Ordered α2 to ωo phase transformations in high Nb-containing TiAl alloys

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ScienceDirect Acta Materialia 91 (2015) 330–339 www.elsevier.com/locate/actamat

Ordered a2 to xo phase transformations in high Nb-containing TiAl alloys ⇑

Lin Song,a Xiangjun Xu,b Li You,a Yongfeng Liang,a, Yanli Wanga and Junpin Lina, a

⇑

State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, China b Materials and Chemistry School, Zhongyuan University of Technology, Zhengzhou 450007, China Received 6 January 2015; revised 11 March 2015; accepted 12 March 2015

Abstract—The transformation of the D019-a2 phase to the B82-xo phase is a new type of phase transformation in high Nb-containing TiAl alloys; experimental results concerning this phase transformation are still lacking. Moreover, studies on the orientation relationships (ORs) between these two phases are scarce compared with those reported between the disordered x and a phases, which can be more complicated due to their ordered structures. In this study, the direct a2 to xo phase transformation is observed by transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM). The xo phase is transformed from the a2 laths in the lamellar structure after annealing over long periods at 850 °C. The various ORs observed between these two phases can be merged into two typical ORs: ½1 1 2 0a2 ==½0 0 0 1xo ; ð0 0 0 2Þa2 ==ð1 1 2 0Þxo and 1 0 0a2 ==½2 2  4 3xo ; ð0 0 0 2Þa2 ==ð0 1 1 2Þxo . The other ORs observed are subsets of these two ORs. The edge-to-edge matching model is applied to ½1  predict the possible ORs between the ordered a2 and xo phases based on the calculated close-packed planes of the two phases. The simulation results agree well with the experimental results. Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Titanium aluminides; Phase transformation; TEM; Orientation relationship; Edge-to-edge matching

1. Introduction High Nb-containing TiAl (Nb-TiAl) alloys are considered to be promising high temperature structural materials for use in aerospace engineering [1–4]. However, due to the high concentration of Nb in these materials, the bo phase (B2 structure, space group: Pm 3m), which results from ordering of the b phase (A2 structure, space group: Im 3m), is usually retained as a constituent of the as-cast microstructure. Recent publications revealed that the high-temperature b phase is beneficial for the thermomechanical processing of TiAl alloys and some alloys are modified to possess a microstructure containing more bo phase to improve workability [5–7]. However, the bo phase and the coexisting ordered x phases inside deteriorate the room temperature ductility of the alloys, because these areas are commonly observed to be the source of cracks and thus they are not desirable [8–10]. As a result, efforts have been made to eliminate the bo(x) phase by thermomechancial processing or heat treatments. In recent years, the ordered x phases in high Nb-TiAl alloys have garnered increasing attention due to their variable structures and morphologies, which can be induced by different heat treatment processes [10–20]. Commonly, the designation x is

⇑ Corresponding

authors. Tel.: +86 10 62332192; fax: +86 10 62332508; e-mail addresses: [email protected]; linjunpin@ ustb.edu.cn

restricted to the disordered x phase (space group P6/ mmm) in Ti based alloys. In intermetallics alloys, phases with similar crystal structures but with two or more differently occupied atom sites are designated x-related phases or ordered x phases. These phases include the trigonal x0 and x00 phases as well as the hexagonal xo in the B82 structure [11]. Among the different ordered variants, the xo phase is the most commonly reported phase in research literature [13–18], in which three Wykoff positions (i.e. 2a, 2c and 2d) are occupied by proportional Ti, Al and Nb atoms. In the disordered x phase, the 1a and 2d Wykoff positions are occupied by the same type of atom [11]. On the other hand, the a2-Ti3Al phase in the D019 structure is a main phase in TiAl intermetallics, in which the Wykoff positions 2c and 6 h are occupied by Al and Ti atoms, respectively. In disordered a phase, the 2c positions are occupied by the same type of atom. To better understand the phases considered in this study, the crystal structures of the ordered phases are compared with those of the corresponding disordered phases, as shown in Fig. 1 and Table 1. Numerous studies have demonstrated that the xo phase is stable at intermediate temperatures (700–900 °C) in high Nb-TiAl alloys. However, these studies have mainly focused on the interconversion between the ordered x phases and the parent bo phase [10–16] or the a2 to bo phase transformation [21–24]; few reports have concentrated on the relationship between the ordered x phases and the a2 phase. Recently, Huang et al. [25–29] claimed that after annealing

http://dx.doi.org/10.1016/j.actamat.2015.03.025 1359-6462/Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

L. Song et al. / Acta Materialia 91 (2015) 330–339

331

Fig. 1. Crystal structures and Wyckoff positions of the disordered (b, x and a) and ordered (bo, xo and a2) phases.

