#
Relation between Electronic Structure and Thermoelectric Properties of Heusler-Type Ru_{2}VAl Compounds

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

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## Abstract

**:**

_{2}VAl, a candidate material for next-generation thermoelectric conversion, by first-principle calculations of its thermoelectric conversion properties and direct experimental observations of its electronic structures, employing photoemission and infrared spectroscopy. Our results show that Ru

_{2}VAl has a wider pseudogap near the Fermi level compared to Fe

_{2}VAl. Accordingly, a higher thermoelectric conversion performance can be expected in Ru

_{2}VAl at higher temperatures.

## 1. Introduction

_{2}Te

_{3}[1,2,3], PbTe [4], and SiGe [5,6,7] are typical thermoelectric materials used in practical applications. Bi

_{2}Te

_{3}, in particular, is used in thermoelectric power generation and laser diode cooling units, and its ZT is approximately 1.2 to 1.4 [8,9,10,11]. However, the performance of these materials has not significantly improved in recent years, and the development of new thermoelectric materials is desired.

_{F}, such as pseudogap-like electronic structures, are promising for thermoelectric conversion [12,13]. Based on Mott’s theory [14], the Seebeck coefficient of a typical metal can be expressed as follows:

_{B}is Boltzmann’s constant. According to this equation, the Seebeck coefficient is inversely proportional to the absolute value of the DOS at E

_{F}and proportional to its energy gradient. Therefore, by adjusting E

_{F}to the appropriate DOS position through carrier doping by elemental substitution, high Seebeck coefficients can be expected for both p- and n-type materials. In fact, it has been shown that high thermoelectric performance can be achieved by controlling the position of E

_{F}in the pseudogap in Heusler-type Fe

_{2}VAl with an ideal pseudogap-like electronic structure [15,16,17,18,19,20,21,22,23,24].

_{2}VAl

_{1-x}Si

_{x}compound [15], P = 5.4 × 10

^{−3}W/mK

^{2}, is larger than the power factor of n-type Bi

_{2}Te

_{3}material. In contrast, P = 2.3 × 10

^{−3}W/mK

^{2}for hole-doped Fe

_{2}V

_{1–x}Ti

_{x}Al [16]. However, the shortcomings of the Heusler compounds are that their high power factor ranges from room temperature to 400 K and their performance is low in the mid-temperature range of 400 to 600 K. In addition, cubic Heusler-type crystal structures have a high crystal symmetry, resulting in a thermal conductivity of approximately 25 W/mK

^{2}, [25] which is approximately 10 times higher than that of Bi

_{2}Te

_{3}. To further improve the thermoelectric performance, it is necessary to search for materials that form pseudogap-like electronic structures even with low thermal conductivity.

_{2}VAl, a wider pseudogap is formed in E

_{F}compared to Fe

_{2}VAl [26,27]. In addition, Ru

_{2}VAl, synthesized by Ramachandran et al., has a thermal conductivity of 10 W/mK

^{2}, which is approximately 40% lower than that of Fe

_{2}VAl [28]. Thus, Heusler-type Ru

_{2}VAl is a candidate for next-generation thermoelectric conversion materials, surpassing the thermoelectric performance of Fe

_{2}VAl.

_{2}VAl, the relationship between the electronic structure and thermoelectric conversion properties by photoelectron spectroscopy [29,30,31,32,33,34,35,36] and infrared (IR) spectroscopy [37,38] has been discussed in detail. The pseudogap width in Fe2VAl is actually much smaller than predicted by band calculations due to the strong electron correlation induced by the Fe atoms [39]. Based on the understanding of this difference in electronic structure, significant performance improvements have been achieved based on the material design utilizing the electronic structure of Fe

_{2}VAl. Therefore, knowledge of the electronic structure is essential for improving the performance of thermoelectric conversion materials. However, for Ru

_{2}VAl, only band-structure calculations are available and there are no experimental observations. Therefore, in this work, we discuss the potential of Ru

_{2}VAl as a thermoelectric conversion material by attempting to relate the electronic structure and thermoelectric conversion properties using first-principle calculations and experimental observations.

