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Seebeck coefficient of (Fe,V)3Al alloys
Journal of Alloys and Compounds 329 (2001) 63–68
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Seebeck coefficient of (Fe,V ) 3 Al alloys 1
Yoshinori Hanada , Ryosuke O. Suzuki*, Katsutoshi Ono Department of Energy Science and Technology, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606 -8501, Japan Received 9 May 2001; accepted 30 May 2001
Abstract The Seebeck coefficient in the ternary system (Fe,V ) 3 Al with D0 3 structure was measured. It increased modestly with 0–20 mol%V replacement. A large increase for 20–25 mol%V replacement and a subsequent sharp drop to a negative value was found at room temperature. The maximum and the minimum value were 175 mV/ K and 2165 mV/ K at Fe–23 mol%V–25 mol%Al and at Fe–27 mol%V–25 mol%Al, respectively. These values were better than the reported values in the Fe-based thermoelectric materials, but became smaller at higher temperatures. The compositional dependency of the Seebeck coefficient reflects the density of state at the Fermi level, because V atoms selectively replace Fe atoms in the ordered D0 3 crystal lattice. 2001 Elsevier Science B.V. All rights reserved. Keywords: Intermetallics; Semiconductors; Crystal structure; Electronic transport; Electronic band structure
1. Introduction Thermoelectric power generation employs low-temperature heat sources to create electricity. It is particularly intriguing as it offers long-term maintenance-free operation owing to the absence of moving parts. It holds the possibility of enabling large-scale electric power generation [1]. Regarding generator materials, the semiconductors have been developed because of high Seebeck coefficient, a. On the other hand, the iron-based alloys appear to be promising for their large-scale productivity. In the previous studies on Fe-based alloys [2–5], a relatively high Seebeck coefficient, a, could be obtained in the compositional range of the D0 3 crystal structure. The maximum and minimum Seebeck coefficients were recorded to be 145 mV/ K at Fe–21 mol%Al–20 mol%Si [3,4], and of 245 mV/ K at Fe–20 mol%V–25 mol%Si [5], respectively. For construction of a thermoelectric device, both the material with the high positive a and the one with the negative a are needed. Note that the Fe–V–Si system is known as one of the Heusler alloys, and its crystal structure is described as L2 1 A, a higher ordered phase than the D0 3 type.
*Corresponding author. Tel.: 181-75-753-5453; fax: 181-75-7534745. E-mail address: [email protected] (R.O. Suzuki). 1 Deceased.
The purpose of this work is to examine the Seebeck coefficient in the ternary Fe–V–Al alloys. In Fe 3 Al with the ordered D0 3 structure, V can replace Fe in a wide compositional range as shown in Fig. 1 [6]. The addition of V in Fe 3 Al stabilizes the D0 3 structure [7], and the existence of the intermetallic compound, Fe 2 VAl, was suggested as one of the Heusler alloys [8,9]. The negative
Fig. 1. Isothermal section of the Fe-rich Fe–V–Al ternary system at 773 K [6], where the closed circles show the compositions of the alloys used here.
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01677-2
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Y. Hanada et al. / Journal of Alloys and Compounds 329 (2001) 63 – 68
temperature dependency of the electrical resistivity, electronic properties and the abnormal magnetic properties were tentatively studied at the composition Fe 2 VAl [7–15].
