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Applied Surface Science 276 (2013) 198– 202

Contents lists available at SciVerse ScienceDirect

Applied Surface Science

jou rn al h omepa g e: www.elsev ier .com/ locate /apsusc

irst principles study of �2-Ti3Al(0 0 0 1) surface and-TiAl(1 1 1)/�2-Ti3Al(0 0 0 1) interfaces

u Wanga, Jia-Xiang Shanga,∗, Fu-He Wangb, Yue Zhanga

School of Materials Science and Engineering, Beihang University, Beijing 100191, PR ChinaDepartment of Physics, Capital Normal University, Beijing 100048, PR China

a r t i c l e i n f o

rticle history:eceived 22 September 2012eceived in revised form 8 March 2013ccepted 8 March 2013vailable online 23 March 2013

a b s t r a c t

The �2-Ti3Al(0 0 0 1) surface and �-TiAl(1 1 1)/�2-Ti3Al(0 0 0 1) interfaces with six orientation relation-ships are studied by using the first-principle density functional theory. The calculated results indicatethat the Ti3Al(0 0 0 1) surface has a higher surface energy (1.964 J/m2) and larger surface relaxations, com-pared with the �-TiAl(1 1 1) surface. For the �-TiAl(1 1 1)/�2-Ti3Al(0 0 0 1) interface structures, the work

eywords:itanium aluminidesnterfaceirst-principles calculation

of separation along Ti3Al(0 0 0 1) cleavage plane is larger than that along TiAl(1 1 1) plane. In the inter-face region, the bonding strengths between Ti3Al layers and between TiAl layers are smaller than thosealong Ti3Al(0 0 0 1) plane and TiAl(1 1 1) plane in the bulk materials, respectively. The heterogeneousinterface would be the weak link in the material, and the bonding strength of interface depends on theweaker one of the two phases. The bonding characteristics of interface are analyzed by the electron localfunction.

. Introduction

Two-phase TiAl alloys, composed of �-TiAl and smaller amountsf �2-Ti3Al, are nowadays attracting a great deal of interests due toheir better ductility and toughness than single-phase �-TiAl alloys1]. Experimentally, considerable research efforts are devoted tohe detailed characterization of the mechanical properties of two-hase TiAl alloys in relation to microstructure [2–9]. It has beenlearly established that the lamellar microstructure offers goodechanical behavior at high temperature [2], relatively high frac-

ure toughness [3–5], superplasticity [6], and creep resistance [7,8].n the other hand, adding alloying elements or light elements iniAl-based alloys to improve various performances also has beenxtensively studied [10–12]. Moreover, the orientation relationshipf {1 1 1}�//(0 0 0 1)�2

and 〈1 1 0〉�//〈1 1 2 0〉�2between TiAl and

i3Al in the lamellar structure of two-phase TiAl alloys has beenonfirmed by transmission electron microscopy. There are six pos-ible orientations for the [1 1 0] direction of �-TiAl with respect tohe 〈1 1 2 0〉 direction of �2-Ti3Al [13,14].

The improvement in mechanical properties is partly due to theresence of lamellar boundaries in the material. In order to better

nderstand the �/� and �/�2 interfaces in TiAl lamellar structure,any theoretical studies were reported. Vitek et al. [15] investi-

ated the effect of covalent-type bonding and segregation upon

∗ Corresponding author. Tel.: +86 10 8231 6500; fax: +86 10 8231 6500.E-mail address: shangjx@buaa.edu.cn (J.-X. Shang).

