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α2-Ti3Al(0 0 0 1) interfaces
Applied Surface Science 276 (2013) 198–202
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First principles study of ␣2 -Ti3 Al(0 0 0 1) surface and ␥-TiAl(1 1 1)/␣2 -Ti3 Al(0 0 0 1) interfaces Lu Wang a , Jia-Xiang Shang a,∗ , Fu-He Wang b , Yue Zhang a a b
School of Materials Science and Engineering, Beihang University, Beijing 100191, PR China Department of Physics, Capital Normal University, Beijing 100048, PR China
a r t i c l e
i n f o
Article history: Received 22 September 2012 Received in revised form 8 March 2013 Accepted 8 March 2013 Available online 23 March 2013 Keywords: Titanium aluminides Interface First-principles calculation
a b s t r a c t The ␣2 -Ti3 Al(0 0 0 1) surface and ␥-TiAl(1 1 1)/␣2 -Ti3 Al(0 0 0 1) interfaces with six orientation relationships are studied by using the first-principle density functional theory. The calculated results indicate that the Ti3 Al(0 0 0 1) surface has a higher surface energy (1.964 J/m2 ) and larger surface relaxations, compared with the ␥-TiAl(1 1 1) surface. For the ␥-TiAl(1 1 1)/␣2 -Ti3 Al(0 0 0 1) interface structures, the work of separation along Ti3 Al(0 0 0 1) cleavage plane is larger than that along TiAl(1 1 1) plane. In the interface region, the bonding strengths between Ti3 Al layers and between TiAl layers are smaller than those along Ti3 Al(0 0 0 1) plane and TiAl(1 1 1) plane in the bulk materials, respectively. The heterogeneous interface would be the weak link in the material, and the bonding strength of interface depends on the weaker one of the two phases. The bonding characteristics of interface are analyzed by the electron local function. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Two-phase TiAl alloys, composed of ␥-TiAl and smaller amounts of ␣2 -Ti3 Al, are nowadays attracting a great deal of interests due to their better ductility and toughness than single-phase ␥-TiAl alloys [1]. Experimentally, considerable research efforts are devoted to the detailed characterization of the mechanical properties of twophase TiAl alloys in relation to microstructure [2–9]. It has been clearly established that the lamellar microstructure offers good mechanical behavior at high temperature [2], relatively high fracture toughness [3–5], superplasticity [6], and creep resistance [7,8]. On the other hand, adding alloying elements or light elements in TiAl-based alloys to improve various performances also has been extensively studied [10–12]. Moreover, the orientation relationship of {1 1 1}␥ //(0 0 0 1)␣2 and 1 1¯ 0␥ //1 1 2¯ 0␣2 between TiAl and Ti3 Al in the lamellar structure of two-phase TiAl alloys has been confirmed by transmission electron microscopy. There are six possible orientations for the [1 1 0] direction of ␥-TiAl with respect to the 1 1 2 0 direction of ␣2 -Ti3 Al [13,14]. The improvement in mechanical properties is partly due to the presence of lamellar boundaries in the material. In order to better understand the ␥/␥ and ␥/␣2 interfaces in TiAl lamellar structure, many theoretical studies were reported. Vitek et al. [15] investigated the effect of covalent-type bonding and segregation upon
∗ Corresponding author. Tel.: +86 10 8231 6500; fax: +86 10 8231 6500. E-mail address: [email protected] (J.-X. Shang). 0169-4332/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.apsusc.2013.03.065
the structure of ␥/␥ interfaces in the lamellar structures of Ti–Al alloys and suggested that in Ti-rich alloys a significant segregation took place in some ␥/␥ interfaces leading to the formation of a very narrow region of the DO19 -Ti3 Al. Moreover, atomistic studies of interactions between the dominant lattice dislocations and ␥/␥lamellar boundaries in lamellar ␥-TiAl were studied by Katzarov et al. [16]. There are three types of ␥/␥ interface formed by rotation about the [1 1 1] axis at angles of 60◦ , 120◦ and 180◦ . The interfacial energies and interfacial work of adhesion of these ␥/␥ interfaces were reported by Fu et al. [17]. They used the full-potential linearized augmented plane-wave method to calculate the interfacial energy and the planar fault energies at the ␥/␣2 interface and evaluate interfacial work of adhesion [18], and the results indicated that the cleavage energy of the ␥/␣2 interface was the same as that of (1 1 1) plane of the ␥ phase and the cleavage energy on the (0 0 0 1) plane of the ␣2 phase was larger than those of any other ␥/␥ interfaces. Recently, Wei et al. [19,20] investigated the effect of oxygen on the ␥-TiAl/␣2 -Ti3 Al interface, and indicated that oxygen weakened the interface strength but strongly stabilized the TiAl/Ti3 Al interface. However, the above studies are mainly concerning on the ␥/␥ interfaces and one of the ␥/␣2 interfaces. Therefore, the microstructures and fracture properties of clean ␥-TiAl(1 1 1)/␣2 Ti3 Al(0 0 0 1) interfaces with six orientation relationships are still unclear. In this paper, we calculate the surface energy of the Ti3 Al(0 0 0 1) surface, the interface energies and work of separation along different cleave planes near to interfaces of the six ␥-TiAl(1 1 1)/␣2 Ti3 Al(0 0 0 1) interfaces by first-principles calculations.