Table 1. Crystal parameters of the disordered (b, x and a) and ordered (bo, xo and a2) phases. Phase

Pearson symbol

x-Ti

hP3

xo

hP6

a-Ti a2

Strukturbericht designation

Space group

Wyckoff position

Coordinate x

Coordinate y

Coordinate z

Lattice parameters (nm)

c/a

P6/ mmm

1a 2d

0 0.3333

0 0.6667

0 0.5

a = 0.463 c = 0.281

0.61 [48]

B82

P63/ mmc

2a 2c 2d

0 0.3333 0.3333

0 0.6667 0.6667

0 0.25 0.75

a = 0.459 c = 0.556

1.21

hP2

A3

P63/ mmc

2c

0.3333

0.6667

0.25

a = 0.291 c = 0.467

1.60 [49]

hP8

D019

P63/ mmc

2c

0.3333

0.6667

0.25

a = 0.579 c = 0.461

0.80

certain high Nb-TiAl alloys at intermediate temperatures for long periods, the bo(x) precipitated along the a2 laths or at parts of the lamellar structures, which are composed of closely spaced a2/c laths. The orientation relationship (OR) can be expressed as follows: h1 1  2 0ia2 ==h111ibo == h0 0 0 1ix ; f0 0 0 1ga2 ==f110gbo ==f1 1  2 0gx . Bystrzanowski et al. [17] observed that the applied stress could enhance the xo precipitation and suspected that the observed xo particles were directly derived from the a2 phase. The xo phase is generally observed within the bo phase without direct contact with other phases, which is most likely the reason for the limited number of investigations on the a2 to xo phase transformation. In contrast, some reports have focused on the ORs between disordered x and a phases [30–41], mostly for Zr-based metals. However, the results of these studies have shown to be controversial. Early studies by Usikov et al. [30] indicated that the a ! x transformation in pure Ti and Zr happens via the unstable b phase, i.e., via the transformation path a ! b ! x. Because the a ! b and b ! x transformations are both clearly understood with respect to their crystallographic characters, the ORs between these two phases can be deduced to be as follows:  0i ==h0 0 0 1i ; f0 0 0 1g ==f1 1 2  0g h1 1 2 ðORIÞ a

x

a

x

and h1 1  2 0ia ==h1 0  1 1ix ==f0 0 0 1ga ==f0 1  1 1gx

ðORIIÞ

More recently, experimental evidence of an a ! b ! x transformation was reported by Vohra et al. [31] and Gupta et al. [32]. Nevertheless, neither of these studies could completely dismiss the pre-existing b phase. Song et al. [35] reported a new OR in Zr that is different from the two abovementioned ORs: h1 0  1 0ia ==h1 1  2 3ix ==f0 0 0 1ga ==f1 0  1 1gx

ðORIIIÞ

However, Jyoti et al. [36–37] proved that ORIII was a subset of ORII, claiming that the a ! x transformation could be directly achieved without the precipitation of an intermediate b phase. Other investigations have indicated that the a ! x transformation could be realized through heat treatment or shear strain [39–41]. In summary, the aforementioned studies have mainly focused on displacive/diffusionless phase transformations, whereas few works have attempted to elucidate a diffusion-controlled mechanism. Qiu et al. [39] reported that the plate-shaped, athermal x phase nucleates at the a0 martensite plate, using the edge-toedge matching (E2EM) model to predict the ORs between

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these two phases and fitting the model results well with experimental results. The E2EM is a simple model for predicting the ORs between parent and product phases and has been proven to be applicable to more complex structures [42–45]. In addition, the ORs observed over a range of lattice parameters between hexagonal close-packed and body-centered cubic (hcp/bcc) structures have also been predicted [45]. As a complement to the aforementioned studies, Yang et al. [46] successfully applied the E2EM model to a hcp/hcp system. The parameters required for the E2EM model are crystal structures, lattice parameters and atom positions of the two phases. In early applications of this model [42–46], the close-packed directions were deduced based on crystal structures, whereas the close-packed planes were roughly estimated from structural factors and from Xray diffraction data. To improve these estimations, Kelly et al. [47] recently developed a new method for identifying close-packed planes, making the E2EM model more reliable. According to their calculations [39], the close-packed planes are f1 1 2 0g, f1 0  1 1g and {0 0 0 2} for the x phase and {0 0 0 2}, f1 0 1 1g and f1 0  1 0g for the a phase. In the present work, the ordered a2 to ordered xo phase transformation in Ti-45Al-9Nb alloys was monitored by selected area diffraction (SAD) and examined using E2EM analyses.