169-4332/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.apsusc.2013.03.065

© 2013 Elsevier B.V. All rights reserved.

the structure of �/� interfaces in the lamellar structures of Ti–Alalloys and suggested that in Ti-rich alloys a significant segrega-tion took place in some �/� interfaces leading to the formation of avery narrow region of the DO19-Ti3Al. Moreover, atomistic studiesof interactions between the dominant lattice dislocations and �/�-lamellar boundaries in lamellar �-TiAl were studied by Katzarovet al. [16]. There are three types of �/� interface formed by rotationabout the [1 1 1] axis at angles of 60◦, 120◦ and 180◦. The interfacialenergies and interfacial work of adhesion of these �/� interfaceswere reported by Fu et al. [17]. They used the full-potential lin-earized augmented plane-wave method to calculate the interfacialenergy and the planar fault energies at the �/�2 interface and eval-uate interfacial work of adhesion [18], and the results indicated thatthe 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 �/� inter-faces. Recently, Wei et al. [19,20] investigated the effect of oxygenon the �-TiAl/�2-Ti3Al interface, and indicated that oxygen weak-ened the interface strength but strongly stabilized the TiAl/Ti3Alinterface. However, the above studies are mainly concerning onthe �/� interfaces and one of the �/�2 interfaces. Therefore, themicrostructures and fracture properties of clean �-TiAl(1 1 1)/�2-Ti3Al(0 0 0 1) interfaces with six orientation relationships are stillunclear.

In this paper, we calculate the surface energy of the Ti3Al(0 0 0 1)surface, the interface energies and work of separation alongdifferent cleave planes near to interfaces of the six �-TiAl(1 1 1)/�2-Ti3Al(0 0 0 1) interfaces by first-principles calculations.

L. Wang et al. / Applied Surface Sc

Fig. 1. Top view of the Ti3Al(0 0 0 1) surface. Large and small brown (black) andylt

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ellow (gray) balls represent the Ti and Al atoms in the first and second surfaceayers for color (grayscale) figures, respectively. (For interpretation of the referenceso color in this figure legend, the reader is referred to the web version of the article.)

. Methodology

The calculations presented in this paper are carried out bysing the Vienna ab initio simulation package (VASP) [21–23]ased on density functional theory. The calculation is con-ucted in a plane-wave basis, using the projector-augmentedave (PAW) method [24,25]. For the exchange-correction energy

unctional, the PW91 generalized gradient approximation (GGA)26] is employed. We use a kinetic-energy cutoff of 400 eV and1 × 11 × 11 Monkhorst–Pack k points in the Brillouin zone for bulk2-Ti3Al calculations. All atomic positions in our models have been

ully relaxed until the force of every atom is less than 0.01 eV/Å. Thealculated lattice constants of bulk �2-Ti3Al are a = 5.73 A, c/a = 0.81,hich are in excellent agreement with the experimental values

= 5.76 A, c/a = 0.8 [27].For the Ti3Al(0 0 0 1) surface, the surface calculation is done in

× 1 surface unit cells with 11 × 11 × 1 Monkhorst–Pack k pointsn the Brillouin zone. In order to prevent unwanted interactionsetween the slab and its periodic images, the surface is modeledy a slab of seven atomic layers separated by a vacuum region of5 A. All atomic positions in the slab are optimized until the forcef each atom is less than 0.01 eV A−1. For Ti3Al(0 0 0 1) surface, theatio of Ti atom and Al atom is 3:1 at every layer, shown in Fig. 1.

The present interface calculations were focused on the coherentnterface structures formed by �-TiAl(1 1 1) and �2-Ti3Al(0 0 0 1)urfaces. According to the experimental observation [14], the two-hase TiAl compounds exhibit the lamellar structure consisting ofhe twin-related �-TiAl and �2-Ti3Al phase with the orientationelationship of {1 1 1}�//(0 0 0 1)�2

and 〈1 1 0〉�//〈1 1 2 0〉�2. There

re six orientation variants of the � phase with respect to the basallane of the �2 phase [13]. The lattice lengths of a〈1 1 0〉{1 1 1}� are

