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Microstructure and texture evolution during cold rolling and annealing of Ni3Fe alloy
Materials Science and Engineering A 431 (2006) 328–338
Microstructure and texture evolution during cold rolling and annealing of Ni3Fe alloy Yasuyuki Kaneno, Akira Takahashi, Takayuki Takasugi ∗ Department of Materials Science, Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan Received 10 January 2006; received in revised form 5 June 2006; accepted 9 June 2006
Abstract Just-stoichiometric Ni3 Fe alloy with L12 ordered and A1 (fcc) disordered structures were cold rolled and annealed below and above the critical ordering temperature (Tc ) to study the effects of ordered and disordered structures on texture and microstructure evolution during deformation and recrystallization. The cold rolling textures of the Ni3 Fe alloy basically showed a copper (pure-metal) type irrespective of ordered or disordered state before cold rolling. However, for the rolling texture of the initially ordered specimen, Bs {0 1 1}2 1 1 component was enhanced in comparison with C {1 1 2}1 1 1 and S {1 2 3}6 3 4 components. The intensity of the rolling texture was weaker in the initially ordered structure than in the initially disordered structure. Also, the intensity of a cube {0 0 1}1 0 0 texture, which was formed after recrystallization above Tc , was significantly reduced in the initially ordered structure. During annealing, the Ni3 Fe alloy slightly hardened up to Tc and then softened rapidly, regardless of ordered or disordered state before cold rolling. It was also found that the recrystallization occurred faster and at lower temperature in the initially ordered structure than in the initially disordered structure. © 2006 Elsevier B.V. All rights reserved. Keywords: Ni3 Fe; L12 structure; Cold rolling texture; Annealing texture; Recrystallization; Ordered structure
1. Introduction In general, intermetallic alloys and compounds possess high strength at elevated temperatures and good properties in oxidizing and corrosive environments, and therefore are considered to be a potential high temperature structural material. However, their applications are limited because of low ductility at low temperature, which is caused by weak lattice or grain boundary cohesion due to their complex crystal structures. Among various crystal structures, low temperature ductility of L12 ordered intermetallic alloys which have been suffered from propensity for intergranular fracture has been improved by micro- and macro-alloying [1–3]. At present, boron-doped Ni3 Al, Co3 Ti and Ni3 (Si,Ti) polycrystals can be plastically deformed in air at room temperature. These L12 intermetallic alloys show a positive temperature dependence of yield strength as well as good chemical properties and thereby attract a considerable attention particularly from practical point of view. Using thermomechan-
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Corresponding author. Tel.: +81 72 254 9314; fax: +81 72 254 9912. E-mail address: [email protected] (T. Takasugi).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.06.054
ical processing, microstructural controls for grain size, crystallographic texture and grain boundary character, which may strongly affect mechanical and physical properties of polycrystalline materials, are of importance for developing intermetallic alloys. Particularly, it is necessary to understand deformation and recrystallization behavior of intermetallic alloys and compounds. Also, texture evolution during these processes is important for intermetallic alloys because they generally show strong anisotropy in various physical and mechanical properties. In the past literatures, recovery and recrystallization behavior of some ordered intermetallic alloys have been outlined and reviewed [4,5], but their deformation and recrystallization textures have been little studied, although several pioneer studies have been done on Ni3 Al [6–11], Co3 Ti [12,13] and Ni3 (Si,Ti) [14]. A comprehensive understanding is required for deformation and recrystallization behavior of ordered intermetallic alloys including L12 alloys. For example, what is an essential difference in deformation and recrystallization behavior, and also in the associated textures between ordered intermetallic alloys, and disordered metals and alloys? To study using Ni3 Fe alloy is appropriate to answer this question. Ni3 Fe shows order (L12 )–disordered (fcc) transition at Tc = 776 K. In the Ni3 Fe
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alloy, both of ordered and disordered structures with an identical chemical composition are obtained by adopting proper heat treatments. For Ni3 Fe alloy, annealing behavior was studied by Vidoz et al. [15], but rolling and recrystallization texture has not been reported so far. For Cu3 Au with order (L12 )–disorder (fcc) transition at Tc = ∼663 K, annealing textures were studied by Hutchinson et al. [16]. In this case, cold rolling was however conducted only for the disordered alloy. In the present study, the Ni3 Fe alloy in initially ordered and disordered states were cold rolled at room temperature and then annealed at temperatures below and above the Tc . The rolling and recrystallization textures were characterized by the orientation distribution functions (ODFs), and the grain boundary character distributions (GBCDs) of the recrystallized alloys were determined by the electron backscattered diffraction (EBSD) method. Also, recrystallization kinetics was evaluated by the hardness test and microstructural observation. Based on these results, the effect of ordered and disordered structures on texture and microstructure evolutions during deformation and recrystallization was discussed. 2. Experimental procedures Raw materials used in this study were 99.9 wt.% nickel and 99.99 wt.% iron. Just-stoichiometric Ni3 Fe alloy was prepared by arc melting in an argon gas atmosphere on a copper hearth using a non-consumable tungsten electrode. The Ni3 Fe button ingot was homogenized in a vacuum at 1373 K for 48 h, followed by furnace cooling. These homogenized-ingots were cold rolled, and then annealed at 973 K for 1 h. This procedure was repeated several times until a desired thickness (∼5 mm) was obtained. The rolled materials were fully recrystallized at 973 K for 2 h. The ordered specimens were prepared by annealing in a salt bath at 743 K for 30 days followed by water quenching. The longrange order parameter was determined by the X-ray diffraction method using the integrated intensity ratio of (1 1 0) superlattice reflection to (2 2 0) fundamental lattice reflection, using Cu K␣ radiation. The degree of long-range order parameter obtained in the ordered Ni3 Fe specimen is assumed to be more than 0.9 [17,18]. On the other hand, the disordered specimens were prepared by annealing in a vacuum at 823 K for 10 h, followed by water quenching. These ordered and disordered specimens will
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be expressed as Ni3 Fe (O) and Ni3 Fe (D), respectively. These ordered and disordered specimens were cold rolled at room temperature up to 90% reduction. The cold-rolled materials were annealed at various temperatures (i.e., below and above Tc ) and time lengths. Microstructural observation was carried out by an optical microscope (OM), a scanning electron microscope (SEM) and a transmission electron microscope (TEM). TEM foils were prepared by mechanical thinning to 0.1 mm and jet-polishing. TEM observation was conducted using a JEM 2000FX operating at 200 kV. For microhardness measurement, more than ten points were measured using mainly a load of 200 g. Textures were measured in a central part along the thickness of a sheet by Cu K␣ radiation. Three incomplete pole figures {1 1 1}, {2 0 0} and {2 2 0} were measured up to a maximal tilt angle of 75◦ and corrected with respect to defocusing error by using the randomly oriented powder sample. From these pole figures, the complete orientation distribution functions (ODFs) including odd terms for ghost correction were determined up to an order of l = 22 by the iterative series expansion method, using positivity conditions in pole figures and an ODF [19,20]. For microtexture including grain boundary character distribution (GBCD), local orientations were determined by the SEM-EBSD equipped with the software (INCA Crystal® ) developed by OXFORD INSTRUMENTS® . The Brandon criterion: θ max = 15◦ Σ −1/2 was used to classify the grain boundary character in terms of the coincidence site lattice (CSL) model [21]. Also, the area fraction of the recrystallized (or unrecrystallized) region was calculated, based on pattern quality image or crystal orientation maps (COMs) obtained by SEM-EBSD. 3. Results 3.1. Cold rolled state Two kinds of starting materials before cold rolling, i.e., the ordered and disordered specimens exhibited a fully recrystallized microstructure with an almost identical grain size and almost no preferential orientation (i.e., random texture). Fig. 1 shows optical micrographs of the longitudinal section of the 90% cold-rolled specimens. The disordered specimen exhibits the deformed microstructure consisting of homogeneously elongated grains along rolling direction. On the other hand, the
Fig. 1. Optical micrographs of longitudinal section of the 90% cold-rolled (a) Ni3 Fe (O) and (b) Ni3 Fe (D) alloys.