## 2. Theoretical and Experimental Methods

_{2}VAl and Ru

_{2}VAl were calculated using the full-potential linearized augmented plane-wave method and generalized gradient approximation as implemented in the WIEN2k package [39]. The equilibrium crystal structure was determined by minimizing the total energy, which was achieved by relaxing the lattice parameters. The convergence energy threshold was set to 0.0001 Ry. The theoretical thermoelectric properties were calculated using the Boltzmann transport equation within the constant relaxation time approximation using the BoltzTraP code based on the WIEN2k electronic structure [40].

_{2}VAl and Ru

_{2}VAl alloys were prepared by repeated arc melting of appropriate mixtures of 99.99% pure Fe, Ru and Al, and 99.9% pure V in an argon atmosphere. For hard X-ray photoemission spectroscopy (HAXPES) and IR measurements, 1 mm × 1 mm × 3 mm and 3 mm × 3 mm × 2 mm samples were used. Each sample was cut from a disk with a SiC blade, sealed in an evacuated quartz capsule, and annealed at 1273 K for 1 h and then at 673 K for 4 h, followed by furnace cooling.

_{2}standard sample. The VESTA program was used to simulate XRD patterns [42].

_{F}and total energy resolution were determined from the Fermi edge of the gold films. The total energy resolution of the HAXPES measurements was set to 310 meV at an excitation photon energy (hν) of 6916 eV.

## 3. Results and Discussions

_{2}VAl and Ru

_{2}VAl, respectively. As shown in Table 1, the lattice parameters and Young’s moduli were derived by fitting the obtained volume dependence of the total energy to the Birch–Murnaghan equation of state. Experimental lattice constants were calculated from XRD measurements on the fabricated materials. The calculated lattice parameters and Young’s moduli were in good agreement with previously reported calculations for both Fe

_{2}VAl [43,44] and Ru

_{2}VAl [26,27]. Comparing the experimental and calculated lattice parameters obtained from SR-XRD measurements, which will be discussed in the next session, the experimental lattice parameter is larger for Fe

_{2}VAl but comparable for Ru

_{2}VAl. In general, the lattice parameter calculated by the GGA method tends to be slightly larger than the experimental value. The discrepancy in the trend of the difference between the experimental and calculated lattice parameters of Ru

_{2}VAl is discussed in the next section. The calculated Young’s modulus is larger for Ru

_{2}VAl than for Fe

_{2}VAl, indicating a higher strength. This is expected to increase the overall strength of the module and improve its reliability when a thermoelectric conversion module is fabricated using Ru

_{2}VAl.

_{2}VAl and Ru

_{2}VAl, respectively. Both the DOSs exhibit a pseudogap-like feature with a sharp drop in DOS close to E

_{F}. The magnitude of the DOS at E

_{F}was similar for Fe

_{2}VAl and Ru

_{2}VAl. In Fe

_{2}VAl, the sizes of the hole and electron pockets were almost the same, whereas, in Ru

_{2}VAl, the hole pocket was larger than the electron pocket. As a result, the pseudogap structure of Ru

_{2}VAl is asymmetric between the valence and conduction band sides, with a gradual increase on the conduction band side, resulting in a wider pseudogap than that of Fe

_{2}VAl. Because of this larger pseudogap width in Ru

_{2}VAl compared to Fe

_{2}VAl, the peak temperature of the absolute Seebeck coefficient is expected to shift to a higher temperature. This shift is caused by the thermal excitation of carriers that are suppressed in Ru

_{2}VAl compared to Fe

_{2}VAl at high temperatures. To discuss the effect of the difference in DOS between Fe

_{2}VAl and Ru

_{2}VAl on the Seebeck coefficient and power factor, we next discuss the electronic transport properties calculated from the obtained electronic structures using the Boltzmann transport equation.