2. Experimental details A Ti-45Al-9Nb alloy ingot used in this study was produced by a ZG-2XF induction levitation melting furnace manufactured in Jinzhou, China. First, the melting furnace was vacuumized to a pressure of 1  102 Pa and then back-filled with argon to approximately 400 Pa. The raw materials of the ingot were melted in a water-cooled copper hearth and then levitated and stirred for 10 min. The ingot was remelted and stirred 3 times in the hearth to ensure homogeneity. Then, an alloy ingot measuring approximately u50 mm  160 mm was obtained by pouring the remelted ingot into a graphite crucible in the furnace. A part of the ingot was sealed in a vacuum quartz tube back-filled with argon and heat treated within the single a phase field at 1350 °C for 4 h, followed by furnace cooling to obtain a fully-lamellar microstructure. After the high temperature treatment, part of the sample was cut off for microstructure observation, whereas the rest was sealed again in a vacuum quartz tube and annealed at 850 °C for 500 h (21 days) to reach a near-equilibrium state, then followed by water quenching. All of the heat treatments were performed in a furnace preset to the experimental temperatures to minimize the influence induced by the heating process. The microstructures before and after annealing were observed using the back-scattered electron (BSE) mode on a Zeiss SUPRA 55 field emission scanning electron microscope (SEM) operated at 15 kV and at a working distance of 11 mm. For SEM observation, samples in sizes of 10  10  10-mm were cut from the center of the heattreated ingot using an electron discharge cutting machine and then polished to a final surface finish of 0.05 lm using standard mechanical polishing procedures. Transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM) observations were conducted on a Tecnai G2 F30 (FEI Company) fieldemission TEM operated at 300 kV. TEM specimens were

cut from the center of the SEM samples and then mechanically polished to 0.1 mm. Thin foils were prepared by twin-jet electropolishing the samples in a solution of 30 ml perchloric acid, 175 ml butan-l-ol, and 300 ml methanol at 30 V and 30 °C. The compositions of the a2 and xo phases in the annealed samples were determined using the EDAX energy dispersive X-ray spectrometry (EDS) function of the TEM. Every composition parameter is the mean value of at least ten points measured in different lamellar colonies. To identify the close-packed planes and perform E2EM modeling, the lattice parameters of the related a2 and xo phases in this alloy were measured using a combination of powder X-ray diffraction, reciprocal vector analyses and direct HRTEM observations, and the results are shown in Table 1 [48–49]. The lattice parameter measurement errors were within 2% and thus negligible in the E2EM calculations. 3. Results 3.1. Experimental observation of a2 ! xo transformation SEM-BSE and multiple-beam bright-field TEM images of Ti-45Al-9Nb alloys before and after annealing are shown in Fig. 2. After heat treatment at the single a phase field, fully-lamellar microstructures composed of alternating a2 and c laths were obtained, with large lamellar colony sizes (approximately 200 lm), as shown in Fig. 2(a)–(b). The homogeneous contrast in Fig. 2(a) indicates that Nb-containing microsegregation was eliminated. After annealing at 850 °C, the xo phase precipitated at the lamellar colony boundaries and within the lamellar colony (Fig. 2(c)). A magnified xo precipitation image is shown in the inset of Fig. 2(c). The xo particles in white contrast precipitated within the a2 laths, and the particles in dark contrast that precipitated within the white xo area are the c (cp) phase [18]. This phenomenon is similar to that observed by Huang et al. [25–29], i.e., the white-contrast particles in the microstructures could be frequently observed within the a2 laths, which were Nb-rich. A local TEM image of the a2 laths is shown in Fig. 2(d). Two xo precipitations can be observed in a single a2 lath, dividing the lath into alternating xo and a2 areas. The SAD data of the xo particle inserted in Fig. 2(d) indicate a B82 structure symmetry, in accord with Bendersky et al. [11], who claimed that the odd {0 0 0 l} reflections should be absent in the B82-x phase. Notably, no intermediate bo phase was observed during TEM investigation. Fig. 3 shows TEM images of one a2 lath and the corresponding SAD patterns. Several xo variants (designated xo1, xo2 and xo3) can be observed within a single a2 lath, as demonstrated in Fig. 3(a). The SAD data of the circled areas in Fig. 3(a) are shown in Fig. 3(c)–(e), and the corresponding indexed pattern is presented in Fig. 3(g). The SAD shown in Fig. 3(c) was obtained at the interface between the a2 and xo1 areas, and the OR could be derived as follows: ½1 1  ðORIVÞ 2 0 ==½0 0 0 1 ; ð0 0 0 2Þ ==ð1 1  2 0Þ a2

xo

a2

xo

The SAD of xo2 under the same incident direction is shown in Fig. 3(d). However, the zone axis of xo2 is not consistent with that of xo1 and can be indexed as ½2 0  2 1xo , indicating another OR between the a2 and xo phases:

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Fig. 2. SEM-BSE and TEM images of microstructures before (a)–(b) and after (c)–(d) annealing; the absence of {0 0 0 l} reflections in (d) indicates ordered x precipitation with a B82 structure.