2. Experimental Iron and vanadium (99.9% purity) were firstly melted in a MgO crucible using a high-frequency induction furnace. Under Ar gas atmosphere of 8310 4 Pa, silicon (99.9% purity) was added to the melt, considering the higher vapor pressure of pure silicon. After mixing sufficiently, about 0.5 kg ingots were cast in 10310 mm rectangular columns. They solidified with a typical columnar crystal growth from the mould surface. These cast samples were cut into 30–50 mm lengths and annealed in atmospheric pressure of Ar gas for 21.6 ks at 1573 K (near the melting point) for homogenization. They were quenched into water. The bulk composition was analyzed using an energy dispersive X-ray (EDX) analyzer in scanning electron microscopy (SEM). The analytical values for the homogenized samples were consistent with the nominal compositions within 0.5 mol%. The nominal compositions for the samples were, therefore, used for this paper and shown in Fig. 1. Some samples after homogenization were cooled to an annealing temperature for ordering, and after holding for 21.6 ks, they were quenched into water. The phases in the samples were identified by X-ray diffraction measurement (XRD) using CuK a radiation. The Seebeck coefficient, a, was measured using a longitudinal heat flow method. Since the details have been already reported [2–5], only a modification pertaining to the brittle samples will be given here. The temperatures were measured by two pairs of chromel–constantan thermocouples glued into two parallel ditches of 0.25 mm width and 1.0 mm depth at the sample surface. The values a were measured by two chromel leads and also by two constantan leads. When these two values agreed well, their average was adopted as a at a given temperature difference between two thermocouples. When the difference of a values was larger than 10%, the sample contained a local compositional segregation. It often occurred at the stoichiometric composition of Fe 2 VAl, even if a homogenizing annealing was made. These scattered data were not used. The average of the two temperatures was defined as the temperature where a was measured. This temperature difference was not larger than 100 K, although the small Seebeck coefficients in some alloys needed a larger temperature difference for higher accuracy. Many small cracks were introduced during heat cycles. Because heat conductivity is sensitive to these cracks, it could not be measured. Electrical resistivity was measured only at room temperature by standard four-probe method using the samples cut into 233320 mm.
3. Results
3.1. As-cast samples Fig. 2 shows the temperature dependencies of the Seebeck coefficients for the as-cast samples. In the compositional range from 0 to 20 mol%V, a was almost constant against temperature. However, in the higher compositional range, a approached zero when the temperature increased. Fig. 3 shows the Seebeck coefficients measured at 323 K. In the range from 0 to 20 mol%V, a had small positive values and its compositional dependency was weak. At the compositional range near Fe 2 VAl, a depended strongly on the composition and a changed from a high positive value to a large negative value, when the vanadium concentration increased. The minimum a was 2165.0 mV/ K at Fe–27 mol%V–25 mol%Al, while the maximum was 174.6 mV/ K at Fe–24 mol%V–25 mol%Al. Combining these values, Da becomes 240 mV/ K, which is 2.6 times larger than the values reported in the iron based alloys [4,5]. The lattice parameter in the (Fe,V ) 3 Al system decreased monotonically from Fe 3 Al to (Fe 2 V) 3 Al, corresponding to
Fig. 2. Temperature dependency of the Seebeck coefficient for the as-cast samples.
Y. Hanada et al. / Journal of Alloys and Compounds 329 (2001) 63 – 68
65
where the previous values of Nishino et al. [9–14] are also plotted. The resistivity of the as-cast samples increased as the vanadium concentration increased. The measured resistivity at 300 K agreed well with their data for the wellannealed samples that have the Heusler structure. The temperature dependency of electrical resistivity reflects semiconductor-like behavior, although it decreased monotonically from Fe 3 Al to Fe 2 VAl [9–14].
3.2. Annealed samples Fig. 5 shows the SEM images for the as-cast sample and for the sample annealed at 1573 K for 21.6 ks. The annealing removed the V segregation that was sometimes found in the as-cast sample. The X-ray diffraction measurement (XRD) for the annealed samples did not differ from that for the as-cast sample. The existence of the ordered D0 3 phase was verified for all the specimens
Fig. 3. Compositional dependency of the Seebeck coefficient, a, and its temperature dependency, da / dT.
the development of ordering in the D0 3 structure [7–15]. However, the Seebeck coefficients and their temperature dependencies as shown in Fig. 3 showed a characteristic change near the composition Fe 2 VAl. The resistivity at room temperature is shown in Fig. 4,
Fig. 4. Compositional dependency of electrical resistivity, r, and its temperature dependency, dr / dT, at 300 K.
