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Experimental determination of domain orientations and domain orientation relationships across lamellar interfaces in polysynthetically twinned TiAl crystals
Materials Science and Engineering A231 (1997) 62 – 71
Experimental determination of domain orientations and domain orientation relationships across lamellar interfaces in polysynthetically twinned TiAl crystals Zhe Jin *, George T. Gray III Materials Science and Technology Di6ision, Los Alamos National Laboratory, MST-5, MS G755, Los Alamos, NM 87 545, USA Received 26 September 1996; revised 6 January 1997
Abstract Six domain orientations in an as-grown polysynthetically twinned (PST) TiAl crystal are unambiguously determined. Fifteen domain orientation relationships across lamellar interfaces (not including those across order-translational lamellar interfaces) are uniquely identified. The atomic arrangements of these 15 domain orientation relationships are investigated. Domains within a lamellar lath are related to each other by a 120°-rotation: either domains [I] to [III] or domains [IV] to [VI] are within a lamellar lath. Diffraction patterns across the lamellar interfaces show that a B 1( 01] zone disordered twin diffraction pattern (the twin diffraction pattern without superlattice diffraction spots) taken parallel to the lamellar interfaces cannot unambiguously determine whether the interface is a true-twin related interface or a pseudo-twin related interface. A second different zone diffraction pattern is necessary to characterize the twin-related interfaces but B2( 11\ zone diffraction patterns can not be used to determine the twin relationships since the diffraction spots from both crystals are coincident. A diffraction criterion for an unambiguous determination of domain orientations and domain orientation relationships across lamellar interfaces is proposed. © 1997 Elsevier Science S.A. Keywords: Domain orientation; Lamellar structure; Lamellar interface; PST crystal
1. Introduction The lamellar structure of g +a2 phases plays an important role in the mechanical response of g-TiAlbased compounds subjected to various external loading conditions [1–4]. Lamellar orientation effects on the mechanical properties of polysynthetically twinned (PST) TiAl crystals have been systematically studied [5,6]. PST crystals inclined 45° to the loading direction (the easy deformation orientation) exhibit the lowest yield strength and the highest ductility while both the 0and 90°-inclined PST crystals (the hard deformation orientations) exhibit a much higher yield strength but a very low ductility [7]. Deformation in the easy orientation is controlled by the activation of parallel twinning and slip of 1/2B 110] normal dislocations. However, deformation in the hard orientation is dominated by
* Corresponding author. Tel.: +1 505 6659473; fax: + 1 505 6678021; e-mail: [email protected] 0921-5093/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved. PII S 0 9 1 - 5 0 9 3 ( 9 7 ) 0 0 0 3 6 - 1
cross twinning and the same 1/2B 110] normal dislocations [7]. The differences in the mechanical properties and deformation behavior between the easy and the hard orientations are characterized as being due to the restriction of deformation across the lamellar interfaces. Thus the domain orientations and lamellar interfaces play a critical role in the mechanical response of PST crystals. Much effort has been carried out to understand the lamellar structures and lamellar interfacial characters and the crystallographical orientation relationships between six domains are well known to us [8–16]. Although some experimental effort has been performed to determine individual domain orientations in lamellar structures [17,18], an unambiguously experimental determination of all six domain orientations in the lamellar structures has not been reported. A recent study on a high rate deformation of a PST-TiAl crystal shows that individual domains deform differently depending on their orientations with respect to loading axis. Ac-
Z. Jin, G.T. Gray III / Materials Science and Engineering A231 (1997) 62–71
cordingly, the deformation transition across the lamellar interfaces depends on the orientations of domains that form the interfaces. Therefore, a systematic investigation of lamellar structures and an unambiguous determination of individual domain orientations become necessary to understand the deformation of individual domains under the specific loading conditions and the role of lamellar interfaces playing in the deformation of lamellar structures. In this paper, the lamellar structure in a PST crystal is systematically characterized. All six domain orientations within the lamellar structure are unambiguously determined by taking diffraction patterns in different zone directions. Fifteen domain orientation relationships across the lamellar interfaces (not including those across order-translational lamellar interfaces) are identified. Accordingly, 15 lamellar interface structures are determined.
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so that the g= [111] vector in all the diffraction patterns points vertically upward. This will be the same for all the diffraction patterns presented in this paper except for the diffraction patterns in Fig. 6. Diffraction patterns in Fig. 2 were taken from each domain in different zone directions by tilting the TEM foil about the [111] lamellar interface normal. The SADPs in Fig. 2(a)–(f) were taken without tilting the foil such that the zone directions are the foil normal directions in reference to the individual domains. The SADPs in Fig. 2(g)–(l) were obtained from the same domains by tilting the foil 19° away from the foil normal, which determine the domain variants. The SADPs in Fig. 2(m)–(r) were also from the same domains but obtained by tilting the TEM foil 41° from the foil normal in an opposite tilting direction. Comparing diffraction patterns between any two domains, we can see that each domain has its own unique combination of three
2. Experimental procedure The material used in this study was an as-grown polysynthetically twinned (PST) TiAl crystal, which was made by Kyoto University, Kyoto, Japan. The nominal composition is Ti-49.3Al. Details of the crystal growing process are described in [5]. Slices for TEM foils were cut perpendicular to both lamellar interfaces and B 3( 21\ directions which are in the lamellar interfaces. The slices were ground to about 100 mm in thickness and then thinned using a twin-jet electropolishing system with a solution of 7.5% sulphuric acid plus methanol at −20°C. The TEM investigation was performed using a Philips CM-30 Analytical Electron Microscope operating at 300 kV.
3. Experimental results The six domains are defined using B 1( 10 \ directions in the (111) lamellar interface and labeled as domain [I]=[1( 10], domain [II]= [01( 1], domain [III]= [101( ], domain [IV] =[11( 0], domain [V]= [011( ], domain [VI] =[1( 01]. Domains in this study are determined by the B 1( 10\ directions closest to the TEM foil normal.
3.1. Diffraction patterns from indi6idual domains in the lamellae Fig. 1(a) is an edge-on image of the lamellar structure that was taken from the as-grown PST TiAl crystal. A schematic of this image is shown in Fig. 1(b) where different domains in Fig. 1(a) are labeled using capital letters. Fig. 2 shows select area diffraction patterns (SADPs) from all the labeled domains in Fig. 1. In Fig. 2, the lamellar interfaces are assumed to be horizontal
Fig. 1. (a)Domains in the lamellar structure of an PST-TiAl crystal. (b) A schematic illustration of domains in (a). Domains investigated are labeled using capital letters.
