- Email: [email protected]
Crystal structure and phase stability of AlSc in the near-equiatomic Al–Sc alloy
Journal of Alloys and Compounds 618 (2015) 192–196
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Crystal structure and phase stability of AlSc in the near-equiatomic Al–Sc alloy Juan Li a, Li Huang a, Yongfeng Liang a, Feng Ye a,⇑, Junpin Lin a, Shunli Shang b, Zikui Liu b a b
State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, 30 Xueyuan Road, Beijing 100083, China Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA
a r t i c l e
i n f o
Article history: Received 8 January 2014 Received in revised form 1 July 2014 Accepted 11 August 2014 Available online 23 August 2014 Keywords: Intermetallics Crystal structure Phase transitions Transmission electron microscopy
a b s t r a c t Intermetallic compound AlSc is found in the equiatomic Al–Sc binary alloy. The present work indicates that the orthorhombic AlSc with the Au2CuZn-type structure can be formed at 50 at.% Sc, while the CsCl-type (B2) AlSc will be formed at 55 at.% Sc. After annealing at 1100 °C, some orthorhombic AlSc grains transit to the B2 structure, and the annealing at lower temperatures leads to the disappearance of B2 phase, indicating that the B2 AlSc is also a metastable phase in the alloy at lower Sc content (<50 at.%). First-principle calculations at 0 K reveal that the orthorhombic AlSc is more stable than the B2 AlSc with the energy difference between them being 5.4 meV/atom. The fast transition between these two phases, which cannot be interpreted by the mechanism of atomic diffusion, was tentatively analyzed by the volume change based on the calculated atomic positions of these two phases. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Considerable works have been performed to determine the Al–Sc phase diagram. However, the crystal structure of the stoichiometric AlSc compound remains controversial in the literature. In 1965, Schob and Parthé [1] reported that the B2 structure with lattice parameter of 3.450 Å could be identified for the equiatomic Al–Sc alloy after induction melting in a boron-nitride crucible. However, a second phase was observed in the X-ray powder diffraction pattern and could not be identified. In 1985, Schuster [2] claimed that the arc melted AlSc alloy was a orthorhombic phase (lattice parameters a = 5.0299 Å, b = 9.8945 Å, and c = 3.1263 Å), and AlSc formed the B2-type structure (a = 3.388 Å) in the ternary Sc–Al–N alloy because the oxygen or nitrogen stabilizes the B2 structure of AlSc. Murray [3] and Gschneidner and Calderwood [4] investigated the Al–Sc system and reported that the equiatomic AlSc alloy was the B2 structure. The latest Al–Sc phase diagram was revised by Cacciamani et al. [5], and the scan electron microscopy (SEM) micrograph of an as-cast 49 at.% Sc alloy indicated the presence of two phases of AlSc and Al2Sc due to an off-stoichiometric composition (approximately 52–54 at.% Sc) of the AlSc phase. Meanwhile, previous first-principles studies [6–8] of the B2 and the orthorhombic (orth-) AlSc compounds cannot confirm the stability of these two phases. In addition, the aforementioned
⇑ Corresponding author. Tel.: +86 10 62333899; fax: +86 10 6233 2508. E-mail address: [email protected] (F. Ye). http://dx.doi.org/10.1016/j.jallcom.2014.08.111 0925-8388/Ó 2014 Elsevier B.V. All rights reserved.
researches did not provide details regarding the space group and atomic positions of the orth-AlSc. Our previous experiments [9] revealed that both orth-AlSc and B2 AlSc can be formed, and their crystal structures showed a distinct influence on the diffusion behavior of elements when bulk alloy of either phase is coupled with Ti. Therefore, the present work aims to investigate the structural details of these two AlSc compounds with a close attention paid to phase transformation of the orthorhombic AlSc. Based on the experimental results, firstprinciple calculations are also employed to explore phase stability of AlSc compounds.
2. Details of experiments and first-principles calculations The Al–45 at.% Sc (Al–45Sc), Al–50 at.% Sc (Al–50Sc) and Al–55 at.% Sc (Al–55Sc) alloys were prepared by arc melting using pure scandium (99.9 wt.%) and aluminum (99.99 wt.%) in a non-consumable vacuum furnace under argon atmosphere. The buttons were turned upside down and re-melted several times to ensure homogenization. Samples cut from buttons were either annealed at 900 (24 h), 1000 (24 h), and 1100 °C (12 h) in vacuum quartz capsules (103 Pa) and cooled in the furnace, or annealed at 1000 (24 h) and 1100 °C (12 h) followed by quenching in water. Structural characterization was performed at a scanning rate of 3° min1 with an X-ray diffractometer (XRD, Rigaku D/MAX-RB, Cu Ka1), scanning electron microscopy (SEM, Zeiss SUPRA™ 55, 20 kV) with electron-dispersive X-ray spectroscopy (EDS) and transmission electron microscopy (TEM, Tecnai T20, 200 kV). The TEM samples were mechanically thinned to 65–70 lm and then jet-electro polished with an electrolyte containing 5 vol.% perchloric acid in methanol at 30 °C. A JEOL JXA-8100 electron-probe micro-analyzer (EPMA) equipped with wavelengthdispersive X-ray spectroscopy (WDS) was employed for local composition analysis
J. Li et al. / Journal of Alloys and Compounds 618 (2015) 192–196 (working at 15 kV). We employed the Fullprof program [10] for Rietveld analysis to refine the lattice parameters of the orthorhombic AlSc. These parameters were used to construct the AlSc unit cell for the analysis of transition between two AlSc compounds. In an effort to investigate phase stability between B2 and orth-AlSc, first-principles calculations were performed by the Vienna ab initio simulation package (VASP) [11] with the ion-electron interaction described by the projector augmented wave (PAW) method [12] and the exchange-correlation functional described by the generalized gradient approximation (GGA) [13]. During VASP calculations, the plane wave energy cutoff was set as 350 eV, and the k-point meshes were set as 13 7 21 for orth-AlSc and 27 27 27 for B2 AlSc. After relaxations of cell shapes and atomic positions by the Methfessel–Paxton technique [14], the final calculations of total energy were performed by the tetrahedron method incorporating Blöchl correction [15]. In order to determine the equilibrium properties for the phase of interest, first-principles calculated energy vs. volume (E–V) data points are fitted by a four-parameter Birch–Murnaghan equation of state (EOS) [16]
EðVÞ ¼ a þ bV
2=3
þ cV 4=3 þ dV
2
ð1Þ
where a, b, c, and d are fitting parameters. The equilibrium properties estimated from this EOS include the volume (V0), energy (E0), bulk modulus (B0) and its pressure derivative (B00 ). Usually nine E–V data points are used for EOS fitting for each phase.