Fig. 5. SEM images of cross-sections of Fe–23 mol%V–25 mol%Al alloys.
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analyzed, although the more ordered L2 1 A structure was hardly identified by XRD, partially because the ordered reflections were very weak. The Seebeck coefficients (a ) for the samples homogenized at 1573 K and for the samples subsequently annealed at 1473–873 K are shown in Fig. 6. The temperature dependency of a for the homogenized sample of Fe–25 mol%V–25 mol%Al was similar to that of 27 mol%V (Fig. 2). a scattered heavily in the annealed samples especially at the composition Fe 2 VAl, because a changes sharply due to the compositional fluctuation near Fe 2 VAl. The small compositional segregation in these samples may disturb reproducible measurements. Therefore, the annealing effect was studied at the offstoichiometric compositions, i.e. Fe–23 mol%V–25 mol%Al and Fe–27 mol%V–25 mol%Al. Fig. 7 shows the temperature dependency of a for the annealed samples. Generally a approached zero when the temperature increased. Fig. 8 summarizes the Seebeck coefficient measured at 350 K and 450 K for these annealed samples. a for the annealed 23 mol%V alloy was almost constant,
Fig. 7. Temperature dependency of the Seebeck coefficient for the annealed samples of 23 and 27 mol%V.
while a for the 27 mol%V alloy decreased for low temperature annealing.
4. Discussion
4.1. Compositional dependency of a
Fig. 6. Temperature dependency of the Seebeck coefficient for the annealed Fe–25 mol%V–25 mol%Al alloys.
Thermoelectric properties of metals can be explained by phonon drag and the diffusion of carriers. The former can be ignored in the temperature range examined. The thermal behavior of electrons and holes at the Fermi level, therefore, affects the Seebeck coefficient, a. In the range of 0–23 mol%V, enough electrons may exist in the conducting band at any temperature, and the number of the carriers does not change significantly even if heated. This metallic character is reflected in the low electric resistivity and in its weak temperature coefficients, as shown in Fig. 4. Therefore a adopts low values in this metallic region. Supposing that Fe 2 VAl is a semiconductor, the sharp
Y. Hanada et al. / Journal of Alloys and Compounds 329 (2001) 63 – 68
67
Fig. 9. Density of state (DOS) for Fe 2 VAl calculated by Botton et al. [16]. The energy scale is relative to the Fermi energy. Fig. 8. Seebeck coefficient measured at 300 K and 450 K for the samples annealed at Ta for 21.6 ks.
change of the Seebeck coefficient in the vicinity of 25 mol%V (Fig. 2) will be explained as follows: The large positive a and the large negative a should correspond to the holes in Fe 2 VAl as a positive carrier, and to the electrons in Fe 2 VAl as a negative carrier, respectively. When the vanadium replacement is not sufficient in Fe 2 VAl, Fe atoms supply the holes for conduction, because Fe has a lower valence than Al. When V is over-doped, V atoms supply the extra electrons. This qualitative explanation agrees with the compositional behavior of a. The carrier density and its mobility in the semiconductive Fe 2 VAl are sensitive to the temperature. The electric resistivity increases abruptly, and its temperature dependency becomes negative (Fig. 4). However, the resistivity and its temperature coefficient increase monotonously for the over-doped compositions. This does not suggest that Fe 2 VAl is an intrinsic semiconductor. The temperature dependency of the density of state (DOS) dominates the thermoelectric phenomenon in the metallic alloys [5]. Several calculations of DOS for Fe 2 VAl [16–18] showed that DOS has a minimum at the Fermi level (EF ) but does not reach zero. For example, Fig. 9 shows DOS calculated by Botton et al. [16]. Both the pseudogap for the majority spin state and that for the minority spin state are generated around EF only at the
composition of Fe 2 VAl in the (Fe,V ) 3 Al system [18], and it may play a role in the anomalous behavior for the compositional dependency of a. Note that no anomaly for a was found in (Fe,V ) 3 Si alloys [5], where no pseudogap was reported [18]. Because the temperature dependency of DOS was not clarified, the compositional dependency of a will be discussed phenomenologically here. When the temperature dependency of the carrier density or mobility at the conducting band is strong, the carriers at the hot end of the sample can move easily toward the cold end. Experimentally these temperature dependencies of Fe 2 VAl were stronger when the Seebeck coefficient was larger. This may be because the electron distribution shifts to the higher band and DOS below the Fermi level decreases, when the temperature rises. There is also another reason in that the sharp valley in DOS at the Fermi level disappears in the higher temperature region due to the thermally activated lattice vibrations, and that the gradient of DOS at the Fermi level becomes lower.