½1 1  2 0a2 ==½2 0 2 1xo ; ð0 0 0 2Þa2 ==ð1 1  1 2Þxo

ðORVÞ

When examining the orientation of xo3, the [0 0 0 1]xo zone axis was recorded again (Fig. 3(e)), and it was determined that the orientation is identical to that of xo1. These results suggest that multiple variants can be generated during the a2 to xo transformation. Moreover, Fig. 3(b) demonstrates another xo precipitation within an a2 lath. The SAD data of these two phases are presented in Fig. 3(f) and indexed in Fig. 3(h), which indicate the following OR:  0 0 ==½2 2 4 3  ; ð0 0 0 2Þ ==ð0 1 1  2Þ ½1 1 ðORVIÞ a2

xo

a2

xo

These results are essentially identical to those reported for ORs in disordered a to x transformations (ORI-III) [30–35], which will be discussed in Section 4.1. Fig. 4 shows HRTEM images of the a2/xo interface. Generally, smooth interfaces are observed between the a2 and xo phases. Fig. 4(a) demonstrates the interface dislocations observed at the interface of a2 and xo in ORV, and the corresponding localized HRTEM image of the interface is shown in Fig. 4(b). Due to the difference between the interplanar spacings of the (0 0 0 2)a2 and ð0 1  1 2Þxo planes, the interface dislocations are required to accommodate the mismatch. According to the measured lattice parameters, the interplanar (0 0 0 2)a2 spacing is 0.231 nm, whereas the interplanar ð0 1  1 2Þxo spacing is 0.228 nm (misfit of 1.2%), indicating that an interface dislocation should exist at every 83 ð0 1 1 2Þxo planes, i.e., at a distance of 19 nm. The average distance between the dislocations is approximately 19.7 nm, which agrees well with the estimated distance. Due to the regularly arranged dislocations, the habit plane slightly deviates from ð1  1 0 0Þa2 .

Fig. 4(c) shows the interface of the a2 and xo phases in ORVI, where ð0 0 0 1Þa2 ==ð0 1  1 2Þxo . The interface is rather smooth with ledges and interface dislocations at random locations. The interface is coherent at the ledges with some atoms belonging to the xo phase and others to the a2 phase, indicating that the transformation is still ongoing. The dark contrast observed at the interface suggests that a strain field exists near the dislocation. Although the determination of the exact habit plane is difficult due to the coherent ledges, the habit plane is approximately parallel to (0 0 0 1)a2. 3.2. E2EM prediction of the ORs between the xo and a2 phases An E2EM prediction is based on the atom-row matching between the parent and the product phase [43]. The close-packed direction of the xo and a2 phases should first be defined. According to the crystal structures of these two phases, the close-packed directions of the xo phase can be deduced to be h0 0 0 1ixo, h1  1 0 0ixo , h2 0  2 1ixo and h2 2  4 3ixo . The first direction is a straight row in which the atom centers are all arranged in a straight line; the last three directions are zigzag rows in which some atom centers are off the line, but the deviation between their centers and the line is less than the atomic radius [42]. Similarly, the close-packed directions in the a2 phase are h1 1  2 0ia2 , h1  1 0 0ia2 and h2  1 1 6ia2 . The first direction is a straight row, whereas the last two directions are zigzag rows. Commonly, a straight row in one phase will match a straight row in other phase, whereas a zigzag row will match a zigzag row [42–43]. Thus, seven matching direction pairs can be deduced, together with their corresponding misfit values (Table 2).

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Fig. 3. (a)–(b) Bright-field TEM images of xo precipitations within a single a2 lath; SAD data of the corresponding circled areas are presented in (c)–(f).

The second step is to identify the matching plane pairs. Kelly et al. [47] developed a simple method to identify close-packed planes in complex structures, which can be applied to study the a2 and xo phases considered in this work. The calculations of the close-packed planes in the a2 and xo phases are indicated in Appendix A. The results show that the close-packed planes in the xo phase are ð1 1 2 0Þxo , ð0 1 1 2Þxo and (0 0 0 4)xo and that those in the a2 phase are (0 0 0 2)a2, ð0 2  2 1Þa2 and ð2 2  4 0Þa2 . Thus, nine matching plane pairs can be determined (Table 3). However, before the ORs are truly defined, the critical value of the interatomic spacing misfit and d-value mismatch should first be specified. Zhang and Kelly et al. [42,45–46] concluded, based on their systematic examinations of different alloy systems, that if one OR can possibly form, the interatomic spacing misfit should not exceed 10%, whereas the d-value mismatch between the matching planes should not exceed 6%. These same critical values were applied in this study. From Tables 2 and 3, the possible ORs between the a2 and xo phases were predicted (Table 4). In fact, some of the ORs listed are essentially identical to one another, which will be discussed in the following section.