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Fig. 2. Select area diffraction patterns from all labeled domains in (a – f) are the diffraction patterns without tilting the TEM foil. The zone directions of these patterns are the foil normal directions in terms of the corresponding domains. (g – l) Diffraction patterns obtained by tilting the foil 19° about the [111] lamellar interface normal clockwise from the foil normal. (m – r) Diffraction patterns obtained by tilting the foil 41° about the [111] lamellar interface normal counter-clockwise from the foil normal. (a), (g) and (m) are from domain A; (b), (h) and (n) are from domains B and D; (c), (i) and (o) from domain C; (d), (j) and (p) from domain E; (e), (k) and (q) from domain F; (f), (l) and (r) from domain G.
diffraction patterns, indicating the possibility of unambiguous determination of each domain orientation.
3.2. Diffraction patterns across lamellar interfaces and domain boundaries A large area of lamellar structure as shown in Fig. 3(a) was investigated to obtain all the possible domain orientation relationships across lamellar interfaces. Fig. 1 is only a small portion (the upper-left corner) of Fig. 3(a). The SADPs across the twin-related lamellar interfaces between any two adjacent domains in Fig. 3 are presented in Fig. 4. Similar to the SADPs obtained from each domain in Section 3.1, the SADPs in Fig. 4 (a1)–(i1) were obtained by tilting the TEM foil 19°. Fig. 4 (a2)–(i2) were obtained by rotating the foil 41° in an opposite direction. Although the lamellar interface between domains [II] and [IV] does not exist in Fig. 3, the diffraction patterns across the interface between them can be easily determined by comparing individual diffraction patterns from both domains. The SADPs across domain boundaries within a lamellar lath in the 19° tilted directions are presented in Fig. 5.
4. Analysis
4.1. Domain orientation determination The diffraction zone direction in Fig. 2 (n) for domains B and D can be uniquely indexed as [11( 0]
according to the superlattice spots and the (111) plane spot in the diffraction pattern. However, the diffraction patterns in Fig. 2(b) and (h) from the same domains can not be unambiguously indexed without knowing the foil tilting directions because these two patterns can be indexed as either B= [31( 2( ] and B= [101( ] or B= [13( 2] and B= [01( 1], respectively, where B is a diffraction zone direction. Similarly, although the diffraction pattern shown in Fig. 2(q) for domain F can be indexed as B= [1( 10] unambiguously, the diffraction patterns in Fig. 2(e) and (k) still have two possibilities: either B= [3( 12] and B= [1( 01] or B=[1( 32( ] and B= [011( ], respectively. This ambiguity was eliminated by determining the TEM foil tilting directions. Fig. 6 shows diffraction patterns of B= [2( 1( 1] in Fig. 6 (a) and B= [1( 1( 0] in Fig. 6(b) which were obtained by tilting the TEM foil about the g= B 11( 1\ vector in Fig. 2(k) in such a way that the electron beam was brought towards the g= [1( 1( 1( ] vector. This result indicates that the zone direction of Fig. 2(k) is [1( 01] and the zero-tilt zone direction (the foil normal) of Fig. 2(e) is [3( 12] in terms of domain F. Therefore, Fig. 2(k) was obtained by tilting the foil clockwise about the [111] lamellar interface normal and Fig. 2(q) was obtained by tilting counter-clockwise about the [111] direction from the foil normal, where the [111] direction points toward the reader. Accordingly, Fig. 2(g)–(l) were obtained by tilting the foil clockwise and Fig. 2(m)–(r) were obtained by tilting the foil counterclockwise about the [111] lamellar interface normal, respectively.
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Fig. 3. (a) Edge-on image of lamellae observed in an as-grown PST TiAl crystal. (b) Schematic illustration of the lamellae showing the domain distribution within the lamellae. The roman numbers indicate the domain variants of those domains. The true-twin, the pseudo-twin and the 120°-rotation related crystal orientation relationships are observed across the lamellar interfaces, but only the 120°-rotational crystal orientation relationship is between the domains within a lamellar lath.
In Fig. 2, the diffraction zone directions of Fig. 2(g)–(l) define the domain variants since they are the B 1( 10\ zone directions closest to the foil normal. Thus, the domain variants in Fig. 1 can be easily determined, as shown in Table 1, since the relative tilting directions between diffraction zone directions in Fig. 2 are known. The indexed B 1( 10 \ and B 3( 21\ zone diffraction patterns for each domain variant are summarized in Table 2, where the foil rotation axis is the [111] lamellar interface normal and points toward the reader. For determination of domain orientations except for domains [I] and [IV], two different zone diffraction patterns are required. The B 2( 11 \ zone
diffraction patterns can also be used to determine domain orientations although the B 2( 11\ zone diffraction patterns are not shown in Table 2. All domains in Fig. 3(a) are identified as shown in Fig. 3(b). We can see from Fig. 3(b) that domains within a lamellar lath are all 120°-rotation-related domains.
4.2. Twin relationships between two domains across lamellar interfaces Both true-twin and pseudo-twin relationships between two domains across lamellar interfaces have identical diffraction patterns when B01( 1]M//B1( 01]T,
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Fig. 4. Select area diffraction patterns across the twin-related lamellar interfaces formed by two domains. (a – i) Diffraction patterns across the domain interfaces of [I]/[IV], [I]/[V], [I]/[VI], [II]/[IV], [II]/[V], [II]/[VI], [III]/[IV], [III]/[V] and [III]/[VI], sequentially. Diffraction patterns in the figures with subscript ‘1’ are obtained by tilting the TEM foil 19° about the [111] lamellar interface normal clockwise from the foil normal. Diffraction patterns in the figures with subscript ‘2’ are obtained by tilting the foil 41° about the [111] lamellar interface normal counter-clockwise from the foil normal.