3. Results 3.1. Phases and microstructure evolution Prior to heat treatment, the as-cast Al–50Sc diffraction peaks are dispersed; in addition to Al2Sc and orth-AlSc, an extra peak at diffraction angle 37.2° (to the left of the strongest peak) cannot
193
be identified (C-Al–50Sc in Fig. 1a). After annealing at 1100 °C, all peaks become sharper and the intensity of the peak at diffraction angle 37.2° becomes stronger. The presence of B2 AlSc can be confirmed by three diffraction lines (other two at about 26.0° and 53.8°, respectively). The as-cast Al–45Sc alloys exhibited a mixed XRD pattern correspond to orth-AlSc and Al2Sc (C-Al–45Sc in Fig. 1a). However, after annealing at 1100 °C, the strongest diffraction peak of B2 AlSc can be observed in Al–45Sc (1100A-Al–45Sc in Fig. 1b). Contrastively, the B2 AlSc cannot be formed in the alloy by annealing or quenching at lower temperatures. In the present work, if the annealing takes place at 1000 or 900 °C, the B2 phase will not be formed (900A-Al–50Sc in Fig. 1b). By employing this heat treatment, the B2 phase disappears in the Al–50Sc or Al– 45Sc alloy after annealing at 1000 °C. The reaction of B2 phase seems to appear during the procedure of slow cooling rather than the rapid cooling. As the sample was quenched in water, no orthAlSc transformed to B2 AlSc, and the distortion of orth-AlSc was preserved, which was demonstrated by the dispersed and widen diffraction peaks in Fig. 1b (1000/1100q-Al–50Sc). C-Al–55Sc in Fig. 1a indicates that the B2 AlSc is the major phase in Al–55Sc, which was also verified by the TEM diffraction patterns, and the two extra lines are attributed to the precipitated phase. This phase is hard to eliminate even though we remelted the Al–55Sc alloy several times. It demonstrates that the B2-type aluminides could not be obtained as a single phase [1]. The matrix composition of the Al–50Sc alloys annealed at 1100 and 900 °C was approximately 49 at.% Sc as measured by EPMA, which indicated that no composition segregation occurred in the annealed Al–50Sc alloys. The EPMA analysis revealed that the composition of the stable B2 AlSc in Al–55Sc is close to 55 at.% Sc. On the basis of the above observations, the following results about orthorhombic AlSc and B2 AlSc can be concluded. The orthorhombic AlSc is formed with the composition of around 50 at.% Sc in alloys of Al–45Sc and Al–50Sc. The B2 AlSc can be transformed from the orthorhombic AlSc when the associated alloy undergoes a high-temperature annealing. Under this condition, B2 AlSc was observed as a metastable phase resulting from a non-equilibrium transformation. However, B2 AlSc is formed as a stable phase in the Al–Sc alloys with 55 at.% Sc. In the micrograph of the as-cast Al–45Sc alloy (Fig. 2a), a massive proeutectic Al2Sc dendrite and a typical orth-AlSc + Al2Sc eutectic lamellar were observed. By contrast, in the micrograph of the annealed sample (Fig. 2b), the eutectic lamellar of orth-AlSc + Al2Sc disappears completely followed by the growth of orth-AlSc grain, which confirms a coalescence mechanism and provides a continuous matrix of the orth-AlSc phase. However, no obvious difference between the B2 and orth-AlSc was observed in the micrograph of this sample. The eutectic structure of orthAlSc and Al2Sc appears to be the same as that in the as-cast Al– 45Sc annealed at 1100 °C for 5 h (not shown here), and no B2 AlSc was observed in the X-ray pattern, which may be due to the insufficient evolution of eutectic lamellar resulting from the short-time annealing. 3.2. Lattice structure of the orthorhombic AlSc and B2 AlSc
Fig. 1. X-ray diffraction patterns for the Al–45Sc, Al–50Sc and Al–55Sc alloys under different treatments. ‘‘?’’ indicate an un-identified structure in the Al–50Sc and Al– 55Sc.
The space group of orth-AlSc was determined to be Pbam with lattice parameters a = 5.032, b = 9.902, and c = 3.129 Å by XRD pattern of the Al–50Sc alloy annealed at 900 °C (Fig. 1b, 900A-Al– 50Sc). Atomic positions were refined by Fullprof to construct the unit cell of orthorhombic while occupancy values were fixed to unity one to minimize the difficulty in the refinement, since effort was mainly put on the understanding of the orthorhombic structure of AlSc. The unit cell of orthorhombic AlSc contains 8 atoms (Fig. 3a), which is 4 times the number of atoms in B2 AlSc
194
J. Li et al. / Journal of Alloys and Compounds 618 (2015) 192–196
Fig. 2. SEM micrograph of Al–45Sc: (a) as-cast microstructure and (b) microstructure after annealing for 12 h at 1100 °C.
Fig. 3. Unit cells of orthorhombic AlSc phase (a) and B2 AlSc (b).
