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Microstructural evolution and stability of (Fe1−xVx)3Al alloys in relation to the electronic structure
Intermetallics 8 (2000) 1209±1214
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Microstructural evolution and stability of (Fe1ÿxVx)3Al alloys in relation to the electronic structure G.A. Botton a,*, Y. Nishino b, C.J. Humphreys c a
Materials Technology Laboratory, Natural Resources Canada, 568 Booth Street, Ottawa K1A 0G1, Canada Department of Materials Science and Engineering, Nagoya Institute of Technology, Showa-Ku, Nagoya 466-8555, Japan c Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK b
Received 13 August 1999; accepted 15 February 2000
Abstract The evolution of the microstructure of (Fe1ÿxVx)3Al alloys in the D03 structure has been studied as function of composition by transmission electron microscopy. The domain size of the D03 structure signi®cantly increases as V is added to the alloy. An increase in long range order parameter is also shown. This microstructural evolution is discussed in terms of the increased second nearest neighbor interactions induced by the V additions. Electronic structure calculations are also presented in this paper. The density of states shows a strong pseudogap for the Fe2VAl compound and thus strong hybridization induced by the alloying element. This electronic structure feature is discussed in terms of interesting physical properties of the system and in relation to the density of states, stability and properties of similar compounds [Fe2MAl (M=Ti, Cr, Mn)]. Electron energy loss spectra of the Al L2ÿ3 edge show that the strong hybridization induced by V does not aect the unoccupied Al s and d states. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Aluminides, miscellaneous; B. Bonding; D. Defects: antiphase domains; E. Electronic structure, calculation; E. Phase stability, prediction; F. Spectroscopic methods, various
1. Introduction Intermetallic materials are potential candidates for high temperature structural applications. Iron aluminides based on the Fe3Al system in particular are of great interest as they present an anomalous peak in the yield stress and show high temperature strength and excellent oxidation and corrosion resistance. Improvements in the mechanical properties for these alloys can be reached by suitable ternary alloying additions that also extend the temperature range over which the D03 structure is stable over the B2 structure. Additions of Ti, V and Mo have been shown to be very eective in increasing the D03±B2 transformation temperature and in changing the lattice parameter [1]. For the (Fe1ÿxVx)3Al system there are signi®cant improvements in high temperature strength that extends up to 1000 K and at the same time there are remarkable changes in physical properties. Nishino and coworkers have reported for (Fe1ÿxVx)3Al an anomalous temperature dependence of the electrical resistivity and magnetic properties [2,3] near the Fe2VAl (a Heusler-type phase) composition with strong similarities to the * Corresponding author. E-mail address: [email protected] (G.A. Botton).
behavior observed in ``heavy-fermion'' compounds. The Heusler-type Fe2VAl exhibits a semiconductor-like negative temperature dependence of the resistivity. Although the electronic structure calculations [4,5] and spectroscopic data of occupied electronic states [6] give some insight into the measured physical properties, no microstructural observations and correlation with other properties have been reported to date. The aim of the present paper is to present some initial results on the microstructural evolution of the alloy as a function of composition and link the observations to changes in electronic structure and physical properties. A comparison of the electronic structure of Fe2VAl with other Heusler alloys Fe2MAl (M= Ti, Cr, Mn) will also be presented in order to gain a better insight into the properties of the Heusler-type Fe2VAl phase. Energy loss spectra showing unoccupied electronic states are also shown and discussed in terms of the hybridization of electronic states of dierent atoms. 2. Experimental methods The pseudo-binary alloys (Fe1ÿxVx)3Al were prepared by repeated melting of a mixture of the 99.99% pure