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and 400 eV of kinetic-energy cutoff are used. All atomic coordinates are optimized until the force of each atom is less than 0.01 eV A˚ −1 , and the lattice parameters are fixed. The surface energy is defined as a difference between the total energy of surface atoms (Eslab ) and that of atoms in bulk (Ebulk ) [28]. Therefore, the surface energy s of Ti3 Al(0 0 0 1) surface can be written as s = [Eslab (N) − Ebulk (N)]/(2As )
Fig. 1. Top view of the Ti3 Al(0 0 0 1) surface. Large and small brown (black) and yellow (gray) balls represent the Ti and Al atoms in the first and second surface layers for color (grayscale) figures, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
2. Methodology The calculations presented in this paper are carried out by using the Vienna ab initio simulation package (VASP) [21–23] based on density functional theory. The calculation is conducted in a plane-wave basis, using the projector-augmented wave (PAW) method [24,25]. For the exchange-correction energy functional, the PW91 generalized gradient approximation (GGA) [26] is employed. We use a kinetic-energy cutoff of 400 eV and 11 × 11 × 11 Monkhorst–Pack k points in the Brillouin zone for bulk ␣2 -Ti3 Al calculations. All atomic positions in our models have been fully relaxed until the force of every atom is less than 0.01 eV/Å. The ˚ c/a = 0.81, calculated lattice constants of bulk ␣2 -Ti3 Al are a = 5.73 A, which are in excellent agreement with the experimental values ˚ c/a = 0.8 [27]. a = 5.76 A, For the Ti3 Al(0 0 0 1) surface, the surface calculation is done in 1 × 1 surface unit cells with 11 × 11 × 1 Monkhorst–Pack k points in the Brillouin zone. In order to prevent unwanted interactions between the slab and its periodic images, the surface is modeled by a slab of seven atomic layers separated by a vacuum region of ˚ All atomic positions in the slab are optimized until the force 15 A. of each atom is less than 0.01 eV A˚ −1 . For Ti3 Al(0 0 0 1) surface, the ratio of Ti atom and Al atom is 3:1 at every layer, shown in Fig. 1. The present interface calculations were focused on the coherent interface structures formed by ␥-TiAl(1 1 1) and ␣2 -Ti3 Al(0 0 0 1) surfaces. According to the experimental observation [14], the twophase TiAl compounds exhibit the lamellar structure consisting of the twin-related ␥-TiAl and ␣2 -Ti3 Al phase with the orientation relationship of {1 1 1}␥ //(0 0 0 1)␣2 and 1 1¯ 0␥ //1 1 2¯ 0␣2 . There are six orientation variants of the ␥ phase with respect to the basal plane of the ␣2 phase [13]. The lattice lengths of a1 1 0{1 1 1}␥ are ˚ while that of a ˚ Therefore, the is 5.73 A. 5.63 and 5.70 A, 1 1 2 0(0 0 0 1)␣ 2
lattice misfits of X and Y directions of ␥-TiAl(1 1 1)/␣2 -Ti3 Al(0 0 0 1) are 1.76% and 0.52%, which possess a good matching. The average lattice parameters of ␥-TiAl(1 1 1) and ␣2 -Ti3 Al(0 0 0 1) are adopted in our interface models. We denote the stacking sequences of Ti3 Al and TiAl as AB and A’B’C’, respectively. The six models that we have constructed are represented by: (a) (b) (c) (d) (e) (f)
A C B A C B A —ABABABA; A B C A B C A —ABABABA; B A C B A C B —ABABABA; C A B C A B C —ABABABA; C B A C B A C —ABABABA; B C A B C A B —ABABABA;
Fig. 2 shows the six interface structures. For each interface model, there are seven ␥-TiAl layers and seven ␣2 -Ti3 Al layers with 15 A˚ vacuum layers. The 5 × 5 × 1 Monkhorst–Pack K-point
(1)
where N symbolizes that Eslab and Ebulk correspond to the same number N of the Ti3 Al(0 0 0 1) surface and Ti3 Al bulk, and As is the corresponding area of the surface. The work of interface separation (Wsep ) is calculated according to the following equation [29–31]: Wsep = (EsTi3 Al + EsTiAl − ETi3 Al/TiAl )/A
(2)
where EsTi3 Al and EsTiAl denote the total energies of the relaxed, isolated Ti3 Al and TiAl surface, respectively. ETi3 Al/TiAl is the total energy of the Ti3 Al/TiAl interface model, and A is the area of interface. It should be pointed out that the work of separation is the work required to reversibly separate the interface into two free surfaces, and Wsep is therefore a direct measure of the interface bond strength. The interface energy i is related to the thermodynamic properties of interface [31]. In our interface models, there are one interface and two surfaces. Therefore, the interface energy i is determined by the equation as follows: TiAl Ti3 Al i = [ETi3 Al/TiAl − (Ebulk + Ebulk )]/A − (sTiAl + sTi3 Al )
(3)
where ETi3 Al/TiAl and A have the same meaning as described in
TiAl and E Ti3 Al are the bulk energies, and TiAl and Ti3 Al are Eq. (2), Ebulk s s bulk the surface energies of the TiAl and Ti3 Al surfaces.
3. Results and discussion 3.1. Ti3 Al(0 0 0 1) surface In our previous work [32], the low-index surfaces of ␥-TiAl have been investigated in detail. The calculated surface energy of TiAl(1 1 1) surface is 1.691 J/m2 . In this paper, the calculated surface energy of ␣2 -Ti3 Al(0 0 0 1) surface is 1.964 J/m2 . This indicates that the cleavage energy along the ␣2 -Ti3 Al(0 0 0 1) surface is larger (2 s = 3.928 J/m2 ) than that along the ␥-TiAl(1 1 1) surface (2 s = 3.382 J/m2 ). This is consistent with the result of Wei et al. [19], in which the cleavage energies of the Ti3 Al(0 0 0 1) and TiAl(1 1 1) are 4.03 J/m2 and 3.45 J/m2 , respectively. Surface relaxation and surface rumpling are important features of the surface structure. Interlayer relaxation can be evaluated by = d − d0 . Here d and d0 are the interlayer distances of the relaxed surface and bulk materials, respectively. We also calculate the surface rumpling ε, which is defined by the following relation [33]: ε = LAl − LTi . Here LAl and LTi are the heights of Al and Ti atoms in the same layer. The calculated results of surface relaxation and surface rumpling of ␣2 -Ti3 Al(0 0 0 1) compared with that in ␥-TiAl(1 1 1) surfaces [32] are listed in Table 1. It is observed that the surface interlayer relaxation between the first and second layers 12 contracted and interlayer relaxation 23 has a little expansion for the ␣2 Ti3 Al(0 0 0 1) surface, and the interlayer relaxation 12 is larger than 23 . In addition, our previous work [32] indicated that the higher surface energy may lead to the larger surface relaxation. Compared with the TiAl(1 1 1) surface, the Ti3 Al(0 0 0 1) surface has relatively larger interlayer relaxation. This indicates that the Ti3 Al(0 0 0 1) surface is less stable than the TiAl(1 1 1) surface, which is consistent with the results of the surface energy.