(Fig. 3b). It belongs to the Au2CuZn-type structure (s1) [18]. The refined atomic positions are Wyckoff site 4 g for Al atoms, i.e., (0.168, 0.138, 0), and Wyckoff site 4 h for Sc atoms, i.e., (0.706, 0.107, 0.5). A goodness of fit from about 1.0 to about 2.0 may indicate sufficient accuracy of the theoretical diffraction pattern, while the goodness of the Rietveld fit is about 2.5 (with Rp = 11.1%, Rwp = 14.5%, Rexp = 5.53%) in our program. Notwithstanding the space group Pbam was retained in the present work, space groups of other orthorhombic structures were also tested but were rejected because the only satisfactory packing and diffraction patterns were obtained when the Sc and Al atoms have the similar parameters to those of Au2CuZn. Lattice parameters of B2 AlSc with both compositions are all around 3.410 Å. In addition, atomic occupations of B2 AlSc with 50 at.% Sc in the Al–50Sc alloy can be determined easily with Al in Wyckoff site 1a and Sc in 1b, whereas B2 AlSc with Sc around 55 at.% in the Al–55Sc alloy has an off-stoichiometric composition, indicating that some 1a positions may be occupied by Sc atoms or vacancies. It is possible, however, to conclude that two kinds of B2 AlSc with different compositions are highly ordered and belong to the same structure because of considerable intensities of {1 0 0} peaks in both phases. 3.3. B2 and orth-AlSc in Al–50Sc alloy annealed at 1100 °C Because two alloys that contain orth-AlSc indicate the presence of B2 AlSc after annealing at 1100 °C for a long time, we therefore performed a detailed microscopic observation and microprobe analysis of the Al–50Sc alloy. The micrograph of the Al–50Sc hypereutectic alloy (Fig. 4a) indicates that the orth-AlSc + Al2Sc lamellar structure distributes at the boundaries of the massive orth-AlSc proeutectic phase and forms a continuous or quasi-continuous network-shaped microstructure. Similar to the annealed Al–45Sc alloy, the eutectic
lamellar of orth-AlSc + Al2Sc disappears completely after annealing at 1100 °C for 12 h, and the SEM micrograph does not indicate the presence of B2 AlSc. To confirm the structures of both AlSc compounds and to investigate the potential orientation relationship between orth-AlSc and B2 AlSc, SADPs are employed. Fig. 4c and d indicate that two selected patterns of the orth-AlSc phase (marked by A) in Fig. 4b exhibit typical superlattice diffractions of a crystal structure with the space group Pbam, which confirms the XRD results. The bright field TEM micrograph of the Al–50Sc alloy annealed at 1100 °C indicates the presence of the B2 phase (Fig. 4b) surrounded by orth-AlSc grains, because the corresponding SADP (top right inset in Fig. 4b) shows a regular hexagon, indicating a cubic structure. In addition, B2 AlSc is not similar to the typical non-equilibrium precipitates composed of small particles, laths or needles dispersed in the matrix [17,19]. The size of the B2 AlSc grain is on the micrometer scale (>1 lm) with obvious boundaries in the orth-AlSc phase. Most of the B2 AlSc grains observed in the TEM are surrounded by the orth-AlSc grains. Few defects are observed in the orth-AlSc grain, which is next to the B2 AlSc grain (Fig. 4 b). However, far away from the B2 AlSc, the orth-AlSc displays more defects and submicrostructures (Fig. 5). The SADP (top right inset in Fig. 5) of the black stripes has a zone axis, while the SADP of the white stripes cannot be ½1 0 3 rotated to a right zone axis. The sharp contrast between the two stripes may be explained in terms of a large disorientation in the two submicrostructures, which also indicates the low stacking fault energy of orth-AlSc. In addition, differences in two kinds of microstructure in orthorhombic AlSc indicate that the formation of B2 AlSc can relax the stress and distortion in the orthorhombic AlSc via high-temperature annealing. Unfortunately, we cannot determine the orientation between the two phases from the TEM diffraction patterns because B2 AlSc has no common orientation with the peripheral ortho-AlSc grains in our current experiment. Therefore, additional studies are required.
195
J. Li et al. / Journal of Alloys and Compounds 618 (2015) 192–196
Fig. 4. Microstructure of the orth-AlSc phase: (a) Backscattered-electron SEM image of the as-cast Al–50Sc and (b) bright field TEM images of the orth- and B2 AlSc. The top right inset displays the SADP from the corresponding region. (c) and (d) are the SADP of region A in (b) along the directions of [1 0 0] and ½1 0 1.
Fig. 5. Bright field TEM image of the orth-AlSc phase with sharp contrast submicrostructures.
Table 1 First-principles (F-P) predicted equilibrium properties of AlSc, including equilibrium volume (V0 (Å3/atom)), relative energy (DE0 (meV/atom)), bulk modulus (B0 (GPa)) and the first derivative of bulk modulus with respect to pressure (B0 ). Structure
a
b
c d
Space group
V0 a
DE0
B0
B0
Note
orth-AlSc
Pbam
19.579 19.489b
0
74.9
3.67
This work, F-P
B2 AlSc
pm3m
19.329 19.826b
5.4
76.1 72c 79.92d
4.00
This work, F-P
First-principles predicted lattice parameters at 0 K (without the effect of zero point vibrational energy) are a = 5.040, b = 9.910, and c = 3.140 Å. In addition, the relaxed atomic positions are (0.178, 0.106, 0.0) for Al and (0.685, 0.137, 0.5) for Sc. Measured room temperature lattice parameters in the present work are a = 5.032, b = 9.902, and c = 3.129 Å for orth-AlSc and a = 3.410 Å for B2 AlSc. Note that the measured atomic positions for Al atom (Wyckoff site 4 g) and Sc atom (Wyckoff site 4 h) are (0.168, 0.138, 0) and (0.706, 0.107, 0.5), respectively. Other first-principles calculations using the full-potential linear muffin-tin orbitals method within local-density-functional approximation [20]. Other first-principles calculations using the generalized gradient approximation [6].
3.4. First-principles results Table 1 summarizes the first-principles results for both orthand B2 AlSc, including equilibrium volume, relative energy (with respect to B2 AlSc), bulk modulus and its pressure derivative. In
addition, the present measurements of lattice parameters and other first-principles results [6,20] of bulk modulus of B2 phase are also included for comparison. It is found that the present first-present equilibrium volume and lattice parameters agree well with experimental data, especially for orth-AlSc (19.579 vs.