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components of Fe and Al and 99.7% pure V in an arc furnace. Since the weight loss after melting was less than 0.3%, the nominal composition was accepted as being accurate. The ingots were homogenized at 1273 K for more than 170 ks in vacuum. Specimens (approximately 20101 mm3 in size) cut from ingots were held at 1273 K for 3.6 ks and annealed for D03 ordering at 673 K for 14.4 ks in an evacuated quartz capsule. Sample preparation for TEM was carried out by mechanically polishing the annealed specimens, down to 200 mm, followed by cutting 3 mm diameter disks with the spark erosion method to minimize mechanical damage. After ®nal mechanical polishing, electron transparency was achieved by electropolishing the disks in 5% perchloric acid in ethanol. TEM observations were carried out on Philips CM30 and CM20-FEG electron microscopes using 111 superlattice re¯ections near the 110 zone axis in order to observe the antiphase domain boundaries. The electronic structure calculations presented in this work were carried out using the linear mun tin orbital (LMTO) method [7] using the local density approximation. For Fe2VAl, the density of states (DOS) obtained with this method was comparable to that obtained with the full-potential linear augmented plane wave (FLAPW) technique of Guo et al. [4]. For the series of compound Fe2TiAl, Fe2VAl, Fe2CrAl and Fe2MnAl, the experimental lattice parameters (for Fe2TiAl a=0.588 nm [8], for Fe2VAl a=0.576 nm [2], for Fe2CrAl a=0.578 nm [8] and for Fe2MnAl a=0.580 nm [9]) were used in the calculation of the electronic structure. For all calculations, convergence with respect to the number of k points was checked and the number of divisions in the Brillouin zone was set at 24. 3. Results and discussion 3.1. Microstructural observations The D03 domains evolve dramatically over the range of composition studied in the (Fe1ÿxVx)3Al system (Fig. 1). The antiphase boundaries are very irregular in shape with no preferential crystallographic orientation. Although the domain size evolution is clearly evident from the electron micrographs, it is dicult to evaluate quantitatively the domain size and only a qualitative description of the APB separation is given in this paper. For the pure Fe3Al (Fig. 1a), the average separation of APB boundaries is approximately 0.3±0.4 mm and as V is introduced in the structure the separation of the APB increases. For x=0.1 (Fig. 1b) the APB separation is typically 0.5±1.5 mm and for x=0.18 (Fig. 1c) it is, on the average, larger than 1.5 mm. The increase in the D03 domain size has also been reported for the additions of Ti [10,11] and Mo [12]. The most important feature of the evolution is that at x=0.2 and x=0.33 (i.e. for the Heusler-type
phase Fe2VAl) the closed domains are no longer observed. Some residual occasional contrast is observed for x=0.2 (Fig. 1d) but microanalysis did not resolve any chemical inhomogeneities. At the composition of Fe2VAl, the alloy is perfectly homogenous with no second phase precipitation visible. Since both the formation and growth of domains are diusion-controlled processes taking place below the D03-B2 transformation temperature Tc, a higher value of Tc could lead to a greater rate of domain coarsening, and thus to a larger domain size [10]. Indeed, the value of Tc for the V addition is 200±400 K higher than that of Fe3Al, which may be enough to allow the domains to grow to larger sizes as seen in Fig. 1. Since the ordering within the domains is also dependent on diusion, the addition of V could give rise to an increase in the degree of D03 long-range order. In fact, as shown in Fig. 2, there is a continuous increase in the D03 long range order parameter as a function of composition and a decrease in the lattice parameter up to the Fe2VAl composition and then a rapid increase above the Heusler phase composition [13]. Although the replacement of smaller Fe atoms with larger V atoms would give an increase in the lattice parameter, the lattice contraction occurs presumably because of an enhanced cohesion due to the D03 ordering. These microstructural and diraction observations strongly suggest an increase in stability of the D03 structure with the addition of V up to the Fe2VAl composition. These results correlate with the reports of Rimlinger [14] who found a linear relationship between the degree of long range order and antiphase domain size. The stabilization of the D03 structure and thus Fe3Al type ordering has been linked to an increase in second nearest neighbor interactions [15,16] and this eect is likely to occur with the addition of V. In fact V, being an early transition metal has more delocalized d orbitals than Fe and the late transition aluminides (as compared to a simple atomic size eect). This suggestion is supported by the fact that the increase in Tc for the (Fe1ÿx Tix)3Al system is much stronger since d orbitals are even further delocalized in Ti. An additional factor contributing to the stabilization is the electron per atom (e/a) ratio which has been shown previously to be linked to the variation of Tc for the various transition metal additions [3]. Despite the sharpest increase in Tc for the Ti addition, the variation of Tc becomes close to that for the V addition when plotted as a function of e/a. This observation will be linked, later in this paper, to the electronic structure variations in the various alloys based on the (Fe1ÿxMx)3Al (M=Ti, Cr, Mn) system. 4. Electronic structure The electronic structure of the system also shows very interesting features and supports the stabilization eects discussed above. With respect to the DOS of Fe3Al (Fig.