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Fig. 2. Change in Vickers hardness by cold rolling of the Ni3 Fe alloy.
ordered specimen exhibits elongated grains along rolling direction, accompanied with shear bands. Fig. 2 shows the change in hardness by cold rolling of the Ni3 Fe alloy. For starting material (i.e. unrolled state), the hardness of the ordered specimen is higher than that of the disordered specimen. Until 30% reduction, both the ordered and disordered specimens show a significant increase, indicating a large work-hardening at the early stage of cold rolling. Above 30% reduction, the ordered and disorder specimens generally show a moderate increase of hardness although the ordered Ni3 Fe alloy shows a saturation or a slight decrease of hardness beyond 50% reduction. It should be noted that after 90% cold rolling, the hardness of the ordered specimen is still higher than that of the disordered specimen. The ϕ2 sections of ODFs for the 90% cold-rolled specimen are given in Fig. 3. Some ideal orientations observed in
Fig. 4. Ideal orientations in Euler angle space.
the present alloy are illustrated in Fig. 4. It is well known that rolling texture of fcc materials is divided into two types, i.e., copper type (pure metal type) and brass type (alloy type) [22]. The rolling textures of the Ni3 Fe alloy are basically a copper
Fig. 3. ϕ2 sections of (ϕ2 = 0◦ , 5◦ , . . ., 90◦ ) of the orientation distribution functions (ODFs) for the 90% cold-rolled (a) Ni3 Fe (O) and (b) Ni3 Fe (D) alloys.
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Fig. 5. Texture index J [15] for the 90% cold-rolled Ni3 Fe alloy.
type irrespective of the initially ordered or disordered state, but the intensity of rolling textures is extremely weak in the initially ordered specimen. Fig. 5 shows the texture index J [23] for the 90% cold-rolled specimens. The texture index J, which is a single parameter to characterize the intensity of texture, is defined by the follow equation, J = [f (g)]2 dg (1) Here, f(g) represents the orientation distribution function (i.e., an orientation density) of the crystallites of a polycrystalline material. The texture index J varies between 1 (in the case of random orientation) and ∞ (in the case of one or more ideal single orientations) [23]. Again, it is apparent from Fig. 5 that the intensity of the rolling texture is low in the initially ordered specimen. The copper type rolling texture is known to be composed of the ␣-fiber that runs from the {0 1 1}1 0 0 (G) orientation to
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the {0 1 1}2 1 1 (Bs) orientation, and -fiber that runs from the {1 1 2}1 1 1 (C) orientation, through the {1 2 3}6 3 4 (S) orientation, to the {0 1 1}2 1 1 (Bs) orientation [20]. Fig. 6 shows the orientation density along the ␣- and -fibers in the rolling texture for the 90% cold-rolled specimen. Generally, the copper type rolling texture of the heavily (e.g., more than 90% reduction) rolled metals and alloys consists of a weak ␣-fiber and strong -fiber in which the C and S orientations are stronger than the Bs orientation [24]. For the initially disordered Ni3 Fe alloy, the orientation density of the C and S orientations is higher than that of the Bs orientation, that is, a typical copper type texture is formed. On the other hand, for the initially ordered Ni3 Fe alloy, the orientation density of the C and S orientations is not higher than that of the Bs orientation, and the -fiber is not so much developed, that is, the development of a copper type texture is suppressed. In other words, the rolling texture of the initially ordered Ni3 Fe alloy can be described as a copper type texture with a prominent Bs component (i.e., a transition type texture). 3.2. Recrystallized state The cold-rolled specimens were isochronally (for 1 h) annealed at various temperatures below and above Tc . Fig. 7 shows the hardness change by 1 h annealing for the 90% coldrolled specimens. In this figure, the long-range order parameter is also included. The hardness of the Ni3 Fe alloy increases gradually with increasing temperature (<700 K) and then shows a peak at a lower temperature by about 75 K than Tc (i.e., ∼700 K) for the initially ordered specimen and at a temperature just below Tc (i.e., ∼770 K) for the initially disordered specimen, respectively. Above this peak temperature, the hardness rapidly decreases probably due to the recrystallization. The observed increase of hardness have been called as strain-age hardening
Fig. 6. Orientation density f(g) of orientations along the (a) ␣-fiber and (b) -fiber for the 90% cold-rolled Ni3 Fe alloy.
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Fig. 7. Changes in Vickers hardness of the Ni3 Fe alloy by isochronal annealing for 1 h at various temperatures. Change in long-range order parameter for the Ni3 Fe alloy is also included in this figure.
and repeatedly observed in some L12 ordered alloys [15,25]. Also, the softening, i.e., the recrystallization occurs at lower temperature in the initially ordered specimen than in the initially disordered specimen. The long-range order parameter remains at a very low level at low temperatures and then shows a peak at a lower temperature by about 75 K than Tc for the initially ordered
Fig. 8. Changes in Vickers hardness and long-range parameter during isothermal annealing at 753 K for the Ni3 Fe alloy.
specimen and at a temperature just below Tc for the initially disordered specimen, respectively. Above this peak temperature, the long-range order parameter rapidly decreases. Interestingly, the behavior of the long-range order parameter quite coincides
Fig. 9. (a) Pattern quality image and crystal orientation maps (COMs) at the (b) normal and (c) rolling directions for the Ni3 Fe (O) alloy annealed at 753 K for 5.4 × 106 s.