_{2}VAl and Ru

_{2}VAl calculated in the range 300–1000 K. Fe

_{2}VAl shows a maximum positive value of 140 μV/K, a maximum negative value of −110 μV/ K, and large Seebeck coefficients for both p- and n-type materials. In contrast, Ru

_{2}VAl has a large Seebeck coefficient for p-type materials with a maximum positive value of 70 μV/K but a small Seebeck coefficient value of −30 μV/K for n-type materials. Figure 2c,d show the chemical potential dependence of the calculated power factors for Fe

_{2}VAl and Ru

_{2}VAl in the 300–1000 K range. The power factor of the calculation is not directly comparable to the power factor of the experiment because the units are different from those of the experiment, since the relaxation time cannot be calculated in the band calculation. The Seebeck coefficient is generally smaller for Ru

_{2}VAl than for Fe

_{2}VAl, but the power factor is similar for both p-type materials with 125 × 10

^{10}W/K

^{2}cm s at 1000 K. The smaller n-type thermoelectric properties can be attributed to the larger hole pocket in Figure 1d. In other words, when the material is electron-doped, E

_{F}shifts to the conduction band side, but the large hole pocket reduces the slope of the DOS at E

_{F}, resulting in a smaller Seebeck coefficient and thus a smaller power factor in Ru

_{2}VAl.

_{2}VAl and Ru

_{2}VAl. The overall X-ray diffraction patterns of Fe

_{2}VAl and Ru

_{2}VAl were identified as a single-phase Heusler-type (L2

_{1}) structure. However, the diffraction peak due to the (111) mirror plane, which should be observed around 7°, was not observed for Ru

_{2}VAl. This result, together with the fact that the experimental and calculated lattice parameter are comparable, suggests that Ru

_{2}VAl may not be completely ordered L2

_{1}structure, but may have a partially disordered B2 structure. In order to obtain the L2

_{1}ordered phase of Ru

_{2}VAl in the future, it is necessary to explore for the optimum heat treatment conditions for ordering.

_{2}VAl and Ru

_{2}VAl for each core–electron state of the constituent elements in Fe

_{2}VAl and Ru

_{2}VAl. The observed photoelectron spectra can be entirely attributed to the core–electron states of the constituent elements, and oxygen and carbon adsorbed on the surface before the sample was introduced into the HAXPES chamber. The core–electron states of Al 1s (b), V 2p

_{3/2}(c), Fe 2p

_{3/2}(d), and Ru 3d

_{5/2}(e) in Fe

_{2}VAl and Ru

_{2}VAl are shown in Figure 4. Two peaks are observed near 1558 eV and 1562 eV for the Al 1s state. The broad peak observed at the high-binding-energy side is attributed to Al

_{2}O

_{3}associated with surface oxidation [45]. In contrast, no oxidation-induced peak structures are visible for the other constituent elements Ru, Fe, and V. In general, Al

_{2}O

_{3}is a stable surface oxide film, and when an Al

_{2}O

_{3}surface-oxide film is formed, oxygen is less likely to diffuse into the interior at high temperatures, improving the oxidation resistance [46]. Therefore, Ru

_{2}VAl, like Fe

_{2}VAl, is expected to have high thermal stability at high temperatures and can be adapted to thermoelectric conversion modules that are stable at high temperatures. The peak positions of Al 1s and V 2p

_{3/2}shift towards higher binding energies in Ru

_{2}VAl than in Fe

_{2}VAl. As shown in Figure 4b,c, the trend of this shift is consistent with the energy difference of the core–electron states expected from the all-electron calculations shown in Figure 1. The probability of the existence of the wave function in the Ru 4d state is more spatially extended than that in the Fe 3d state. Therefore, the DOS near E

_{F}in Ru

_{2}VAl is expected to be strongly hybridized than that in Fe

_{2}VAl, resulting in a wider pseudogap. Therefore, the peaks of the Al and V core electron states in Ru

_{2}VAl with stronger hybridization are located on the higher binding energy side compared to Fe

_{2}VAl, and this interpretation is consistent with the experimental and calculated results.

_{2}VAl and Fe

_{2}VAl. The calculated valence band photoelectron spectra were obtained by considering the photoexcitation cross-sections [47] at the excitation photon energies used for the HAXPES measurements for each constituent element in DOS in Figure 1c,d. The SR-XRD results suggest that Ru

_{2}VAl may not be a completely ordered-L2

_{1}structure, but the effect of the disordered-B2 structure on the electronic structure is considered to be very small because no broadening of the photoelectron spectrum was observed when comparing the photoelectron spectra of Ru

_{2}VAl and Fe

_{2}VAl. The photoelectron spectrum of Ru

_{2}VAl shows a large peak around 1.5 eV, which is not observed in Fe

_{2}VAl. This state is emphasized because the photoexcitation cross-section of Ru 4d state is larger than that of the Fe 3d state. Similar to Fe

_{2}VAl, Ru

_{2}VAl has a pseudogap electronic structure with low photoelectron intensity near the E

_{F}. The increase in the intensity of the photoelectron spectrum from the E

_{F}in Ru

_{2}VAl is comparable to that in Fe

_{2}VAl. This result is in agreement with the band calculation results, where the DOS on the valence band side is similar for both, and the difference in the pseudogap width is attributed to the different density of states on the conduction band side.