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Fig. 2. The six different interface structures of TiAl(1 1 1)/Ti3 Al(0 0 0 1), which is denoted by a, b, c, d, e, f, respectively. The brown (black) and yellow (gray) balls represent the Ti and Al atoms for color (grayscale) figures, respectively. The different layers in the interface region are labeled by 1–8 to discuss clearly. The TiAl(1 1 1)/Ti3 Al(0 0 0 1) interface is between 4 and 5 layers. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
From Table 1, it is also found that the rumpling of the ␣2 Ti3 Al(0 0 0 1) surface decreases from the first to the third surface layer, which indicates that the atoms in the top-layer are active. The surface rumpling ε1 is positive, indicating that the Al atoms are displaced outward relative to the Ti atoms in the top surface layer. This suggests that Al atoms prefer to stay the outer layer in ␣2 -Ti3 Al(0 0 0 1) surface, which is similar to that of ␥-TiAl(1 1 1). Moreover, the surface rumpling of the ␣2 -Ti3 Al(0 0 0 1) surface are the larger than those of the ␥-TiAl(1 1 1) surface, due to its higher surface energy. In order to better understand the surface characteristic, the electronic structures are calculated. Fig. 3 shows the comparisons of the partial densities of states (PDOSs) for one Ti and one Al atom on the Ti3 Al(0 0 0 1) top surface and center layers. It is obvious that the peaks of the PDOSs for Ti-d, Ti-p and Al-p of the Ti3 Al surface layer are located at Fermi level, while the peaks of those in the center layer are located at lower energy region, showing the activity of surface atoms. It is also seen that the peaks of PDOSs for Al-s are rather higher and for Ti-p are slightly higher in the Ti3 Al surface layer at −5 eV below the Fermi energy compared with those in the center layer, which indicates that there are the strong interactions between Ti-p and Al-s in surface at this energy.
3.2. Interface of TiAl/Ti3 Al As mentioned in Section 2, the geometries of the six interface models are optimized. The work of separation, interface energy and
Table 1 Surface relaxation (in Å) and surface rumpling ε (in Å) of Ti3 Al(0 0 0 1) and TiAl(1 1 1) surfaces. Ti3 Al(0 0 0 1)
TiAl(1 1 1)
Interlayer
12 23
−0.02 0.007
−0.012a −0.003a
Rumpling
ε1 ε2 ε3
0.188 −0.101 0.031
0.151a 0.022a −0.010
a
Reference [32].
Fig. 3. The comparison of PDOSs for one Ti and one Al atom on the first layer of Ti3 Al(0 0 0 1) surface and center layer. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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Table 2 Work of separation Wsep (J/m2 ), interface energy ␥i (J/m2 ) and interface separation d for coherent interfaces between ␥-TiAl and ␣2 -Ti3 Al. Interface configuration
a b c d e f
␥i (J/m2 )
0.410 0.350 0.405 0.416 0.328 0.336
Wsep (J/m2 )
d (Å)
TiAl(3)/TiAl(4)
TiAl(4)/Ti3 Al(5)
Ti3 Al(5)/Ti3 Al(6)
3.171 3.231 3.178 3.216 3.302 3.245
3.262 3.322 3.268 3.257 3.345 3.336
3.716 3.724 3.721 3.711 3.743 3.735
interface separation are calculated and listed in Table 2. In order to better understand the bond strength in the interface region, we assume the interfaces cleave at TiAl(3)/TiAl(4), TiAl(4)/Ti3 Al(5) and Ti3 Al(5)/Ti3 Al(6) (see Fig. 2). From Table 2, it is found that the structure (e) has the smallest value of i and the largest value of Wsep among the six interface configurations, indicating that the interface structure (e) is the most stable. However, the energy differences of the six interfaces are very small. It is also seen that the “on-top site” interfacial structures (a) and (b) have small interface separation, and the values of Wsep and i are close to those of other four “vacancy-site” interface structures, which is different from NiAl/Cr interface model [31]. This may be caused by the attraction of heterogeneous atoms Ti–Al near interfacial layers. From Table 2, it is found that in the interface region, the work of interface separation between Ti3 Al(5) and Ti3 Al(6) layers is the largest, followed by TiAl(4)/Ti3 Al(5) interface layer, and that between TiAl(3) and TiAl(4) layers is the smallest. Comparing with the energy required to split the bulk into two surfaces of TiAl(1 1 1) (2 s = 3.382 J/m2 ) or of Ti3 Al(0 0 0 1) (2 s = 3.928 J/m2 ), we can know that the work of separation between Ti3 Al(5) and Ti3 Al(6) layers in the interface region is smaller than that along Ti3 Al(0 0 0 1) plane in the bulk. Similarly, the work of separation between TiAl(4) and TiAl(5) layers in the interface region is smaller than that along TiAl(1 1 1) plane in the bulk. In addition, the work of separation of TiAl(4)/Ti3 Al(5) interface is closer to that of TiAl(1 1 1) plane, which is consistent with the results of Fu et al. [17] and Wei et al. [19]. Fu et al. and Wei et al. reported that the calculated cleavage energies of the TiAl/Ti3 Al interface, the TiAl(1 1 1) plane, and the Ti3 Al(0 0 0 1) plane are 4.5 J/m2 , 4.5 J/m2 , 4.8 J/m2 and 3.62 J/m2 , 3.45 J/m2 , 4.03 J/m2 , respectively. We can conclude that the bonding strength of interface depends on the weaker one of the two phases and the heterogeneous interface would be the weak link in the material, which can be also confirmed in the other two-phase materials [29,34,35]. From above analysis, we have known that there are different work of separation and bonding strengths when the ␥-TiAl(1 1 1)/␣2 -Ti3 Al(0 0 0 1) interface is cleaved along different cleavage planes. In order to better understand the bonding characteristics between different layers, we employ the electron localization function (ELF) [36–38] to describe the chemical bonds and electron pairs for the most stable interface structure (e). The
2.307 2.319 2.306 2.321 2.327 2.320