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with that of hardness, irrespective of the initially ordered or disordered-specimen. Therefore, the observed hardness increase is attributed to the increase of the long-range order parameter, i.e., reordering, and may be interpreted in terms of dislocation dragging anti-phase domain (APD) tubes [4], because such a dislocation movement leads to increase of flow stress. The hardness change by isothermal annealing at a temperature (753 K) below Tc is given in Fig. 8, together with the change of the long-range order parameter. For both the initially ordered and disordered states, the degree of the longrange order parameter reaches approximately 1 by annealing at 753 K for ∼106 s (12 days). On the other hand, the hardness appears to show saturation by an annealing for 1.8 × 107 s (210 days). Figs. 9 and 10 show the pattern quality images and the crystal orientation maps (COMs) at normal and rolling directions for the initially ordered and disordered Ni3 Fe alloys annealed at 753 K for 5.4 × 106 s, respectively. Interestingly, the recrystallized grains are formed in the initially ordered specimen, while no distinct recrystallized grains are formed in the initially disordered specimen. The color maps for orientations reveal that the orientation of recrystallized grains is various (random orientation) while recovered regions have near {0 1 1}2 1 1–1 1 1 orientation (Figs. 9b and c). Consequently, the recrystallization partially occurs in the initially ordered specimen at temperature below Tc . On the other hand, for the initially disordered specimen, the orientations of the recovered regions are mainly {0 1 1}2 1 1 and {1 1 2}1 1 1 but a small amount of a cube {0 0 1}1 0 0 oriented region is also recognized.
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Fig. 11 shows the change in hardness of the Ni3 Fe alloy by isothermal annealing at several temperatures above Tc . The softening took place without showing a moderate increase and a subsequent peak, in contrast with the case of annealing at temperature below Tc (see Fig. 8). The softening due to recrystallization occurs at an earlier time with increasing annealing temperature both in the initially ordered and disordered specimens. Also, the initially ordered specimen softens at an earlier time than the initially disordered specimen, irrespective of annealing temperature. Fig. 12 shows the pattern quality image and the crystal orientation maps for the partially recrystallized Ni3 Fe alloy in the initially ordered state. Obviously, new grains with various orientations are preferentially formed in the shear bands. Fig. 13 shows semi log plots of ‘time to 50% recrystallization’ as a function of reciprocal temperature for the initially ordered and disordered Ni3 Fe alloys. The first point to be noted in this figure is that the recrystallization kinetics is faster in the initially ordered specimen than in the initially disordered specimen, regardless of annealing temperatures above or below Tc . The second point is that the recrystallization kinetics abruptly increases like a step function around Tc with increasing temperature, regardless of the initially ordered and disordered specimens. Extrapolation of data from above Tc to below Tc reveals that the ordered structure decelerates the recrystallization. The retardation of recrystallization in the temperature range of ordered structure (i.e., below Tc ) is essentially the same as that observed in Cu3 Au [16] and (Co,Fe)3 V [26]. Fig. 14 shows the distribution of grain boundary character and the EBSD grain maps for the specimen fully recrystallized
Fig. 10. (a) Pattern quality image and crystal orientation maps (COMs) at the (b) normal and (c) rolling directions for the Ni3 Fe (D) alloy annealed at 753 K for 5.4 × 106 s.
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Fig. 13. Arrhenius plots of time to 50% recrystallization for the initially ordered and disordered Ni3 Fe alloys. The time to 50% recrystallization was determined from the pattern quality image or crystal orientation maps (COMs) obtained by SEM-EBSD.
Fig. 11. Changes in Vickers hardness by isothermal annealing at 823, 923 and 973 K for the Ni3 Fe alloy.
at 973 K for 1 h. In these grain maps, Σ3 twin boundary is colored as yellow. From the boundary maps, the grain size of the initially ordered specimen is found to be smaller than those of the initially disordered specimen. Further, a large amount of Σ3 boundaries are observed in all the specimens. It is recognized that the grain boundary character distributions (GBCDs) of both the specimens are featured by a high frequency of Σ3 boundary. Also, low but recognizable frequency is observed for Σ1 and Σ9 boundaries of all the specimens. The occurrence of Σ9 boundary (and also Σ27 boundary), i.e., Σ3n boundaries, may be due to geometric interactions of twin related variants [27]. The occurrence of other special boundaries (i.e., Σ ≤ 29) is very low in all the specimens. Here, it is noted that the frequency of Σ3
Fig. 12. (a) Pattern quality image and (b) crystal orientation maps (COMs) at the (b) normal and (c) rolling directions for the Ni3 Fe (O) alloy annealed at 873 K for 30 s (longitudinal section).
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Fig. 14. Distributions of grain boundary character and EBSD boundary maps (pattern quality images) for (a) Ni3 Fe (O) and (b) Ni3 Fe (D) alloys annealed at 973 K for 1 h.
boundary is found to be somewhat less in the initially ordered specimen than in the initially disordered specimen. Although the observed specimens are fully recrystallized above Tc (i.e., in the disordered state), the GBCDs including Σ3 twin boundaries are apparently affected by the initial state before cold rolling, that is, ordered or disordered state.
The ϕ2 sections of ODFs for the specimens annealed at 973 K for 1 h are shown in Fig. 15 (see their microstructures in Fig. 14). It is well known that a cube {0 0 1}1 0 0 texture is formed by recrystallization of heavily rolled copper, aluminum and nickel [e.g., 28–30] where the copper-type texture is well developed. A marked cube texture was formed in the initially disordered
Fig. 15. ϕ2 sections of (ϕ2 = 0◦ , 5◦ , . . ., 90◦ ) of the orientation distribution functions (ODFs) for the (a) Ni3 Fe (O) and (b) Ni3 Fe (D) alloys annealed at 973 K for 1 h.