.63 and 5.70 A, while that of a〈1 1 2 0〉(0 0 0 1)�2is 5.73 A. Therefore, the

attice misfits of X and Y directions of �-TiAl(1 1 1)/�2-Ti3Al(0 0 0 1)re 1.76% and 0.52%, which possess a good matching. The averageattice parameters of �-TiAl(1 1 1) and �2-Ti3Al(0 0 0 1) are adoptedn our interface models. We denote the stacking sequences of Ti3Alnd TiAl as AB and A’B’C’, respectively. The six models that we haveonstructed are represented by:

a) A′C′B′A′C′B′A′—ABABABA;b) A′B′C′A′B′C′A′—ABABABA;c) B′A′C′B′A′C′B′—ABABABA;d) C′A′B′C′A′B′C′—ABABABA;e) C′B′A′C′B′A′C′—ABABABA;f) B′C′A′B′C′A′B′—ABABABA;

Fig. 2 shows the six interface structures. For each interfaceodel, there are seven �-TiAl layers and seven �2-Ti3Al layersith 15 A vacuum layers. The 5 × 5 × 1 Monkhorst–Pack K-point

ience 276 (2013) 198– 202 199

and 400 eV of kinetic-energy cutoff are used. All atomic coordinatesare 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 totalenergy of surface atoms (Eslab) and that of atoms in bulk (Ebulk)[28]. Therefore, the surface energy �s of Ti3Al(0 0 0 1) surface canbe written as

�s = [Eslab(N) − Ebulk(N)]/(2As) (1)

where N symbolizes that Eslab and Ebulk correspond to the samenumber N of the Ti3Al(0 0 0 1) surface and Ti3Al bulk, and As is thecorresponding area of the surface.

The work of interface separation (Wsep) is calculated accordingto the following equation [29–31]:

Wsep = (ETi3Als + ETiAl

s − ETi3Al/TiAl)/A (2)

where ETi3Als and ETiAl

s denote the total energies of the relaxed,isolated Ti3Al and TiAl surface, respectively. ETi3Al/TiAl is the totalenergy of the Ti3Al/TiAl interface model, and A is the area of inter-face. It should be pointed out that the work of separation is thework required to reversibly separate the interface into two freesurfaces, and Wsep is therefore a direct measure of the interfacebond strength.

The interface energy � i is related to the thermodynamic proper-ties of interface [31]. In our interface models, there are one interfaceand two surfaces. Therefore, the interface energy � i is determinedby the equation as follows:

�i = [ETi3Al/TiAl − (ETiAlbulk + ETi3Al

bulk )]/A − (�TiAls + �Ti3Al

s ) (3)

where ETi3Al/TiAl and A have the same meaning as described inEq. (2), ETiAl

bulk and ETi3Albulk are the bulk energies, and �TiAl

s and �Ti3Als are

the surface energies of the TiAl and Ti3Al surfaces.

3. Results and discussion

3.1. Ti3Al(0 0 0 1) surface

In our previous work [32], the low-index surfaces of �-TiAlhave been investigated in detail. The calculated surface energy ofTiAl(1 1 1) surface is 1.691 J/m2. In this paper, the calculated sur-face energy of �2-Ti3Al(0 0 0 1) surface is 1.964 J/m2. This indicatesthat the cleavage energy along the �2-Ti3Al(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 Ti3Al(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 featuresof the surface structure. Interlayer relaxation can be evaluated by� = d − d0. Here d and d0 are the interlayer distances of the relaxedsurface and bulk materials, respectively. We also calculate the sur-face 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 inthe same layer.

The calculated results of surface relaxation and surface rumplingof �2-Ti3Al(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 inter-layer relaxation between the first and second layers �12 contractedand interlayer relaxation �23 has a little expansion for the �2-Ti3Al(0 0 0 1) surface, and the interlayer relaxation �12 is largerthan �23. In addition, our previous work [32] indicated that thehigher surface energy may lead to the larger surface relaxation.

Compared with the TiAl(1 1 1) surface, the Ti3Al(0 0 0 1) surfacehas relatively larger interlayer relaxation. This indicates that theTi3Al(0 0 0 1) surface is less stable than the TiAl(1 1 1) surface, whichis consistent with the results of the surface energy.