value of ELF is restricted to 0 ≤ ELF ≤ 1, with ELF = 1 corresponding to completely electron pair localization, and ELF = 0.5 representing a homogeneous electron gas-like pair probability (electron delocalization). Generally, the ELF in the region of 0.5 < ELF ≤ 1 corresponds to some degree of covalent bonding. The larger the ELF is, the stronger the covalent nature of the bond is. The ELF of different cleavage planes are showed in Fig. 4. (a) and (e) are the ELF of the TiAl(1 1 1) and Ti3 Al(0 0 0 1) cleavage planes in the bulk materials, respectively. Fig. 4(b), (c) and (d) are the ELF of the TiAl(1 1 1)/Ti3 Al(0 0 0 1) interface along TiAl(3)/TiAl(4), TiAl(4)/Ti3 Al(5) and Ti3 Al(5)/Ti3 Al(6) cleavage planes (see Fig. 2). To maintain consistency, all the cleavage planes in Fig. 4 are selected in the middle area between two layers. From Fig. 4, it is observed that the Ti3 Al(0 0 0 1) cleavage plane in the bulk has the strongest bonding, where the ELF attains the maximum value of 0.74. Therefore, the Ti3 Al(0 0 0 1) cleavage plane needs to break the stronger covalent bond to separate the bulk into two surfaces, compared with TiAl(1 1 1) cleavage plane. Thus the work of separation along Ti3 Al(0 0 0 1) plane (3.928 J/m2 ) is larger than that along the TiAl(1 1 1) cleavage plane (3.382 J/m2 ) in the bulk. Comparing Fig. 4(a) with (b), the red regions representing the strongest bonding have the same proportions, but the TiAl(3)/TiAl(4) cleavage plane has a slightly lower ELF maximum value than the TiAl(1 1 1) plane, so the TiAl(3)/TiAl(4) cleavage plane breaks the relatively weaker covalent bond. Therefore, the work of separation between TiAl(3) and TiAl(4) layers in the interface region (3.302 J/m2 ) is slightly smaller than that along TiAl(1 1 1) plane (3.382 J/m2 ) in the bulk. Similarly, comparing Fig. 4(d) with (e), the Ti3 Al(5)/Ti3 Al(6) cleavage plane has a lower ELF maximum value than the Ti3 Al(0 0 0 1) plane in the bulk. Therefore, the work of separation between Ti3 Al(5) and Ti3 Al(6) layers in the interface region (3.743 J/m2 ) is smaller than that along Ti3 Al(0 0 0 1) plane (3.928 J/m2 ) in the bulk. Moreover, it can be seen that the ELF plot of the interface between TiAl(1 1 1) and Ti3 Al(0 0 0 1) (see Fig. 4(c)) is completely different from TiAl phase or Ti3 Al phase. The TiAl(4)/Ti3 Al(5) cleavage plane has the relatively smaller ELF value than the TiAl(1 1 1) and Ti3 Al(0 0 0 1) planes, so there is the weaker covalent bonding in the TiAl(1 1 1)/Ti3 Al(0 0 0 1) interface. Therefore, the heterogeneous interface would be the weak link in the material. In addition, it is seen from Fig. 4 that the ELF maximum value of TiAl(1 1 1)/Ti3 Al(0 0 0 1) interface is closer to the TiAl(1 1 1) phase than Ti3 Al(0 0 0 1) phase, which explains the reason why
Fig. 4. The ELF along different cleavage planes. (a) TiAl(1 1 1) plane in the bulk; (b) TiAl(3)/TiAl(4) plane; (c) TiAl(4)/Ti3 Al(5) plane; (d) Ti3 Al(5)/Ti3 Al(6); (e) Ti3 Al(0 0 0 1) plane in the bulk. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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the work of separation of TiAl/Ti3 Al interface is closer to that of TiAl(1 1 1) plane, and further indicates that the bonding strength of interface depends on the weaker one of the two phases. 4. Conclusions In conclusion, the first-principle method based on DFT is employed to study the surface properties of ␣2 -Ti3 Al(0 0 0 1) and the interface properties including interface energy and interfacial work of separation of the six different ␥-TiAl(1 1 1)/␣2 -Ti3 Al(0 0 0 1) interface configurations. It is found that Ti3 Al(0 0 0 1) surface has higher surface energy and larger surface relaxation than TiAl(1 1 1) surface. The surface atomic layer is rather active and Al atoms prefer to stay the outer layer in Ti3 Al(0 0 0 1) surface. It is also revealed that the interface structure (e) is the most stable among the six TiAl(1 1 1)/Ti3 Al(0 0 0 1) interface structures. The work of separation along Ti3 Al(0 0 0 1) cleavage plane is larger than that along TiAl(1 1 1) plane. The bonding strengths between Ti3 Al layers and between TiAl layers in the interface region are smaller than those of the corresponding Ti3 Al(0 0 0 1)/Ti3 Al(0 0 0 1) plane and TiAl(1 1 1)/TiAl(1 1 1) plane in the bulk, respectively. The heterogeneous interface would be the weak link in the material. In addition, the work of separation of TiAl(1 1 1)/Ti3 Al(0 0 0 1) interface is closer to that of TiAl(1 1 1) plane, indicating that the bonding strength of interface depends on the weaker one of the two phases. The electron local function is used to analyze the bonding characteristic of interface. It is found that the ELF of interface is different from both TiAl(1 1 1) and Ti3 Al(0 0 0 1). Acknowledgment The work was financially supported by National Natural Science Foundation of China under Grant Nos. 50871071 and 51071011. References [1] F. Appel, R. Wagner, Microstructure and deformation of two-phase-titanium aluminides, Materials Science and Engineering: R: Reports 22 (1998) 187–268. [2] J.X. Zhang, H.Q. Ye, The deformation twin in lamellar Ti3 Al/TiAl structure, Solid State Communications 126 (2003) 217–221. [3] K. Chan, Toughening mechanisms in titanium aluminides, Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science 24 (1993) 569–583. [4] K. Chan, Y.W. Kim, Relationships of slip morphology, microcracking, and fracture resistance in a lamellar TiAl-alloy, Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science 25 (1994) 1217–1228. [5] K. Chan, D. Shih, Fatigue and fracture behavior of a fine-grained lamellar TiAl alloy, Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science 28 (1997) 79–90. [6] S. Cheng, J. Wolfenstine, O. Sherby, Superplastic behavior of two-phase titanium aluminides, Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science 23 (1992) 1509–1513. [7] S. Karthikeyan, G.B. Viswanathan, P.I. Gouma, V.K. Vasudevan, Y.W. Kim, M.J. Mills, Mechanisms and effect of microstructure on creep of TiAl-based alloys, Materials Science and Engineering A 329–331 (2002) 621–630. [8] X.W. Du, J. Zhu, Y.W. Kim, Microstructural characterization of creep cavitation in a fully-lamellar TiAl alloy, Intermetallics 9 (2001) 137–146. [9] J. Kumpfert, Y.W. Kim, D.M. Dimiduk, Effect of microstructure on fatigue and tensile properties of the gamma TiAl alloy Ti-46.5Al-3.0Nb-2.1Cr-0.2 W, Materials Science and Engineering A 192–193 (Part 1) (1995) 465–473. [10] P.I. Gouma, K. Subramanian, Y.W. Kim, M.J. Mills, Annealing studies of ␥titanium aluminides alloyed with light elements for creep strengthening, Intermetallics 6 (1998) 689–693.