4. Discussion 4.1. Observed ORs between a2 and xo phases Although most of the a to x phase transformations in disordered alloys are displacive/diffusionless [30–35], the xo to a2 phase transformation in high Nb-TiAl alloys appears to be diffusion-controlled because the volume fraction of the xo phase increases with increasing Nb content and annealing time [14–15,27–29]. Many reports have indicated that the xo phase precipitates at 700–900 °C [10–20], and the xo phase is an equilibrium phase at these temperatures. This falls within the temperature range over which the high Nb-TiAl alloys examined herein are applied. Moreover, the quasi-binary Ti–Al phase diagram with 10% Nb addition also suggests that the bo(x) phase is an equilibrium phase at lower temperatures [8,50]. However, few studies have focused on the relationship between the a2 and xo phases. Our TEM and HRTEM results indicate a direct a2 to xo transformation without an intermediate bo formation, in contrast to previously reported results [30– 32]. Three ORs between the disordered a and x phases in diffusionless transformations have been reported [30–35].

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Fig. 4. (a) Bright-field TEM image of the a2 and xo interface and HRTEM images of the a2 and xo interface in ORV (b) and ORVI (c).

Table 2. Misfit value (%) of possible straight/straight (S–S) and zigzag/zigzag (Z–Z) direction matching pairs between a2 and xo phases. S–S Z–Z  0 =½0 0 0 1 1 0 0 =½1 1 0 0 1 0 0 =½2 0 2 1         ½1 1 2 ½1 ½1 a2 xo a2 xo a2 xo ½1 1 0 0a2 =½2 2 4 3xo ½2 1 1 6a2 =½1 1 0 0xo ½2 1 1 6a2 =½2 0 2 1xo ½2 1 1 6a2 =½2 2 4 3xo 4.1 5.7 12 7 2.7 3.1 1.5 The misfit values lower than 10% are labeled in bold.

Meanwhile, in a diffusion-controlled a2 to xo transformation, the ORs are essentially identical to those in disordered alloys. Considering the variation in the crystal orientation and lattice plane indices mentioned in Appendix A, ORIV, ORV and ORVI are identical to ORI, ORII and ORIII, respectively. Furthermore, these ORs are clearly depicted in the superimposed stereographic projections in Fig. 5. Fig. 5(a) shows superimposed (0 0 0 1)a2 and ð1 1 2 0Þxo projections, where the ð1 1  2 0Þxo stereographic projection is rotated around the ½1 1  2 0xo direction to maintain a coincidence between the [0 0 0 1]xo and ½1 1 2 0a2 directions. Consequently, ½1  1 0 0xo and ½1  1 0 0a2 coincide at the same position (i.e., the angles 1 0 0xo directions and ½1 1  2 0a2 between [0 0 0 1]xo and ½1  and ½1 1 0 0a2 directions are precisely 90o), as indicated by the arrows in Fig. 5(a). Thus, ORIV can be further defined as follows: ½11  20a2 ==½0001xo ; ½1  100a2 ==½1  100xo ; ð0002Þa2 ==ð11 20Þxo :

Similar results can also be obtained from the superim1 2Þxo posed stereographic projections of (0 0 0 1)a2 and ð0 1 

shown in Fig. 5(b). The ð0 1  1 2Þxo stereographic projection is rotated to maintain a coincidence between the ½1 0  1 0a2 and ½ 2 2 4 3xo directions. Accordingly, the ½2  1 1 0a2 direction, which is also on the (0 0 0 1)a2 plane but 30o away from 1 0a2 direction, is nearly coincident with ½ 2 0 2 1xo , the ½1 0  which is also on the ð0 1  1 2Þxo plane but 29.5o away from the ½ 2 2 4 3xo direction. As shown by the arrows in Fig. 5(b), ORV and ORVI can be further defined as follows: 2  4 3 ; ½2  ½1 0  1 0a2 ==½2 1 1 0a2 0:5 from½ 2 0 2 1xo ; xo  ð0 0 0 1Þa2 ==ð0 1 1 2Þxo : Thus, the observed ORV and ORVI can be defined as the same OR viewed along different zone axes, because the 0.5° deviation is actually difficult to detect in conventional SAD analyses. Because ordered structures are mainly induced by high Nb addition, the redistribution of Nb atoms between two structures should play an important role. According to the crystal structure of the xo phase, Nb atoms partly occupy the 2a position at the non-collapsed planes.

