Interfacial energies in two-phase TiAl-Ti3Al alloy

Scripta Materialia, Vol. 37, No. 10, pp. 1453-1459, 1997 Published by Elsevier Science Ltd Printed in the USA. All rights reserved 1359~6462/97 $0.00 + .oO

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INTERFACIAL ENERGIES IN TWO-PHASE TiAI-T&AI ALLOY C.L. Fu and M.H. Yoo Metals and Ceramics Division, Oak Ridge National Laboratory P. 0. Box 2008, Oak Ridge, TN 3783 l-61 14 (Received September 23, 1996) (Accepted July 24, 1997) Introduction Mechanical properties of polycrystalline two-phase y-TiAl alloys depend sensitively on the microstructure, which can be controlled by chemical composition and processing methods (l-4). Balanced properties of relatively high fracture toughness and tensile elongation together with high yield strength and creep resistance have been obtained recently in fully lamellar Ti-47Al-2Cr-2Nb (in atom %) alloys with fine grain size and lamellar spacing (5;6). Fundamental understanding of deformation and fracture behavior of fully lamellar y-TiAl has been substantially improved since experimental findings based on the so-called polysynthetically twinned (PST) crystals were made available, e.g., (7,8). Quantitative determination of specific energies for various y/y interfacial variants and c~z/yinterface is an important prerequisite for better understanding of phase stability, lamellar microstructure, and mechanical behavior of two-phase y-TiAl; particularly, of the anisotropic yield strength and tensile elongation (7,9) and fracture behavior (8,lO) with respect to the lamellar orientation in PST TiAl crystals. Crystallographic descriptions for each of 60°, 120”, and 180’ -y/yinterfaces and their relative energies have been discussed by Rao et al. (11) on the basis of Bollman’s O-lattice theory and an empirical Embedded Altom Method (EAM). In this paper, we report the interfacial energies of these y/y variants that were determined from first-principles local-density-functional (LDF) calculations including atomic relaxation near the interfaces. We show that the planar fault energies at these interfaces are significantly different from those in the bulk y-TiAl. We also discuss the work of adhesion at these interfaces. Theoretical Approach We use the full-potential linearized augmented plane-wave (FLAPW) method (12)to solve the LDF equations. There is no shape approximation to the potential and charge density. The uniqueness of these features makes it possible to determine the energetics associated with shape deformations and lattice defects accurately. In this investigation angular momentum components up to l = 8 and approximately 60 plane waves per atom are used for expansion of wave functions. Relaxed structures of interfaces are optimized by calculating Helhnann-Feynman forces acting on the atoms.

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[llll

(a)

Figure 1.(a) Schematic illustration of translation and rotation operations and (b) Atomic stacking (ABC) sequence on the (111) plane of the L lo structure.

For the calculation of ‘y/ylamellar interface energies, supercell sizes of 5 x 5 (i.e., repeated layer stacking sequence of 5 layers of TiAl separating the interfaces) are used. For the calculation of antiphase boundary (APB) and complex stacking fault (CSF) energies in bulk TiAl, supercell sizes with 12 and 11 layers seperating adjacent interfaces were used. Calculated Results Figure 1(a) shows schematically how three different types of planar faults are created at three different types of rh interfaces. When the angle of rotation, 8, and the fault shift vector, f, are both zero, the top and bottom halves together constitute the reference state of a single crystal, i.e., the total internal energy is set to Eo = 0. Interfacial energies calculated for the three different types, i.e., pseudo-twin (0 = 609, 120°-rotational @ = 1209 and true-twin (0 = 180”) boundaries, are listed in the first column (f = 0) of Table 1. Fault energies calculated for the three types on the (111) plane, i.e., APB with f = b, - b3 or bl - b3 = < iO1]/2, superlattice intrinsic stacking fault (SISF) with f = b3 = [112]/6, and

TABLE 1 Interfacial Energies of y/y Lameliar Boundaries in TiAl (in Units of mJ/m’) lnlerfa2c

type Bldk Pseudo-twin

f-0

f c

~[1121

+<2111

l-i

APB

SISP

CSP

0”