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First principles study of ␣2 -Ti3 Al(0 0 0 1) surface and ␥-TiAl(1 1 1)/␣2 -Ti3 Al(0 0 0 1) interfaces Lu Wang a , Jia-Xiang Shang a,∗ , Fu-He Wang b , Yue Zhang a a b
School of Materials Science and Engineering, Beihang University, Beijing 100191, PR China Department of Physics, Capital Normal University, Beijing 100048, PR China
a r t i c l e
i n f o
Article history: Received 22 September 2012 Received in revised form 8 March 2013 Accepted 8 March 2013 Available online 23 March 2013 Keywords: Titanium aluminides Interface First-principles calculation
a b s t r a c t The ␣2 -Ti3 Al(0 0 0 1) surface and ␥-TiAl(1 1 1)/␣2 -Ti3 Al(0 0 0 1) interfaces with six orientation relationships are studied by using the first-principle density functional theory. The calculated results indicate that the Ti3 Al(0 0 0 1) surface has a higher surface energy (1.964 J/m2 ) and larger surface relaxations, compared with the ␥-TiAl(1 1 1) surface. For the ␥-TiAl(1 1 1)/␣2 -Ti3 Al(0 0 0 1) interface structures, the work of separation along Ti3 Al(0 0 0 1) cleavage plane is larger than that along TiAl(1 1 1) plane. In the interface region, the bonding strengths between Ti3 Al layers and between TiAl layers are smaller than those along Ti3 Al(0 0 0 1) plane and TiAl(1 1 1) plane in the bulk materials, respectively. The heterogeneous interface would be the weak link in the material, and the bonding strength of interface depends on the weaker one of the two phases. The bonding characteristics of interface are analyzed by the electron local function. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Two-phase TiAl alloys, composed of ␥-TiAl and smaller amounts of ␣2 -Ti3 Al, are nowadays attracting a great deal of interests due to their better ductility and toughness than single-phase ␥-TiAl alloys [1]. Experimentally, considerable research efforts are devoted to the detailed characterization of the mechanical properties of twophase TiAl alloys in relation to microstructure [2–9]. It has been clearly established that the lamellar microstructure offers good mechanical behavior at high temperature [2], relatively high fracture toughness [3–5], superplasticity [6], and creep resistance [7,8]. On the other hand, adding alloying elements or light elements in TiAl-based alloys to improve various performances also has been extensively studied [10–12]. Moreover, the orientation relationship of {1 1 1}␥ //(0 0 0 1)␣2 and 1 1¯ 0␥ //1 1 2¯ 0␣2 between TiAl and Ti3 Al in the lamellar structure of two-phase TiAl alloys has been confirmed by transmission electron microscopy. There are six possible orientations for the [1 1 0] direction of ␥-TiAl with respect to the 1 1 2 0 direction of ␣2 -Ti3 Al [13,14]. The improvement in mechanical properties is partly due to the presence of lamellar boundaries in the material. In order to better understand the ␥/␥ and ␥/␣2 interfaces in TiAl lamellar structure, many theoretical studies were reported. Vitek et al. [15] investigated the effect of covalent-type bonding and segregation upon
∗ Corresponding author. Tel.: +86 10 8231 6500; fax: +86 10 8231 6500. E-mail address: [email protected] (J.-X. Shang). 0169-4332/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.apsusc.2013.03.065
the structure of ␥/␥ interfaces in the lamellar structures of Ti–Al alloys and suggested that in Ti-rich alloys a significant segregation took place in some ␥/␥ interfaces leading to the formation of a very narrow region of the DO19 -Ti3 Al. Moreover, atomistic studies of interactions between the dominant lattice dislocations and ␥/␥lamellar boundaries in lamellar ␥-TiAl were studied by Katzarov et al. [16]. There are three types of ␥/␥ interface formed by rotation about the [1 1 1] axis at angles of 60◦ , 120◦ and 180◦ . The interfacial energies and interfacial work of adhesion of these ␥/␥ interfaces were reported by Fu et al. [17]. They used the full-potential linearized augmented plane-wave method to calculate the interfacial energy and the planar fault energies at the ␥/␣2 interface and evaluate interfacial work of adhesion [18], and the results indicated that the cleavage energy of the ␥/␣2 interface was the same as that of (1 1 1) plane of the ␥ phase and the cleavage energy on the (0 0 0 1) plane of the ␣2 phase was larger than those of any other ␥/␥ interfaces. Recently, Wei et al. [19,20] investigated the effect of oxygen on the ␥-TiAl/␣2 -Ti3 Al interface, and indicated that oxygen weakened the interface strength but strongly stabilized the TiAl/Ti3 Al interface. However, the above studies are mainly concerning on the ␥/␥ interfaces and one of the ␥/␣2 interfaces. Therefore, the microstructures and fracture properties of clean ␥-TiAl(1 1 1)/␣2 Ti3 Al(0 0 0 1) interfaces with six orientation relationships are still unclear. In this paper, we calculate the surface energy of the Ti3 Al(0 0 0 1) surface, the interface energies and work of separation along different cleave planes near to interfaces of the six ␥-TiAl(1 1 1)/␣2 Ti3 Al(0 0 0 1) interfaces by first-principles calculations.