336

Table 3. d-Value mismatch (%) of possible close-packed plane matching pairs between a2 and xo phases. ð0 0 0 2Þa2 =ð1 1  2 0Þxo

(0 0 0 2)a2/(0 0 0 2)xo

ð0 0 0 2Þa2 =ð0 1 1 2Þxo

ð1 1 2 0Þa2 =ð1 1 2 0Þxo

ð1 1 2 0Þa2 =ð0 0 0 2Þxo

ð1 1 2 0Þa2 =ð0 1 1 2Þxo

ð0 2 2 1Þa2 =ð1 1 2 0Þxo

ð0 2 2 1Þa2 =ð0 0 0 2Þxo

ð0 2 2 1Þa2 =ð0 1 1 2Þxo

0.4

20.6

1.2

26.1

4.1

27.1

4.2

26.2

3.4

The d-value mismatches lower than 6% are labeled in bold.

L. Song et al. / Acta Materialia 91 (2015) 330–339

Table 4. Calculated ORs between a2 and xo phases from the E2EM model. OR(1) ½1 1  2 0a2 ==½0 0 0 1xo ð0 0 0 2Þa2 ==ð1 1  2 0Þxo

OR(2) ½1 1 0 0a2 ==½1 1 0 0xo ð0 0 0 2Þa2 ==ð1 1 2 0Þxo

OR(3) ½1 1 0 0a2 ==½1 1 0 0xo ð1 1 2 0Þ ==ð0 0 0 2Þ a2

xo

OR(4) ½2116a2 ==½2 2 4 3xo  ==ð0 1 1 2Þ ð2 0 2 1Þ a2

xo

OR(5) ½2 1 1 0a2 ==½0 0 0 1xo ð0 2 2 1Þ ==ð1 1 2 0Þ a2

xo

OR(6) ½2 1 1 6a2 ==½1 1 0 0xo  ==ð1 1 2 0Þ ð2 0 2 1Þ a2

xo

OR(7) ½1 1 0 0a2 ==½2 2 4 3xo ð0 0 0 2Þa2 ==ð0 1 1 2Þxo

OR(8) ½2 1 1 6a2 ==½2 0 2 1xo  ==ð1 2 1 0Þ ð2 0 2 1Þ a2

xo

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Fig. 5. Superimposed stereographic projections of (a) (0 0 0 1)a2 and ð1 1 2 0Þxo projections and (b) (0 0 0 1)a2 and ð0 1 1 2Þxo projections.

Fig. 6. Schematic diagrams of atom arrangements on the habit planes in ORIV–VI; the edge-on views of each plane are shown to the left of the corresponding diagrams.

However, for the a2 phase, although the exact site occupation of Nb is not clear, Nb atoms mainly substitute the Ti sites [51], i.e., the 6 h position. According to the results obtained by EDS analyses, the average compositions of the a2 and xo phases are Ti-37.2 ± 0.3Al-7.3 ± 0.4Nb and Ti-37.6 ± 0.3Al-10.8 ± 0.4Nb, respectively. The difference in composition mainly arises from the Ti and Nb content. The supersaturated Nb at Ti sites in the a2 phase stimulates the formation of the ordered xo phase. Because the composition of the a2 phase largely deviates from the nominal composition, Nb and Al can substitute the Ti sites on a large scale. As the Nb content increases, ordering occurs by the redistribution of Nb and Al between neighboring planes to maximize Al-Ti interactions because Al–Ti interactions are stronger than Al–Nb and Ti–Nb interactions [11,19,52]. Fig. 6 shows the schematic diagrams of the atom arrangement at the habit planes of ORIV-VI. Edge-on views of the habit planes along the close-packed directions are shown to the left of each diagram. In ORIV, and as indicated by the diagram, the nearest distance between the atoms in the a2 phase is 0.290 nm (0.285 nm between

the nearest atoms on neighboring (0 0 0 1)a2 planes), whereas the distances between the 2c (Al) and 2d (Ti) positions in the xo phase are 0.265 or 0.278 nm, which are smaller than 0.285 nm. Moreover, the distance between the 2a and 2c (or 2d) positions in the xo phase is 0.299 nm. Thus, the distance between the Al–Ti interactions is reduced, and the distance characterizing the Al–Nb and Ti–Nb interactions are increased by the formation of the xo phase from the a2 phase. Therefore, the xo phase can be more stable than the a2 phase at intermediate temperatures as the Nb content increases, which is consistent with the results reported by Bendersky et al., wherein a limited volume fraction of a2 phase was detected in authors’ samples [11]. The growth mechanism of the xo phase can be attributed to the motion of the ledges at the interfaces [45]. Ledges are commonly observed at the boundaries, and the ledge heights are limited to several interatomic distances. The atomic attachment at the ledges makes the ledges move laterally on the habit planes, resulting in a continuous transition at the interfaces [53]. However, for ORV and ORVI, although the atom positions are identical to