as shown in Fig. 4 (e1),(f1),(h1),(i1),(a2),(b2),(d2) and (e2), in which Fig. 4(f1),(h1),(b2) and (d2) are from the pseudo-twin relationship between two domains in Fig. 3. The reason for this can be understood from the crystal orientation relationships between two TiAl crystals. The twin relationship between two domains can be obtained by a (2n −1)60° rotation of one domain with respect to the other within any one of the {111} planes in TiAl if no atomic species at lattice points are considered. Atomic arrangements across all twin-related lamellar interfaces in TiAl are shown in Fig. 7, where the crystals are projected onto the {1( 10} planes along B1( 10\ directions. Circles represent atoms in the projection plane and squares represent atoms in the plane above the projection plane. Ti and Al atoms are represented by the shaded and open symbols, respectively. Atoms in the lamellar interfaces are all from the lower crystals. Considering the atomic characters at lattice points, we can see that atoms only in Fig. 7(a),(e) and (i) are symmetric about the interfaces, indicating that they have a true-twin relationship. Many atoms in the remaining orientation relationships as in Fig. 7(b),(c),(d),(f),(g) and (h) occupy anti-atomic positions so that they have a pseudo-twin relationship. The truetwin relationship has the same conjugate twin plane and direction in the matrix and twin portions, as shown
in Fig. 7(a),(e) and (i). In the pseudo-twin relationship, the conjugate twin elements in the matrix are different from those in the twin. For example, in Fig. 7(b), if the lower crystal is considered as the matrix, the conjugate twin plane (111( ) and the conjugate twin direction [112] in terms of the matrix are changed to the corresponding conjugate twin plane of (1( 11) and the conjugate twin direction of [211], respectively. The twin direction (h1) is also different in terms of the lower and the upper crystals for both true-twin and pseudo-twin relationships. However, for the true-twin relationship, the twin directions in terms of the two crystals are anti-parallel. In the case of the pseudo-twin relationship, the twin directions are related by a 60°-rotation. From Fig. 7, we can see that the probabilities of the non-superlattice-spot twin diffraction patterns (or the disordered twin diffraction patterns) for the true-twin relationship and the pseudo-twin relationship between two domains across lamellar interfaces are even. The B 1( 01] zone twin diffraction patterns without superlattice diffraction spots cannot differentiate whether two domains are true-twin related or pseudo-twin related. To distinguish the true-twin relationship from the pseudo-twin relationship across a lamellar interface, we must have at least one domain in a B 1( 10] zone direction, or we must have a second different zone diffrac-
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tion pattern, as shown in Fig. 4. However, for deformation twins, we must use B 1( 01] zone diffraction patterns to distinguish between true-twins and pseudo-twins.
4.3. Lamellar interface structures In Fig. 7, atoms at interfaces for true-twin relationships belong to both the lower and upper crystals. There is no violation of the atomic arrangement at the interface for both crystals. Thus atoms in the true-twinrelated lamellar interfaces as shown in Fig. 7(a), (e) and (i) do not need to be rearranged. For the pseudo-twin-related interfaces, atoms at the interfaces that are from the lower crystals are not consistent with the atomic arrangements of the upper crystals, as shown in Fig. 7(b), (c), (d), (f), (g) and (h). Many atoms are in the anti-atomic positions at the interfaces with respect to the upper crystals. These anti-phase configurations of the pseudo-twin-related interfaces may result in a higher interfacial energy compared to the true-twin-related interfaces. To reduce the energy of the pseudo-twin-related interfaces, the atomic arrangements at the interfaces shown in Fig. 7(b), (c), (d), (f), (g) and (h) should be adjusted to reduce the anti-phase components between the interface atoms and the atoms in both side crystals. Thus the atomic arrangements at the pseudo-twin-related lamellar inter-
Fig. 6. Diffraction patterns taken from domain [VI] by moving the electron beam toward the (1( 1( 1( ) diffraction spot and rotating the foil about [11( 1] from B =[1( 01]. (a) [2( 1( 1] zone diffraction pattern; (b) [1( 1( 0] zone diffraction pattern.
faces should not be like those shown in Fig. 7(b), (c), (d), (f), (g) and (h). The large proportion of pseudotwin-related lamellar interfaces in Fig. 3 indicates that this type of pseudo-twin-related lamellar interfaces is stable during the solidification and/or the phase transformation in PST crystals. Therefore, it may not be necessary to form a second phase (the a2-phase) layer at the pseudo-twin-related lamellar interface to reduce the interfacial energy, at least for the alloy used in this study. In Fig. 3, a thin a2-phase layer is observed at the true-twin-related lamellar interface, the interface of domain [III]/domain [VI] and domain [I]/domain [IV]. This indicates that the formation of a2-phase layers in the lamellar structures of TiAl may be due to compositional effects and solidification processing conditions rather than the reduction of the interfacial energy. The lamellar lath of domain [IV] within the lath of domain [I] as indicated by arrows in Fig. 3 is not Table 1 Domain identification and foil normal in Fig. 1
Fig. 5. Select area diffraction patterns across the 120°-rotational domain boundaries within a lamellar lath. The diffraction patterns are taken by tilting the foil 19° about the [111] lamellar interface normal clockwise from the foil normal. (a) Diffraction pattern for domain boundaries [I]/[II] and [I]/[III]; (b) diffraction pattern for [II]/[III]; (c) for [IV]/[V] and [IV]/[VI]; (d) for [V]/[VI].
Domain variant
Domain
Foil normal
[I] [II] [III] [IV] [V] [VI]
E A B, D G C F
[2( 31( ] [1( 2( 3] [31( 2( ] [23( 1] [123( ] [3( 12]
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Table 2 The indexed B1( 10\ and B3( 21\ zone diffraction patterns for six domains in TiAl
parallel to the other lamellar laths. A comparison of the diffraction pattern of this inclined lath with those of other domain [IV] laths in Fig. 3 indicates that this inclined lath has the same crystal orientation as the other domain [IV] laths. Therefore, the reason that this lath is inclined may be due to the (111) facets at interfaces. The lamellar interface between domain [I] and domain [II] at the lower portion in Fig. 3 indicates that 120°-rotational interfaces also exist within the lamellar structure of TiAl. The atomic arrangements of three 120°-rotational interfaces are shown in Fig. 8, the projections of which are the same as those in Fig. 7. Atoms at the interfaces shown in Fig. 8(a) and (c) violate the atomic arrangements of the upper crystals. Thus some atomic rearrangements within the interfaces may also be necessary to maintain the minimum interfacial energy. The crystal orientation relationships across lamellar interfaces observed in this study are summarized as the true-twin related lamellar interface, the pseudotwin related lamellar interface and the 120°-rotational lamellar interface. However, the proportion of the 120°-rotational lamellar interface is small compared to the other two interfaces. Domains within a lamellar lath are observed to be related all by a 120°-rotation, i.e. domains in a lamellar lath are either domains [I]
to [III] or domains [IV] to [VI].
5. Discussion An attempt to experimentally determine domain orientations within lamellar structures has been reported in the literature [17,18]. Yang and Wu defined six domain variants with respect to the crystallographic orientation relationship between g- and a2phases in the lamellae [17]. However, only four domain variants (variants A, B, C and D which are identical to domains [IV], [I], [VI] and [III] in this study, respectively) were determined. Variants C and E (domains [VI] and [V] in this study) or variants D and F (domains [III] and [II] in this study) could not be distinguished for the reason described in Section 4.1 so that they concluded that only four orientation variants between g and a2 could be distinguished from SADPs. Accordingly, domain orientation relationships across lamellar interfaces could not be completely determined. Misorientations between domains across lamellar interfaces were measured using both SADPs and convergent-beam electron diffraction patterns (CBEDPs) by Dimiduk, Sun and Hazzledine [18]. However, details of domain orientation determination were not described.