200 L. Wang et al. / Applied Surface Science 276 (2013) 198– 202

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3.2. Interface of TiAl/Ti3Al

As mentioned in Section 2, the geometries of the six interfacemodels are optimized. The work of separation, interface energy and

ig. 2. The six different interface structures of TiAl(1 1 1)/Ti3Al(0 0 0 1), which is dehe Ti and Al atoms for color (grayscale) figures, respectively. The different layers

nterface is between 4 and 5 layers. (For interpretation of the references to color in

From Table 1, it is also found that the rumpling of the �2-i3Al(0 0 0 1) surface decreases from the first to the third surfaceayer, which indicates that the atoms in the top-layer are active.he surface rumpling �ε1 is positive, indicating that the Al atomsre displaced outward relative to the Ti atoms in the top surfaceayer. This suggests that Al atoms prefer to stay the outer layer in

2-Ti3Al(0 0 0 1) surface, which is similar to that of �-TiAl(1 1 1).oreover, the surface rumpling of the �2-Ti3Al(0 0 0 1) surface are

he larger than those of the �-TiAl(1 1 1) surface, due to its higherurface energy.

In order to better understand the surface characteristic, the elec-ronic structures are calculated. Fig. 3 shows the comparisons of theartial densities of states (PDOSs) for one Ti and one Al atom on thei3Al(0 0 0 1) top surface and center layers. It is obvious that theeaks of the PDOSs for Ti-d, Ti-p and Al-p of the Ti3Al surface layerre located at Fermi level, while the peaks of those in the centerayer are located at lower energy region, showing the activity ofurface atoms. It is also seen that the peaks of PDOSs for Al-s areather higher and for Ti-p are slightly higher in the Ti3Al surface

ayer at −5 eV below the Fermi energy compared with those in theenter layer, which indicates that there are the strong interactionsetween Ti-p and Al-s in surface at this energy.

able 1urface relaxation � (in Å) and surface rumpling �ε (in Å) of Ti3Al(0 0 0 1) andiAl(1 1 1) surfaces.

Ti3Al(0 0 0 1) TiAl(1 1 1)

Interlayer �12 −0.02 −0.012a

�23 0.007 −0.003a

Rumpling �ε1 0.188 0.151a

�ε2 −0.101 0.022a

�ε3 0.031 −0.010

a Reference [32].

by a, b, c, d, e, f, respectively. The brown (black) and yellow (gray) balls represent interface region are labeled by 1–8 to discuss clearly. The TiAl(1 1 1)/Ti3Al(0 0 0 1)gure legend, the reader is referred to the web version of the article.)

Fig. 3. The comparison of PDOSs for one Ti and one Al atom on the first layer ofTi3Al(0 0 0 1) surface and center layer. (For interpretation of the references to colorin this figure legend, the reader is referred to the web version of the article.)

L. Wang et al. / Applied Surface Science 276 (2013) 198– 202 201

Table 2Work of separation Wsep (J/m2), interface energy �i (J/m2) and interface separation d for coherent interfaces between �-TiAl and �2-Ti3Al.

Interface configuration �i (J/m2) Wsep (J/m2) d (Å)

TiAl(3)/TiAl(4) TiAl(4)/Ti3Al(5) Ti3Al(5)/Ti3Al(6)

a 0.410 3.171 3.262 3.716 2.307b 0.350 3.231 3.322 3.724 2.319c 0.405 3.178 3.268 3.721 2.306

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d 0.416 3.216e 0.328 3.302

f 0.336 3.245

nterface separation are calculated and listed in Table 2. In order toetter understand the bond strength in the interface region, wessume the interfaces cleave at TiAl(3)/TiAl(4), TiAl(4)/Ti3Al(5) andi3Al(5)/Ti3Al(6) (see Fig. 2).

