scan probe with a large thermal mass, which locally draws heat fromthe sample surface to create the local temperature difference ∆T. The procedure is similarto that described in [12,13]. In this work, the spatial resolution of the Seebeck coefficientmeasurements is ~150 µm, reflecting the wire diameter of the T-type thermocouple used inthis work. At each distance from the top cap of the furnace, measurements were done forfive different points and the five values were averaged.3. Results and DiscussionCompositions of the sintered samples measured by EPMA are Fe38.7±0.7Al23.6±0.5Si37.7±0.4for p-FAST and Fe39.9±0.7Al21.8±2.2Si38.4±1.8 for n-FAST, where the error ranges correspondto the standard deviations of seven measured points. Three-phase microstructures with tensof micrometers size scales are observed in the as-sintered samples, as shown in Figure 2a,j.Since τ8 and FeSi phases cannot be in equilibrium with each other according to the equilib-rium phase diagram [14], the three-phase state is thought to be in a non-equilibriumstate reflecting the solidification microstructure after the solidification processing bygas atomization.Microstructures after the heat treatment are shown for various heat treatment tem-peratures in Figure 2b–i,k–r. The chemical compositions of phases observed in the mi-crostructures at respective temperatures are shown in Figure S1 together with the phasediagram [6]. Three-phase microstructures consisting of τ1, τ8, and FeSi are observed attemperatures up to 1033 K in both the p- and n-type samples, while the volume fraction ofthe τ8 phase decreases with increasing temperature. Above 1033 K, microstructures arecomposed of the τ1 and FeSi phases with a decreasing trend in the FeSi phase fraction.In addition, there are precipitates at grain boundaries at 1273 K in the n-FAST sample,while this phase has not been identified. The phase fractions were evaluated using X-rayintensity maps for each element obtained by EPMA; results of analysis from the n-typesample at 993 K are shown as examples in Figure 3. Since the samples were prepared bysintering, significant fractions of voids were observed. The phase fractions were evaluatedwithin solid regions. The cumulative phase fractions and Seebeck coefficients are shownin Figure 4. Absolute values of the Seebeck coefficients of both p- and n-types increaseMaterials 2024, 17, 5899 4 of 9up to around 1173 K. As the spatial resolution of the Seebeck coefficient measurements is~150 µm, which is larger than the length scale of the phase variation shown in Figure 2, eachSeebeck coefficient at a single measured point represents the average values of multiplephases shown in Figure 2. At each distance from the top cap of the furnace, measurementswere done for five different points and the five values were averaged. The standard de-viations of five measured values were used to show the range of error in Figure 4. Thetrend of absolute values of the Seebeck coefficients is accompanied by the increase in the τ1fraction and the decrease in the τ8 fraction, and is reasonable because the τ8 phase showsmetallic behavior and hence is expected to exhibit a low Seebeck coefficient while the τ1 isknown for its excellent thermoelectric properties arising from the formation of a narrowgap near the Fermi level according to first principle calculations [8]. Such variations of thephase fractions can be attributed to atomic diffusion; diffusion distance due to the 24 hannealing is not large enough at low temperatures up to 1173 K compared to the size scalesshowing inhomogeneity in the as-sintered state shown in Figure 2, while it is large enoughto homogenize the samples and achieve the equilibrium compositions of phases at 1173 Kand above. Actually, the compositions measured from respective phases are consistent withthe reported phase diagram, as shown in Figure 5 for 1173 K [14].Materials 2024, 17, x FOR PEER REVIEW 4 of 9   1173 K. As the spatial resolution of the Seebeck coefficient measurements is ~150 µm, which is larger than the length scale of the phase variation shown in Figure 2, each Seebeck coefficient at a single measured point represents the average values of multiple phases shown in Figure 2. At each distance from the top cap of the furnace, measurements were done for five different points and the five values were averaged. The standard deviations of five measured values were used to show the range of error in Figure 4. The trend of absolute values of the Seebeck coefficients is accompanied by the increase in the τ1 fraction and the decrease in the τ8 fraction, and is reasonable because the τ8 phase shows metallic behavior and hence is expected to exhibit a low Seebeck coefficient while the τ1 is known for its excellent thermoelectric properties arising from the formation of a narrow gap near the Fermi level according to first principle calculations [8]. Such variations of the phase fractions can be attributed to atomic diffusion; diffusion distance due to the 24 h annealing is not large enough at low temperatures up to 1173 K compared to the size scales showing inhomogeneity in the as-sintered state shown in Figure 2, while it is large enough to ho-mogenize the samples and achieve the equilibrium compositions of phases at 1173 K and above. Actually, the compositions measured from respective phases are consistent with the reported phase diagram, as shown in Figure 5 for 1173 K [14].  