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Ni3 Fe alloy. In the initially ordered Ni3 Fe alloy, a cube texture with an additional component of near {1 2 2}2 2 1 orientation that has a twin relationship with {0 0 1}1 0 0 was formed. Here, it is noted that a cube component is formed in the recrystallization texture of the initially ordered Ni3 Fe alloy although no cube recrystallization textures has been observed in the strongly ordered L12 intermetallic alloys such as Ni3 Al [6,8,9], Ni3 (Si,Ti) [14] and Co3 Ti [12,13]. It is emphasized that the intensity of the recrystallization texture is extremely lower in the initially ordered specimen than in the initially disordered specimen. 4. Discussion 4.1. Cold-rolled state It was found by the present observation that the cold rolling texture of the Ni3 Fe alloy basically shows a copper type composed of -fiber component accompanied by ␣-fiber component, regardless of the L12 ordered or fcc disordered structure. This result stems from the fact that the slip system for L12 type ordered structure is the same as that for fcc structure, i.e., 1 0 1{1 1 1}. In general, deformation texture is formed by crystal lattice rotation due to slip deformation. The intensity of the rolling texture was lower in the initially ordered specimen than in the initially disordered specimen. In addition, the -fiber, particularly the S and C orientations, was not so developed in the initially ordered specimen, resulting in the prominent Bs orientation, while the S and C components (i.e., a typical main component of the -fiber) were remarkable in the initially disordered specimen. The feature for the rolling texture has also been so far observed in the strongly ordered L12 alloys such as Ni3 Al [8–10], Co3 Ti [13] and Ni3 (Si,Ti) [14] alloys. The difference in the rolling texture between the ordered and disordered alloys is correlated with the difficulty of octahedral cross slip from {1 1 1} to {1 1 1} planes. The difficulty or the easiness of octahedral cross slip is closely related to the width of the extended dislocation; the larger the width of extended dislocation becomes, the harder the octahedral cross slip becomes. The width of the extended dislocation is presumed to be inversely proportional to the energy of the stacking-faultlike defect (i.e., antiphase boundary in the case of L12 ordered structure or stacking fault in the case of fcc disordered structure). Consequently, it is suggested that the octahedral cross slip becomes easier and then the deformation texture becomes more intense with increasing energy of the stacking-fault-like defect (SFLD) [31]. The superlattice dislocation 1 1 0 in L12 ordered structure is dissociated into two (1/2)1 1 0 dislocations bounded for the antiphase boundary (APB), while the dislocation (1/2)1 1 0 in fcc disordered structure is dissociated into two Shockley partials (1/6)2 1 1 bounded for the stacking fault (SF). These dissociation manners of the dislocation are expressed by the followings: a1 1 0 → 2a 1 1 0 + APB + 2a 1 1 0 (for L12 structure) (2) a 2 1 1 0
→ a6 2 1 1 + SF + a6 1 2 1
(for fcc structure)
(3)
Here, a is the lattice parameter. The width (w) of the extended dislocation for the L12 ordered alloy is given as follows [32]: Gbh2 sin2 ϕ w= cos2 ϕ + (4) 2πγAPB 1−ν Similarly, w for fcc material is given as follows [33]: Gbh2 2 − ν 2ν w= 1− cos2ϕ 8πγSF 1 − ν 2−ν
(5)
Here, G is the shear modulus, bh the Burgers vector for super partial dislocation in the case of L12 ordered alloy and for Shockley partial dislocation in the case of fcc material, γ APB the antiphase boundary energy per unit area, γ SF the stacking fault energy per unit area, ϕ the angle between the dislocation and the Burgers vector of the perfect dislocation (ϕ = 0◦ in the case of screw dislocation and ϕ = 90◦ in the case of edge dislocation) and ν is the Poisson’s ratio (ν = 1/3 was used in the present calculation). The lattice parameters (a) of ordered and disordered Ni3 Fe are 0.3524 √nm [34] and 0.3551 nm [18], respectively. b is given as a/ 2 for the L12 structure and h √ a/ 6 for fcc structure, respectively. The shear modulus (G) of ordered Ni3 Fe has been reported as 84.7 GPa [35]. The same value of shear modulus of the ordered Ni3 Fe was used in the calculation of the disordered Ni3 Fe [35]. Also, the value of γ APB for Ni3 Fe has been reported to be 133 (±8) mJ/m2 [36], while the value of γ SF for pure nickel has been reported to be 95 mJ/m2 [37]. By using these values, the widths of screw dislocation for ordered and disordered Ni3 Fe are calculated as 6.40 and 1.11 nm, respectively. In fact, the TEM observation revealed that the dislocations of ordered Ni3 Fe deformed at low temperature widely extended (or dissociated) [38]. This result is consistent well with the intensity of the observed rolling textures (Figs. 3 and 5). As mentioned above, the octahedral cross slips become more difficult with increasing width of the extended dislocation. As a result, the development of the -fiber texture is suppressed and alternatively the Bs orientation (the ␣-fiber texture) remains as a main component of rolling textures in the L12 ordered specimen. Strictly describing, the superlattice dislocation introduced in ordered Ni3 Fe shows a four-fold dissociation scheme [38], i.e., a1 0 1 → (a/6)2 1 1 + CSF + (a/6)1 1 2 + APB + (a/6)2 1 1 + CSF + (a/6)112 (where CSF is a complex stacking fault). Such a dissociation scheme may make the cross slip event hard and at the same time result in unusual (unexpected) crystal rotation, leading to the observed weak (undeveloped) rolling texture in the ordered Ni3 Fe (Figs. 3 and 5). 4.2. Recrystallized state The initially ordered alloy showed faster recrystallization kinetics than the initially disordered alloy, whether the annealing is performed at temperatures below or above Tc . The driving force for the primary recrystallization is the stored energy of cold work. The stored energy E for the ordered and disordered materials per unit volume is simply estimated as follows [5]: E = αρGbh2
(6)
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Here, ρ is the dislocation density, G the shear modulus, bh the Burgurs’ vector of the dislocation and α is a constant whose value is assumed to be approximately 0.5. During deformation, the dislocations of Burgers’ vector bh move an average distance L, and the dislocation density (ρ) is related to the shear strain (γ) by γ = ρbh L
(7)
From Eqs. (6) and (7), the stored energy is then given by γ E=α (8) Gbh L For the 90% cold-rolled alloys in the initially ordered and disordered states, the value of γ is the same between both states, and α, L and G are assumed not to change greatly. Therefore, the stored energy E simply depends on the magnitude of the Burgers’ vector bh . Using the lattice parameters described in the previous section, 0.249 and 0.145 nm as the length of bh in the ordered and disordered Ni3 Fe are obtained, respectively. Apparently, the stored energy of the ordered Ni3 Fe alloy is greater than that of the disordered Ni3 Fe alloy, and consequently results in the fast recrystallization in the initially ordered specimen. Also, it is suggested that such a high stored energy introduced in the ordered Ni3 Fe alloy results in the earlier reordering and hardness increase (shown in Figs. 7 and 8). It was shown that the annealing in the ordered structure decelerates the recrystallization kinetics whether the specimen is deformed in initially ordered or disordered state (Fig. 13). The discontinuous change in recrystallization kinetics is primarily attributed to either a sharp change in diffusivity or a change in recrystallization