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Fig. 1. Transmission electron micrographs of the (Fe1ÿxVx)3Al alloys as a function of composition: (a) Fe3Al, (b) (Fe0.9V0.1)3Al, (c) (Fe0.82V0.18)3Al, and (d) (Fe0.8V0.2)3Al. All micrographs have been obtained at the same magni®cation.
3a), the Fe2VAl DOS shows a very pronounced pseudogap right at the Fermi level (EF) (Fig. 3b) separating bonding states from antibonding states. The creation of such a pseudogap has been associated in general to very strong hybridization of the s and p bands with the d bands [17,18] which would also result in increased stability of the D03 structure. A similar pseudogap and semiconducting properties have been shown for Al2Ru and Ga2Ru [17] and attributed to strong hybridization. The clear separation of the antibonding states from the completely full bonding states is also an indication of a maximum in cohesive energy (see, for example [17,19]) and would also explain the decrease in lattice parameter as a
function of composition. Finally, the low DOS at EF and the pseudogap can give some insight into the conductivity properties of the Fe2VAl compound shown in the literature [2,3]. Guo et al. [4] have shown that Fe2VAl is a semimetal and the predicted Fermi surface consists of hole pockets (originating from the Fe 3d bands) and electron pockets (originating from the V 3d bands). These features and the low density of states at EF were shown to be factors contributing to the semiconducting behavior of the temperature dependent resistivity measurements [4]. In order to understand why this spectacular physical behavior occurs with the V addition (stability, microstructure, resistivity, etc.), it is of crucial importance to
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compare this system with other transition metal additions where such eects are not as marked. Fig. 4 shows the total DOS calculated for a series of the Heusler alloys: (a) Fe2TiAl, (b) Fe2CrAl, (c) Fe2MnAl (for Fe2VAl, see
Fig. 2. Lattice parameter and order parameter in the (Fe1ÿxVx)3Al system as a function of composition x. Data taken from Kato et al. [13].
Fig. 3b). For these initial calculations we assumed that all the alloys are nonmagnetic although Fe2CrAl and Fe2MnAl may be ferromagnetic alloys. Our result for Fe2TiAl is in agreement with that of Weinert and Watson [5]. For Fe2MnAl a direct comparison with the literature [20] is not possible as a dierent lattice parameter (also dierent from the experimental value [9]) was used and ferromagnetic calculations were done. When compared to the DOS of Fe2TiAl, there are similarities for the overall shape including the pseudogap (Fig. 4a) but the Fermi energy is not situated right in the pseudogap. The DOS at EF is in fact very high and this explains why the semiconductor temperature dependence of the resistivity eect is not as strong in (Fe1ÿxTix)3Al as in (Fe1ÿxVx)3Al (see, for example, the resistivity curves of Nishino [3]). In addition to this eect, the lattice parameter reduction observed for (Fe1ÿxVx)3Al is not observed in this system although the change is much smaller than predicted by a simple bcc solid solution. Although hybridization is strong, the separation of the occupied states from the unoccupied states is not optimal as the bonding states are not completely full. As the Ti is replaced by V, Cr and Mn the DOS changes are important (Figs. 3b, 4b and c, respectively). The ``pseudogap'' narrows while moving down relative to EF and the depth decreases so that, for Fe2CrAl and Fe2MnAl the eect is almost no longer observed. The stabilization eect in fact also decreases for Cr and Mn additions as compared to Ti and V alloying. For Cr and Mn additions, the D03±B2 transformation temperature is in fact almost unchanged. This eect would also correlate with the localization of the d orbitals with increasing atomic number in the transition metal series. The variation of the DOS at EF is also interesting. It is a minimum for Fe2VAl and particularly high for Fe2CrAl and Fe2MnAl. Ferromagnetic calculations for Fe2MnAl
Fig. 3. Density of states (DOS) for (a) Fe3Al and (b) Fe2VAl. The energy scale is relative to the Fermi energy.