Figure 2. Microstructures of as-sintered p-FAST (a) and n-FAST (j). Figures (b–i) and (k–r) show microstructures taken from the p-FAST and n-FAST, respectively, after graded temperature heat treatments. Corresponding temperatures of the heat treatments are shown in the respective images. Figure 2. Microstructures of as-sintered p-FAST (a) and n-FAST (j). Figures (b–i) and (k–r) showmicrostructures taken from the p-FAST and n-FAST, respectively, after graded temperature heattreatments. Corresponding temperatures of the heat treatments are shown in the respective images.Materials 2024, 17, 5899 5 of 9Materials 2024, 17, x FOR PEER REVIEW 5 of 9    Figure 3. The analysis to evaluate the volume fractions of constituent phases for the region heat-treated at 993 K in the n-FAST, as an example, after the graded temperature heat treatments.  Figure 3. The analysis to evaluate the volume fractions of constituent phases for the region heat-treated at 993 K in the n-FAST, as an example, after the graded temperature heat treatments.Materials 2024, 17, x FOR PEER REVIEW 5 of 9    Figure 3. The analysis to evaluate the volume fractions of constituent phases for the region heat-treated at 993 K in the n-FAST, as an example, after the graded temperature heat treatments.  Figure 4. Seebeck coefficients mapped at room temperature and cumulative phase fractions after thegraded temperature heat treatment as functions of temperature for p- FAST (a) and n- FAST (b).Materials 2024, 17, 5899 6 of 9Materials 2024, 17, x FOR PEER REVIEW 6 of 9   Figure 4. Seebeck coefficients mapped at room temperature and cumulative phase fractions after the graded temperature heat treatment as functions of temperature for p- FAST (a) and n- FAST (b).  Figure 5. Compositions measured in the p- and n-FAST samples after the graded temperature heat treatment plotted with the reported Al-Fe-Si phase diagram [6]. To examine the validity of the above arguments, we first check the validity of the temperatures within the samples during the graded temperature heat treatments. Samples at the same compositions Fe38Al22+xSi40-x (x = 0 and x = 2.2 for n- and p-type, respectively) were annealed in a uniform-temperature furnace. The microstructure and the chemical composition of the sample annealed at 923 K for 24 h are shown in Figure 6, where micro-structures with the three phases, τ1, FeSi, and τ8, are observed. This phase composition is consistent with that in the samples heat-treated in the graded temperature. This result shows that the temperature during the graded temperature heat treatment is not contra-dictory to that during the uniform temperature annealing. Next, we consider whether the phase composition, τ1, FeSi, and τ8, at 1023 K and lower temperatures in Figure 2 are really of nonequilibrium states. According to Du et al. [15], both experiments and CALPHAD calculations show that, on the Si-rich side of the τ1 phase, τ1 phase is in equilibrium with the FeSi and FeSi2 phases, or with τ8 and FeSi2 phases at 1000 K, and hence the FeSi, τ1, and τ8 phases are not in phase equilibrium. Therefore, the three-phase state with the τ1, FeSi, and τ8 phases at temperature lower than 1000 K should be in a non-equilibrium state. This means that the reason why the microstructure of the three phases of τ1, FeSi, and τ8 is observed at 1023 K and lower temperatures is that the annealing of this material at temperatures lower than 1000 K for 24 h does not give a long diffusion distance enough to equilibrate the samples remaining in the non-equilib-rium state due to solidification processing, including the peritectic reaction. Figure 5. Compositions measured in the p- and n-FAST samples after the graded temperature heattreatment plotted with the reported Al-Fe-Si phase diagram [6].To examine the validity of the above arguments, we first check the validity of thetemperatures within the samples during the graded temperature heat treatments. Samplesat the same compositions Fe38Al22+xSi40-x (x = 0 and x = 2.2 for n- and p-type, respectively)were annealed in a uniform-temperature furnace. The microstructure and the chemicalcomposition of the sample annealed at 923 K for 24 h are shown in Figure 6, where mi-crostructures with the three phases, τ1, FeSi, and τ8, are observed. This phase compositionis consistent with that in the samples heat-treated in the graded temperature. This re-sult shows that the temperature during the graded temperature heat treatment is notcontradictory to that during the uniform temperature annealing.Materials 2024, 17, x FOR PEER REVIEW 7 of 9    Figure 6. Microstructures and compositions obtained in the sample heat-treated using a uniform temperature furnace at 923 K for 24 h. A significant increase in S for n-FAST and a decrease in S for p-FAST is recognized with the absolute values of the Seebeck coefficient above ~1273 K. This region may be affected by compositional change due to annealing at high temperatures. To consider these variations in Seebeck coefficient above 1273 K, first we focus on the effect of grain boundary phase observed in n-FAST as shown Figure 2r. According to a previous study [8], electronic states of phases other than τ1 and τ12 in the Fe-Al-Si phase