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and 400 eV of kinetic-energy cutoff are used. All atomic coordinates are optimized until the force of each atom is less than 0.01 eV A˚ −1 , and the lattice parameters are fixed. The surface energy is defined as a difference between the total energy of surface atoms (Eslab ) and that of atoms in bulk (Ebulk ) [28]. Therefore, the surface energy s of Ti3 Al(0 0 0 1) surface can be written as s = [Eslab (N) − Ebulk (N)]/(2As )
Fig. 1. Top view of the Ti3 Al(0 0 0 1) surface. Large and small brown (black) and yellow (gray) balls represent the Ti and Al atoms in the first and second surface layers for color (grayscale) figures, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
2. Methodology The calculations presented in this paper are carried out by using the Vienna ab initio simulation package (VASP) [21–23] based on density functional theory. The calculation is conducted in a plane-wave basis, using the projector-augmented wave (PAW) method [24,25]. For the exchange-correction energy functional, the PW91 generalized gradient approximation (GGA) [26] is employed. We use a kinetic-energy cutoff of 400 eV and 11 × 11 × 11 Monkhorst–Pack k points in the Brillouin zone for bulk ␣2 -Ti3 Al calculations. All atomic positions in our models have been fully relaxed until the force of every atom is less than 0.01 eV/Å. The ˚ c/a = 0.81, calculated lattice constants of bulk ␣2 -Ti3 Al are a = 5.73 A, which are in excellent agreement with the experimental values ˚ c/a = 0.8 [27]. a = 5.76 A, For the Ti3 Al(0 0 0 1) surface, the surface calculation is done in 1 × 1 surface unit cells with 11 × 11 × 1 Monkhorst–Pack k points in the Brillouin zone. In order to prevent unwanted interactions between the slab and its periodic images, the surface is modeled by a slab of seven atomic layers separated by a vacuum region of ˚ All atomic positions in the slab are optimized until the force 15 A. of each atom is less than 0.01 eV A˚ −1 . For Ti3 Al(0 0 0 1) surface, the ratio of Ti atom and Al atom is 3:1 at every layer, shown in Fig. 1. The present interface calculations were focused on the coherent interface structures formed by ␥-TiAl(1 1 1) and ␣2 -Ti3 Al(0 0 0 1) surfaces. According to the experimental observation [14], the twophase TiAl compounds exhibit the lamellar structure consisting of the twin-related ␥-TiAl and ␣2 -Ti3 Al phase with the orientation relationship of {1 1 1}␥ //(0 0 0 1)␣2 and 1 1¯ 0␥ //1 1 2¯ 0␣2 . There are six orientation variants of the ␥ phase with respect to the basal plane of the ␣2 phase [13]. The lattice lengths of a1 1 0{1 1 1}␥ are ˚ while that of a ˚ Therefore, the is 5.73 A. 5.63 and 5.70 A, 1 1 2 0(0 0 0 1)␣ 2
lattice misfits of X and Y directions of ␥-TiAl(1 1 1)/␣2 -Ti3 Al(0 0 0 1) are 1.76% and 0.52%, which possess a good matching. The average lattice parameters of ␥-TiAl(1 1 1) and ␣2 -Ti3 Al(0 0 0 1) are adopted in our interface models. We denote the stacking sequences of Ti3 Al and TiAl as AB and A’B’C’, respectively. The six models that we have constructed are represented by: (a) (b) (c) (d) (e) (f)
A C B A C B A —ABABABA; A B C A B C A —ABABABA; B A C B A C B —ABABABA; C A B C A B C —ABABABA; C B A C B A C —ABABABA; B C A B C A B —ABABABA;
Fig. 2 shows the six interface structures. For each interface model, there are seven ␥-TiAl layers and seven ␣2 -Ti3 Al layers with 15 A˚ vacuum layers. The 5 × 5 × 1 Monkhorst–Pack K-point
(1)
where N symbolizes that Eslab and Ebulk correspond to the same number N of the Ti3 Al(0 0 0 1) surface and Ti3 Al bulk, and As is the corresponding area of the surface. The work of interface separation (Wsep ) is calculated according to the following equation [29–31]: Wsep = (EsTi3 Al + EsTiAl − ETi3 Al/TiAl )/A
(2)
where EsTi3 Al and EsTiAl denote the total energies of the relaxed, isolated Ti3 Al and TiAl surface, respectively. ETi3 Al/TiAl is the total energy of the Ti3 Al/TiAl interface model, and A is the area of interface. It should be pointed out that the work of separation is the work required to reversibly separate the interface into two free surfaces, and Wsep is therefore a direct measure of the interface bond strength. The interface energy i is related to the thermodynamic properties of interface [31]. In our interface models, there are one interface and two surfaces. Therefore, the interface energy i is determined by the equation as follows: TiAl Ti3 Al i = [ETi3 Al/TiAl − (Ebulk + Ebulk )]/A − (sTiAl + sTi3 Al )
(3)
where ETi3 Al/TiAl and A have the same meaning as described in
TiAl and E Ti3 Al are the bulk energies, and TiAl and Ti3 Al are Eq. (2), Ebulk s s bulk the surface energies of the TiAl and Ti3 Al surfaces.
3. Results and discussion 3.1. Ti3 Al(0 0 0 1) surface In our previous work [32], the low-index surfaces of ␥-TiAl have been investigated in detail. The calculated surface energy of TiAl(1 1 1) surface is 1.691 J/m2 . In this paper, the calculated surface energy of ␣2 -Ti3 Al(0 0 0 1) surface is 1.964 J/m2 . This indicates that the cleavage energy along the ␣2 -Ti3 Al(0 0 0 1) surface is larger (2 s = 3.928 J/m2 ) than that along the ␥-TiAl(1 1 1) surface (2 s = 3.382 J/m2 ). This is consistent with the result of Wei et al. [19], in which the cleavage energies of the Ti3 Al(0 0 0 1) and TiAl(1 1 1) are 4.03 J/m2 and 3.45 J/m2 , respectively. Surface relaxation and surface rumpling are important features of the surface structure. Interlayer relaxation can be evaluated by = d − d0 . Here d and d0 are the interlayer distances of the relaxed surface and bulk materials, respectively. We also calculate the surface rumpling ε, which is defined by the following relation [33]: ε = LAl − LTi . Here LAl and LTi are the heights of Al and Ti atoms in the same layer. The calculated results of surface relaxation and surface rumpling of ␣2 -Ti3 Al(0 0 0 1) compared with that in ␥-TiAl(1 1 1) surfaces [32] are listed in Table 1. It is observed that the surface interlayer relaxation between the first and second layers 12 contracted and interlayer relaxation 23 has a little expansion for the ␣2 Ti3 Al(0 0 0 1) surface, and the interlayer relaxation 12 is larger than 23 . In addition, our previous work [32] indicated that the higher surface energy may lead to the larger surface relaxation. Compared with the TiAl(1 1 1) surface, the Ti3 Al(0 0 0 1) surface has relatively larger interlayer relaxation. This indicates that the Ti3 Al(0 0 0 1) surface is less stable than the TiAl(1 1 1) surface, which is consistent with the results of the surface energy.