0

560

90

410

0

IO11

60

270

270

270

270

1200-rotation

120

250

250

280

280

TmbhViil

180

60

550

60

550

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CSF with f = bl or bz = < 211116, are listed in the first row of Table 1. Figure l(b) shows atomic stacking arrangement of the Llo structure viewed on the (111) plane, wherein the three different fault vectors, bi, arc:described. Degeneracies of fault energies noted in Table 1 are due to geometrically equivalent characteristic patterns of interfaces resulting from certain combinations of rigid-body translations and rotations according to the O-lattice theory (11). An example of these degeneracies can be described with the aid of Fig. 2, where the C-layer of atoms have been rotated and translated with reference to the B-layer. Figure 2(b) sh.ows the geometric pattern of interfaces by 8 = 60” and f = 0, and Fig. 2(c) shows that by 8 = 60” and :I = bz. These two operations result in a geometrically equivalent pattern between two atomic rows of the adjacent B and C layers. Because of the assumption that c/a = 1, the magnitude of bl = bz are equal to that of b3, and the atomic lattices shown in Figs. 1 and 2 are equilateral triangles. With the actual value of c/a = 1.O1 for y-TiAl, this symmetry and the degeneracies are broken for the 8 = 60” rotational boundary, thus giving rise to long-range coherency stresses and interfacial dislocations to accommodate the misfit strain across the interface. In this investigation, we assume the degeneracies in the interface energies are retained for the 8 = 60” rotational boundary. In other words, assuming that the lattice misfit is eliminated at the interface by misfit dislocations, we are effectively modelling the coherent region between dislocations at the interface. All the calculated interfacial energies in Table 1 are the values obtained after atomic relaxations. The APB, SISF, and true-twin boundary energies of E APB= 560, EsrsF= 90, and FT = 60 mJ/m*, respectively, are the ones reported earlier (13). It should be noted that in the earlier paper (13) the relaxation effect was included only for the APB. Since there is no change in the nearest-neighbor coordination of atoms at the SISF, superlattice extrinsic stacking fault (SESF), and true-twin interfaces, atomic relaxation at these j’nterfaces is negligible small. On the other hand, the relaxation energies are more than 10% of the APB and CSF energies once the nearest-neighbor Ti-Al bonds are disrupted. According to a more refined calculation, the present result gives an APB energy which is slightly increased from the previously reported value. With the inclusion of relaxation energy, the CSF energy is reduced from EcsF = 480 mJ/m* to 410 mJ/m2. [Note that the CSF energy is lower than the APB energy in this case.]

(a)

(b)

(c)

Figure 2. Degeneracy of the planar fault at a pseudo-twin interface: (a) reference positions of C-layer (large circles) and B-layer (smaller circles), (b) after rotation of the C-layer by 0 = 60° about the [l 1 l] axis and f = 0, and (c) after 8 = 60” and f = bz.

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Likewise, the pseudo-twin boundary energy is reduced from F p = 310 mJ/m* to 270 mJ/m’ after relaxation. The atomic relaxations are mostly restricted to those Ti atoms on the (111) atomic layers adjacent to the interfaces, and the atomic relaxation just one layer away from the interfaces becomes negligibly small. At pseudo-twin and 120°-rotational y/y interfaces, the magnitudes of atomic displacements are about 1% of the interatomic distance (for the in-plane component) and about l-2% of the interlayer spacing (for the normal-to-the-plane component). The in-plane relaxation of Ti atoms at APB is about 0.06 8, (with Ti atoms at adjacent planes moving closer to each other); a similar pattern of atomic relaxations is also found for CSF. At the pseudo-twin and 120”-rotational boundaries, while both EAPBand ECSFare reduced markedly, by factors of about two, as compared to those in the bulk, E SISFis increased by a factor of three. At the true-twin boundary, on the other hand, changes in the fault energies (from those in the bulk) are relatively small, with slight increases in both E APBand Ecs~ and a decrease in ESISF. At an a2/y interface with the crystallographic habit relationship of (OOOl)[l ITO]-Ti3A1 and (111) [l iO]-TiAl, the interfacial energy is calculated to be 110 mJ/m* (the reference energy in this case is the sum of bulk TiAl and T&Al energies). Substantial reductions in E APB, &SF, and &SF of y-phase to those (280, 20, and 220mJ/m*, respectively) at the Ti3Al/TiA1 interface were reported recently (14). Once a cleavage crack is initiated on a (111) plane, which is of the lowest surface energy in TiAl, it may propagate across a series of y/y interfaces under the influence of mode-II and mode-III components of external loading applied to the coplanar (111) [112] twinning (edge) and (111) [l TO] ordinary slip (screw), leading to translamellar fracture [ 151. Using the calculated surface energies, G,, and the interfacial energies, Fi, one can evaluate interfacial work of adhesion (Gi) by using the relationship,