diagram are metallic, which inherently results in lower Seebeck coefficients than that of τ1. Therefore, the increase in the absolute value of the Seebeck coefficient of n-FAST above 1273 K cannot be explained as the contribution of such metallic phases. On the other hand, the decrease in the absolute value of the Seebeck coefficient above 1273 K in p-FAST (Fig-ure 4a) is unlikely to be attributed to grain boundary phases, even if their Seebeck coeffi-cients are assumed to be very small because the area fraction of the grain boundary phase is too small to explain the observed decrease in Seebeck coefficient. Assuming that the grain boundary phase is the τ12 phase and Seebeck coefficient of the τ12 phase is significantly higher than that of the τ1 phase, it may contribute to the in-crease of the Seebeck coefficient above 1273 K in n-FAST (Figure 4b). According to the phase diagram [6], the composition of the τ12 phase is Al-richer and slightly Fe-deficient compared to τ1, being consistent with the darker contrast observed in SEM. If the grain boundary precipitates in n-FAST (Al-deficient) are really the τ12 phase, it should be more likely that the same thing happens in p-FAST (Al-rich). However, no grain boundary pre-cipitates are observed in p-FAST. Thus, the drastic variations of the Seebeck coefficients above 1273 K are neither due to the contributions from the metallic phases nor the τ12 phase in the Al-Fe-Si system. Considering this, the primary cause of the variation of the Seebeck coefficient ob-served above 1273 K in Figure 4a,b is likely to be an increase in the Al/Si ratio within the τ1 phase itself, rather than the influence of grain boundary phase. According to the Seebeck coefficient estimated by a first principle calculation as a function of chemical potential [4], such behavior of the Seebeck coefficient, that is, increase for n-FAST and decrease for p-FAST in the absolute values by annealing, can occur with the shift to lower chemical potentials for both n- and p-types, which corresponds to the shift of the chemical compositions in the Al-rich direction and cannot be explained by Al evaporation. Therefore, the results of compositional analysis of samples heat-treated un-der a temperature gradient indicate that at 900 °C diffusion occurs, but the effect of tem-perature gradient diffusion does not occur, while at higher temperatures, the effect of tem-perature gradient diffusion may occur. In addition, there is not enough diffusion at lower temperatures because microstructures at lower temperature should be non-equilibrium. The reason for such a compositional variation might be diffusion due to temperature Figure 6. Microstructures and compositions obtained in the sample heat-treated using a uniformtemperature furnace at 923 K for 24 h.Next, we consider whether the phase composition, τ1, FeSi, and τ8, at 1023 K and lowertemperatures in Figure 2 are really of nonequilibrium states. According to Du et al. [15],both experiments and CALPHAD calculations show that, on the Si-rich side of the τ1 phase,τ1 phase is in equilibrium with the FeSi and FeSi2 phases, or with τ8 and FeSi2 phases at1000 K, and hence the FeSi, τ1, and τ8 phases are not in phase equilibrium. Therefore, thethree-phase state with the τ1, FeSi, and τ8 phases at temperature lower than 1000 K shouldbe in a non-equilibrium state. This means that the reason why the microstructure of thethree phases of τ1, FeSi, and τ8 is observed at 1023 K and lower temperatures is that theMaterials 2024, 17, 5899 7 of 9annealing of this material at temperatures lower than 1000 K for 24 h does not give a longdiffusion distance enough to equilibrate the samples remaining in the non-equilibriumstate due to solidification processing, including the peritectic reaction.A significant increase in S for n-FAST and a decrease in S for p-FAST is recognizedwith the absolute values of the Seebeck coefficient above ~1273 K. This region may beaffected by compositional change due to annealing at high temperatures.To consider these variations in Seebeck coefficient above 1273 K, first we focus onthe effect of grain boundary phase observed in n-FAST as shown Figure 2r. Accordingto a previous study [8], electronic states of phases other than τ1 and τ12 in the Fe-Al-Siphase diagram are metallic, which inherently results in lower Seebeck coefficients than thatof τ1. Therefore, the increase in the absolute value of the Seebeck coefficient of n-FASTabove 1273 K cannot be explained as the contribution of such metallic phases. On the otherhand, the decrease in the absolute value of the Seebeck coefficient above 1273 K in p-FAST(Figure 4a) is unlikely to be attributed to grain boundary phases, even if their Seebeckcoefficients are assumed to be very small because the area fraction of the grain boundaryphase is too small to explain the observed decrease in Seebeck coefficient.Assuming that the grain boundary phase is the τ12 phase and Seebeck coefficient ofthe τ12 phase is significantly higher than that of the τ1 phase, it may contribute to theincrease of the Seebeck coefficient above 1273 K in n-FAST (Figure 4b). According to thephase diagram [6], the composition of the τ12 phase is Al-richer and slightly Fe-deficientcompared to τ1, being consistent with the darker contrast observed in SEM. If the