mechanism through the order to disorder transformation. For the former reason, it has been suggested that atomic diffusion in the ordered structure is generally retarded due to the feature that atom cannot migrate to its neighboring fair site position without migrating through wrong site positions [39,40]. The main component of the observed recrystallization texture for the Ni3 Fe alloy was a cube {0 0 1}1 0 0 orientation. The recrystallization texture of the initially ordered alloy was weak compared with those of the initially disordered alloy. Similarly weak recrystallization texture has also been observed in strongly ordered Ni3 Al [8–10], Co3 Ti [13] and Ni3 (Si,Ti) [14]. The weak recrystallization texture observed in the initially ordered specimens appears to be closely related to the deformation microstructure. The weak recrystallization texture may stem from the weak rolling texture and/or the inhomogeneous deformation microstructure including shear bands. It has been reported that the recrystallized grains formed in shear bands had a wide spread of grain orientations, resulting in a weak cube recrystallization texture for cold-rolled and annealed polycrystalline copper (fcc) [41]. Actually, the preferential nucleation in the shear bands accompanied by a wide spread of orientations was observed in the present Ni3 Fe alloy. It is likely that such a preferential nucleation in the inhomogeneously deformed regions is related to the fast recrystallization observed in the initially ordered speci-
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men. There may be the other origin affecting the recrystallization texture. During the early stage of annealing, reordering and recover simultaneously occur in the cold-rolled ordered alloy, and result in nucleation of grains with unusual orientations, i.e., different from orientations formed by cold rolling. In the ordered structure, the migration of grain boundary is retarded because the grain boundary in the ordered lattices has to migrate, keeping or restoring atomic ordering. In fact, the grain sizes after recrystallization of the initially ordered alloy was small compared with those of the initially disordered alloy (Fig. 14). Also, it is unlikely that the preferential growth of the specified grains (such as a cube orientated grains) or the specific grain boundaries occurs in the ordered structure, e.g., as understood from the distributions of grain boundary character (see Fig. 14). Furthermore, it is possible that the annealing twining affects the recrystallization texture. If the multiple twinning occurs, recrystallization texture will be weak. Consequently, the weak recrystallization texture developed in the initially ordered alloy was suggested to be associated with the nucleation of randomly orientated grains and the non-selected grain growth. To furthermore clarify the formation mechanism for deformation and recrystallization textures of ordered alloys, more and atomistic studies on microstructural evolution during deformation and particularly the early stage of recrystallization will be required.
5. Conclusion (1) The 90% cold rolling texture of both the initially ordered and disordered Ni3 Fe alloys was basically a copper (pure-metal) type. However, the rolling texture of the initially ordered Ni3 Fe alloy, the Bs {0 1 1}2 1 1 component was enhanced in comparison with the C {1 1 2}1 1 1 and S {1 2 3}6 3 4 components. The intensity of the rolling texture was lower in the initially ordered alloy than in the initially disordered alloy. (2) After the recrystallization, cube {0 0 1}1 0 0 texture was formed, in both the initially ordered and the initially disordered alloys. However, the intensity of the recrystallization texture was much more reduced in the initially ordered alloy than in the initially disordered alloy. (3) During annealing of the cold-rolled specimen, the hardness showed a broad peak and then decreased rapidly with increasing temperature, regardless of ordered or disordered state before cold rolling. The rapid decease of the hardness due to the recrystallization occurred at lower temperature or faster in the initially ordered alloy than in the initially disordered alloy. (4) The intensity of the observed rolling texture was interpreted by considering the difficulty of the cross slip of superlattice dislocations and ordinary dislocations. Also, the weak recrystallization texture developed in the initially ordered alloy was suggested to be associated with the nucleation of randomly orientated grains and the non-selected grain growth.
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Microstructure and texture evolution during cold rolling and annealing of Ni3Fe alloy Yasuyuki Kaneno, Akira Takahashi, Takayuki Takasugi ∗ Department of Materials Science, Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan Received 10 January 2006; received in revised form 5 June 2006; accepted 9 June 2006
Abstract Just-stoichiometric Ni3 Fe alloy with L12 ordered and A1 (fcc) disordered structures were cold rolled and annealed below and above the critical ordering temperature (Tc ) to study the effects of ordered and disordered structures on texture and microstructure evolution during deformation and recrystallization. The cold rolling textures of the Ni3 Fe alloy basically showed a copper (pure-metal) type irrespective of ordered or disordered state before cold rolling. However, for the rolling texture of the initially ordered specimen, Bs {0 1 1}2 1 1 component was enhanced in comparison with C {1 1 2}1 1 1 and S {1 2 3}6 3 4 components. The intensity of the rolling texture was weaker in the initially ordered structure than in the initially disordered structure. Also, the intensity of a cube {0 0 1}1 0 0 texture, which was formed after recrystallization above Tc , was significantly reduced in the initially ordered structure. During annealing, the Ni3 Fe alloy slightly hardened up to Tc and then softened rapidly, regardless of ordered or disordered state before cold rolling. It was also found that the recrystallization occurred faster and at lower temperature in the initially ordered structure than in the initially disordered structure. © 2006 Elsevier B.V. All rights reserved. Keywords: Ni3 Fe; L12 structure; Cold rolling texture; Annealing texture; Recrystallization; Ordered structure
1. Introduction In general, intermetallic alloys and compounds possess high strength at elevated temperatures and good properties in oxidizing and corrosive environments, and therefore are considered to be a potential high temperature structural material. However, their applications are limited because of low ductility at low temperature, which is caused by weak lattice or grain boundary cohesion due to their complex crystal structures. Among various crystal structures, low temperature ductility of L12 ordered intermetallic alloys which have been suffered from propensity for intergranular fracture has been improved by micro- and macro-alloying [1–3]. At present, boron-doped Ni3 Al, Co3 Ti and Ni3 (Si,Ti) polycrystals can be plastically deformed in air at room temperature. These L12 intermetallic alloys show a positive temperature dependence of yield strength as well as good chemical properties and thereby attract a considerable attention particularly from practical point of view. Using thermomechan-
∗
Corresponding author. Tel.: +81 72 254 9314; fax: +81 72 254 9912. E-mail address: [email protected] (T. Takasugi).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.06.054