196
J. Li et al. / Journal of Alloys and Compounds 618 (2015) 192–196
19.489 Å3/atom, see Table 1). Concerning the bulk modulus of B2 phase, the present prediction (76 GPa) is also in good agreement with other predictions [6,20] (72 and 80 GPa, see Table 1). About the first derivative of bulk modulus with respect to pressure, the present results (3.67 and 4.00) are also fallen in the region for most materials (3–6, see [21]). Regarding phase stability, the present first-principles calculations indicate that the orthorhombic AlSc with the space group Pbam is more stable than B2 AlSc with the space group pm3m, and the energy difference between them is 5.4 meV/atom at 0 K, see Table 1. However, the slight energy difference also indicates that other factors, such as stress and impurity, might reverse the phase stability of orth-AlSc and B2 AlSc. Additionally, phase transition between these two compounds can be generated easily because of such low formation energy barrier. 4. Discussion Based on results in the literature, impurity can cause the disappearance of orth-AlSc and the appearance of B2 AlSc. However, in the present Al–50Sc alloy, B2 and orth-AlSc can coexist with the same composition after annealing at high temperatures, but the B2 AlSc disappears under annealing at low temperatures. It appears that impurities do not play a vital role in the formation of B2 in the annealed Al–50Sc. However, annealing at high temperatures may have some special impact on the microstructures of ortho-AlSc in the Al–50Sc alloy. As mentioned in Section 3.4, the energy difference between these two AlSc compounds is small (5.4 meV/atom), indicating the phase stability can be changed easily in terms of alloying and stress. By considering the influence of local stress, a reasonable mechanism can be tentatively proposed to elucidate the lattice evolution that relieves the tensile stress upon cooling from high temperatures. The annealing temperature of 1100 °C is believed to be higher than the temperature of the alloy above which the orth-AlSc lattice is unstable. In addition, the fast cooling from 1100 to 1000 °C leads to local enrichment in the tensile stress in minor grains enclosed by major grains. Due to the local high tensile stress applied to the crystal plane, the orth ? B2 phase transformation occurs, implying that this transformation can relieve the local stress/strain. However, much faster cooling (quenching) from 1100 °C will maintain the lattice or keep the atoms from moving and preserve the lattice distortion and expansion. The special orientation between the metastable phase and the matrix is not expected during this transition. This mechanism can be confirmed by the volume change during the phase transition. According to the lattice parameters obtained from TEM and XRD for the Al–50Sc sample annealed at 1100 °C, the density of the B2 AlSc phase is approximately 3.013 g cm3, and the density of orth-AlSc ranges from 3.041 (annealed at 1100 °C) to 3.070 (annealed at 900 °C) g cm3. B2 AlSc has a lower density than orth-AlSc, and the B2 AlSc transformation may result in a relative expansion in the volume. Based on the volume change, a local enrichment in tensile stress (resulting from the interaction of stress fields of the peripheral grains) would provide favorable sites for transformation of orth-AlSc to B2 AlSc. As mentioned above, B2 phase is absent in the Al–45Sc alloy annealed at 1100 °C for 5 h. A microscopic observation shows that eutectic lamellar of orthAlSc + Al2Sc changes little and the microstructure of orth-AlSc is fine and insular. This indicates that stress in isolated orthorhombic AlSc grains is insufficient or can be relieved by other phase, and the formation of B2 AlSc requires a continuous matrix of the orthorhombic AlSc grains.
5. Conclusions (1) Two different structures of AlSc were determined in the present work. The phase with 50 at.% Sc exhibits a space group of Pbam with the Au2CuZn-type structure, while the alloys with 55 at.% Sc exhibit a CsCl-type B2 structure. (2) B2 AlSc is a metastable phase in alloys with the orth-AlSc phase (or with scandium less than 50 at.%). The orth-AlSc cooling from high temperatures can transform into B2 AlSc. Decrease of heating temperature to 1000 °C is not favorable for the formation of B2 phase. Microstructure observation reveals that the orthorhombic AlSc grains far away from the B2 AlSc display more defects than those close to the B2 AlSc, indicating that B2 AlSc can lessen the distortion in orthorhombic AlSc from high temperatures. (3) First-principles calculations predict that the orth-AlSc is more stable than B2 AlSc with the energy difference being 5.4 meV/atom. A small energy difference between these two phases implies that the B2 AlSc can become stable and the phase transition between these two compounds is easy. (4) Phase transition between these two AlSc phases can be well understood in terms of volume change; the local tensile stress in the cooling of the orth-AlSc phase from high temperatures plays a major role in the formation of the metastable B2 phase.
Acknowledgments The authors acknowledge the financial support from the National Basic Research Program of China (No. 2011CB606304), the National High Technology Research and Development Program of China (No. 2012AA03A505), the Program for Changjiang Scholars and Innovative Research Team in University, and the Specialized Research Fund for the Doctoral Program of Higher Education (20100006110013). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
O. Schob, E. Parthé, Acta Crystallogr. 19 (1965) 214–224. J.C. Schuster, J. Less-Common Met. 109 (1985) 345–350. J.L. Murray, J. Phase Equilib. 19 (1998) 380–384. K.A. Gschneidner, F.W. Calderwood, Bull. Alloy Phase Diagrams 10 (1989) 34– 36. G. Cacciamani, P. Riani, G. Borzone, N. Parodi, A. Saccone, R. Ferro, A. Pisch, R. Schmid-Fetzer, Intermetallics 7 (1999) 101–108. X.M. Tao, Y.F. Ouyang, H.S. Liu, F.J. Zeng, Y.P. Feng, Z.P. Jin, Physica B 399 (2007) 27–32. M. Asta, V. Ozolinn ß š, Phys. Rev. B 64 (2001). 094104.1–14. G. Trimarchi, A.J. Freeman, A. Zunger, Phys. Rev. B 80 (2009). 092101.1–4. J. Li, F. Ye, L. Huang, Y.F. Liang, Mater. Sci. Forum 747 (2013) 9–13. J. Rodríguez-Carvajal, An Introduction to the Program Fullprof 2000, Version 2001, Laboratoire Léon Brillouin, CEA-CNRS, Saclay (France), 2001. G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169–11186. G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758–1775. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865–3868. M. Methfessel, A.T. Paxton, Phys. Rev. B 40 (1989) 3616–3621. P.E. Blöchl, Phys. Rev. B 50 (1994) 17953–17979. S.L. Shang, Y. Wang, D. Kim, Z.K. Liu, Comput. Mater. Sci. 47 (2010) 1040–1048. F. Prima, P. Vermaut, G. Texier, D. Ansel, T. Gloriant, Scr. Mater. 54 (2006) 645– 648. M. Wilkens, K. Schubert, Z. Metallkd. 48 (1957) 550–557. C.S. Tsao, C.Y. Chen, U.S. Jeng, T.Y. Kuo, Acta Mater. 54 (2006) 4621–4631. D. Nguyen-Manh, D.G. Pettifor, Intermetallics 7 (1999) 1095–1106. S.L. Shang, A. Saengdeejing, Z.G. Mei, D.E. Kim, H. Zhang, S. Ganeshan, Y. Wang, Z.K. Liu, Comput. Mater. Sci. 48 (2010) 813–826.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Crystal structure and phase stability of AlSc in the near-equiatomic Al–Sc alloy Juan Li a, Li Huang a, Yongfeng Liang a, Feng Ye a,⇑, Junpin Lin a, Shunli Shang b, Zikui Liu b a b