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Fig. 2. The six different interface structures of TiAl(1 1 1)/Ti3 Al(0 0 0 1), which is denoted by a, b, c, d, e, f, respectively. The brown (black) and yellow (gray) balls represent the Ti and Al atoms for color (grayscale) figures, respectively. The different layers in the interface region are labeled by 1–8 to discuss clearly. The TiAl(1 1 1)/Ti3 Al(0 0 0 1) interface is between 4 and 5 layers. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
From Table 1, it is also found that the rumpling of the ␣2 Ti3 Al(0 0 0 1) surface decreases from the first to the third surface layer, which indicates that the atoms in the top-layer are active. The surface rumpling ε1 is positive, indicating that the Al atoms are displaced outward relative to the Ti atoms in the top surface layer. This suggests that Al atoms prefer to stay the outer layer in ␣2 -Ti3 Al(0 0 0 1) surface, which is similar to that of ␥-TiAl(1 1 1). Moreover, the surface rumpling of the ␣2 -Ti3 Al(0 0 0 1) surface are the larger than those of the ␥-TiAl(1 1 1) surface, due to its higher surface energy. In order to better understand the surface characteristic, the electronic structures are calculated. Fig. 3 shows the comparisons of the partial densities of states (PDOSs) for one Ti and one Al atom on the Ti3 Al(0 0 0 1) top surface and center layers. It is obvious that the peaks of the PDOSs for Ti-d, Ti-p and Al-p of the Ti3 Al surface layer are located at Fermi level, while the peaks of those in the center layer are located at lower energy region, showing the activity of surface atoms. It is also seen that the peaks of PDOSs for Al-s are rather higher and for Ti-p are slightly higher in the Ti3 Al surface layer at −5 eV below the Fermi energy compared with those in the center layer, which indicates that there are the strong interactions between Ti-p and Al-s in surface at this energy.
3.2. Interface of TiAl/Ti3 Al As mentioned in Section 2, the geometries of the six interface models are optimized. The work of separation, interface energy and
Table 1 Surface relaxation (in Å) and surface rumpling ε (in Å) of Ti3 Al(0 0 0 1) and TiAl(1 1 1) surfaces. Ti3 Al(0 0 0 1)
TiAl(1 1 1)
Interlayer
12 23
−0.02 0.007
−0.012a −0.003a
Rumpling
ε1 ε2 ε3
0.188 −0.101 0.031
0.151a 0.022a −0.010
a
Reference [32].
Fig. 3. The comparison of PDOSs for one Ti and one Al atom on the first layer of Ti3 Al(0 0 0 1) surface and center layer. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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Table 2 Work of separation Wsep (J/m2 ), interface energy ␥i (J/m2 ) and interface separation d for coherent interfaces between ␥-TiAl and ␣2 -Ti3 Al. Interface configuration
a b c d e f
␥i (J/m2 )
0.410 0.350 0.405 0.416 0.328 0.336
Wsep (J/m2 )
d (Å)
TiAl(3)/TiAl(4)
TiAl(4)/Ti3 Al(5)
Ti3 Al(5)/Ti3 Al(6)
3.171 3.231 3.178 3.216 3.302 3.245
3.262 3.322 3.268 3.257 3.345 3.336
3.716 3.724 3.721 3.711 3.743 3.735
interface separation are calculated and listed in Table 2. In order to better understand the bond strength in the interface region, we assume the interfaces cleave at TiAl(3)/TiAl(4), TiAl(4)/Ti3 Al(5) and Ti3 Al(5)/Ti3 Al(6) (see Fig. 2). From Table 2, it is found that the structure (e) has the smallest value of i and the largest value of Wsep among the six interface configurations, indicating that the interface structure (e) is the most stable. However, the energy differences of the six interfaces are very small. It is also seen that the “on-top site” interfacial structures (a) and (b) have small interface separation, and the values of Wsep and i are close to those of other four “vacancy-site” interface structures, which is different from NiAl/Cr interface model [31]. This may be caused by the attraction of heterogeneous atoms Ti–Al near interfacial layers. From Table 2, it is found that in the interface region, the work of interface separation between Ti3 Al(5) and Ti3 Al(6) layers is the largest, followed by TiAl(4)/Ti3 Al(5) interface layer, and that between TiAl(3) and TiAl(4) layers is the smallest. Comparing with the energy required to split the bulk into two surfaces of TiAl(1 1 1) (2 s = 3.382 J/m2 ) or of Ti3 Al(0 0 0 1) (2 s = 3.928 J/m2 ), we can know that the work of separation between Ti3 Al(5) and Ti3 Al(6) layers in the interface region is smaller than that along Ti3 Al(0 0 0 1) plane in the bulk. Similarly, the work of separation between TiAl(4) and TiAl(5) layers in the interface region is smaller than that along TiAl(1 1 1) plane in the bulk. In addition, the work of separation of TiAl(4)/Ti3 Al(5) interface is closer to that of TiAl(1 1 1) plane, which is consistent with the results of Fu et al. [17] and Wei et al. [19]. Fu et al. and Wei et al. reported that the calculated cleavage energies of the TiAl/Ti3 Al interface, the TiAl(1 1 1) plane, and the Ti3 Al(0 0 0 1) plane are 4.5 J/m2 , 4.5 J/m2 , 4.8 J/m2 and 3.62 J/m2 , 3.45 J/m2 , 4.03 J/m2 , respectively. We can conclude that the bonding strength of interface depends on the weaker one of the two phases and the heterogeneous interface would be the weak link in the material, which can be also confirmed in the other two-phase materials [29,34,35]. From above analysis, we have known that there are different work of separation and bonding strengths when the ␥-TiAl(1 1 1)/␣2 -Ti3 Al(0 0 0 1) interface is cleaved along different cleavage planes. In order to better understand the bonding characteristics between different layers, we employ the electron localization function (ELF) [36–38] to describe the chemical bonds and electron pairs for the most stable interface structure (e). The
2.307 2.319 2.306 2.321 2.327 2.320