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Fig. 7. Atomic arrangements across the twin-related lamellar interfaces, which are projected onto {1( 10} planes along B1( 10 \ directions. Circles represent atoms in the projection planes and squares represent atoms in the planes above the projection planes. The shaded and open marks represent Ti and Al atoms, respectively. (a)–(i) are the atomic arrangements across the domain interfaces of [I]/[IV], [I]/[V], [I]/[VI], [II]/[IV], [II]/[V], [II]/[VI], [III]/[IV], [III]/[V] and [III]/[VI], sequentially. Atoms at the interfaces are all from the lower crystals.
The unambiguous determination of domain orientations in lamellar structures is necessary to completely understand the deformation of the lamellar structures.
It has been observed that different behave differently in a specimen under the external loading. Fig. 9 shows a deformation microstructure in domain
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Fig. 8. Atomic arrangements across the 120°-rotational lamellar interfaces, which are projected onto {1( 10} planes along B 1( 10 \ directions. (a)– (c) Interfaces between domains of [I]/[II], [II]/[III] and [III]/[I], respectively. Circles represent atoms in the projection planes and squares represent atoms in the planes above the projection planes. The shaded and open marks represent Ti and Al atoms, respectively. Atoms at the interfaces are all from the lower crystals. (a)–(c) Interfaces between domains of [I]/[II], [II]/[III] and [III]/[I], respectively.
[V] and domain [VI] in a specimen deformed at 800°C and 3000 s − 1. Many cross-twins are seen in domain [V] but only ordinary dislocations are seen in domain [VI], indicating that the deformation of these two domains is different. However, if we take only one diffraction pattern from each of these two domains with the diffraction zone direction in the domain variant direction, like those in Fig. 2(i) and (k), we might wrongly get a conclusion that these two domains are the same domain. In addition, only a simple differentiation of two domains is not sufficient to characterize the deformation of individual domains under the different external loadings. Although there exist only four crystal orientation relationships across lamellar interfaces in TiAl, there are nine twin-related domain relationships (Fig. 7), six
Fig. 9. The deformation microstructure of domain [V] and domain [VI]. The specimen deformed at 800°C and 3000 s − 1.
120°-rotational domain relationships (three of which are presented in Fig. 8) and six order-translational domain relationships. The domain orientation relationships across lamellar interfaces consider the domain orientations with reference to a fixed crystal direction (for instance, the foil normal direction in this study) in addition to the relative crystal orientation relationships between two domains. The mechanical response of lamellar interfaces to the external loading is different depending on the orientations of two domains that form the interfaces although the crystal orientation relationship between these two domains remains the same when the interface between these two domains is rotated to a different orientation with respect to the loading direction. A lamellar interface is transitive to one particular deformation mode in one orientation but may not be transitive to the same deformation mode in another orientation because the domains on this interface behave differently in different orientations. Thus, the identification of only four crystal orientation relationships between two adjacent lamellae (or domains) is not enough to completely characterize the deformation of lamellar structures in TiAl. The definition of domain variants used in this study is relative since the TEM foil normal is dependent upon the cutting directions of the TEM slices from the bulk specimens. The same domain in reference to a fixed loading direction will have different domain variants if the slices are cut in different directions. Even in the same TEM foil, for instance, domain [I] will become domain [IV] if the foil is turned over since the orientations of these two domains are anti-parallel. Therefore, the investigation of domain orientations and mechanical behavior of domains should be performed under the same TEM foil orientation. Similarly, the TEM foil orientation is also critical to the characterization of lamellar interfaces. The current study also provides
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insight toward a more complete understanding of the mechanical behavior of duplex TiAl microstructures that consists of equiaxed g-grains and lamellar grains.
6. Conclusions A lamellar structure in a polysynthetically-twinned (PST) TiAl crystal is characterized for the purpose of unambiguously determining domain orientations and domain orientation relationships across lamellar interfaces in TiAl. By documenting many different zone diffraction patterns in each domain, the domain orientations in lamellar structures have been unambiguously determined so that the lamellar interfaces formed by these domains are also uniquely identified. Among the three crystal orientation relationships observed across lamellar interfaces, the probabilities of the true-twin-related lamellar interface and the pseudo-twin-related lamellar interface are similar. However, the proportion of the 120°-rotational lamellar interface is small. The observed three types of lamellar interfaces in terms of the crystal orientations are further divided into 15 domain interfaces in terms of the domain orientation relationships across the interfaces. These interfaces should be different in their responses to the external loading. Domains within a lamellar lath are all 120°-rotational domains: either domains [I], [II] and [III] or domains [IV], [V] and [VI] are within a lamellar lath. Twin-related lamellar interfaces can not be unambiguously characterized using one B1( 10 \ zone diffraction pattern taken parallel to the lamellar interfaces except for diffraction patterns having at least one domain in a B 1( 10] zone direction. Acknowledgements This work was performed under the auspices of the
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U.S. Department of Energy. The authors are very grateful to Professor M. Yamaguchi for providing the PST crystal for this study and his comments and suggestions to the manuscript. The authors would also like to express their gratitude to Drs. S. Maloy and D.E. Albert for reviewing this manuscript.