ical processing, microstructural controls for grain size, crystallographic texture and grain boundary character, which may strongly affect mechanical and physical properties of polycrystalline materials, are of importance for developing intermetallic alloys. Particularly, it is necessary to understand deformation and recrystallization behavior of intermetallic alloys and compounds. Also, texture evolution during these processes is important for intermetallic alloys because they generally show strong anisotropy in various physical and mechanical properties. In the past literatures, recovery and recrystallization behavior of some ordered intermetallic alloys have been outlined and reviewed [4,5], but their deformation and recrystallization textures have been little studied, although several pioneer studies have been done on Ni3 Al [6–11], Co3 Ti [12,13] and Ni3 (Si,Ti) [14]. A comprehensive understanding is required for deformation and recrystallization behavior of ordered intermetallic alloys including L12 alloys. For example, what is an essential difference in deformation and recrystallization behavior, and also in the associated textures between ordered intermetallic alloys, and disordered metals and alloys? To study using Ni3 Fe alloy is appropriate to answer this question. Ni3 Fe shows order (L12 )–disordered (fcc) transition at Tc = 776 K. In the Ni3 Fe
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alloy, both of ordered and disordered structures with an identical chemical composition are obtained by adopting proper heat treatments. For Ni3 Fe alloy, annealing behavior was studied by Vidoz et al. [15], but rolling and recrystallization texture has not been reported so far. For Cu3 Au with order (L12 )–disorder (fcc) transition at Tc = ∼663 K, annealing textures were studied by Hutchinson et al. [16]. In this case, cold rolling was however conducted only for the disordered alloy. In the present study, the Ni3 Fe alloy in initially ordered and disordered states were cold rolled at room temperature and then annealed at temperatures below and above the Tc . The rolling and recrystallization textures were characterized by the orientation distribution functions (ODFs), and the grain boundary character distributions (GBCDs) of the recrystallized alloys were determined by the electron backscattered diffraction (EBSD) method. Also, recrystallization kinetics was evaluated by the hardness test and microstructural observation. Based on these results, the effect of ordered and disordered structures on texture and microstructure evolutions during deformation and recrystallization was discussed. 2. Experimental procedures Raw materials used in this study were 99.9 wt.% nickel and 99.99 wt.% iron. Just-stoichiometric Ni3 Fe alloy was prepared by arc melting in an argon gas atmosphere on a copper hearth using a non-consumable tungsten electrode. The Ni3 Fe button ingot was homogenized in a vacuum at 1373 K for 48 h, followed by furnace cooling. These homogenized-ingots were cold rolled, and then annealed at 973 K for 1 h. This procedure was repeated several times until a desired thickness (∼5 mm) was obtained. The rolled materials were fully recrystallized at 973 K for 2 h. The ordered specimens were prepared by annealing in a salt bath at 743 K for 30 days followed by water quenching. The longrange order parameter was determined by the X-ray diffraction method using the integrated intensity ratio of (1 1 0) superlattice reflection to (2 2 0) fundamental lattice reflection, using Cu K␣ radiation. The degree of long-range order parameter obtained in the ordered Ni3 Fe specimen is assumed to be more than 0.9 [17,18]. On the other hand, the disordered specimens were prepared by annealing in a vacuum at 823 K for 10 h, followed by water quenching. These ordered and disordered specimens will
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be expressed as Ni3 Fe (O) and Ni3 Fe (D), respectively. These ordered and disordered specimens were cold rolled at room temperature up to 90% reduction. The cold-rolled materials were annealed at various temperatures (i.e., below and above Tc ) and time lengths. Microstructural observation was carried out by an optical microscope (OM), a scanning electron microscope (SEM) and a transmission electron microscope (TEM). TEM foils were prepared by mechanical thinning to 0.1 mm and jet-polishing. TEM observation was conducted using a JEM 2000FX operating at 200 kV. For microhardness measurement, more than ten points were measured using mainly a load of 200 g. Textures were measured in a central part along the thickness of a sheet by Cu K␣ radiation. Three incomplete pole figures {1 1 1}, {2 0 0} and {2 2 0} were measured up to a maximal tilt angle of 75◦ and corrected with respect to defocusing error by using the randomly oriented powder sample. From these pole figures, the complete orientation distribution functions (ODFs) including odd terms for ghost correction were determined up to an order of l = 22 by the iterative series expansion method, using positivity conditions in pole figures and an ODF [19,20]. For microtexture including grain boundary character distribution (GBCD), local orientations were determined by the SEM-EBSD equipped with the software (INCA Crystal® ) developed by OXFORD INSTRUMENTS® . The Brandon criterion: θ max = 15◦ Σ −1/2 was used to classify the grain boundary character in terms of the coincidence site lattice (CSL) model [21]. Also, the area fraction of the recrystallized (or unrecrystallized) region was calculated, based on pattern quality image or crystal orientation maps (COMs) obtained by SEM-EBSD. 3. Results 3.1. Cold rolled state Two kinds of starting materials before cold rolling, i.e., the ordered and disordered specimens exhibited a fully recrystallized microstructure with an almost identical grain size and almost no preferential orientation (i.e., random texture). Fig. 1 shows optical micrographs of the longitudinal section of the 90% cold-rolled specimens. The disordered specimen exhibits the deformed microstructure consisting of homogeneously elongated grains along rolling direction. On the other hand, the
Fig. 1. Optical micrographs of longitudinal section of the 90% cold-rolled (a) Ni3 Fe (O) and (b) Ni3 Fe (D) alloys.
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Fig. 2. Change in Vickers hardness by cold rolling of the Ni3 Fe alloy.
ordered specimen exhibits elongated grains along rolling direction, accompanied with shear bands. Fig. 2 shows the change in hardness by cold rolling of the Ni3 Fe alloy. For starting material (i.e. unrolled state), the hardness of the ordered specimen is higher than that of the disordered specimen. Until 30% reduction, both the ordered and disordered specimens show a significant increase, indicating a large work-hardening at the early stage of cold rolling. Above 30% reduction, the ordered and disorder specimens generally show a moderate increase of hardness although the ordered Ni3 Fe alloy shows a saturation or a slight decrease of hardness beyond 50% reduction. It should be noted that after 90% cold rolling, the hardness of the ordered specimen is still higher than that of the disordered specimen. The ϕ2 sections of ODFs for the 90% cold-rolled specimen are given in Fig. 3. Some ideal orientations observed in
Fig. 4. Ideal orientations in Euler angle space.
the present alloy are illustrated in Fig. 4. It is well known that rolling texture of fcc materials is divided into two types, i.e., copper type (pure metal type) and brass type (alloy type) [22]. The rolling textures of the Ni3 Fe alloy are basically a copper
Fig. 3. ϕ2 sections of (ϕ2 = 0◦ , 5◦ , . . ., 90◦ ) of the orientation distribution functions (ODFs) for the 90% cold-rolled (a) Ni3 Fe (O) and (b) Ni3 Fe (D) alloys.