4.2. Annealing All the samples annealed or gradually cooled were identified as D0 3 ordered phase. It could not be judged only from XRD whether a part of these samples changed to the higher ordered structure, L2 1 A. We consider that the structure of the cast samples may adopt the L2 1 A type, and
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Y. Hanada et al. / Journal of Alloys and Compounds 329 (2001) 63 – 68
that the annealing did not change the degree of ordering. The Seebeck coefficient by annealing decreases due to decomposition of the super-saturated solid solution, probably because the equilibrium homogeneous solution range is narrow and the annealing homogenized the compositional fluctuation. If we could produce perfectly homogenized specimens, the over-doping or under-doping by vanadium against the Fe 2 VAl composition could be minimized.
5. Conclusion Their Seebeck coefficients in the ternary alloys (Fe,V ) 3 Al with D0 3 structure increased modestly with 0–20 mol%V replacement. a near the Fe 2 VAl composition changed significantly from a large positive value (175 mV/ K at Fe–23 mol%V–25 mol%Al) to a large negative value (2165 mV/ K at Fe–27 mol%V–25 mol%Al). Both values were larger than the values reported for the Febased alloys at room temperature, namely, 145 mV/ K (Fe–21 mol%Al–20 mol%Si) [3,4] and 245 mV/ K (Fe– 20 mol%V–25 mol%Si) [5]. a in the (Fe,V ) 3 Al alloys became smaller at higher temperatures. These alloys, offstoichiometric from the Fe 2 VAl composition, can be produced by casting, but their high a s were sensitive to annealing at higher temperatures.
Acknowledgements The authors thank Mr T. Tsuji for his advice throughout the experiments, Mr T. Unesaki and Mr I. Nakagawa for SEM–EDX analysis, Mr M. Hamura for XRD measurements, and Dr Y. Yamada at Shimane University for useful suggestions. This study was supported in part by Grants-
in-Aid for Scientific Research, under Contract No. 10555256, and as Guest-Scientist at the Japan Nuclear Cycle Development Institute (JNC).