_{F}. Figure 6 shows the photon energy dependence of the reflectivity of Ru

_{2}VAl. Overall reflectivity showed a gradual decrease with increasing photon energy, reflecting the semi-metallic electronic structure. The overall shape of the temperature dependence of reflectivity remained unaltered, but the reflectivity gradually decreased with increasing measurement temperature. This result suggests a decrease in the number of carriers with decreasing measurement temperatures. This result is qualitatively consistent with the electronic resistivity measurement results, which show an increase in the electrical resistivity with increasing temperature. The reflectivity changes abruptly at about 0.03 eV and 0.2 eV, with the latter change in reflectivity energy being related to the width of the pseudogap based on previous IR results for Fe

_{2}VAl [39]. This suggests that Ru

_{2}VAl has a larger pseudogap than Fe

_{2}VAl, which is consistent with the band calculations. However, we did not observe an abrupt phenomenon in the DOS below 0.02 eV, as observed in the IR measurements of Fe

_{2}VAl. This may be due to the strong electronic correlation of Fe 3d in Fe

_{2}VAl; such a decrease in reflectivity was not observed in Ru

_{2}VAl, which has a stronger itinerant nature, as observed in SrM

_{4}Sb

_{12}(M = Fe, Ru) [48]. The pseudogap width of Ru

_{2}VAl is expected to be similar to the band calculation result due to the itinerant nature of Ru atoms. Therefore, Ru

_{2}VAl is expected to have a higher Seebeck coefficient peak at higher temperatures than Fe

_{2}VAl due to its wider pseudogap width, and is expected to be a thermoelectric conversion material with higher performance at higher temperatures than Fe

_{2}VAl.

## 4. Conclusions

_{2}VAl alloys as thermoelectric materials. First-principle calculations showed that the n-type power factor is smaller in Ru

_{2}VAl than in Fe

_{2}VAl, but the p-type power factor is comparable. Compared with Fe

_{2}VAl, Ru

_{2}VAl has a lower thermal conductivity owing to its higher density. Therefore, ZT, which is a performance index that includes the thermal conductivity, is expected to be large. A comparison of the electronic structures of Ru

_{2}VAl and Fe

_{2}VAl shows that Ru

_{2}VAl has a wider pseudogap, which was confirmed experimentally and theoretically. This result may be due to the shift of the peak temperature of the thermoelectric conversion property to the higher-temperature side of Ru

_{2}VAl. Based on these results, Ru

_{2}VAl is expected to be a candidate material for next-generation thermoelectric conversion materials with better thermoelectric conversion properties at higher temperatures compared to Fe