value of ELF is restricted to 0 ≤ ELF ≤ 1, with ELF = 1 corresponding to completely electron pair localization, and ELF = 0.5 representing a homogeneous electron gas-like pair probability (electron delocalization). Generally, the ELF in the region of 0.5 < ELF ≤ 1 corresponds to some degree of covalent bonding. The larger the ELF is, the stronger the covalent nature of the bond is. The ELF of different cleavage planes are showed in Fig. 4. (a) and (e) are the ELF of the TiAl(1 1 1) and Ti3 Al(0 0 0 1) cleavage planes in the bulk materials, respectively. Fig. 4(b), (c) and (d) are the ELF of the TiAl(1 1 1)/Ti3 Al(0 0 0 1) interface along TiAl(3)/TiAl(4), TiAl(4)/Ti3 Al(5) and Ti3 Al(5)/Ti3 Al(6) cleavage planes (see Fig. 2). To maintain consistency, all the cleavage planes in Fig. 4 are selected in the middle area between two layers. From Fig. 4, it is observed that the Ti3 Al(0 0 0 1) cleavage plane in the bulk has the strongest bonding, where the ELF attains the maximum value of 0.74. Therefore, the Ti3 Al(0 0 0 1) cleavage plane needs to break the stronger covalent bond to separate the bulk into two surfaces, compared with TiAl(1 1 1) cleavage plane. Thus the work of separation along Ti3 Al(0 0 0 1) plane (3.928 J/m2 ) is larger than that along the TiAl(1 1 1) cleavage plane (3.382 J/m2 ) in the bulk. Comparing Fig. 4(a) with (b), the red regions representing the strongest bonding have the same proportions, but the TiAl(3)/TiAl(4) cleavage plane has a slightly lower ELF maximum value than the TiAl(1 1 1) plane, so the TiAl(3)/TiAl(4) cleavage plane breaks the relatively weaker covalent bond. Therefore, the work of separation between TiAl(3) and TiAl(4) layers in the interface region (3.302 J/m2 ) is slightly smaller than that along TiAl(1 1 1) plane (3.382 J/m2 ) in the bulk. Similarly, comparing Fig. 4(d) with (e), the Ti3 Al(5)/Ti3 Al(6) cleavage plane has a lower ELF maximum value than the Ti3 Al(0 0 0 1) plane in the bulk. Therefore, the work of separation between Ti3 Al(5) and Ti3 Al(6) layers in the interface region (3.743 J/m2 ) is smaller than that along Ti3 Al(0 0 0 1) plane (3.928 J/m2 ) in the bulk. Moreover, it can be seen that the ELF plot of the interface between TiAl(1 1 1) and Ti3 Al(0 0 0 1) (see Fig. 4(c)) is completely different from TiAl phase or Ti3 Al phase. The TiAl(4)/Ti3 Al(5) cleavage plane has the relatively smaller ELF value than the TiAl(1 1 1) and Ti3 Al(0 0 0 1) planes, so there is the weaker covalent bonding in the TiAl(1 1 1)/Ti3 Al(0 0 0 1) interface. Therefore, the heterogeneous interface would be the weak link in the material. In addition, it is seen from Fig. 4 that the ELF maximum value of TiAl(1 1 1)/Ti3 Al(0 0 0 1) interface is closer to the TiAl(1 1 1) phase than Ti3 Al(0 0 0 1) phase, which explains the reason why
Fig. 4. The ELF along different cleavage planes. (a) TiAl(1 1 1) plane in the bulk; (b) TiAl(3)/TiAl(4) plane; (c) TiAl(4)/Ti3 Al(5) plane; (d) Ti3 Al(5)/Ti3 Al(6); (e) Ti3 Al(0 0 0 1) plane in the bulk. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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the work of separation of TiAl/Ti3 Al interface is closer to that of TiAl(1 1 1) plane, and further indicates that the bonding strength of interface depends on the weaker one of the two phases. 4. Conclusions In conclusion, the first-principle method based on DFT is employed to study the surface properties of ␣2 -Ti3 Al(0 0 0 1) and the interface properties including interface energy and interfacial work of separation of the six different ␥-TiAl(1 1 1)/␣2 -Ti3 Al(0 0 0 1) interface configurations. It is found that Ti3 Al(0 0 0 1) surface has higher surface energy and larger surface relaxation than TiAl(1 1 1) surface. The surface atomic layer is rather active and Al atoms prefer to stay the outer layer in Ti3 Al(0 0 0 1) surface. It is also revealed that the interface structure (e) is the most stable among the six TiAl(1 1 1)/Ti3 Al(0 0 0 1) interface structures. The work of separation along Ti3 Al(0 0 0 1) cleavage plane is larger than that along TiAl(1 1 1) plane. The bonding strengths between Ti3 Al layers and between TiAl layers in the interface region are smaller than those of the corresponding Ti3 Al(0 0 0 1)/Ti3 Al(0 0 0 1) plane and TiAl(1 1 1)/TiAl(1 1 1) plane in the bulk, respectively. The heterogeneous interface would be the weak link in the material. In addition, the work of separation of TiAl(1 1 1)/Ti3 Al(0 0 0 1) interface is closer to that of TiAl(1 1 1) plane, indicating that the bonding strength of interface depends on the weaker one of the two phases. The electron local function is used to analyze the bonding characteristic of interface. It is found that the ELF of interface is different from both TiAl(1 1 1) and Ti3 Al(0 0 0 1). Acknowledgment The work was financially supported by National Natural Science Foundation of China under Grant Nos. 50871071 and 51071011. References [1] F. Appel, R. Wagner, Microstructure and deformation of two-phase-titanium aluminides, Materials Science and Engineering: R: Reports 22 (1998) 187–268. [2] J.X. Zhang, H.Q. Ye, The deformation twin in lamellar Ti3 Al/TiAl structure, Solid State Communications 126 (2003) 217–221. [3] K. Chan, Toughening mechanisms in titanium aluminides, Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science 24 (1993) 569–583. [4] K. Chan, Y.W. Kim, Relationships of slip morphology, microcracking, and fracture resistance in a lamellar TiAl-alloy, Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science 25 (1994) 1217–1228. [5] K. Chan, D. Shih, Fatigue and fracture behavior of a fine-grained lamellar TiAl alloy, Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science 28 (1997) 79–90. [6] S. Cheng, J. Wolfenstine, O. Sherby, Superplastic behavior of two-phase titanium aluminides, Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science 23 (1992) 1509–1513. [7] S. Karthikeyan, G.B. Viswanathan, P.I. Gouma, V.K. Vasudevan, Y.W. Kim, M.J. Mills, Mechanisms and effect of microstructure on creep of TiAl-based alloys, Materials Science and Engineering A 329–331 (2002) 621–630. [8] X.W. Du, J. Zhu, Y.W. Kim, Microstructural characterization of creep cavitation in a fully-lamellar TiAl alloy, Intermetallics 9 (2001) 137–146. [9] J. Kumpfert, Y.W. Kim, D.M. Dimiduk, Effect of microstructure on fatigue and tensile properties of the gamma TiAl alloy Ti-46.5Al-3.0Nb-2.1Cr-0.2 W, Materials Science and Engineering A 192–193 (Part 1) (1995) 465–473. [10] P.I. Gouma, K. Subramanian, Y.W. Kim, M.J. Mills, Annealing studies of ␥titanium aluminides alloyed with light elements for creep strengthening, Intermetallics 6 (1998) 689–693.
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