State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, 30 Xueyuan Road, Beijing 100083, China Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA
a r t i c l e
i n f o
Article history: Received 8 January 2014 Received in revised form 1 July 2014 Accepted 11 August 2014 Available online 23 August 2014 Keywords: Intermetallics Crystal structure Phase transitions Transmission electron microscopy
a b s t r a c t Intermetallic compound AlSc is found in the equiatomic Al–Sc binary alloy. The present work indicates that the orthorhombic AlSc with the Au2CuZn-type structure can be formed at 50 at.% Sc, while the CsCl-type (B2) AlSc will be formed at 55 at.% Sc. After annealing at 1100 °C, some orthorhombic AlSc grains transit to the B2 structure, and the annealing at lower temperatures leads to the disappearance of B2 phase, indicating that the B2 AlSc is also a metastable phase in the alloy at lower Sc content (<50 at.%). First-principle calculations at 0 K reveal that the orthorhombic AlSc is more stable than the B2 AlSc with the energy difference between them being 5.4 meV/atom. The fast transition between these two phases, which cannot be interpreted by the mechanism of atomic diffusion, was tentatively analyzed by the volume change based on the calculated atomic positions of these two phases. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Considerable works have been performed to determine the Al–Sc phase diagram. However, the crystal structure of the stoichiometric AlSc compound remains controversial in the literature. In 1965, Schob and Parthé [1] reported that the B2 structure with lattice parameter of 3.450 Å could be identified for the equiatomic Al–Sc alloy after induction melting in a boron-nitride crucible. However, a second phase was observed in the X-ray powder diffraction pattern and could not be identified. In 1985, Schuster [2] claimed that the arc melted AlSc alloy was a orthorhombic phase (lattice parameters a = 5.0299 Å, b = 9.8945 Å, and c = 3.1263 Å), and AlSc formed the B2-type structure (a = 3.388 Å) in the ternary Sc–Al–N alloy because the oxygen or nitrogen stabilizes the B2 structure of AlSc. Murray [3] and Gschneidner and Calderwood [4] investigated the Al–Sc system and reported that the equiatomic AlSc alloy was the B2 structure. The latest Al–Sc phase diagram was revised by Cacciamani et al. [5], and the scan electron microscopy (SEM) micrograph of an as-cast 49 at.% Sc alloy indicated the presence of two phases of AlSc and Al2Sc due to an off-stoichiometric composition (approximately 52–54 at.% Sc) of the AlSc phase. Meanwhile, previous first-principles studies [6–8] of the B2 and the orthorhombic (orth-) AlSc compounds cannot confirm the stability of these two phases. In addition, the aforementioned
⇑ Corresponding author. Tel.: +86 10 62333899; fax: +86 10 6233 2508. E-mail address: [email protected] (F. Ye). http://dx.doi.org/10.1016/j.jallcom.2014.08.111 0925-8388/Ó 2014 Elsevier B.V. All rights reserved.
researches did not provide details regarding the space group and atomic positions of the orth-AlSc. Our previous experiments [9] revealed that both orth-AlSc and B2 AlSc can be formed, and their crystal structures showed a distinct influence on the diffusion behavior of elements when bulk alloy of either phase is coupled with Ti. Therefore, the present work aims to investigate the structural details of these two AlSc compounds with a close attention paid to phase transformation of the orthorhombic AlSc. Based on the experimental results, firstprinciple calculations are also employed to explore phase stability of AlSc compounds.
2. Details of experiments and first-principles calculations The Al–45 at.% Sc (Al–45Sc), Al–50 at.% Sc (Al–50Sc) and Al–55 at.% Sc (Al–55Sc) alloys were prepared by arc melting using pure scandium (99.9 wt.%) and aluminum (99.99 wt.%) in a non-consumable vacuum furnace under argon atmosphere. The buttons were turned upside down and re-melted several times to ensure homogenization. Samples cut from buttons were either annealed at 900 (24 h), 1000 (24 h), and 1100 °C (12 h) in vacuum quartz capsules (103 Pa) and cooled in the furnace, or annealed at 1000 (24 h) and 1100 °C (12 h) followed by quenching in water. Structural characterization was performed at a scanning rate of 3° min1 with an X-ray diffractometer (XRD, Rigaku D/MAX-RB, Cu Ka1), scanning electron microscopy (SEM, Zeiss SUPRA™ 55, 20 kV) with electron-dispersive X-ray spectroscopy (EDS) and transmission electron microscopy (TEM, Tecnai T20, 200 kV). The TEM samples were mechanically thinned to 65–70 lm and then jet-electro polished with an electrolyte containing 5 vol.% perchloric acid in methanol at 30 °C. A JEOL JXA-8100 electron-probe micro-analyzer (EPMA) equipped with wavelengthdispersive X-ray spectroscopy (WDS) was employed for local composition analysis
J. Li et al. / Journal of Alloys and Compounds 618 (2015) 192–196 (working at 15 kV). We employed the Fullprof program [10] for Rietveld analysis to refine the lattice parameters of the orthorhombic AlSc. These parameters were used to construct the AlSc unit cell for the analysis of transition between two AlSc compounds. In an effort to investigate phase stability between B2 and orth-AlSc, first-principles calculations were performed by the Vienna ab initio simulation package (VASP) [11] with the ion-electron interaction described by the projector augmented wave (PAW) method [12] and the exchange-correlation functional described by the generalized gradient approximation (GGA) [13]. During VASP calculations, the plane wave energy cutoff was set as 350 eV, and the k-point meshes were set as 13 7 21 for orth-AlSc and 27 27 27 for B2 AlSc. After relaxations of cell shapes and atomic positions by the Methfessel–Paxton technique [14], the final calculations of total energy were performed by the tetrahedron method incorporating Blöchl correction [15]. In order to determine the equilibrium properties for the phase of interest, first-principles calculated energy vs. volume (E–V) data points are fitted by a four-parameter Birch–Murnaghan equation of state (EOS) [16]
EðVÞ ¼ a þ bV
2=3
þ cV 4=3 þ dV
2
ð1Þ
where a, b, c, and d are fitting parameters. The equilibrium properties estimated from this EOS include the volume (V0), energy (E0), bulk modulus (B0) and its pressure derivative (B00 ). Usually nine E–V data points are used for EOS fitting for each phase.