From Table 2, it is found that the structure (e) has the smallestalue of � i and the largest value of Wsep among the six interface con-gurations, indicating that the interface structure (e) is the mosttable. However, the energy differences of the six interfaces areery small. It is also seen that the “on-top site” interfacial struc-ures (a) and (b) have small interface separation, and the values of

sep and � i are close to those of other four “vacancy-site” interfacetructures, which is different from NiAl/Cr interface model [31].his may be caused by the attraction of heterogeneous atoms Ti–Alear interfacial layers.

From Table 2, it is found that in the interface region, the workf interface separation between Ti3Al(5) and Ti3Al(6) layers ishe largest, followed by TiAl(4)/Ti3Al(5) interface layer, and thatetween TiAl(3) and TiAl(4) layers is the smallest. Comparing withhe energy required to split the bulk into two surfaces of TiAl(1 1 1)2�s = 3.382 J/m2) or of Ti3Al(0 0 0 1) (2�s = 3.928 J/m2), we cannow that the work of separation between Ti3Al(5) and Ti3Al(6)ayers in the interface region is smaller than that along Ti3Al(0 0 0 1)lane in the bulk. Similarly, the work of separation between TiAl(4)nd TiAl(5) layers in the interface region is smaller than that alongiAl(1 1 1) plane in the bulk. In addition, the work of separationf TiAl(4)/Ti3Al(5) interface is closer to that of TiAl(1 1 1) plane,hich 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 cleav-ge energies of the TiAl/Ti3Al interface, the TiAl(1 1 1) plane, andhe Ti3Al(0 0 0 1) plane are 4.5 J/m2, 4.5 J/m2, 4.8 J/m2 and 3.62 J/m2,.45 J/m2, 4.03 J/m2, respectively. We can conclude that the bond-

ng strength of interface depends on the weaker one of the twohases and the heterogeneous interface would be the weak link inhe material, which can be also confirmed in the other two-phase

aterials [29,34,35].From above analysis, we have known that there are dif-

erent work of separation and bonding strengths when the-TiAl(1 1 1)/�2-Ti3Al(0 0 0 1) interface is cleaved along differ-nt cleavage planes. In order to better understand the bonding

haracteristics between different layers, we employ the electronocalization function (ELF) [36–38] to describe the chemical bondsnd electron pairs for the most stable interface structure (e). The

ig. 4. The ELF along different cleavage planes. (a) TiAl(1 1 1) plane in the bulk; (b) TiAllane in the bulk. (For interpretation of the references to color in this figure legend, the r

3.257 3.711 2.3213.345 3.743 2.3273.336 3.735 2.320

value of ELF is restricted to 0 ≤ ELF ≤ 1, with ELF = 1 correspondingto completely electron pair localization, and ELF = 0.5 represent-ing a homogeneous electron gas-like pair probability (electrondelocalization). Generally, the ELF in the region of 0.5 < ELF ≤ 1corresponds to some degree of covalent bonding. The larger theELF is, the stronger the covalent nature of the bond is. The ELFof different cleavage planes are showed in Fig. 4. (a) and (e)are the ELF of the TiAl(1 1 1) and Ti3Al(0 0 0 1) cleavage planesin the bulk materials, respectively. Fig. 4(b), (c) and (d) are theELF of the TiAl(1 1 1)/Ti3Al(0 0 0 1) interface along TiAl(3)/TiAl(4),TiAl(4)/Ti3Al(5) and Ti3Al(5)/Ti3Al(6) cleavage planes (see Fig. 2). Tomaintain consistency, all the cleavage planes in Fig. 4 are selectedin the middle area between two layers.