G.A. Botton et al. / Intermetallics 8 (2000) 1209±1214
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from the literature [20] also show a high DOS at EF. As it has been generally deduced from electronic structure calculations of phase stability [21], this high DOS at EF also suggests that the compounds would not be very stable. This could, in part, explain the lack of a single phase domain in the D03 structure for (Fe1ÿxCrx)3Al [22]. Also the site preference data for Cr and Mn are still incomplete as reviewed elsewhere [3]. Further calculations as a function of lattice parameter and total energy would be necessary to con®rm this eect. The important changes in the DOS of the series also suggest that the rigid band approximation is not valid to explain the electronic structure dierences. This eect is additional evidence that the hybridization eects in these alloys vary very strongly. These changes in hybridization and therefore the dierences in the resulting pseudogap for the series of compounds give therefore further insight into the electron per atom (e/a) variation reported above and discussed by Nishino [3]. When hybridization is strong, the stabilization eect is strongly varying with e/ a (and therefore to the position of the Fermi energy within the band) and is weakly dependent on the dopant atomic number. When the pseudogap is almost non-existent, and therefore hybridization is weak, the stabilization is also weak. Energy loss spectra of the Al L23 edge for Fe3Al and (Fe0.8V0.2)3Al (Fig. 5) are very dierent from those observed in pure Al (see, for example, Botton et al. [23]). This edge probes the unoccupied s and d states at the Al site. As in transition metal aluminides, the hybridization of the Al 3s (and 4s) electrons with the Fe d electrons is present (see, for example, the discussion on EELS spectra in late transition metal aluminides [23]). With the addition of V, little changes are observed and this preliminary result suggests that the hybridization due to V either
Fig. 4. Density of states (DOS) for (a) Fe2TiAl, (b) Fe2CrAl and (c) Fe2MnAl.
Fig. 5. Electron energy-loss spectra of the Al L2ÿ3 edge for Fe3Al and (Fe0.8 V0.2)3Al. The two spectra have been shifted vertically for clarity.
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occurs with Al p states (and thus, because of the EELS transition selection rules, not visible at the Al L23 edge) or with the Fe atoms. Further work is in progress to analyze the EELS spectra of Fe2VAl and model the spectra with ab-initio electronic structure methods. 5. Conclusion We have presented the microstructural evolution of the (Fe1ÿxVx)3Al compound and analyzed the results based on electronic structure calculations. A rapid increase of D03 domain size is observed and has been correlated to measurements of long range order parameter. The increased stability deduced from the evolution of domain sizes and from the long-range order parameter of this structure has been linked to strong hybridization in the bonding induced by the presence of V. This strong hybridization is shown in the density of states calculated from ab-initio electronic structure methods by the presence of a strong pseudogap. This pseudogap evolves signi®cantly when the Ti, Cr and Mn are substituted for V. Several physical properties (lattice parameter, resistivity behavior, stability, and energy loss spectra) have been discussed in terms of the electronic structure calculations. The results indicate that the signi®cant dierences in properties observed with various alloying additions (Ti, V, Cr and Mn) can be correlated to the strong hybridization dierences between the various compounds. These dierences in bonding give new insight into the electron per atom ratio dependence previously reported. Acknowledgements It is a pleasure to acknowledge the contribution of M. Kato for providing the order and lattice parameter data shown in Fig. 2. The authors are grateful for funding