3. Results 3.1. Phases and microstructure evolution Prior to heat treatment, the as-cast Al–50Sc diffraction peaks are dispersed; in addition to Al2Sc and orth-AlSc, an extra peak at diffraction angle 37.2° (to the left of the strongest peak) cannot
193
be identified (C-Al–50Sc in Fig. 1a). After annealing at 1100 °C, all peaks become sharper and the intensity of the peak at diffraction angle 37.2° becomes stronger. The presence of B2 AlSc can be confirmed by three diffraction lines (other two at about 26.0° and 53.8°, respectively). The as-cast Al–45Sc alloys exhibited a mixed XRD pattern correspond to orth-AlSc and Al2Sc (C-Al–45Sc in Fig. 1a). However, after annealing at 1100 °C, the strongest diffraction peak of B2 AlSc can be observed in Al–45Sc (1100A-Al–45Sc in Fig. 1b). Contrastively, the B2 AlSc cannot be formed in the alloy by annealing or quenching at lower temperatures. In the present work, if the annealing takes place at 1000 or 900 °C, the B2 phase will not be formed (900A-Al–50Sc in Fig. 1b). By employing this heat treatment, the B2 phase disappears in the Al–50Sc or Al– 45Sc alloy after annealing at 1000 °C. The reaction of B2 phase seems to appear during the procedure of slow cooling rather than the rapid cooling. As the sample was quenched in water, no orthAlSc transformed to B2 AlSc, and the distortion of orth-AlSc was preserved, which was demonstrated by the dispersed and widen diffraction peaks in Fig. 1b (1000/1100q-Al–50Sc). C-Al–55Sc in Fig. 1a indicates that the B2 AlSc is the major phase in Al–55Sc, which was also verified by the TEM diffraction patterns, and the two extra lines are attributed to the precipitated phase. This phase is hard to eliminate even though we remelted the Al–55Sc alloy several times. It demonstrates that the B2-type aluminides could not be obtained as a single phase [1]. The matrix composition of the Al–50Sc alloys annealed at 1100 and 900 °C was approximately 49 at.% Sc as measured by EPMA, which indicated that no composition segregation occurred in the annealed Al–50Sc alloys. The EPMA analysis revealed that the composition of the stable B2 AlSc in Al–55Sc is close to 55 at.% Sc. On the basis of the above observations, the following results about orthorhombic AlSc and B2 AlSc can be concluded. The orthorhombic AlSc is formed with the composition of around 50 at.% Sc in alloys of Al–45Sc and Al–50Sc. The B2 AlSc can be transformed from the orthorhombic AlSc when the associated alloy undergoes a high-temperature annealing. Under this condition, B2 AlSc was observed as a metastable phase resulting from a non-equilibrium transformation. However, B2 AlSc is formed as a stable phase in the Al–Sc alloys with 55 at.% Sc. In the micrograph of the as-cast Al–45Sc alloy (Fig. 2a), a massive proeutectic Al2Sc dendrite and a typical orth-AlSc + Al2Sc eutectic lamellar were observed. By contrast, in the micrograph of the annealed sample (Fig. 2b), the eutectic lamellar of orth-AlSc + Al2Sc disappears completely followed by the growth of orth-AlSc grain, which confirms a coalescence mechanism and provides a continuous matrix of the orth-AlSc phase. However, no obvious difference between the B2 and orth-AlSc was observed in the micrograph of this sample. The eutectic structure of orthAlSc and Al2Sc appears to be the same as that in the as-cast Al– 45Sc annealed at 1100 °C for 5 h (not shown here), and no B2 AlSc was observed in the X-ray pattern, which may be due to the insufficient evolution of eutectic lamellar resulting from the short-time annealing. 3.2. Lattice structure of the orthorhombic AlSc and B2 AlSc
Fig. 1. X-ray diffraction patterns for the Al–45Sc, Al–50Sc and Al–55Sc alloys under different treatments. ‘‘?’’ indicate an un-identified structure in the Al–50Sc and Al– 55Sc.
The space group of orth-AlSc was determined to be Pbam with lattice parameters a = 5.032, b = 9.902, and c = 3.129 Å by XRD pattern of the Al–50Sc alloy annealed at 900 °C (Fig. 1b, 900A-Al– 50Sc). Atomic positions were refined by Fullprof to construct the unit cell of orthorhombic while occupancy values were fixed to unity one to minimize the difficulty in the refinement, since effort was mainly put on the understanding of the orthorhombic structure of AlSc. The unit cell of orthorhombic AlSc contains 8 atoms (Fig. 3a), which is 4 times the number of atoms in B2 AlSc
194
J. Li et al. / Journal of Alloys and Compounds 618 (2015) 192–196
Fig. 2. SEM micrograph of Al–45Sc: (a) as-cast microstructure and (b) microstructure after annealing for 12 h at 1100 °C.
Fig. 3. Unit cells of orthorhombic AlSc phase (a) and B2 AlSc (b).