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Fig. 5. Texture index J [15] for the 90% cold-rolled Ni3 Fe alloy.
type irrespective of the initially ordered or disordered state, but the intensity of rolling textures is extremely weak in the initially ordered specimen. Fig. 5 shows the texture index J [23] for the 90% cold-rolled specimens. The texture index J, which is a single parameter to characterize the intensity of texture, is defined by the follow equation, J = [f (g)]2 dg (1) Here, f(g) represents the orientation distribution function (i.e., an orientation density) of the crystallites of a polycrystalline material. The texture index J varies between 1 (in the case of random orientation) and ∞ (in the case of one or more ideal single orientations) [23]. Again, it is apparent from Fig. 5 that the intensity of the rolling texture is low in the initially ordered specimen. The copper type rolling texture is known to be composed of the ␣-fiber that runs from the {0 1 1}1 0 0 (G) orientation to
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the {0 1 1}2 1 1 (Bs) orientation, and -fiber that runs from the {1 1 2}1 1 1 (C) orientation, through the {1 2 3}6 3 4 (S) orientation, to the {0 1 1}2 1 1 (Bs) orientation [20]. Fig. 6 shows the orientation density along the ␣- and -fibers in the rolling texture for the 90% cold-rolled specimen. Generally, the copper type rolling texture of the heavily (e.g., more than 90% reduction) rolled metals and alloys consists of a weak ␣-fiber and strong -fiber in which the C and S orientations are stronger than the Bs orientation [24]. For the initially disordered Ni3 Fe alloy, the orientation density of the C and S orientations is higher than that of the Bs orientation, that is, a typical copper type texture is formed. On the other hand, for the initially ordered Ni3 Fe alloy, the orientation density of the C and S orientations is not higher than that of the Bs orientation, and the -fiber is not so much developed, that is, the development of a copper type texture is suppressed. In other words, the rolling texture of the initially ordered Ni3 Fe alloy can be described as a copper type texture with a prominent Bs component (i.e., a transition type texture). 3.2. Recrystallized state The cold-rolled specimens were isochronally (for 1 h) annealed at various temperatures below and above Tc . Fig. 7 shows the hardness change by 1 h annealing for the 90% coldrolled specimens. In this figure, the long-range order parameter is also included. The hardness of the Ni3 Fe alloy increases gradually with increasing temperature (<700 K) and then shows a peak at a lower temperature by about 75 K than Tc (i.e., ∼700 K) for the initially ordered specimen and at a temperature just below Tc (i.e., ∼770 K) for the initially disordered specimen, respectively. Above this peak temperature, the hardness rapidly decreases probably due to the recrystallization. The observed increase of hardness have been called as strain-age hardening
Fig. 6. Orientation density f(g) of orientations along the (a) ␣-fiber and (b) -fiber for the 90% cold-rolled Ni3 Fe alloy.
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Fig. 7. Changes in Vickers hardness of the Ni3 Fe alloy by isochronal annealing for 1 h at various temperatures. Change in long-range order parameter for the Ni3 Fe alloy is also included in this figure.
and repeatedly observed in some L12 ordered alloys [15,25]. Also, the softening, i.e., the recrystallization occurs at lower temperature in the initially ordered specimen than in the initially disordered specimen. The long-range order parameter remains at a very low level at low temperatures and then shows a peak at a lower temperature by about 75 K than Tc for the initially ordered
Fig. 8. Changes in Vickers hardness and long-range parameter during isothermal annealing at 753 K for the Ni3 Fe alloy.
specimen and at a temperature just below Tc for the initially disordered specimen, respectively. Above this peak temperature, the long-range order parameter rapidly decreases. Interestingly, the behavior of the long-range order parameter quite coincides
Fig. 9. (a) Pattern quality image and crystal orientation maps (COMs) at the (b) normal and (c) rolling directions for the Ni3 Fe (O) alloy annealed at 753 K for 5.4 × 106 s.
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with that of hardness, irrespective of the initially ordered or disordered-specimen. Therefore, the observed hardness increase is attributed to the increase of the long-range order parameter, i.e., reordering, and may be interpreted in terms of dislocation dragging anti-phase domain (APD) tubes [4], because such a dislocation movement leads to increase of flow stress. The hardness change by isothermal annealing at a temperature (753 K) below Tc is given in Fig. 8, together with the change of the long-range order parameter. For both the initially ordered and disordered states, the degree of the longrange order parameter reaches approximately 1 by annealing at 753 K for ∼106 s (12 days). On the other hand, the hardness appears to show saturation by an annealing for 1.8 × 107 s (210 days). Figs. 9 and 10 show the pattern quality images and the crystal orientation maps (COMs) at normal and rolling directions for the initially ordered and disordered Ni3 Fe alloys annealed at 753 K for 5.4 × 106 s, respectively. Interestingly, the recrystallized grains are formed in the initially ordered specimen, while no distinct recrystallized grains are formed in the initially disordered specimen. The color maps for orientations reveal that the orientation of recrystallized grains is various (random orientation) while recovered regions have near {0 1 1}2 1 1–1 1 1 orientation (Figs. 9b and c). Consequently, the recrystallization partially occurs in the initially ordered specimen at temperature below Tc . On the other hand, for the initially disordered specimen, the orientations of the recovered regions are mainly {0 1 1}2 1 1 and {1 1 2}1 1 1 but a small amount of a cube {0 0 1}1 0 0 oriented region is also recognized.
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Fig. 11 shows the change in hardness of the Ni3 Fe alloy by isothermal annealing at several temperatures above Tc . The softening took place without showing a moderate increase and a subsequent peak, in contrast with the case of annealing at temperature below Tc (see Fig. 8). The softening due to recrystallization occurs at an earlier time with increasing annealing temperature both in the initially ordered and disordered specimens. Also, the initially ordered specimen softens at an earlier time than the initially disordered specimen, irrespective of annealing temperature. Fig. 12 shows the pattern quality image and the crystal orientation maps for the partially recrystallized Ni3 Fe alloy in the initially ordered state. Obviously, new grains with various orientations are preferentially formed in the shear bands. Fig. 13 shows semi log plots of ‘time to 50% recrystallization’ as a function of reciprocal temperature for the initially ordered and disordered Ni3 Fe alloys. The first point to be noted in this figure is that the recrystallization kinetics is faster in the initially ordered specimen than in the initially disordered specimen, regardless of annealing temperatures above or below Tc . The second point is that the recrystallization kinetics abruptly increases like a step function around Tc with increasing temperature, regardless of the initially ordered and disordered specimens. Extrapolation of data from above Tc to below Tc reveals that the ordered structure decelerates the recrystallization. The retardation of recrystallization in the temperature range of ordered structure (i.e., below Tc ) is essentially the same as that observed in Cu3 Au [16] and (Co,Fe)3 V [26]. Fig. 14 shows the distribution of grain boundary character and the EBSD grain maps for the specimen fully recrystallized
Fig. 10. (a) Pattern quality image and crystal orientation maps (COMs) at the (b) normal and (c) rolling directions for the Ni3 Fe (D) alloy annealed at 753 K for 5.4 × 106 s.
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Fig. 13. Arrhenius plots of time to 50% recrystallization for the initially ordered and disordered Ni3 Fe alloys. The time to 50% recrystallization was determined from the pattern quality image or crystal orientation maps (COMs) obtained by SEM-EBSD.