References [1] K. Ono, R.O. Suzuki, J. Metals Dec (1998) 49–51. [2] K. Ono, R.O. Suzuki, R. Nakahashi, M. Shoda, Hetsu-to-Hagane´ 83 (2) (1997) 157–161. [3] M. Shoda, M. Kado, T. Tsuji, R.O. Suzuki, K. Ono, Tetsu-toHagane´ 84 (2) (1998) 154–158. [4] K. Ono, M. Kado, R.O. Suzuki, Steel Res. 69 (9) (1998) 387–390. [5] T. Tsuji, R.O. Suzuki, K. Ono, J. Jpn. Inst. Met. 63 (11) (1999) 1435–1442. [6] P.Z. Zhao, T. Kozakai, T. Miyazaki, J. Jpn. Inst. Met. 53 (3) (1989) 266–272. [7] E. Popiel, M. Tuszynski, W. Zarek, T. Rendecki, J. Less-Comm. Met. 146 (1989) 127–135. [8] D.E. Okpalugo, J.G. Booth, C.A. Faunce, J. Phys. F Met. Phys. 15 (1985) 681–692. [9] Y. Nishino, Intermetallics 8 (2000) 1233–1241. [10] Y. Nishino, S. Asano, T. Ogawa, Mat. Sci. Eng. A234–A236 (1997) 271–274. [11] Y. Nishino, C. Kumada, S. Asano, Scripta Mater. 36 (4) (1997) 461–466. [12] Y. Nishino, M. Kato, S. Asano, K. Soda, M. Hayasaki, U. Mizutani, Phys. Rev. Lett. 79 (1997) 1909–1912. [13] Y. Nishino, Mater. Sci. Eng. A258 (1998) 50–58. [14] M. Kato, Y. Nishino, S. Asano, S. Ohara, J. Jpn. Inst. Met. 62 (7) (1998) 669–674. [15] W. Zarek, T. Talik, J. Heimann, M. Kulpa, A. Winiarska, M. Neumann, J. Alloys Comp. 297 (1–2) (2000) 53–58. [16] G.A. Botton, Y. Nishino, C.J. Humphreys, Intermetallics 8 (2000) 1209–1214. [17] G.Y. Guo, G.A. Botton, Y. Nishino, J. Phys. Condens. Matter 10 (1998) L119–L126. [18] A. Bansil, S. Kaprzyk, P.E. Mijnarends, J. Tobola, Phys. Rev. B 60 (19) (1999) 13396–13412.
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Seebeck coefficient of (Fe,V ) 3 Al alloys 1
Yoshinori Hanada , Ryosuke O. Suzuki*, Katsutoshi Ono Department of Energy Science and Technology, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606 -8501, Japan Received 9 May 2001; accepted 30 May 2001
Abstract The Seebeck coefficient in the ternary system (Fe,V ) 3 Al with D0 3 structure was measured. It increased modestly with 0–20 mol%V replacement. A large increase for 20–25 mol%V replacement and a subsequent sharp drop to a negative value was found at room temperature. The maximum and the minimum value were 175 mV/ K and 2165 mV/ K at Fe–23 mol%V–25 mol%Al and at Fe–27 mol%V–25 mol%Al, respectively. These values were better than the reported values in the Fe-based thermoelectric materials, but became smaller at higher temperatures. The compositional dependency of the Seebeck coefficient reflects the density of state at the Fermi level, because V atoms selectively replace Fe atoms in the ordered D0 3 crystal lattice. 2001 Elsevier Science B.V. All rights reserved. Keywords: Intermetallics; Semiconductors; Crystal structure; Electronic transport; Electronic band structure
1. Introduction Thermoelectric power generation employs low-temperature heat sources to create electricity. It is particularly intriguing as it offers long-term maintenance-free operation owing to the absence of moving parts. It holds the possibility of enabling large-scale electric power generation [1]. Regarding generator materials, the semiconductors have been developed because of high Seebeck coefficient, a. On the other hand, the iron-based alloys appear to be promising for their large-scale productivity. In the previous studies on Fe-based alloys [2–5], a relatively high Seebeck coefficient, a, could be obtained in the compositional range of the D0 3 crystal structure. The maximum and minimum Seebeck coefficients were recorded to be 145 mV/ K at Fe–21 mol%Al–20 mol%Si [3,4], and of 245 mV/ K at Fe–20 mol%V–25 mol%Si [5], respectively. For construction of a thermoelectric device, both the material with the high positive a and the one with the negative a are needed. Note that the Fe–V–Si system is known as one of the Heusler alloys, and its crystal structure is described as L2 1 A, a higher ordered phase than the D0 3 type.
*Corresponding author. Tel.: 181-75-753-5453; fax: 181-75-7534745. E-mail address: [email protected] (R.O. Suzuki). 1 Deceased.