_{2}VAl.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Amin Bhuiyan, M.R.; Mamur, H.; Dilmaç, Ö.F. A Review on Performance Evaluation of Bi2Te3-based and some other Thermoelectric Nanostructured Materials. Curr. Nanosci.
**2021**, 17, 423–446. [Google Scholar] [CrossRef] - Chen, Y.; Hou, X.; Ma, C.; Dou, Y.; Wu, W. Review of Development Status of Bi
_{2}Te_{3}-Based Semiconductor Thermoelectric Power Generation. Adv. Mater. Sci. Eng.**2018**, 2018, 1210562. [Google Scholar] [CrossRef][Green Version] - Mamur, H.; Bhuiyan, M.R.A.; Korkmaz, F.; Nil, M. A review on bismuth telluride (Bi
_{2}Te_{3}) nanostructure for thermoelectric applications. Renew. Sust. Energ. Rev.**2018**, 82, 4159. [Google Scholar] [CrossRef] - Su, C.-H. Design, growth and characterization of PbTe-based thermoelectric materials. Prog. Cryst. Growth Charact. Mater.
**2019**, 65, 47–94. [Google Scholar] [CrossRef] - Nozariasbmarz, A.; Agarwal, A.; Coutant, Z.A.; Hall, M.J.; Liu, J.; Liu, R.; Malhotra, A.; Norouzzadeh, P.; Öztürk, M.C.; Ramesh, V.P.; et al. Thermoelectric silicides: A review. Jpn. J. Appl. Phys.
**2017**, 56, 05DA04. [Google Scholar] [CrossRef] - Basu, R.; Singh, A. High temperature Si–Ge alloy towards thermoelectric applications: A comprehensive review. Mater. Today Phys.
**2021**, 21, 100468. [Google Scholar] [CrossRef] - Li, Y.; Wang, G.; Akbari-Saatlu, M.; Procek, M.; Radamson, H.H. Si and SiGe Nanowire for Micro-Thermoelectric Generator: A Review of the Current State of the Art. Front. Mater.
**2021**, 8, 611078. [Google Scholar] [CrossRef] - Chen, Z.; lin, M.Y.; Xu, G.D.; Chen, S.; Zhang, J.H.; Wang, M.M. Hydrothermal synthesized nanostructure Bi–Sb–Te thermoelectric materials. J. Alloys Compd.
**2014**, 588, 384–387. [Google Scholar] [CrossRef] - Tan, M.; Deng, Y.; Hao, Y. Enhancement of thermoelectric properties induced by oriented nanolayer in Bi
_{2}Te_{2.7}Se_{0.3}columnar films. Mater. Chem. Phys.**2014**, 146, 153–158. [Google Scholar] [CrossRef] - Tan, M.; Hao, Y.; Wang, G. Improvement of thermoelectric properties induced by uniquely ordered lattice field in Bi
_{2}Se_{0.5}Te_{2.5}pillar array. J. Solid State Chem.**2014**, 215, 219–224. [Google Scholar] [CrossRef] - Ahmad, K.; Wan, C. Enhanced thermoelectric performance of Bi2Te3 through uniform dispersion of single wall carbon nanotubes. Nanotechnology
**2017**, 28, 415402. [Google Scholar] [CrossRef] [PubMed] - Nishino, Y.; Kato, M.; Asano, S.; Soda, K.; Hayasaki, M.; Mizutani, U. Semiconductorlike Behavior of Electrical Resistivity in Heusler-type Fe
_{2}VAl Compound. Phys. Rev. Lett.**1997**, 79, 1909. [Google Scholar] [CrossRef][Green Version] - Nishino, Y. The Science of Complex Alloy Phases; TMS: Warrendale, PA, USA, 2005; pp. 325–344. [Google Scholar]
- Mott, N.F.; Jones, H. The Theory of the Properties of Metals; Clarendon Press: Oxford, UK, 1936. [Google Scholar]
- Kato, H.; Kato, M.; Nishino, Y.; Mizutani, U.; Asano, S. Effect of Silicon Substitution on Thermoelectric Properties of Heusler-type Fe
_{2}VAl Alloy. J Jpn. Inst. Metal.**2001**, 65, 652. [Google Scholar] [CrossRef][Green Version] - Matsuura, H.; Nishino, Y.; Mizutani, U.; Asano, S. Doping Effects on Thermoelectric Properties of the Pseudogap Fe
_{2}VAl System. J Jpn. Inst. Metal.**2002**, 66, 767. [Google Scholar] [CrossRef][Green Version] - Lue, C.S.; Chen, C.F.; Lin, J.Y.; Yu, Y.T.; Kuo, Y.K. Thermoelectric properties of quaternary Heusler alloys Fe
_{2}VAl_{1−x}Si_{x}. Phys. Rev. B**2007**, 75, 064204. [Google Scholar] [CrossRef] - Vasundhara, M.; Srinivas, V.; Rao, V.V. Electronic transport in Heusler-type Fe