References [1] Y.-W. Kim, Acta Metall. 40 (1992) 1121. [2] K.S. Chen, Y.-W. Kim, Metall. Trans. A 23A (1992) 1663. [3] M. Yamaguchi and H. Inui, in: R. Darolia, J.J. Levandowski, C.T. Liu, P.L. Martin, D.B. Miracle and M.V. Nathal (Eds.), Structural Intermetallics, TMS, Warrendale, PA, 1993, p. 127. . [4] Y.-W. Kim, in: Y-W. Kim, R. Wagner and M. Yamaguchi (Eds.), Gamma Titanium Aluminides, TMS, Warrendale, PA, 1995, p. 637. [5] T. Fujiwara, A. Nakanura, M. Hosomi, S.R. Nishitani, Y. Shirai, M. Yamaguchi, Phil. Mag. A 61 (1990) 591. [6] H. Inui, M.H. Oh, A. Nakamura, M. Yamaguchi, Acta Metall. 40 (1992) 3095. [7] H. Inui, A. Nakamura, M.H. Oh, M. Yamaguchi, Phil. Mag. A 66 (1992) 557. [8] C.R. Feng, D.J. Michel, C.R. Crowe, Scripta Metall. 22 (1988) 1481. [9] H. Inui, A. Nakamura, M.H. Oh, M. Yamaguchi, Ultramicroscopy 39 (1991) 268. [10] L. Zhao, K. Tangri, Phil. Mag. A 64 (1991) 361. [11] H. Inui, M.H. Oh, A. Nakamura, M. Yamaguchi, Phil. Mag. A 66 (1992) 539. [12] S.R. Singh, J.M. Howe, Phil. Mag. A 65 (1992) 233. [13] S.R. Singh, J.M. Howe, Phil. Mag. A 66 (1992) 739. [14] L.L. He, H.Q. Ye, X.G. Ning, M.Z. Cao, D. Han, Phil. Mag. A 67 (1993) 1161. [15] Ch. Ricolleau, A. Denquin, S. Naka, Phil. Mag. A 69 (1994) 197. [16] H. Inui, K. Kishida, M. Misaki, M. Kobayashi, Y. Shirai, M. Yamaguchi, Phil. Mag. A 72 (1995) 1609. [17] Y.S. Yang, S.K. Wu, Scripta Metall. 24 (1990) 1801. [18] D.M. Dimiduk, Y.Q. Sun and P.M. Hazzledine, in: J.A. Horton, I. Baker, S. Hanada, R.D. Noebe and D.S. Schwartz (Eds.), High-Temperature Ordered Intermetallic Alloys VI, Mat. Soc. Symp. Proc. Vol. 364, 1995, p. 599.
Experimental determination of domain orientations and domain orientation relationships across lamellar interfaces in polysynthetically twinned TiAl crystals Zhe Jin *, George T. Gray III Materials Science and Technology Di6ision, Los Alamos National Laboratory, MST-5, MS G755, Los Alamos, NM 87 545, USA Received 26 September 1996; revised 6 January 1997
Abstract Six domain orientations in an as-grown polysynthetically twinned (PST) TiAl crystal are unambiguously determined. Fifteen domain orientation relationships across lamellar interfaces (not including those across order-translational lamellar interfaces) are uniquely identified. The atomic arrangements of these 15 domain orientation relationships are investigated. Domains within a lamellar lath are related to each other by a 120°-rotation: either domains [I] to [III] or domains [IV] to [VI] are within a lamellar lath. Diffraction patterns across the lamellar interfaces show that a B 1( 01] zone disordered twin diffraction pattern (the twin diffraction pattern without superlattice diffraction spots) taken parallel to the lamellar interfaces cannot unambiguously determine whether the interface is a true-twin related interface or a pseudo-twin related interface. A second different zone diffraction pattern is necessary to characterize the twin-related interfaces but B2( 11\ zone diffraction patterns can not be used to determine the twin relationships since the diffraction spots from both crystals are coincident. A diffraction criterion for an unambiguous determination of domain orientations and domain orientation relationships across lamellar interfaces is proposed. © 1997 Elsevier Science S.A. Keywords: Domain orientation; Lamellar structure; Lamellar interface; PST crystal
1. Introduction The lamellar structure of g +a2 phases plays an important role in the mechanical response of g-TiAlbased compounds subjected to various external loading conditions [1–4]. Lamellar orientation effects on the mechanical properties of polysynthetically twinned (PST) TiAl crystals have been systematically studied [5,6]. PST crystals inclined 45° to the loading direction (the easy deformation orientation) exhibit the lowest yield strength and the highest ductility while both the 0and 90°-inclined PST crystals (the hard deformation orientations) exhibit a much higher yield strength but a very low ductility [7]. Deformation in the easy orientation is controlled by the activation of parallel twinning and slip of 1/2B 110] normal dislocations. However, deformation in the hard orientation is dominated by
* Corresponding author. Tel.: +1 505 6659473; fax: + 1 505 6678021; e-mail: [email protected] 0921-5093/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved. PII S 0 9 1 - 5 0 9 3 ( 9 7 ) 0 0 0 3 6 - 1
cross twinning and the same 1/2B 110] normal dislocations [7]. The differences in the mechanical properties and deformation behavior between the easy and the hard orientations are characterized as being due to the restriction of deformation across the lamellar interfaces. Thus the domain orientations and lamellar interfaces play a critical role in the mechanical response of PST crystals. Much effort has been carried out to understand the lamellar structures and lamellar interfacial characters and the crystallographical orientation relationships between six domains are well known to us [8–16]. Although some experimental effort has been performed to determine individual domain orientations in lamellar structures [17,18], an unambiguously experimental determination of all six domain orientations in the lamellar structures has not been reported. A recent study on a high rate deformation of a PST-TiAl crystal shows that individual domains deform differently depending on their orientations with respect to loading axis. Ac-
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cordingly, the deformation transition across the lamellar interfaces depends on the orientations of domains that form the interfaces. Therefore, a systematic investigation of lamellar structures and an unambiguous determination of individual domain orientations become necessary to understand the deformation of individual domains under the specific loading conditions and the role of lamellar interfaces playing in the deformation of lamellar structures. In this paper, the lamellar structure in a PST crystal is systematically characterized. All six domain orientations within the lamellar structure are unambiguously determined by taking diffraction patterns in different zone directions. Fifteen domain orientation relationships across the lamellar interfaces (not including those across order-translational lamellar interfaces) are identified. Accordingly, 15 lamellar interface structures are determined.
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so that the g= [111] vector in all the diffraction patterns points vertically upward. This will be the same for all the diffraction patterns presented in this paper except for the diffraction patterns in Fig. 6. Diffraction patterns in Fig. 2 were taken from each domain in different zone directions by tilting the TEM foil about the [111] lamellar interface normal. The SADPs in Fig. 2(a)–(f) were taken without tilting the foil such that the zone directions are the foil normal directions in reference to the individual domains. The SADPs in Fig. 2(g)–(l) were obtained from the same domains by tilting the foil 19° away from the foil normal, which determine the domain variants. The SADPs in Fig. 2(m)–(r) were also from the same domains but obtained by tilting the TEM foil 41° from the foil normal in an opposite tilting direction. Comparing diffraction patterns between any two domains, we can see that each domain has its own unique combination of three
2. Experimental procedure The material used in this study was an as-grown polysynthetically twinned (PST) TiAl crystal, which was made by Kyoto University, Kyoto, Japan. The nominal composition is Ti-49.3Al. Details of the crystal growing process are described in [5]. Slices for TEM foils were cut perpendicular to both lamellar interfaces and B 3( 21\ directions which are in the lamellar interfaces. The slices were ground to about 100 mm in thickness and then thinned using a twin-jet electropolishing system with a solution of 7.5% sulphuric acid plus methanol at −20°C. The TEM investigation was performed using a Philips CM-30 Analytical Electron Microscope operating at 300 kV.