Gi= G, -Ti - Em, where E, is the misfit energy estimated using the Frank and van der Merwe method (16) and the calculated lattice parameters of TiAl and T&Al (13,14). The calculated results are summarized in Table 2. Because of the approximations involved in determining the misfit energies, the final interfacial fracture energies are only estimates. Nevertheless, these results enable us to set a relative measure of interfacial bonding strength, indicating that the interfacial work of adhesion is slightly stronger along a2/yand true-twin boundaries than other types of y/y lamellar interfaces. Fracture behavior and toughness of PST TiAl crystals at room temperature were investigated using three-point bending tests of Chevron-notched crystals in five different lamellar orientations (10). While TABLE 2 Interfacial Work of Adhesion(Gi) in Two-phaseTiAl (in Units of J/m*).G, is the Sum of Surface Energies of the Two CleavagePlanes. The Em’sof Pseudo-twinand True-twin Boundaries are Lower than the E, of 120”-Rotational Boundary

v-t pseudo-twin

4.5

0.27

12O%olalion

4.5

0.25

true-twin

4.5

0.06

wi

4.65

0.11

-4.2 0.03

4.2 -4.4

0.01

4.5

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the preliminary results suggest that delamination-type separation occurs in a2 lamellae, examinations to clarify whether fracture occurs along y/y, a&, or in a2 lamellae have not been completed. On the other hand, in the fracture tests using microcompact tension specimens of TiAl PST cry>tals (8) it was found that a microcrack was initiated on the a2 plate and easily developed into a main crack on the (0001) plane, finally leading to failure because of the hydrogen embrittlement of the a2 phase. Although the calculated cleavage energies of the a2/yinterface (G, = 4.5 J/m2) and the (0001) plane of the a2 phase (G, = 4.8 J/m’) are higher than those of any other ylyinterfaces listed in Table 2, it could be reduced appreciably, due probably to the relatively high solubility of interstitials (hydrogen, in this case) in the a2phase. In fact, our first-principles calculation shows that hydrogen preferentially segregates to the a21yboundary and also to the a2 phase in two-phase Ti-Al alloys. The (0001) surface energy of T&Al is reduced by -15% with a hydrogen coverage of -0.2 on the surface. (The effect of atomic hydrogen on the interfacial cohesion will be published separately.) Environmental embrittlement can have a pronounced effect on the fracture mode in Ti-Al alloy. Discussion

The ratio of y!y-type interfacial energies calculated for true-twin, pseudo-twin, and 120“-rotational boundaries (r~:rp; r~) is 1:4.5:4.2. This is consistent with more frequent observation of true-twin type lamellar interfaces in two-phase TiAl alloys of binary compositions, compared with the 120”-rotational and pseudo-twin types (17). On the other hand, the reason why the lamellar domain boundaries of higher energies than that of the true-twin type, by a factor of four, do appear in the TiAl phase is not entirely clear. One possible explanation for the formation of these lamellar domain boundaries may be closely related to the preexisting anti-phase domain boundaries of Ti,AI before the a2--> a2 + y transformation (18). According to the recent review by Wiezorek and Humphreys (19), the hierarchy of planar fault energies in Ti-54Al is EAPB> EC~F> ESISF,and the values for TiAl are E~pe> 2.50 mJ/m’ and EslsF= 140 mJ/m2. Our calculated results of E APB= 560 mJ/m2 and Esrs~= 90 mJm2 for TiAl (at stoichiometry) indicate that there is a dependence of planar fault energies on composition. Further theoretical and experimental studies are needed to assess this dependence in order to better understand the role of interfaces in Ti-Al alloys. A screw dislocation of Burgers vector, [I iO]/2, is dissociated into a pair of Shockley partials on -either the (111) or (1 1 1) slip plane by,