_{2}VAl_{1−x}M_{x}alloys (M = B,In,Si). Phys. Rev. B**2008**, 77, 224415. [Google Scholar] [CrossRef] - Mikami, M.; Tanaka, S.; Kobayashi, K. Thermoelectric properties of Sb-doped Heusler Fe
_{2}VAl alloy. J. Alloys Compd.**2009**, 484, 444. [Google Scholar] [CrossRef] - Terazawa, Y.; Mikami, M.; Itoh, T.; Takeuchi, T. Effects of Heavy Element Substitution on Electronic Structure and Lattice Thermal Conductivity of Fe
_{2}VAl Thermoelectric Material. J. Electron. Mater.**2012**, 41, 1348. [Google Scholar] [CrossRef] - Miyazaki, H.; Renard, K.; Inukai, M.; Soda, K.; Nishino, Y. Electronic structure of Heusler-type Fe
_{2}V_{1+x}Al_{1−x}thermoelectric materials. J. Electron Spectros. Relat. Rhenomena**2014**, 195, 185–188. [Google Scholar] [CrossRef] - Nishino, Y.; Tamada, Y. Doping effects on thermoelectric properties of the off-stoichiometric Heusler compounds Fe
_{2−x}V_{1+x}Al. J. Appl. Phys.**2014**, 115, 123707. [Google Scholar] [CrossRef] - Renard, K.; Mori, A.; Yamada, Y.; Tanaka, S.; Miyazaki, H.; Nishino, Y. Thermoelectric properties of the Heusler-type Fe
_{2}VTa_{x}Al_{1−x}alloys. J. Appl. Phys.**2014**, 115, 033707. [Google Scholar] [CrossRef] - Nishino, Y.; Kamizono, S.; Miyazaki, H.; Kimura, K. Effects of off-stoichiometry and Ti doping on thermoelectric performance of Fe
_{2}VAl Heusler compound. AIP Adv.**2019**, 9, 125003. [Google Scholar] [CrossRef][Green Version] - Miyazaki, H.; Tanaka, S.; Ide, N.; Soda, K.; Nishino, Y. Thermoelectric properties of Heusler-type off-stoichiometric Fe
_{2}V_{1+x}Al_{1−x}alloys. Mater. Res. Express**2014**, 1, 015901. [Google Scholar] [CrossRef] - Guezmir, A.; Rached, H.; Bentouaf, A.; Caid, M.; Benkhettou, N.; Rached, D.; Sidoumou, M. Theoretical insight of stabilities and optoelectronic features of Ru-based Heusler alloys: Ab-initio calculations. Comput. Condens. Matter.
**2021**, 28, e00573. [Google Scholar] [CrossRef] - Abbassa, H.; Hadjri-Mebarki, S.; Amrani, B.; Belaroussi, T.; Driss Khodja, K.; Aubert, P. Theoretical investigation of new Heusler alloys Ru
_{2}VGa_{1−x}Al_{x}. J. Alloys Compd.**2015**, 637, 557–563. [Google Scholar] [CrossRef] - Ramachandran, B.; Lin, Y.H.; Kuo, Y.K.; Kuo, C.N.; Gippius, A.A.; Lue, C.S. Thermoelectric properties of Heusler-type Ru
_{2}VAl_{1−x}Ga_{x}alloys. Intermetallics**2018**, 92, 36–41. [Google Scholar] [CrossRef] - Soda, K.; Mizutani, T.; Yoshimoto, O.; Yagi, S.; Mizutani, U.; Sumi, H.; Nishino, Y.; Yamada, Y.; Yokoya, T.; Shin, A.; et al. High-resolution photoelectron spectroscopyof Heusler-type Fe
_{2}VAl alloy. J. Synchrotron Radiat.**2002**, 9, 233. [Google Scholar] [CrossRef][Green Version] - Miyazaki, H.; Soda, K.; Yagi, S.; Kato, M.; Takeuchi, T.; Mizutani, U.; Nishino, Y. Surface and bulk electronic structures of Heusler-type Fe
_{2}VAl. J. Vac. Sci. Technol. A**2006**, 24, 1464. [Google Scholar] [CrossRef] - Miyazaki, H.; Soda, K.; Kato, M.; Yagi, S.; Takeuchi, T.; Nishino, Y. Soft X-ray photoemission study of the Heusler-type Fe
_{2}VAl_{1−z}Ge_{z}alloys. J. Electron Spectros. Relat. Rhenomena**2007**, 156-158, 347. [Google Scholar] [CrossRef] - Soda, K.; Harada, S.; Kato, M.; Yagi, S.; Inukai, M.; Miyazaki, H.; Sandaiji, Y.; Tamada, Y.; Tanaka, S.; Sugiura, T.; et al. Soft X-ray photoemission study of thermoelectric alloys Fe
_{2−x−y}Ir_{y}V_{1+x}Al and Fe_{2−x}V_{1+x−y}Ti_{y}Al. J. Electron Spectros. Relat. Rhenomena**2011**, 184, 236. [Google Scholar] [CrossRef] - Miyazaki, H.; Inukai, M.; Nishino, Y. Effect of Ta substitution on the electronic structure of Heusler-type Fe
_{2}VAl-based alloy. J. Appl. Phys.**2016**, 120, 125106. [Google Scholar] [CrossRef] - Miyazaki, H.; Tateishi, S.; Matsunami, M.; Soda, K.; Yamada, S.; Hamaya, K.; Nishino, Y. Direct observation of pseudo-gap electronic structure in the Heusler-type Fe