from the Engineering and Physical Sciences Research Council of the UK for a ROPA award and from Natural Resources Canada. References [1] Nishino Y, Asano S, Ogawa T. Mater Sci Eng 1997;A234±236:271. [2] Nishino Y, Kato M, Asano S, Soda K, Hayasaki M, Mizutani U. Phys Rev Lett 1997;79:1909. [3] Nishino Y. Mater Sci Eng 1998;A258:50. [4] Guo GY, Botton GA, Nishino Y. J Phys Condens Matter 1998;10:L119. [5] Weinert M, Watson RE. Phys Rev B 1998;58:9732. [6] Soda K, Takeuchi T, Yanagida Y, Mizutani U, Kato M, Nishino Y et al. Jpn J Appl Phys 1999;38(Suppl. 1):496. [7] Skriver HL. The LMTO method. Berlin: Springer Verlag, 1984. [8] Okpalugo DE, Booth JG, Faunce CA. J Phys F 1985;15:681. [9] Ilyushin AS, Wallace WE. J Solid State Chem 1976;17:385. [10] Longworth HP, Mikkola DE. Mater Sci Eng 1987;96:213. [11] Prakash U, Muraleedhars K, Buckley RA, Jones H, Shenton PA. J Mater Sci 1996;31:1569. [12] Nishino Y, Inkson BJ, Ogawa T, Humphreys CJ. Phil Mag Lett 1998;78:97. [13] Kato M, Nishino Y, Asano S, Ohara S. J Jpn Inst Metals 1998;62:669. [14] Rimlinger L. Scripta Metall 1971;5:357. [15] Rudman PS. Acta Metall 1960;8:321. [16] Mendiratta MG, Lipsitt HA. In: Koch CC, Liu CT, Stolo NS, editors. High temperature ordered intermetallic alloys. Mater Res Soc, Symp Proc, vol. 39. Pittsburg: MRS, 1985. p. 155. [17] Nguyen-Mahn D, Trambly de Laissardiere G, Julien JP, Mayou D, Cyrot-Lanckmann F. Solid State Commun 1992;82:329. [18] Trambly de Laissardiere G, Nguyen-Mahn D, Magaud L, Julien JP, Cyrot-Lanckmann F, Mayou D. Phys Rev B 1995;52:7920. [19] Gelatt Jr CD, Williams AR, Moruzzi VL. Phys Rev B 1983;27:2005. [20] Fujii S, Ishida S, Asano S. J Phys Soc Japan 1995;64:185. [21] Freeman AJ, Hong T, Lin W, Xu Jian-Hua. In: Johnson LA, Pope DP, Stiegler JO, editors. High-temperature ordered intermetallic alloys IV. Materials Res Soc, Symp Proc, vol. 213. Pittsburg: MRS, 1991. p. 3. [22] Nishino Y, Kumada C, Asano S. Scripta Mater 1997;36:461. [23] Botton GA, Guo GY, Temmerman WM, Humphreys CJ. Phys Rev B 1996;54:1682.
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Microstructural evolution and stability of (Fe1ÿxVx)3Al alloys in relation to the electronic structure G.A. Botton a,*, Y. Nishino b, C.J. Humphreys c a
Materials Technology Laboratory, Natural Resources Canada, 568 Booth Street, Ottawa K1A 0G1, Canada Department of Materials Science and Engineering, Nagoya Institute of Technology, Showa-Ku, Nagoya 466-8555, Japan c Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK b
Received 13 August 1999; accepted 15 February 2000
Abstract The evolution of the microstructure of (Fe1ÿxVx)3Al alloys in the D03 structure has been studied as function of composition by transmission electron microscopy. The domain size of the D03 structure signi®cantly increases as V is added to the alloy. An increase in long range order parameter is also shown. This microstructural evolution is discussed in terms of the increased second nearest neighbor interactions induced by the V additions. Electronic structure calculations are also presented in this paper. The density of states shows a strong pseudogap for the Fe2VAl compound and thus strong hybridization induced by the alloying element. This electronic structure feature is discussed in terms of interesting physical properties of the system and in relation to the density of states, stability and properties of similar compounds [Fe2MAl (M=Ti, Cr, Mn)]. Electron energy loss spectra of the Al L2ÿ3 edge show that the strong hybridization induced by V does not aect the unoccupied Al s and d states. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Aluminides, miscellaneous; B. Bonding; D. Defects: antiphase domains; E. Electronic structure, calculation; E. Phase stability, prediction; F. Spectroscopic methods, various
1. Introduction Intermetallic materials are potential candidates for high temperature structural applications. Iron aluminides based on the Fe3Al system in particular are of great interest as they present an anomalous peak in the yield stress and show high temperature strength and excellent oxidation and corrosion resistance. Improvements in the mechanical properties for these alloys can be reached by suitable ternary alloying additions that also extend the temperature range over which the D03 structure is stable over the B2 structure. Additions of Ti, V and Mo have been shown to be very eective in increasing the D03±B2 transformation temperature and in changing the lattice parameter [1]. For the (Fe1ÿxVx)3Al system there are signi®cant improvements in high temperature strength that extends up to 1000 K and at the same time there are remarkable changes in physical properties. Nishino and coworkers have reported for (Fe1ÿxVx)3Al an anomalous temperature dependence of the electrical resistivity and magnetic properties [2,3] near the Fe2VAl (a Heusler-type phase) composition with strong similarities to the * Corresponding author. E-mail address: [email protected] (G.A. Botton).