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those of ORIV, a small shuffle is required to displace the atom centers from the ð0 1  1 2Þxo plane resulting in a “flat” (0 0 0 1)a2 plane parallel to a “rumple” ð0 1  1 2Þxo plane during xo precipitation, which may require a rotation angle between the habit planes. As a result, the energy barriers to forming ORV and ORVI can be larger than the energy barrier to forming ORIV, consistent with the experimental observations, in which only seven a2/xo pairs were found in ORV and ORVI after examining a total of 23. 4.2. Relationship between the E2EM prediction and experimental results In a previous study, researchers used the E2EM model to effectively predict the ORs between disordered a and x phases in Ti–Cr alloys [39]. In this work, the model successfully predicted the ORs between ordered a2 and xo phases, and the predictions fit well with the experimental results. When compared to ORIV (as discussed in Section 4.1), the calculated OR(1)–(3) were found to be identical. The matching direction misfits, i.e., 4.1% in ½1 1  2 0a2 =½0 0 0 1xo and 5.7% in ½1  1 0 0a2 =½1  1 0 0xo , are relatively low. Actually, in this OR, the c and a axes of the two phases are transposed, and the interatomic misfit in the ½1 1 2 0xo =½0 0 0 1a2 directions is also effectively low (0.4%). Thus, ORIV is of low strain energy, consistent with the experimental results, which indicate that most ORs observed are in this category. OR(4) is close to ORIV, with coincident ½2 1 1 6a2 and ½2 2  4 3xo directions in the stereographic projection, as shown by the black circles in Fig. 5(a). However, the habit planes of OR(4) deviate from each other at approximately 10o, as indicated by the great circles of ð2 0 2 1Þa2 and ð0 1  1 2Þxo in Fig. 5(a). Because matching directions are of the zigzag/zigzag type, an additional restriction (i.e., the planes defined by the zigzag directions should be parallel or inclined to each other by a small angle) should be considered [43,45]. Both the ð2 0 2 1Þa2 and ð0 1  1 2Þxo are “rumple” planes, i.e., not the planes defined by their own zigzag rows, and the matching between the TypeII and TypeII rows mentioned in literature [45] would be generated, which is generally improbable due to the large angle of rotation. OR(5) (i.e., ½2 1 1 0a2 ==½0 0 0 1xo ; ð0 2  2 1Þa2 ==ð1 1 2 0Þxo ) is actually a subset of ORIV. The matching direction ½ 2 1 1 0a2 is identical to ½1 1  2 0a2 ; however, the matching plane ð0 2 2 1Þa2 is a “rumple” plane and 61.5o away from (0 0 0 1)a2, resulting in a 1.5o deviation between the “flat” ð1  2 1 0Þxo and (0 0 0 1)a2 planes (and also between the ½1  2 1 0xo and [0 0 0 1]a2 directions). In addition, considering that the d-value mismatch in the ð0 2  2 1Þa2 =ð1 1  2 0Þxo pair is 4.2% and greater than a 0.4% mismatch in the ð0 0 0 1Þa2 =ð1 1 2 0Þxo , OR(5) should be less likely to be observed when compared to ORIV. In other words, if the matching direction between the two phases follows ½ 2 1 1 0a2 ==½0 0 0 1xo , the ð0 2  2 1Þa2 ==ð1 1  2 0Þxo (OR(5)) is unlikely to form compared to ð0 0 0 1Þa2 ==ð1 1  2 0Þxo (OR(1)–OR(3)). A similar condition occurred in OR(6), where an angle of approximately 30o was observed between ½2  1 1 6a2 and ½1 1 0 0xo (Fig. 5(a)). If OR(6) forms, no closepacked atom rows in the a2 phase form to match the ½1 1 2 0xo and [0 0 0 1]xo rows, and a “rumple” to “flat” plane matching would be produced. Thus, this OR is less likely to be observed.