The purpose of this work is to examine the Seebeck coefficient in the ternary Fe–V–Al alloys. In Fe 3 Al with the ordered D0 3 structure, V can replace Fe in a wide compositional range as shown in Fig. 1 [6]. The addition of V in Fe 3 Al stabilizes the D0 3 structure [7], and the existence of the intermetallic compound, Fe 2 VAl, was suggested as one of the Heusler alloys [8,9]. The negative
Fig. 1. Isothermal section of the Fe-rich Fe–V–Al ternary system at 773 K [6], where the closed circles show the compositions of the alloys used here.
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01677-2
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Y. Hanada et al. / Journal of Alloys and Compounds 329 (2001) 63 – 68
temperature dependency of the electrical resistivity, electronic properties and the abnormal magnetic properties were tentatively studied at the composition Fe 2 VAl [7–15].
2. Experimental Iron and vanadium (99.9% purity) were firstly melted in a MgO crucible using a high-frequency induction furnace. Under Ar gas atmosphere of 8310 4 Pa, silicon (99.9% purity) was added to the melt, considering the higher vapor pressure of pure silicon. After mixing sufficiently, about 0.5 kg ingots were cast in 10310 mm rectangular columns. They solidified with a typical columnar crystal growth from the mould surface. These cast samples were cut into 30–50 mm lengths and annealed in atmospheric pressure of Ar gas for 21.6 ks at 1573 K (near the melting point) for homogenization. They were quenched into water. The bulk composition was analyzed using an energy dispersive X-ray (EDX) analyzer in scanning electron microscopy (SEM). The analytical values for the homogenized samples were consistent with the nominal compositions within 0.5 mol%. The nominal compositions for the samples were, therefore, used for this paper and shown in Fig. 1. Some samples after homogenization were cooled to an annealing temperature for ordering, and after holding for 21.6 ks, they were quenched into water. The phases in the samples were identified by X-ray diffraction measurement (XRD) using CuK a radiation. The Seebeck coefficient, a, was measured using a longitudinal heat flow method. Since the details have been already reported [2–5], only a modification pertaining to the brittle samples will be given here. The temperatures were measured by two pairs of chromel–constantan thermocouples glued into two parallel ditches of 0.25 mm width and 1.0 mm depth at the sample surface. The values a were measured by two chromel leads and also by two constantan leads. When these two values agreed well, their average was adopted as a at a given temperature difference between two thermocouples. When the difference of a values was larger than 10%, the sample contained a local compositional segregation. It often occurred at the stoichiometric composition of Fe 2 VAl, even if a homogenizing annealing was made. These scattered data were not used. The average of the two temperatures was defined as the temperature where a was measured. This temperature difference was not larger than 100 K, although the small Seebeck coefficients in some alloys needed a larger temperature difference for higher accuracy. Many small cracks were introduced during heat cycles. Because heat conductivity is sensitive to these cracks, it could not be measured. Electrical resistivity was measured only at room temperature by standard four-probe method using the samples cut into 233320 mm.
3. Results
3.1. As-cast samples Fig. 2 shows the temperature dependencies of the Seebeck coefficients for the as-cast samples. In the compositional range from 0 to 20 mol%V, a was almost constant against temperature. However, in the higher compositional range, a approached zero when the temperature increased. Fig. 3 shows the Seebeck coefficients measured at 323 K. In the range from 0 to 20 mol%V, a had small positive values and its compositional dependency was weak. At the compositional range near Fe 2 VAl, a depended strongly on the composition and a changed from a high positive value to a large negative value, when the vanadium concentration increased. The minimum a was 2165.0 mV/ K at Fe–27 mol%V–25 mol%Al, while the maximum was 174.6 mV/ K at Fe–24 mol%V–25 mol%Al. Combining these values, Da becomes 240 mV/ K, which is 2.6 times larger than the values reported in the iron based alloys [4,5]. The lattice parameter in the (Fe,V ) 3 Al system decreased monotonically from Fe 3 Al to (Fe 2 V) 3 Al, corresponding to
Fig. 2. Temperature dependency of the Seebeck coefficient for the as-cast samples.