behavior observed in ``heavy-fermion'' compounds. The Heusler-type Fe2VAl exhibits a semiconductor-like negative temperature dependence of the resistivity. Although the electronic structure calculations [4,5] and spectroscopic data of occupied electronic states [6] give some insight into the measured physical properties, no microstructural observations and correlation with other properties have been reported to date. The aim of the present paper is to present some initial results on the microstructural evolution of the alloy as a function of composition and link the observations to changes in electronic structure and physical properties. A comparison of the electronic structure of Fe2VAl with other Heusler alloys Fe2MAl (M= Ti, Cr, Mn) will also be presented in order to gain a better insight into the properties of the Heusler-type Fe2VAl phase. Energy loss spectra showing unoccupied electronic states are also shown and discussed in terms of the hybridization of electronic states of dierent atoms. 2. Experimental methods The pseudo-binary alloys (Fe1ÿxVx)3Al were prepared by repeated melting of a mixture of the 99.99% pure
0966-9795/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0966-9795(00)00043-1
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components of Fe and Al and 99.7% pure V in an arc furnace. Since the weight loss after melting was less than 0.3%, the nominal composition was accepted as being accurate. The ingots were homogenized at 1273 K for more than 170 ks in vacuum. Specimens (approximately 20101 mm3 in size) cut from ingots were held at 1273 K for 3.6 ks and annealed for D03 ordering at 673 K for 14.4 ks in an evacuated quartz capsule. Sample preparation for TEM was carried out by mechanically polishing the annealed specimens, down to 200 mm, followed by cutting 3 mm diameter disks with the spark erosion method to minimize mechanical damage. After ®nal mechanical polishing, electron transparency was achieved by electropolishing the disks in 5% perchloric acid in ethanol. TEM observations were carried out on Philips CM30 and CM20-FEG electron microscopes using 111 superlattice re¯ections near the 110 zone axis in order to observe the antiphase domain boundaries. The electronic structure calculations presented in this work were carried out using the linear mun tin orbital (LMTO) method [7] using the local density approximation. For Fe2VAl, the density of states (DOS) obtained with this method was comparable to that obtained with the full-potential linear augmented plane wave (FLAPW) technique of Guo et al. [4]. For the series of compound Fe2TiAl, Fe2VAl, Fe2CrAl and Fe2MnAl, the experimental lattice parameters (for Fe2TiAl a=0.588 nm [8], for Fe2VAl a=0.576 nm [2], for Fe2CrAl a=0.578 nm [8] and for Fe2MnAl a=0.580 nm [9]) were used in the calculation of the electronic structure. For all calculations, convergence with respect to the number of k points was checked and the number of divisions in the Brillouin zone was set at 24. 3. Results and discussion 3.1. Microstructural observations The D03 domains evolve dramatically over the range of composition studied in the (Fe1ÿxVx)3Al system (Fig. 1). The antiphase boundaries are very irregular in shape with no preferential crystallographic orientation. Although the domain size evolution is clearly evident from the electron micrographs, it is dicult to evaluate quantitatively the domain size and only a qualitative description of the APB separation is given in this paper. For the pure Fe3Al (Fig. 1a), the average separation of APB boundaries is approximately 0.3±0.4 mm and as V is introduced in the structure the separation of the APB increases. For x=0.1 (Fig. 1b) the APB separation is typically 0.5±1.5 mm and for x=0.18 (Fig. 1c) it is, on the average, larger than 1.5 mm. The increase in the D03 domain size has also been reported for the additions of Ti [10,11] and Mo [12]. The most important feature of the evolution is that at x=0.2 and x=0.33 (i.e. for the Heusler-type