The calculated OR(7) is identical to ORV and ORVI. The matching directions ½2  1 1 0a2 ==½ 2 0 2 1xo in ORV deviate from each other by 0.5o in OR(7), i.e., the matching direction in ORV can be nearly fulfilled in this OR. However, although the interatomic spacing misfit in ½2  1 1 0a2 =½ 2 0 2 1xo is only 3.1%, the ½2  1 1 0a2 direction is a  straight atom row, whereas the ½2 0 2 1xo is a zigzag row. The straight/zigzag matching is of low probability [45], thus the preferred matching direction in this OR should be ½1 0  1 0a2 =½ 2 2 4 3xo , i.e., zigzag/zigzag matching (ORVI). The misfit in this matching pair is 7%, and the mismatch between matching planes ð0 0 0 2Þa2 =ð0 1  1 2Þxo is 1.2%, which is still a low value such that ORVI is possible. Nevertheless, (0 0 0 2)a2 is the plane defined by the zigzag ½1 0  1 0a2 row, whereas ð0 1  1 2Þxo is not, and a rotation angle between the matching planes is required. Considering the reasons discussed in Section 4.1, ORVI (or ORV) should be of lower probability when compared to ORIV, explaining the fewer incidences of ORVI observed in our TEM experiments. Finally, OR(8) deviates from ORV and ORVI, and the matching directions can be observed in two stereographic projections (Fig. 5(a) and (b)), whereas the pole of ½2 0  2 1xo is not coincident with that of ½2  1 1 6a2 . Similarly to OR(6), a large strain energy is produced if OR(8) is created. The precipitates should follow an OR where most of the atom rows can match another row in the parent phase, or the strain energy would hinder the precipitation; thus, atom rows in low strain energy ORs will dominate. Other ORs, e.g., ½2  1 1 0a2 ==½2 0  2 1xo and ð0 2  2 1Þa2 == o  ð0 1 1 2Þxo , where [0 0 0 2]a2 is 1.7 away from ½ 12 1 0xo , are either subsets of the abovementioned category or of straight/zigzag type, which contain high misfits. Compared to ORIV–ORVI, these ORs are of much lower probability. The predictions from the E2EM model, to a great extent, can be attributed to an equilibrium state because the annealing time applied in this work was of sufficient length. In contrast, as previously reported [42–43], elastic anisotropy can play an important role in determining the final OR between the two phases. Thus, the ORs observed maybe the most favorable ORs between the two phases with the lowest energies. The ORs predicted by the E2EM model fit well with the observed ones, and the misfit or mismatch in the predicted ORs can be used to evaluate the relative stability of the observed ORs to a certain extent. Further studies should focus on the thermal stability of different ORs. The combined results obtained from our experiments and calculations serve as a good reference for the OR study of disordered a and x phases.

5. Conclusions In the present work, we observed the a2 to xo phase transformation via TEM. The ORs between these two phases are in good agreement with those predicted using the E2EM model. Our main conclusions are as follows: 1. xo precipitated within the a2 phase occurring in fullylamellar Ti-45Al-9Nb alloys after annealing at 850 °C for 500 h. The phase transformation was diffusion-controlled, and the intermediate bo phase was not observed during the transformation. The lattice misfit between the two phases was accommodated by interface dislocations. The xo phase was an equilibrium phase at 850 °C.

L. Song et al. / Acta Materialia 91 (2015) 330–339

2. Two main ORs between a2 and xo phases were observed via TEM experiments:  100 ==½1  100 ; ð0002Þ ==ð11  20Þ ½11 20 ==½0001 ; ½1  a2

xo

a2

xo

a2

xo

½1 0  1 0a2 ==½2 2 4 3xo ; ½2  1 1 0a2 0:5 from ½ 2 0 2 1xo ;  ð0 0 0 1Þa2 ==ð0 1 1 2Þxo : These ORs are essentially identical to those observed in disordered a and x phases. ORV (½1 1  2 0a2 ==½2 0  2 1xo ; ð0 0 0 2Þa2 ==ð0 1 1 2Þxo ) and ORVI (½1  1 0 0a2 ==½2 2  4 3xo ; ð0 0 0 2Þa2 ==ð0 1 1 2Þxo ) are identical, which are obtained under different zone axes. 3. The E2EM model was successfully applied in this study to predict the possible ORs between a2 and xo phases. ORIV (½1 1  2 0a2 ==½0 0 0 1xo ; ð0 0 0 2Þa2 ==ð1 1  2 0Þxo ) is of a lower misfit compared to ORV and ORVI. Other ORs were also deduced; however, they are unlikely to occur in terms of strain energy. Acknowledgments The authors thank the National Basic Research Program of China (973 Program) for their financial support under contract No. 2011CB605501 and the National Natural Science Foundation of China for their financial support under contract Nos. 51171015 and U1204508, The authors also thank Ms. Cassie Marker for her careful reading of the manuscript.

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.actamat.2015.03.025.

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