3. Experimental results The six domains are defined using B 1( 10 \ directions in the (111) lamellar interface and labeled as domain [I]=[1( 10], domain [II]= [01( 1], domain [III]= [101( ], domain [IV] =[11( 0], domain [V]= [011( ], domain [VI] =[1( 01]. Domains in this study are determined by the B 1( 10\ directions closest to the TEM foil normal.
3.1. Diffraction patterns from indi6idual domains in the lamellae Fig. 1(a) is an edge-on image of the lamellar structure that was taken from the as-grown PST TiAl crystal. A schematic of this image is shown in Fig. 1(b) where different domains in Fig. 1(a) are labeled using capital letters. Fig. 2 shows select area diffraction patterns (SADPs) from all the labeled domains in Fig. 1. In Fig. 2, the lamellar interfaces are assumed to be horizontal
Fig. 1. (a)Domains in the lamellar structure of an PST-TiAl crystal. (b) A schematic illustration of domains in (a). Domains investigated are labeled using capital letters.
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Fig. 2. Select area diffraction patterns from all labeled domains in (a – f) are the diffraction patterns without tilting the TEM foil. The zone directions of these patterns are the foil normal directions in terms of the corresponding domains. (g – l) Diffraction patterns obtained by tilting the foil 19° about the [111] lamellar interface normal clockwise from the foil normal. (m – r) Diffraction patterns obtained by tilting the foil 41° about the [111] lamellar interface normal counter-clockwise from the foil normal. (a), (g) and (m) are from domain A; (b), (h) and (n) are from domains B and D; (c), (i) and (o) from domain C; (d), (j) and (p) from domain E; (e), (k) and (q) from domain F; (f), (l) and (r) from domain G.
diffraction patterns, indicating the possibility of unambiguous determination of each domain orientation.
3.2. Diffraction patterns across lamellar interfaces and domain boundaries A large area of lamellar structure as shown in Fig. 3(a) was investigated to obtain all the possible domain orientation relationships across lamellar interfaces. Fig. 1 is only a small portion (the upper-left corner) of Fig. 3(a). The SADPs across the twin-related lamellar interfaces between any two adjacent domains in Fig. 3 are presented in Fig. 4. Similar to the SADPs obtained from each domain in Section 3.1, the SADPs in Fig. 4 (a1)–(i1) were obtained by tilting the TEM foil 19°. Fig. 4 (a2)–(i2) were obtained by rotating the foil 41° in an opposite direction. Although the lamellar interface between domains [II] and [IV] does not exist in Fig. 3, the diffraction patterns across the interface between them can be easily determined by comparing individual diffraction patterns from both domains. The SADPs across domain boundaries within a lamellar lath in the 19° tilted directions are presented in Fig. 5.
4. Analysis
4.1. Domain orientation determination The diffraction zone direction in Fig. 2 (n) for domains B and D can be uniquely indexed as [11( 0]
according to the superlattice spots and the (111) plane spot in the diffraction pattern. However, the diffraction patterns in Fig. 2(b) and (h) from the same domains can not be unambiguously indexed without knowing the foil tilting directions because these two patterns can be indexed as either B= [31( 2( ] and B= [101( ] or B= [13( 2] and B= [01( 1], respectively, where B is a diffraction zone direction. Similarly, although the diffraction pattern shown in Fig. 2(q) for domain F can be indexed as B= [1( 10] unambiguously, the diffraction patterns in Fig. 2(e) and (k) still have two possibilities: either B= [3( 12] and B= [1( 01] or B=[1( 32( ] and B= [011( ], respectively. This ambiguity was eliminated by determining the TEM foil tilting directions. Fig. 6 shows diffraction patterns of B= [2( 1( 1] in Fig. 6 (a) and B= [1( 1( 0] in Fig. 6(b) which were obtained by tilting the TEM foil about the g= B 11( 1\ vector in Fig. 2(k) in such a way that the electron beam was brought towards the g= [1( 1( 1( ] vector. This result indicates that the zone direction of Fig. 2(k) is [1( 01] and the zero-tilt zone direction (the foil normal) of Fig. 2(e) is [3( 12] in terms of domain F. Therefore, Fig. 2(k) was obtained by tilting the foil clockwise about the [111] lamellar interface normal and Fig. 2(q) was obtained by tilting counter-clockwise about the [111] direction from the foil normal, where the [111] direction points toward the reader. Accordingly, Fig. 2(g)–(l) were obtained by tilting the foil clockwise and Fig. 2(m)–(r) were obtained by tilting the foil counterclockwise about the [111] lamellar interface normal, respectively.
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Fig. 3. (a) Edge-on image of lamellae observed in an as-grown PST TiAl crystal. (b) Schematic illustration of the lamellae showing the domain distribution within the lamellae. The roman numbers indicate the domain variants of those domains. The true-twin, the pseudo-twin and the 120°-rotation related crystal orientation relationships are observed across the lamellar interfaces, but only the 120°-rotational crystal orientation relationship is between the domains within a lamellar lath.
In Fig. 2, the diffraction zone directions of Fig. 2(g)–(l) define the domain variants since they are the B 1( 10\ zone directions closest to the foil normal. Thus, the domain variants in Fig. 1 can be easily determined, as shown in Table 1, since the relative tilting directions between diffraction zone directions in Fig. 2 are known. The indexed B 1( 10 \ and B 3( 21\ zone diffraction patterns for each domain variant are summarized in Table 2, where the foil rotation axis is the [111] lamellar interface normal and points toward the reader. For determination of domain orientations except for domains [I] and [IV], two different zone diffraction patterns are required. The B 2( 11 \ zone
diffraction patterns can also be used to determine domain orientations although the B 2( 11\ zone diffraction patterns are not shown in Table 2. All domains in Fig. 3(a) are identified as shown in Fig. 3(b). We can see from Fig. 3(b) that domains within a lamellar lath are all 120°-rotation-related domains.