grainboundary precipitates in n-FAST (Al-deficient) are really the τ12 phase, it should be morelikely that the same thing happens in p-FAST (Al-rich). However, no grain boundaryprecipitates are observed in p-FAST.Thus, the drastic variations of the Seebeck coefficients above 1273 K are neither due tothe contributions from the metallic phases nor the τ12 phase in the Al-Fe-Si system.Considering this, the primary cause of the variation of the Seebeck coefficient observedabove 1273 K in Figure 4a,b is likely to be an increase in the Al/Si ratio within the τ1 phaseitself, rather than the influence of grain boundary phase.According to the Seebeck coefficient estimated by a first principle calculation as afunction of chemical potential [4], such behavior of the Seebeck coefficient, that is, increasefor n-FAST and decrease for p-FAST in the absolute values by annealing, can occur withthe shift to lower chemical potentials for both n- and p-types, which corresponds to theshift of the chemical compositions in the Al-rich direction and cannot be explained by Alevaporation. Therefore, the results of compositional analysis of samples heat-treated undera temperature gradient indicate that at 900 ◦C diffusion occurs, but the effect of temperaturegradient diffusion does not occur, while at higher temperatures, the effect of temperaturegradient diffusion may occur. In addition, there is not enough diffusion at lower tem-peratures because microstructures at lower temperature should be non-equilibrium. Thereason for such a compositional variation might be diffusion due to temperature gradient,i.e., thermal diffusion [16]. However, the argument cannot be conclusive at present andis beyond the scope of this work. Thus, in general, if the temperature of heat treatmentis too high, unexpected effects may be caused, and hence one needs to choose the righttemperature for heat treatments. These results show that combining the graded tempera-ture heat treatments and spatial mapping measurements of thermoelectric properties giveseffective routes to determine the suitable heat treatment temperature for materials withmultiphase microstructure.4. ConclusionsWe have applied graded temperature heat treatments to p- and n-FAST materialsprepared by induction melting followed by gas atomization and sintering, which enabled usto examine microstructures, chemical compositions, and Seebeck coefficients as continuousfunctions of temperature. As a result, the Seebeck coefficient was improved by heattreatment at 1173 K for 24 h. This is accompanied by the microstructure change fromMaterials 2024, 17, 5899 8 of 9a non-equilibrium state containing the τ1, FeSi, and τ8 phases to an equilibrium statecontaining the τ1 and FeSi phases. Thus, eliminating the τ8 phase, which is harmful tothermoelectric properties, effectively optimizes thermoelectric properties. Heat treatmentsunder a temperature gradation give effective routes to determine the proper temperatureof heat treatments.Supplementary Materials: The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/ma17235899/s1, Figure S1: Compositions of phases observed inn-FAST after the graded-temperature heat treatments.Author Contributions: Conceptualization, R.Y., T.I. and A.I.; methodology, R.Y. and A.I.; software,R.Y.; validation, R.Y.; formal analysis, R.Y. and Y.T.; investigation, R.Y. and T.I.; resources, A.I and Y.T.;data curation, R.Y.; writing—original draft preparation, R.Y. and T.I.; writing—review and editing,A.I. and Y.T; visualization, R.Y.; supervision, T.I.; project administration, T.I.; funding acquisition, T.I.,A.I. and Y.T. All authors have read and agreed to the published version of the manuscript.Funding: This paper is based on results obtained from a project, JPNP14004, commissioned by theNew Energy and Industrial Technology Development Organization (NEDO). This work was partlysupported by JSPS KAKENHI Grant Number 20K15054 and by NIMS Joint Research Hub ProgramNo. 2024-095.Institutional Review Board Statement: Not applicable.Informed Consent Statement: Not applicable.Data Availability Statement: The raw data supporting the conclusions of this article will be madeavailable by the authors on request.Acknowledgments: We would like to thank Thomas Höfler for invaluable assistance in creating thefigures in this paper.Conflicts of Interest: The authors declare no conflicts of interest. The funders had no role in the designof the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; orin the decision to publish the results.References1. Snyder, G.J.; Toberer, E.S. 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A thermodynamicdescription of the Al–Fe–Si system over the whole composition and temperature ranges via a hybrid approach of CALPHAD andkey experiments. Intermetallics 2008, 16, 554–570. [CrossRef]16. Shewmon, P. Diffusion in Solids; Wiley: Hoboken, NJ, USA, 1989.Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individualauthor(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury topeople or property resulting from any ideas, methods, instructions or products referred to in the content.https://doi.org/10.1016/j.intermet.2008.01.003 Introduction  Materials and Methods  Sample Preparation  Heat Treatments Under Temperature Gradation  Characterization  Results and Discussion  Conclusions  References