Y. Hanada et al. / Journal of Alloys and Compounds 329 (2001) 63 – 68
65
where the previous values of Nishino et al. [9–14] are also plotted. The resistivity of the as-cast samples increased as the vanadium concentration increased. The measured resistivity at 300 K agreed well with their data for the wellannealed samples that have the Heusler structure. The temperature dependency of electrical resistivity reflects semiconductor-like behavior, although it decreased monotonically from Fe 3 Al to Fe 2 VAl [9–14].
3.2. Annealed samples Fig. 5 shows the SEM images for the as-cast sample and for the sample annealed at 1573 K for 21.6 ks. The annealing removed the V segregation that was sometimes found in the as-cast sample. The X-ray diffraction measurement (XRD) for the annealed samples did not differ from that for the as-cast sample. The existence of the ordered D0 3 phase was verified for all the specimens
Fig. 3. Compositional dependency of the Seebeck coefficient, a, and its temperature dependency, da / dT.
the development of ordering in the D0 3 structure [7–15]. However, the Seebeck coefficients and their temperature dependencies as shown in Fig. 3 showed a characteristic change near the composition Fe 2 VAl. The resistivity at room temperature is shown in Fig. 4,
Fig. 4. Compositional dependency of electrical resistivity, r, and its temperature dependency, dr / dT, at 300 K.
Fig. 5. SEM images of cross-sections of Fe–23 mol%V–25 mol%Al alloys.
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analyzed, although the more ordered L2 1 A structure was hardly identified by XRD, partially because the ordered reflections were very weak. The Seebeck coefficients (a ) for the samples homogenized at 1573 K and for the samples subsequently annealed at 1473–873 K are shown in Fig. 6. The temperature dependency of a for the homogenized sample of Fe–25 mol%V–25 mol%Al was similar to that of 27 mol%V (Fig. 2). a scattered heavily in the annealed samples especially at the composition Fe 2 VAl, because a changes sharply due to the compositional fluctuation near Fe 2 VAl. The small compositional segregation in these samples may disturb reproducible measurements. Therefore, the annealing effect was studied at the offstoichiometric compositions, i.e. Fe–23 mol%V–25 mol%Al and Fe–27 mol%V–25 mol%Al. Fig. 7 shows the temperature dependency of a for the annealed samples. Generally a approached zero when the temperature increased. Fig. 8 summarizes the Seebeck coefficient measured at 350 K and 450 K for these annealed samples. a for the annealed 23 mol%V alloy was almost constant,
Fig. 7. Temperature dependency of the Seebeck coefficient for the annealed samples of 23 and 27 mol%V.
while a for the 27 mol%V alloy decreased for low temperature annealing.
4. Discussion
4.1. Compositional dependency of a
Fig. 6. Temperature dependency of the Seebeck coefficient for the annealed Fe–25 mol%V–25 mol%Al alloys.
Thermoelectric properties of metals can be explained by phonon drag and the diffusion of carriers. The former can be ignored in the temperature range examined. The thermal behavior of electrons and holes at the Fermi level, therefore, affects the Seebeck coefficient, a. In the range of 0–23 mol%V, enough electrons may exist in the conducting band at any temperature, and the number of the carriers does not change significantly even if heated. This metallic character is reflected in the low electric resistivity and in its weak temperature coefficients, as shown in Fig. 4. Therefore a adopts low values in this metallic region. Supposing that Fe 2 VAl is a semiconductor, the sharp
Y. Hanada et al. / Journal of Alloys and Compounds 329 (2001) 63 – 68
67
Fig. 9. Density of state (DOS) for Fe 2 VAl calculated by Botton et al. [16]. The energy scale is relative to the Fermi energy. Fig. 8. Seebeck coefficient measured at 300 K and 450 K for the samples annealed at Ta for 21.6 ks.