_{2}VAl thin film. J. Electron Spectros. Relat. Rhenomena**2019**, 232, 1–4. [Google Scholar] [CrossRef] - Asai, M.; Miyazaki, H.; Watanabe, K.; Yasui, A.; Takagi, Y.; Nishino, Y. Hard X-Ray Photoemission Study of Heusler-Type Fe
_{2−x}Re_{x}VAl Thermoelectric Compounds. Phys. Stat. Sol. (b)**2022**, 259, 2100567. [Google Scholar] [CrossRef] - Soda, K.; Ikedo, W.; Hayashi, T.; Shirakawa, T.; Miyazaki, H.; Nishino, Y. Hard X-Ray Photoemission Study on Bulk Electronic Structure of Heusler-Type Fe
_{2−x}V_{1+x}Al Alloys. J. Phys. Soc. Jpn.**2022**, 91, 064713. [Google Scholar] [CrossRef] - Okamura, H.; Kawahara, J.; Nanba, T.; Kimura, S.; Soda, K.; Mizutani, U.; Nishino, Y.; Kato, M.; Shimoyama, I.; Miura, H.; et al. Pseudogap Formation in the Intermetallic Compounds (Fe
_{1-x}V_{x})_{3}Al. Phys. Rev. Lett.**2000**, 84, 3674. [Google Scholar] [CrossRef] [PubMed][Green Version] - Feng, Y.; Rhee, J.Y.; Wiener, T.A.; Lynch, D.W.; Hubbard, B.E.; Sievers, A.J.; Schlagel, D.L.; Lograsso, T.A.; Miller, L.L. Physical properties of Heusler-like Fe
_{2}VAl. Phys. Rev. B**2001**, 63, 165109. [Google Scholar] [CrossRef][Green Version] - Blaha, P.; Schwarz, K.; Tran, F.; Laskowski, R.; Madsen, G.K.H.; Marks, L.D. WIEN2k: An APW+lo program for calculating the properties of solids. J. Chem. Phys.
**2020**, 152, 074101. [Google Scholar] [CrossRef][Green Version] - Madsen, G.K.H.; Singh, D.J. BoltzTraP. A code for calculating band-structure dependent quantities. Comput. Phys. Commun.
**2006**, 175, 67–71. [Google Scholar] [CrossRef][Green Version] - Kawaguchi, S.; Takemoto, M.; Osaka, K.; Nishibori, E.; Moriyoshi, C.; Kubota, Y.; Kuroiwa, Y.; Sugimoto, K. High-throughput powder diffraction measurement system consisting of multiple MYTHEN detectors at beamline BL02B2 of SPring-8. Rev. Sci. Instrum.
**2017**, 88, 085111. [Google Scholar] [CrossRef][Green Version] - Momma, K.; Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr.
**2011**, 44, 1272–1276. [Google Scholar] [CrossRef] - Xu, B.; Li, X.; Yu, G.; Zhang, J.; Ma, S.; Wang, Y.; Yi, L. The structural, elastic and thermoelectric properties of Fe
_{2}VAl at pressures. J. Alloys Compd.**2013**, 565, 22. [Google Scholar] [CrossRef] - Khalfa, M.; Khachai, H.; Chiker, F.; Baki, N.; Bougherara, K.; Yakoubi, A.; Murtaza, G.; Harmel, M.; Abu-Jafar, M.S.; Omran, S.B.; et al. Mechanical, electronic and thermodynamic properties of full Heusler compounds Fe
_{2}VX(X = Al, Ga). International J. Mod. Phys. B**2015**, 29, 1550229. [Google Scholar] [CrossRef] - Weiland, C.; Lysaght, P.; Price, J.; Huang, J.; Woicik, J.C. Hard x-ray photoelectron spectroscopy study of As and Ga out-diffusion in In
_{0.53}Ga_{0.47}As/Al_{2}O_{3}film systems. Appl. Phys. Lett.**2012**, 101, 061602. [Google Scholar] [CrossRef] - Song, T.T.; Yang, M.; Chai, J.W.; Callsen, M.; Zhou, J.; Yang, T.; Zhang, Z.; Pan, J.S.; Chi, D.Z.; Feng, Y.P.; et al. The stability of aluminium oxide monolayer and its interface with two-dimensional materials. Sci. Rep.
**2016**, 6, 29221. [Google Scholar] [CrossRef][Green Version] - Yeh, J.J.; Lindau, I. Atomic subshell photoionization cross sections and asymmetry parameters: 1 ≤ Z ≤ 103. At. Data Nucl. Data Tables
**1985**, 32, 1. [Google Scholar] [CrossRef] - Kimura, S.-I.; Im, H.; Mizuno, T.; Narazu, S.; Matsuoka, E.; Takabatake, T. Infrared study on the electronic structure of the alkaline-earth-filled skutterudites AM
_{4}Sb_{12}(A = Sr, Ba; M = Fe, Ru, Os). Phys. Rev. B**2007**, 75, 245106. [Google Scholar] [CrossRef]