phase Fe2VAl) the closed domains are no longer observed. Some residual occasional contrast is observed for x=0.2 (Fig. 1d) but microanalysis did not resolve any chemical inhomogeneities. At the composition of Fe2VAl, the alloy is perfectly homogenous with no second phase precipitation visible. Since both the formation and growth of domains are diusion-controlled processes taking place below the D03-B2 transformation temperature Tc, a higher value of Tc could lead to a greater rate of domain coarsening, and thus to a larger domain size [10]. Indeed, the value of Tc for the V addition is 200±400 K higher than that of Fe3Al, which may be enough to allow the domains to grow to larger sizes as seen in Fig. 1. Since the ordering within the domains is also dependent on diusion, the addition of V could give rise to an increase in the degree of D03 long-range order. In fact, as shown in Fig. 2, there is a continuous increase in the D03 long range order parameter as a function of composition and a decrease in the lattice parameter up to the Fe2VAl composition and then a rapid increase above the Heusler phase composition [13]. Although the replacement of smaller Fe atoms with larger V atoms would give an increase in the lattice parameter, the lattice contraction occurs presumably because of an enhanced cohesion due to the D03 ordering. These microstructural and diraction observations strongly suggest an increase in stability of the D03 structure with the addition of V up to the Fe2VAl composition. These results correlate with the reports of Rimlinger [14] who found a linear relationship between the degree of long range order and antiphase domain size. The stabilization of the D03 structure and thus Fe3Al type ordering has been linked to an increase in second nearest neighbor interactions [15,16] and this eect is likely to occur with the addition of V. In fact V, being an early transition metal has more delocalized d orbitals than Fe and the late transition aluminides (as compared to a simple atomic size eect). This suggestion is supported by the fact that the increase in Tc for the (Fe1ÿx Tix)3Al system is much stronger since d orbitals are even further delocalized in Ti. An additional factor contributing to the stabilization is the electron per atom (e/a) ratio which has been shown previously to be linked to the variation of Tc for the various transition metal additions [3]. Despite the sharpest increase in Tc for the Ti addition, the variation of Tc becomes close to that for the V addition when plotted as a function of e/a. This observation will be linked, later in this paper, to the electronic structure variations in the various alloys based on the (Fe1ÿxMx)3Al (M=Ti, Cr, Mn) system. 4. Electronic structure The electronic structure of the system also shows very interesting features and supports the stabilization eects discussed above. With respect to the DOS of Fe3Al (Fig.
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Fig. 1. Transmission electron micrographs of the (Fe1ÿxVx)3Al alloys as a function of composition: (a) Fe3Al, (b) (Fe0.9V0.1)3Al, (c) (Fe0.82V0.18)3Al, and (d) (Fe0.8V0.2)3Al. All micrographs have been obtained at the same magni®cation.
3a), the Fe2VAl DOS shows a very pronounced pseudogap right at the Fermi level (EF) (Fig. 3b) separating bonding states from antibonding states. The creation of such a pseudogap has been associated in general to very strong hybridization of the s and p bands with the d bands [17,18] which would also result in increased stability of the D03 structure. A similar pseudogap and semiconducting properties have been shown for Al2Ru and Ga2Ru [17] and attributed to strong hybridization. The clear separation of the antibonding states from the completely full bonding states is also an indication of a maximum in cohesive energy (see, for example [17,19]) and would also explain the decrease in lattice parameter as a
function of composition. Finally, the low DOS at EF and the pseudogap can give some insight into the conductivity properties of the Fe2VAl compound shown in the literature [2,3]. Guo et al. [4] have shown that Fe2VAl is a semimetal and the predicted Fermi surface consists of hole pockets (originating from the Fe 3d bands) and electron pockets (originating from the V 3d bands). These features and the low density of states at EF were shown to be factors contributing to the semiconducting behavior of the temperature dependent resistivity measurements [4]. In order to understand why this spectacular physical behavior occurs with the V addition (stability, microstructure, resistivity, etc.), it is of crucial importance to
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compare this system with other transition metal additions where such eects are not as marked. Fig. 4 shows the total DOS calculated for a series of the Heusler alloys: (a) Fe2TiAl, (b) Fe2CrAl, (c) Fe2MnAl (for Fe2VAl, see
Fig. 2. Lattice parameter and order parameter in the (Fe1ÿxVx)3Al system as a function of composition x. Data taken from Kato et al. [13].