change of the Seebeck coefficient in the vicinity of 25 mol%V (Fig. 2) will be explained as follows: The large positive a and the large negative a should correspond to the holes in Fe 2 VAl as a positive carrier, and to the electrons in Fe 2 VAl as a negative carrier, respectively. When the vanadium replacement is not sufficient in Fe 2 VAl, Fe atoms supply the holes for conduction, because Fe has a lower valence than Al. When V is over-doped, V atoms supply the extra electrons. This qualitative explanation agrees with the compositional behavior of a. The carrier density and its mobility in the semiconductive Fe 2 VAl are sensitive to the temperature. The electric resistivity increases abruptly, and its temperature dependency becomes negative (Fig. 4). However, the resistivity and its temperature coefficient increase monotonously for the over-doped compositions. This does not suggest that Fe 2 VAl is an intrinsic semiconductor. The temperature dependency of the density of state (DOS) dominates the thermoelectric phenomenon in the metallic alloys [5]. Several calculations of DOS for Fe 2 VAl [16–18] showed that DOS has a minimum at the Fermi level (EF ) but does not reach zero. For example, Fig. 9 shows DOS calculated by Botton et al. [16]. Both the pseudogap for the majority spin state and that for the minority spin state are generated around EF only at the
composition of Fe 2 VAl in the (Fe,V ) 3 Al system [18], and it may play a role in the anomalous behavior for the compositional dependency of a. Note that no anomaly for a was found in (Fe,V ) 3 Si alloys [5], where no pseudogap was reported [18]. Because the temperature dependency of DOS was not clarified, the compositional dependency of a will be discussed phenomenologically here. When the temperature dependency of the carrier density or mobility at the conducting band is strong, the carriers at the hot end of the sample can move easily toward the cold end. Experimentally these temperature dependencies of Fe 2 VAl were stronger when the Seebeck coefficient was larger. This may be because the electron distribution shifts to the higher band and DOS below the Fermi level decreases, when the temperature rises. There is also another reason in that the sharp valley in DOS at the Fermi level disappears in the higher temperature region due to the thermally activated lattice vibrations, and that the gradient of DOS at the Fermi level becomes lower.
4.2. Annealing All the samples annealed or gradually cooled were identified as D0 3 ordered phase. It could not be judged only from XRD whether a part of these samples changed to the higher ordered structure, L2 1 A. We consider that the structure of the cast samples may adopt the L2 1 A type, and
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that the annealing did not change the degree of ordering. The Seebeck coefficient by annealing decreases due to decomposition of the super-saturated solid solution, probably because the equilibrium homogeneous solution range is narrow and the annealing homogenized the compositional fluctuation. If we could produce perfectly homogenized specimens, the over-doping or under-doping by vanadium against the Fe 2 VAl composition could be minimized.
5. Conclusion Their Seebeck coefficients in the ternary alloys (Fe,V ) 3 Al with D0 3 structure increased modestly with 0–20 mol%V replacement. a near the Fe 2 VAl composition changed significantly from a large positive value (175 mV/ K at Fe–23 mol%V–25 mol%Al) to a large negative value (2165 mV/ K at Fe–27 mol%V–25 mol%Al). Both values were larger than the values reported for the Febased alloys at room temperature, namely, 145 mV/ K (Fe–21 mol%Al–20 mol%Si) [3,4] and 245 mV/ K (Fe– 20 mol%V–25 mol%Si) [5]. a in the (Fe,V ) 3 Al alloys became smaller at higher temperatures. These alloys, offstoichiometric from the Fe 2 VAl composition, can be produced by casting, but their high a s were sensitive to annealing at higher temperatures.
Acknowledgements The authors thank Mr T. Tsuji for his advice throughout the experiments, Mr T. Unesaki and Mr I. Nakagawa for SEM–EDX analysis, Mr M. Hamura for XRD measurements, and Dr Y. Yamada at Shimane University for useful suggestions. This study was supported in part by Grants-
in-Aid for Scientific Research, under Contract No. 10555256, and as Guest-Scientist at the Japan Nuclear Cycle Development Institute (JNC).
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