(Fig. 3b). It belongs to the Au2CuZn-type structure (s1) [18]. The refined atomic positions are Wyckoff site 4 g for Al atoms, i.e., (0.168, 0.138, 0), and Wyckoff site 4 h for Sc atoms, i.e., (0.706, 0.107, 0.5). A goodness of fit from about 1.0 to about 2.0 may indicate sufficient accuracy of the theoretical diffraction pattern, while the goodness of the Rietveld fit is about 2.5 (with Rp = 11.1%, Rwp = 14.5%, Rexp = 5.53%) in our program. Notwithstanding the space group Pbam was retained in the present work, space groups of other orthorhombic structures were also tested but were rejected because the only satisfactory packing and diffraction patterns were obtained when the Sc and Al atoms have the similar parameters to those of Au2CuZn. Lattice parameters of B2 AlSc with both compositions are all around 3.410 Å. In addition, atomic occupations of B2 AlSc with 50 at.% Sc in the Al–50Sc alloy can be determined easily with Al in Wyckoff site 1a and Sc in 1b, whereas B2 AlSc with Sc around 55 at.% in the Al–55Sc alloy has an off-stoichiometric composition, indicating that some 1a positions may be occupied by Sc atoms or vacancies. It is possible, however, to conclude that two kinds of B2 AlSc with different compositions are highly ordered and belong to the same structure because of considerable intensities of {1 0 0} peaks in both phases. 3.3. B2 and orth-AlSc in Al–50Sc alloy annealed at 1100 °C Because two alloys that contain orth-AlSc indicate the presence of B2 AlSc after annealing at 1100 °C for a long time, we therefore performed a detailed microscopic observation and microprobe analysis of the Al–50Sc alloy. The micrograph of the Al–50Sc hypereutectic alloy (Fig. 4a) indicates that the orth-AlSc + Al2Sc lamellar structure distributes at the boundaries of the massive orth-AlSc proeutectic phase and forms a continuous or quasi-continuous network-shaped microstructure. Similar to the annealed Al–45Sc alloy, the eutectic
lamellar of orth-AlSc + Al2Sc disappears completely after annealing at 1100 °C for 12 h, and the SEM micrograph does not indicate the presence of B2 AlSc. To confirm the structures of both AlSc compounds and to investigate the potential orientation relationship between orth-AlSc and B2 AlSc, SADPs are employed. Fig. 4c and d indicate that two selected patterns of the orth-AlSc phase (marked by A) in Fig. 4b exhibit typical superlattice diffractions of a crystal structure with the space group Pbam, which confirms the XRD results. The bright field TEM micrograph of the Al–50Sc alloy annealed at 1100 °C indicates the presence of the B2 phase (Fig. 4b) surrounded by orth-AlSc grains, because the corresponding SADP (top right inset in Fig. 4b) shows a regular hexagon, indicating a cubic structure. In addition, B2 AlSc is not similar to the typical non-equilibrium precipitates composed of small particles, laths or needles dispersed in the matrix [17,19]. The size of the B2 AlSc grain is on the micrometer scale (>1 lm) with obvious boundaries in the orth-AlSc phase. Most of the B2 AlSc grains observed in the TEM are surrounded by the orth-AlSc grains. Few defects are observed in the orth-AlSc grain, which is next to the B2 AlSc grain (Fig. 4 b). However, far away from the B2 AlSc, the orth-AlSc displays more defects and submicrostructures (Fig. 5). The SADP (top right inset in Fig. 5) of the black stripes has a zone axis, while the SADP of the white stripes cannot be ½1 0 3 rotated to a right zone axis. The sharp contrast between the two stripes may be explained in terms of a large disorientation in the two submicrostructures, which also indicates the low stacking fault energy of orth-AlSc. In addition, differences in two kinds of microstructure in orthorhombic AlSc indicate that the formation of B2 AlSc can relax the stress and distortion in the orthorhombic AlSc via high-temperature annealing. Unfortunately, we cannot determine the orientation between the two phases from the TEM diffraction patterns because B2 AlSc has no common orientation with the peripheral ortho-AlSc grains in our current experiment. Therefore, additional studies are required.
195
J. Li et al. / Journal of Alloys and Compounds 618 (2015) 192–196
Fig. 4. Microstructure of the orth-AlSc phase: (a) Backscattered-electron SEM image of the as-cast Al–50Sc and (b) bright field TEM images of the orth- and B2 AlSc. The top right inset displays the SADP from the corresponding region. (c) and (d) are the SADP of region A in (b) along the directions of [1 0 0] and ½1 0 1.
Fig. 5. Bright field TEM image of the orth-AlSc phase with sharp contrast submicrostructures.
Table 1 First-principles (F-P) predicted equilibrium properties of AlSc, including equilibrium volume (V0 (Å3/atom)), relative energy (DE0 (meV/atom)), bulk modulus (B0 (GPa)) and the first derivative of bulk modulus with respect to pressure (B0 ). Structure
a
b
c d
Space group
V0 a
DE0
B0
B0
Note
orth-AlSc
Pbam
19.579 19.489b
0
74.9
3.67
This work, F-P
B2 AlSc
pm3m
19.329 19.826b
5.4
76.1 72c 79.92d
4.00
This work, F-P
First-principles predicted lattice parameters at 0 K (without the effect of zero point vibrational energy) are a = 5.040, b = 9.910, and c = 3.140 Å. In addition, the relaxed atomic positions are (0.178, 0.106, 0.0) for Al and (0.685, 0.137, 0.5) for Sc. Measured room temperature lattice parameters in the present work are a = 5.032, b = 9.902, and c = 3.129 Å for orth-AlSc and a = 3.410 Å for B2 AlSc. Note that the measured atomic positions for Al atom (Wyckoff site 4 g) and Sc atom (Wyckoff site 4 h) are (0.168, 0.138, 0) and (0.706, 0.107, 0.5), respectively. Other first-principles calculations using the full-potential linear muffin-tin orbitals method within local-density-functional approximation [20]. Other first-principles calculations using the generalized gradient approximation [6].
3.4. First-principles results Table 1 summarizes the first-principles results for both orthand B2 AlSc, including equilibrium volume, relative energy (with respect to B2 AlSc), bulk modulus and its pressure derivative. In
addition, the present measurements of lattice parameters and other first-principles results [6,20] of bulk modulus of B2 phase are also included for comparison. It is found that the present first-present equilibrium volume and lattice parameters agree well with experimental data, especially for orth-AlSc (19.579 vs.