From Fig. 4, it is observed that the Ti3Al(0 0 0 1) cleavage planein the bulk has the strongest bonding, where the ELF attains themaximum value of 0.74. Therefore, the Ti3Al(0 0 0 1) cleavage planeneeds to break the stronger covalent bond to separate the bulkinto two surfaces, compared with TiAl(1 1 1) cleavage plane. Thusthe work of separation along Ti3Al(0 0 0 1) plane (3.928 J/m2) islarger 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 repre-senting the strongest bonding have the same proportions, but theTiAl(3)/TiAl(4) cleavage plane has a slightly lower ELF maximumvalue than the TiAl(1 1 1) plane, so the TiAl(3)/TiAl(4) cleavageplane breaks the relatively weaker covalent bond. Therefore, thework of separation between TiAl(3) and TiAl(4) layers in the inter-face 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 Ti3Al(5)/Ti3Al(6) cleavage plane has a lower ELF maximumvalue than the Ti3Al(0 0 0 1) plane in the bulk. Therefore, the workof separation between Ti3Al(5) and Ti3Al(6) layers in the inter-face region (3.743 J/m2) is smaller than that along Ti3Al(0 0 0 1)plane (3.928 J/m2) in the bulk. Moreover, it can be seen that theELF plot of the interface between TiAl(1 1 1) and Ti3Al(0 0 0 1) (seeFig. 4(c)) is completely different from TiAl phase or Ti3Al phase. TheTiAl(4)/Ti3Al(5) cleavage plane has the relatively smaller ELF valuethan the TiAl(1 1 1) and Ti3Al(0 0 0 1) planes, so there is the weakercovalent bonding in the TiAl(1 1 1)/Ti3Al(0 0 0 1) interface. There-fore, the heterogeneous interface would be the weak link in the

material. In addition, it is seen from Fig. 4 that the ELF maximumvalue of TiAl(1 1 1)/Ti3Al(0 0 0 1) interface is closer to the TiAl(1 1 1)phase than Ti3Al(0 0 0 1) phase, which explains the reason why

(3)/TiAl(4) plane; (c) TiAl(4)/Ti3Al(5) plane; (d) Ti3Al(5)/Ti3Al(6); (e) Ti3Al(0 0 0 1)eader is referred to the web version of the article.)

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he work of separation of TiAl/Ti3Al interface is closer to that ofiAl(1 1 1) plane, and further indicates that the bonding strength ofnterface depends on the weaker one of the two phases.

. Conclusions

In conclusion, the first-principle method based on DFT ismployed to study the surface properties of �2-Ti3Al(0 0 0 1) andhe interface properties including interface energy and interfacialork of separation of the six different �-TiAl(1 1 1)/�2-Ti3Al(0 0 0 1)

nterface configurations. It is found that Ti3Al(0 0 0 1) surface hasigher surface energy and larger surface relaxation than TiAl(1 1 1)urface. The surface atomic layer is rather active and Al atomsrefer to stay the outer layer in Ti3Al(0 0 0 1) surface. It is alsoevealed that the interface structure (e) is the most stable amonghe six TiAl(1 1 1)/Ti3Al(0 0 0 1) interface structures. The work ofeparation along Ti3Al(0 0 0 1) cleavage plane is larger than thatlong TiAl(1 1 1) plane. The bonding strengths between Ti3Al lay-rs and between TiAl layers in the interface region are smaller thanhose of the corresponding Ti3Al(0 0 0 1)/Ti3Al(0 0 0 1) plane andiAl(1 1 1)/TiAl(1 1 1) plane in the bulk, respectively. The heteroge-eous interface would be the weak link in the material. In addition,he work of separation of TiAl(1 1 1)/Ti3Al(0 0 0 1) interface is closero that of TiAl(1 1 1) plane, indicating that the bonding strength ofnterface depends on the weaker one of the two phases. The elec-ron local function is used to analyze the bonding characteristic ofnterface. It is found that the ELF of interface is different from bothiAl(1 1 1) and Ti3Al(0 0 0 1).

cknowledgment

The work was financially supported by National Natural Scienceoundation of China under Grant Nos. 50871071 and 51071011.

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