4.2. Twin relationships between two domains across lamellar interfaces Both true-twin and pseudo-twin relationships between two domains across lamellar interfaces have identical diffraction patterns when B01( 1]M//B1( 01]T,
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Fig. 4. Select area diffraction patterns across the twin-related lamellar interfaces formed by two domains. (a – i) Diffraction patterns across the domain interfaces of [I]/[IV], [I]/[V], [I]/[VI], [II]/[IV], [II]/[V], [II]/[VI], [III]/[IV], [III]/[V] and [III]/[VI], sequentially. Diffraction patterns in the figures with subscript ‘1’ are obtained by tilting the TEM foil 19° about the [111] lamellar interface normal clockwise from the foil normal. Diffraction patterns in the figures with subscript ‘2’ are obtained by tilting the foil 41° about the [111] lamellar interface normal counter-clockwise from the foil normal.
as shown in Fig. 4 (e1),(f1),(h1),(i1),(a2),(b2),(d2) and (e2), in which Fig. 4(f1),(h1),(b2) and (d2) are from the pseudo-twin relationship between two domains in Fig. 3. The reason for this can be understood from the crystal orientation relationships between two TiAl crystals. The twin relationship between two domains can be obtained by a (2n −1)60° rotation of one domain with respect to the other within any one of the {111} planes in TiAl if no atomic species at lattice points are considered. Atomic arrangements across all twin-related lamellar interfaces in TiAl are shown in Fig. 7, where the crystals are projected onto the {1( 10} planes along B1( 10\ directions. Circles represent atoms in the projection plane and squares represent atoms in the plane above the projection plane. Ti and Al atoms are represented by the shaded and open symbols, respectively. Atoms in the lamellar interfaces are all from the lower crystals. Considering the atomic characters at lattice points, we can see that atoms only in Fig. 7(a),(e) and (i) are symmetric about the interfaces, indicating that they have a true-twin relationship. Many atoms in the remaining orientation relationships as in Fig. 7(b),(c),(d),(f),(g) and (h) occupy anti-atomic positions so that they have a pseudo-twin relationship. The truetwin relationship has the same conjugate twin plane and direction in the matrix and twin portions, as shown
in Fig. 7(a),(e) and (i). In the pseudo-twin relationship, the conjugate twin elements in the matrix are different from those in the twin. For example, in Fig. 7(b), if the lower crystal is considered as the matrix, the conjugate twin plane (111( ) and the conjugate twin direction [112] in terms of the matrix are changed to the corresponding conjugate twin plane of (1( 11) and the conjugate twin direction of [211], respectively. The twin direction (h1) is also different in terms of the lower and the upper crystals for both true-twin and pseudo-twin relationships. However, for the true-twin relationship, the twin directions in terms of the two crystals are anti-parallel. In the case of the pseudo-twin relationship, the twin directions are related by a 60°-rotation. From Fig. 7, we can see that the probabilities of the non-superlattice-spot twin diffraction patterns (or the disordered twin diffraction patterns) for the true-twin relationship and the pseudo-twin relationship between two domains across lamellar interfaces are even. The B 1( 01] zone twin diffraction patterns without superlattice diffraction spots cannot differentiate whether two domains are true-twin related or pseudo-twin related. To distinguish the true-twin relationship from the pseudo-twin relationship across a lamellar interface, we must have at least one domain in a B 1( 10] zone direction, or we must have a second different zone diffrac-
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tion pattern, as shown in Fig. 4. However, for deformation twins, we must use B 1( 01] zone diffraction patterns to distinguish between true-twins and pseudo-twins.
4.3. Lamellar interface structures In Fig. 7, atoms at interfaces for true-twin relationships belong to both the lower and upper crystals. There is no violation of the atomic arrangement at the interface for both crystals. Thus atoms in the true-twinrelated lamellar interfaces as shown in Fig. 7(a), (e) and (i) do not need to be rearranged. For the pseudo-twin-related interfaces, atoms at the interfaces that are from the lower crystals are not consistent with the atomic arrangements of the upper crystals, as shown in Fig. 7(b), (c), (d), (f), (g) and (h). Many atoms are in the anti-atomic positions at the interfaces with respect to the upper crystals. These anti-phase configurations of the pseudo-twin-related interfaces may result in a higher interfacial energy compared to the true-twin-related interfaces. To reduce the energy of the pseudo-twin-related interfaces, the atomic arrangements at the interfaces shown in Fig. 7(b), (c), (d), (f), (g) and (h) should be adjusted to reduce the anti-phase components between the interface atoms and the atoms in both side crystals. Thus the atomic arrangements at the pseudo-twin-related lamellar inter-
Fig. 6. Diffraction patterns taken from domain [VI] by moving the electron beam toward the (1( 1( 1( ) diffraction spot and rotating the foil about [11( 1] from B =[1( 01]. (a) [2( 1( 1] zone diffraction pattern; (b) [1( 1( 0] zone diffraction pattern.
faces should not be like those shown in Fig. 7(b), (c), (d), (f), (g) and (h). The large proportion of pseudotwin-related lamellar interfaces in Fig. 3 indicates that this type of pseudo-twin-related lamellar interfaces is stable during the solidification and/or the phase transformation in PST crystals. Therefore, it may not be necessary to form a second phase (the a2-phase) layer at the pseudo-twin-related lamellar interface to reduce the interfacial energy, at least for the alloy used in this study. In Fig. 3, a thin a2-phase layer is observed at the true-twin-related lamellar interface, the interface of domain [III]/domain [VI] and domain [I]/domain [IV]. This indicates that the formation of a2-phase layers in the lamellar structures of TiAl may be due to compositional effects and solidification processing conditions rather than the reduction of the interfacial energy. The lamellar lath of domain [IV] within the lath of domain [I] as indicated by arrows in Fig. 3 is not Table 1 Domain identification and foil normal in Fig. 1
Fig. 5. Select area diffraction patterns across the 120°-rotational domain boundaries within a lamellar lath. The diffraction patterns are taken by tilting the foil 19° about the [111] lamellar interface normal clockwise from the foil normal. (a) Diffraction pattern for domain boundaries [I]/[II] and [I]/[III]; (b) diffraction pattern for [II]/[III]; (c) for [IV]/[V] and [IV]/[VI]; (d) for [V]/[VI].
Domain variant
Domain
Foil normal
[I] [II] [III] [IV] [V] [VI]
E A B, D G C F
[2( 31( ] [1( 2( 3] [31( 2( ] [23( 1] [123( ] [3( 12]
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Table 2 The indexed B1( 10\ and B3( 21\ zone diffraction patterns for six domains in TiAl
parallel to the other lamellar laths. A comparison of the diffraction pattern of this inclined lath with those of other domain [IV] laths in Fig. 3 indicates that this inclined lath has the same crystal orientation as the other domain [IV] laths. Therefore, the reason that this lath is inclined may be due to the (111) facets at interfaces. The lamellar interface between domain [I] and domain [II] at the lower portion in Fig. 3 indicates that 120°-rotational interfaces also exist within the lamellar structure of TiAl. The atomic arrangements of three 120°-rotational interfaces are shown in Fig. 8, the projections of which are the same as those in Fig. 7. Atoms at the interfaces shown in Fig. 8(a) and (c) violate the atomic arrangements of the upper crystals. Thus some atomic rearrangements within the interfaces may also be necessary to maintain the minimum interfacial energy. The crystal orientation relationships across lamellar interfaces observed in this study are summarized as the true-twin related lamellar interface, the pseudotwin related lamellar interface and the 120°-rotational lamellar interface. However, the proportion of the 120°-rotational lamellar interface is small compared to the other two interfaces. Domains within a lamellar lath are observed to be related all by a 120°-rotation, i.e. domains in a lamellar lath are either domains [I]
to [III] or domains [IV] to [VI].