196
J. Li et al. / Journal of Alloys and Compounds 618 (2015) 192–196
19.489 Å3/atom, see Table 1). Concerning the bulk modulus of B2 phase, the present prediction (76 GPa) is also in good agreement with other predictions [6,20] (72 and 80 GPa, see Table 1). About the first derivative of bulk modulus with respect to pressure, the present results (3.67 and 4.00) are also fallen in the region for most materials (3–6, see [21]). Regarding phase stability, the present first-principles calculations indicate that the orthorhombic AlSc with the space group Pbam is more stable than B2 AlSc with the space group pm3m, and the energy difference between them is 5.4 meV/atom at 0 K, see Table 1. However, the slight energy difference also indicates that other factors, such as stress and impurity, might reverse the phase stability of orth-AlSc and B2 AlSc. Additionally, phase transition between these two compounds can be generated easily because of such low formation energy barrier. 4. Discussion Based on results in the literature, impurity can cause the disappearance of orth-AlSc and the appearance of B2 AlSc. However, in the present Al–50Sc alloy, B2 and orth-AlSc can coexist with the same composition after annealing at high temperatures, but the B2 AlSc disappears under annealing at low temperatures. It appears that impurities do not play a vital role in the formation of B2 in the annealed Al–50Sc. However, annealing at high temperatures may have some special impact on the microstructures of ortho-AlSc in the Al–50Sc alloy. As mentioned in Section 3.4, the energy difference between these two AlSc compounds is small (5.4 meV/atom), indicating the phase stability can be changed easily in terms of alloying and stress. By considering the influence of local stress, a reasonable mechanism can be tentatively proposed to elucidate the lattice evolution that relieves the tensile stress upon cooling from high temperatures. The annealing temperature of 1100 °C is believed to be higher than the temperature of the alloy above which the orth-AlSc lattice is unstable. In addition, the fast cooling from 1100 to 1000 °C leads to local enrichment in the tensile stress in minor grains enclosed by major grains. Due to the local high tensile stress applied to the crystal plane, the orth ? B2 phase transformation occurs, implying that this transformation can relieve the local stress/strain. However, much faster cooling (quenching) from 1100 °C will maintain the lattice or keep the atoms from moving and preserve the lattice distortion and expansion. The special orientation between the metastable phase and the matrix is not expected during this transition. This mechanism can be confirmed by the volume change during the phase transition. According to the lattice parameters obtained from TEM and XRD for the Al–50Sc sample annealed at 1100 °C, the density of the B2 AlSc phase is approximately 3.013 g cm3, and the density of orth-AlSc ranges from 3.041 (annealed at 1100 °C) to 3.070 (annealed at 900 °C) g cm3. B2 AlSc has a lower density than orth-AlSc, and the B2 AlSc transformation may result in a relative expansion in the volume. Based on the volume change, a local enrichment in tensile stress (resulting from the interaction of stress fields of the peripheral grains) would provide favorable sites for transformation of orth-AlSc to B2 AlSc. As mentioned above, B2 phase is absent in the Al–45Sc alloy annealed at 1100 °C for 5 h. A microscopic observation shows that eutectic lamellar of orthAlSc + Al2Sc changes little and the microstructure of orth-AlSc is fine and insular. This indicates that stress in isolated orthorhombic AlSc grains is insufficient or can be relieved by other phase, and the formation of B2 AlSc requires a continuous matrix of the orthorhombic AlSc grains.
5. Conclusions (1) Two different structures of AlSc were determined in the present work. The phase with 50 at.% Sc exhibits a space group of Pbam with the Au2CuZn-type structure, while the alloys with 55 at.% Sc exhibit a CsCl-type B2 structure. (2) B2 AlSc is a metastable phase in alloys with the orth-AlSc phase (or with scandium less than 50 at.%). The orth-AlSc cooling from high temperatures can transform into B2 AlSc. Decrease of heating temperature to 1000 °C is not favorable for the formation of B2 phase. Microstructure observation reveals that the orthorhombic AlSc grains far away from the B2 AlSc display more defects than those close to the B2 AlSc, indicating that B2 AlSc can lessen the distortion in orthorhombic AlSc from high temperatures. (3) First-principles calculations predict that the orth-AlSc is more stable than B2 AlSc with the energy difference being 5.4 meV/atom. A small energy difference between these two phases implies that the B2 AlSc can become stable and the phase transition between these two compounds is easy. (4) Phase transition between these two AlSc phases can be well understood in terms of volume change; the local tensile stress in the cooling of the orth-AlSc phase from high temperatures plays a major role in the formation of the metastable B2 phase.
Acknowledgments The authors acknowledge the financial support from the National Basic Research Program of China (No. 2011CB606304), the National High Technology Research and Development Program of China (No. 2012AA03A505), the Program for Changjiang Scholars and Innovative Research Team in University, and the Specialized Research Fund for the Doctoral Program of Higher Education (20100006110013). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
O. Schob, E. Parthé, Acta Crystallogr. 19 (1965) 214–224. J.C. Schuster, J. Less-Common Met. 109 (1985) 345–350. J.L. Murray, J. Phase Equilib. 19 (1998) 380–384. K.A. Gschneidner, F.W. Calderwood, Bull. Alloy Phase Diagrams 10 (1989) 34– 36. G. Cacciamani, P. Riani, G. Borzone, N. Parodi, A. Saccone, R. Ferro, A. Pisch, R. Schmid-Fetzer, Intermetallics 7 (1999) 101–108. X.M. Tao, Y.F. Ouyang, H.S. Liu, F.J. Zeng, Y.P. Feng, Z.P. Jin, Physica B 399 (2007) 27–32. M. Asta, V. Ozolinn ß š, Phys. Rev. B 64 (2001). 094104.1–14. G. Trimarchi, A.J. Freeman, A. Zunger, Phys. Rev. B 80 (2009). 092101.1–4. J. Li, F. Ye, L. Huang, Y.F. Liang, Mater. Sci. Forum 747 (2013) 9–13. J. Rodríguez-Carvajal, An Introduction to the Program Fullprof 2000, Version 2001, Laboratoire Léon Brillouin, CEA-CNRS, Saclay (France), 2001. G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169–11186. G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758–1775. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865–3868. M. Methfessel, A.T. Paxton, Phys. Rev. B 40 (1989) 3616–3621. P.E. Blöchl, Phys. Rev. B 50 (1994) 17953–17979. S.L. Shang, Y. Wang, D. Kim, Z.K. Liu, Comput. Mater. Sci. 47 (2010) 1040–1048. F. Prima, P. Vermaut, G. Texier, D. Ansel, T. Gloriant, Scr. Mater. 54 (2006) 645– 648. M. Wilkens, K. Schubert, Z. Metallkd. 48 (1957) 550–557. C.S. Tsao, C.Y. Chen, U.S. Jeng, T.Y. Kuo, Acta Mater. 54 (2006) 4621–4631. D. Nguyen-Manh, D.G. Pettifor, Intermetallics 7 (1999) 1095–1106. S.L. Shang, A. Saengdeejing, Z.G. Mei, D.E. Kim, H. Zhang, S. Ganeshan, Y. Wang, Z.K. Liu, Comput. Mater. Sci. 48 (2010) 813–826.