where ECsF= 4 10 mJ/m* in they bulk gives the equilibrium width of d = 0.35 nm. Due to lower values of EcsF at the y/y-type interfaces (the last column of Table 1) and at the a2/yinterface (I 4), relatively wider dissociations at interfaces are expected. The widest being at the al/y interface with d = 0.55 nm (if the same elastic interaction between partials as in y bulk is assumed). According to the classical Peierls concept that the wider the dissociation configuration of a dislocation, the more mobile the dislocation is, the mobility of [ITO]/ screw dislocation is expected to be slightly reduced along a true-twin boundary, but significantly enhanced along all other types of interfaces when its glide plane is confined along the interface. On the other hand, for shear deformation proceeding on the { I1 1) plane intersecting the lamellar interfaces, the interfaces can act as an effective barrier impeding propagation of slip across the interfaces (i.e., “hard” mode dislocations).

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Because of more complex dissociation configuration involving all three types of the planar faults, the role of interfaces in the relative mobility of superdislocations is more complicated than that of ordinary dislocations. As listed in Table 1, while EAPBand ECWin the bulk of y-phase are both reduced, by about a half, at pseudo-twin and 120”-rotational boundary interfaces, Esm is increased about threefold. As far as ordinary dislocations are involved, the enhanced mobility along these lamellar interfaces supports the notion of “channeled dislocation motion” (20) or “supersoft deformation mode” (11) in lamellar TiAl. Recently, the experiment by Kad and Asaro (21) has shown direct evidence of y/y interface sliding in PST-TiAl deformed in compression at room temperature. In addition to this evidence of coarse slip parallel to the laminates, localized at the y/y and aZ/y interfaces, they also observed transition from the coarse slip to mode II cracking parallel to lamellar interfaces, and then to mixed mode (I + II) across interfaces. These experimental findings are consistent with the present results indicating inhomogeneous slip along the lamellar interfaces and translamellar crack nucleation due to pileup of ordinary dislocations. The bonding in bulk Ti-Al system is dominated by the directional Ti-Ti bonding (for TiAl) (13) and the multi-centered bonding among Ti atoms (for T&Al) (14). The presence of Al in these alloys enhances these bonding components by charge donation and bonding hybridization between Al-p and Ti-d states. The effect of the TiAl/TisAl interface is to disrupt these long-range bonding characteristics and, as a result, to reduce the planar fault energies at the interface from those of either constituent phase, On the other hand, the geometry of TiAl/TiAl lamellar interfaces produces degeneracies in the interface structures with and without the presence of translation faults. Due to relatively low y/y lamellar boundary energies (compared to the planar fault energies in bulk TiAl), APB and CSF energies at the pseudo-twin and 120“-rotational boundaries are reduced from their counterparts in bulk TiAl. The lower ‘y/y lamellar interface energies are due to a partial preservation of the local ordering of bulk TiAl at these interfaces. It is conceivable that an effective way to improve the ductility of Tirich TiAl alloys is to reduce the interfacial spacings (and thus to increase the number of y/y and a& interfaces). Summary

The intrinsic values of interfacial energies based on first-principles calculations, including atomic relaxation, were obtained for the three types of y/y interfaces and the azly lamellar boundary in twophase TiAl alloy. The pseudo-twin boundary energy is highest, Fp = 270 mJ/m*, and the true-twin boundary energy is lowest, FT = 60 mJ/m*. Planar fault energies at pseudo-twin and 120”-rotational interfaces are markedly different from those in the bulk of the y-phase, i.e., approximately, EAWand Ecs~ decreases by more than 30% and E sis~ increases by threefold. Enhanced mobility of ordinary dislocations along the y/y and a~/y interfaces (except true twin boundaries) is predicted based on the reduced EcsF values at the interfaces. Acknowledgments

This work was sponsored by the Division of Materials Sciences, Office of Basic Energy Sciences, U.S. Department of Energy under contract DE-AC05-960R22464 with Oak Ridge National Laboratory, managed by Lockheed Martin Energy Research Corporation.

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