**Figure 1.**Volume dependence of the total energy of Fe

_{2}VAl (

**a**) and Ru

_{2}VAl (

**b**). The curves are the result of fitting with the Birch–Murnaghan equation of state. Calculated density of states of Fe

_{2}VAl (

**c**) and Ru

_{2}VAl (

**d**). The inset shows the band structure along the Г–X line.

**Figure 2.**Chemical potential dependence of Seebeck coefficients and power factor for Fe

_{2}VAl (

**a**,

**c**) and Ru

_{2}VAl (

**b**,

**d**) calculated in the range of 300–1000 K.

**Figure 4.**Wide photoemission spectra (

**a**) and core level photoemission spectra of Al 1s (

**b**), V 2p

_{3/2}(

**c**), Fe 2p

_{3/2}(

**d**) and Ru 3d

_{3/2}(

**e**) states Fe

_{2}VAl and Ru

_{2}VAl.

**Figure 5.**Experimental (

**a**) and simulated (

**b**) photoemission spectra of Fe

_{2}VAl and Ru

_{2}VAl with hν= 6916 eV.

Fe_{2}VAl | Ru_{2}VAl | |
---|---|---|

Lattice parameter (nm) | 0.5709 | 0.6011 |

Experimental Lattice parameter (nm) | 0.5761 | 0.5994 |

Young module (GPa) | 223.05 | 256.03 |

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## Share and Cite

**MDPI and ACS Style**

Miyazaki, H.; Kimura, S.-i.; Onishi, K.; Hihara, T.; Yoshimura, M.; Ishii, H.; Mikami, M.; Nishino, Y. Relation between Electronic Structure and Thermoelectric Properties of Heusler-Type Ru_{2}VAl Compounds. *Crystals* **2022**, *12*, 1403.
https://doi.org/10.3390/cryst12101403

**AMA Style**

Miyazaki H, Kimura S-i, Onishi K, Hihara T, Yoshimura M, Ishii H, Mikami M, Nishino Y. Relation between Electronic Structure and Thermoelectric Properties of Heusler-Type Ru_{2}VAl Compounds. *Crystals*. 2022; 12(10):1403.
https://doi.org/10.3390/cryst12101403

**Chicago/Turabian Style**

Miyazaki, Hidetoshi, Shin-ichi Kimura, Kensuke Onishi, Takehiko Hihara, Masato Yoshimura, Hirofumi Ishii, Masashi Mikami, and Yoichi Nishino. 2022. "Relation between Electronic Structure and Thermoelectric Properties of Heusler-Type Ru_{2}VAl Compounds" *Crystals* 12, no. 10: 1403.
https://doi.org/10.3390/cryst12101403