Fig. 3b). For these initial calculations we assumed that all the alloys are nonmagnetic although Fe2CrAl and Fe2MnAl may be ferromagnetic alloys. Our result for Fe2TiAl is in agreement with that of Weinert and Watson [5]. For Fe2MnAl a direct comparison with the literature [20] is not possible as a dierent lattice parameter (also dierent from the experimental value [9]) was used and ferromagnetic calculations were done. When compared to the DOS of Fe2TiAl, there are similarities for the overall shape including the pseudogap (Fig. 4a) but the Fermi energy is not situated right in the pseudogap. The DOS at EF is in fact very high and this explains why the semiconductor temperature dependence of the resistivity eect is not as strong in (Fe1ÿxTix)3Al as in (Fe1ÿxVx)3Al (see, for example, the resistivity curves of Nishino [3]). In addition to this eect, the lattice parameter reduction observed for (Fe1ÿxVx)3Al is not observed in this system although the change is much smaller than predicted by a simple bcc solid solution. Although hybridization is strong, the separation of the occupied states from the unoccupied states is not optimal as the bonding states are not completely full. As the Ti is replaced by V, Cr and Mn the DOS changes are important (Figs. 3b, 4b and c, respectively). The ``pseudogap'' narrows while moving down relative to EF and the depth decreases so that, for Fe2CrAl and Fe2MnAl the eect is almost no longer observed. The stabilization eect in fact also decreases for Cr and Mn additions as compared to Ti and V alloying. For Cr and Mn additions, the D03±B2 transformation temperature is in fact almost unchanged. This eect would also correlate with the localization of the d orbitals with increasing atomic number in the transition metal series. The variation of the DOS at EF is also interesting. It is a minimum for Fe2VAl and particularly high for Fe2CrAl and Fe2MnAl. Ferromagnetic calculations for Fe2MnAl
Fig. 3. Density of states (DOS) for (a) Fe3Al and (b) Fe2VAl. The energy scale is relative to the Fermi energy.
G.A. Botton et al. / Intermetallics 8 (2000) 1209±1214
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from the literature [20] also show a high DOS at EF. As it has been generally deduced from electronic structure calculations of phase stability [21], this high DOS at EF also suggests that the compounds would not be very stable. This could, in part, explain the lack of a single phase domain in the D03 structure for (Fe1ÿxCrx)3Al [22]. Also the site preference data for Cr and Mn are still incomplete as reviewed elsewhere [3]. Further calculations as a function of lattice parameter and total energy would be necessary to con®rm this eect. The important changes in the DOS of the series also suggest that the rigid band approximation is not valid to explain the electronic structure dierences. This eect is additional evidence that the hybridization eects in these alloys vary very strongly. These changes in hybridization and therefore the dierences in the resulting pseudogap for the series of compounds give therefore further insight into the electron per atom (e/a) variation reported above and discussed by Nishino [3]. When hybridization is strong, the stabilization eect is strongly varying with e/ a (and therefore to the position of the Fermi energy within the band) and is weakly dependent on the dopant atomic number. When the pseudogap is almost non-existent, and therefore hybridization is weak, the stabilization is also weak. Energy loss spectra of the Al L23 edge for Fe3Al and (Fe0.8V0.2)3Al (Fig. 5) are very dierent from those observed in pure Al (see, for example, Botton et al. [23]). This edge probes the unoccupied s and d states at the Al site. As in transition metal aluminides, the hybridization of the Al 3s (and 4s) electrons with the Fe d electrons is present (see, for example, the discussion on EELS spectra in late transition metal aluminides [23]). With the addition of V, little changes are observed and this preliminary result suggests that the hybridization due to V either
Fig. 4. Density of states (DOS) for (a) Fe2TiAl, (b) Fe2CrAl and (c) Fe2MnAl.
Fig. 5. Electron energy-loss spectra of the Al L2ÿ3 edge for Fe3Al and (Fe0.8 V0.2)3Al. The two spectra have been shifted vertically for clarity.
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occurs with Al p states (and thus, because of the EELS transition selection rules, not visible at the Al L23 edge) or with the Fe atoms. Further work is in progress to analyze the EELS spectra of Fe2VAl and model the spectra with ab-initio electronic structure methods. 5. Conclusion We have presented the microstructural evolution of the (Fe1ÿxVx)3Al compound and analyzed the results based on electronic structure calculations. A rapid increase of D03 domain size is observed and has been correlated to measurements of long range order parameter. The increased stability deduced from the evolution of domain sizes and from the long-range order parameter of this structure has been linked to strong hybridization in the bonding induced by the presence of V. This strong hybridization is shown in the density of states calculated from ab-initio electronic structure methods by the presence of a strong pseudogap. This pseudogap evolves signi®cantly when the Ti, Cr and Mn are substituted for V. Several physical properties (lattice parameter, resistivity behavior, stability, and energy loss spectra) have been discussed in terms of the electronic structure calculations. The results indicate that the signi®cant dierences in properties observed with various alloying additions (Ti, V, Cr and Mn) can be correlated to the strong hybridization dierences between the various compounds. These dierences in bonding give new insight into the electron per atom ratio dependence previously reported. Acknowledgements It is a pleasure to acknowledge the contribution of M. Kato for providing the order and lattice parameter data shown in Fig. 2. The authors are grateful for funding
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