5. Discussion An attempt to experimentally determine domain orientations within lamellar structures has been reported in the literature [17,18]. Yang and Wu defined six domain variants with respect to the crystallographic orientation relationship between g- and a2phases in the lamellae [17]. However, only four domain variants (variants A, B, C and D which are identical to domains [IV], [I], [VI] and [III] in this study, respectively) were determined. Variants C and E (domains [VI] and [V] in this study) or variants D and F (domains [III] and [II] in this study) could not be distinguished for the reason described in Section 4.1 so that they concluded that only four orientation variants between g and a2 could be distinguished from SADPs. Accordingly, domain orientation relationships across lamellar interfaces could not be completely determined. Misorientations between domains across lamellar interfaces were measured using both SADPs and convergent-beam electron diffraction patterns (CBEDPs) by Dimiduk, Sun and Hazzledine [18]. However, details of domain orientation determination were not described.
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Fig. 7. Atomic arrangements across the twin-related lamellar interfaces, which are projected onto {1( 10} planes along B1( 10 \ directions. Circles represent atoms in the projection planes and squares represent atoms in the planes above the projection planes. The shaded and open marks represent Ti and Al atoms, respectively. (a)–(i) are the atomic arrangements across the domain interfaces of [I]/[IV], [I]/[V], [I]/[VI], [II]/[IV], [II]/[V], [II]/[VI], [III]/[IV], [III]/[V] and [III]/[VI], sequentially. Atoms at the interfaces are all from the lower crystals.
The unambiguous determination of domain orientations in lamellar structures is necessary to completely understand the deformation of the lamellar structures.
It has been observed that different behave differently in a specimen under the external loading. Fig. 9 shows a deformation microstructure in domain
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Fig. 8. Atomic arrangements across the 120°-rotational lamellar interfaces, which are projected onto {1( 10} planes along B 1( 10 \ directions. (a)– (c) Interfaces between domains of [I]/[II], [II]/[III] and [III]/[I], respectively. Circles represent atoms in the projection planes and squares represent atoms in the planes above the projection planes. The shaded and open marks represent Ti and Al atoms, respectively. Atoms at the interfaces are all from the lower crystals. (a)–(c) Interfaces between domains of [I]/[II], [II]/[III] and [III]/[I], respectively.
[V] and domain [VI] in a specimen deformed at 800°C and 3000 s − 1. Many cross-twins are seen in domain [V] but only ordinary dislocations are seen in domain [VI], indicating that the deformation of these two domains is different. However, if we take only one diffraction pattern from each of these two domains with the diffraction zone direction in the domain variant direction, like those in Fig. 2(i) and (k), we might wrongly get a conclusion that these two domains are the same domain. In addition, only a simple differentiation of two domains is not sufficient to characterize the deformation of individual domains under the different external loadings. Although there exist only four crystal orientation relationships across lamellar interfaces in TiAl, there are nine twin-related domain relationships (Fig. 7), six
Fig. 9. The deformation microstructure of domain [V] and domain [VI]. The specimen deformed at 800°C and 3000 s − 1.
120°-rotational domain relationships (three of which are presented in Fig. 8) and six order-translational domain relationships. The domain orientation relationships across lamellar interfaces consider the domain orientations with reference to a fixed crystal direction (for instance, the foil normal direction in this study) in addition to the relative crystal orientation relationships between two domains. The mechanical response of lamellar interfaces to the external loading is different depending on the orientations of two domains that form the interfaces although the crystal orientation relationship between these two domains remains the same when the interface between these two domains is rotated to a different orientation with respect to the loading direction. A lamellar interface is transitive to one particular deformation mode in one orientation but may not be transitive to the same deformation mode in another orientation because the domains on this interface behave differently in different orientations. Thus, the identification of only four crystal orientation relationships between two adjacent lamellae (or domains) is not enough to completely characterize the deformation of lamellar structures in TiAl. The definition of domain variants used in this study is relative since the TEM foil normal is dependent upon the cutting directions of the TEM slices from the bulk specimens. The same domain in reference to a fixed loading direction will have different domain variants if the slices are cut in different directions. Even in the same TEM foil, for instance, domain [I] will become domain [IV] if the foil is turned over since the orientations of these two domains are anti-parallel. Therefore, the investigation of domain orientations and mechanical behavior of domains should be performed under the same TEM foil orientation. Similarly, the TEM foil orientation is also critical to the characterization of lamellar interfaces. The current study also provides
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insight toward a more complete understanding of the mechanical behavior of duplex TiAl microstructures that consists of equiaxed g-grains and lamellar grains.
6. Conclusions A lamellar structure in a polysynthetically-twinned (PST) TiAl crystal is characterized for the purpose of unambiguously determining domain orientations and domain orientation relationships across lamellar interfaces in TiAl. By documenting many different zone diffraction patterns in each domain, the domain orientations in lamellar structures have been unambiguously determined so that the lamellar interfaces formed by these domains are also uniquely identified. Among the three crystal orientation relationships observed across lamellar interfaces, the probabilities of the true-twin-related lamellar interface and the pseudo-twin-related lamellar interface are similar. However, the proportion of the 120°-rotational lamellar interface is small. The observed three types of lamellar interfaces in terms of the crystal orientations are further divided into 15 domain interfaces in terms of the domain orientation relationships across the interfaces. These interfaces should be different in their responses to the external loading. Domains within a lamellar lath are all 120°-rotational domains: either domains [I], [II] and [III] or domains [IV], [V] and [VI] are within a lamellar lath. Twin-related lamellar interfaces can not be unambiguously characterized using one B1( 10 \ zone diffraction pattern taken parallel to the lamellar interfaces except for diffraction patterns having at least one domain in a B 1( 10] zone direction. Acknowledgements This work was performed under the auspices of the
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U.S. Department of Energy. The authors are very grateful to Professor M. Yamaguchi for providing the PST crystal for this study and his comments and suggestions to the manuscript. The authors would also like to express their gratitude to Drs. S. Maloy and D.E. Albert for reviewing this manuscript.
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