Fig. 11. Changes in Vickers hardness by isothermal annealing at 823, 923 and 973 K for the Ni3 Fe alloy.
at 973 K for 1 h. In these grain maps, Σ3 twin boundary is colored as yellow. From the boundary maps, the grain size of the initially ordered specimen is found to be smaller than those of the initially disordered specimen. Further, a large amount of Σ3 boundaries are observed in all the specimens. It is recognized that the grain boundary character distributions (GBCDs) of both the specimens are featured by a high frequency of Σ3 boundary. Also, low but recognizable frequency is observed for Σ1 and Σ9 boundaries of all the specimens. The occurrence of Σ9 boundary (and also Σ27 boundary), i.e., Σ3n boundaries, may be due to geometric interactions of twin related variants [27]. The occurrence of other special boundaries (i.e., Σ ≤ 29) is very low in all the specimens. Here, it is noted that the frequency of Σ3
Fig. 12. (a) Pattern quality image and (b) crystal orientation maps (COMs) at the (b) normal and (c) rolling directions for the Ni3 Fe (O) alloy annealed at 873 K for 30 s (longitudinal section).
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Fig. 14. Distributions of grain boundary character and EBSD boundary maps (pattern quality images) for (a) Ni3 Fe (O) and (b) Ni3 Fe (D) alloys annealed at 973 K for 1 h.
boundary is found to be somewhat less in the initially ordered specimen than in the initially disordered specimen. Although the observed specimens are fully recrystallized above Tc (i.e., in the disordered state), the GBCDs including Σ3 twin boundaries are apparently affected by the initial state before cold rolling, that is, ordered or disordered state.
The ϕ2 sections of ODFs for the specimens annealed at 973 K for 1 h are shown in Fig. 15 (see their microstructures in Fig. 14). It is well known that a cube {0 0 1}1 0 0 texture is formed by recrystallization of heavily rolled copper, aluminum and nickel [e.g., 28–30] where the copper-type texture is well developed. A marked cube texture was formed in the initially disordered
Fig. 15. ϕ2 sections of (ϕ2 = 0◦ , 5◦ , . . ., 90◦ ) of the orientation distribution functions (ODFs) for the (a) Ni3 Fe (O) and (b) Ni3 Fe (D) alloys annealed at 973 K for 1 h.
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Ni3 Fe alloy. In the initially ordered Ni3 Fe alloy, a cube texture with an additional component of near {1 2 2}2 2 1 orientation that has a twin relationship with {0 0 1}1 0 0 was formed. Here, it is noted that a cube component is formed in the recrystallization texture of the initially ordered Ni3 Fe alloy although no cube recrystallization textures has been observed in the strongly ordered L12 intermetallic alloys such as Ni3 Al [6,8,9], Ni3 (Si,Ti) [14] and Co3 Ti [12,13]. It is emphasized that the intensity of the recrystallization texture is extremely lower in the initially ordered specimen than in the initially disordered specimen. 4. Discussion 4.1. Cold-rolled state It was found by the present observation that the cold rolling texture of the Ni3 Fe alloy basically shows a copper type composed of -fiber component accompanied by ␣-fiber component, regardless of the L12 ordered or fcc disordered structure. This result stems from the fact that the slip system for L12 type ordered structure is the same as that for fcc structure, i.e., 1 0 1{1 1 1}. In general, deformation texture is formed by crystal lattice rotation due to slip deformation. The intensity of the rolling texture was lower in the initially ordered specimen than in the initially disordered specimen. In addition, the -fiber, particularly the S and C orientations, was not so developed in the initially ordered specimen, resulting in the prominent Bs orientation, while the S and C components (i.e., a typical main component of the -fiber) were remarkable in the initially disordered specimen. The feature for the rolling texture has also been so far observed in the strongly ordered L12 alloys such as Ni3 Al [8–10], Co3 Ti [13] and Ni3 (Si,Ti) [14] alloys. The difference in the rolling texture between the ordered and disordered alloys is correlated with the difficulty of octahedral cross slip from {1 1 1} to {1 1 1} planes. The difficulty or the easiness of octahedral cross slip is closely related to the width of the extended dislocation; the larger the width of extended dislocation becomes, the harder the octahedral cross slip becomes. The width of the extended dislocation is presumed to be inversely proportional to the energy of the stacking-faultlike defect (i.e., antiphase boundary in the case of L12 ordered structure or stacking fault in the case of fcc disordered structure). Consequently, it is suggested that the octahedral cross slip becomes easier and then the deformation texture becomes more intense with increasing energy of the stacking-fault-like defect (SFLD) [31]. The superlattice dislocation 1 1 0 in L12 ordered structure is dissociated into two (1/2)1 1 0 dislocations bounded for the antiphase boundary (APB), while the dislocation (1/2)1 1 0 in fcc disordered structure is dissociated into two Shockley partials (1/6)2 1 1 bounded for the stacking fault (SF). These dissociation manners of the dislocation are expressed by the followings: a1 1 0 → 2a 1 1 0 + APB + 2a 1 1 0 (for L12 structure) (2) a 2 1 1 0
→ a6 2 1 1 + SF + a6 1 2 1
(for fcc structure)
(3)
Here, a is the lattice parameter. The width (w) of the extended dislocation for the L12 ordered alloy is given as follows [32]: Gbh2 sin2 ϕ w= cos2 ϕ + (4) 2πγAPB 1−ν Similarly, w for fcc material is given as follows [33]: Gbh2 2 − ν 2ν w= 1− cos2ϕ 8πγSF 1 − ν 2−ν
(5)
Here, G is the shear modulus, bh the Burgers vector for super partial dislocation in the case of L12 ordered alloy and for Shockley partial dislocation in the case of fcc material, γ APB the antiphase boundary energy per unit area, γ SF the stacking fault energy per unit area, ϕ the angle between the dislocation and the Burgers vector of the perfect dislocation (ϕ = 0◦ in the case of screw dislocation and ϕ = 90◦ in the case of edge dislocation) and ν is the Poisson’s ratio (ν = 1/3 was used in the present calculation). The lattice parameters (a) of ordered and disordered Ni3 Fe are 0.3524 √nm [34] and 0.3551 nm [18], respectively. b is given as a/ 2 for the L12 structure and h √ a/ 6 for fcc structure, respectively. The shear modulus (G) of ordered Ni3 Fe has been reported as 84.7 GPa [35]. The same value of shear modulus of the ordered Ni3 Fe was used in the calculation of the disordered Ni3 Fe [35]. Also, the value of γ APB for Ni3 Fe has been reported to be 133 (±8) mJ/m2 [36], while the value of γ SF for pure nickel has been reported to be 95 mJ/m2 [37]. By using these values, the widths of screw dislocation for ordered and disordered Ni3 Fe are calculated as 6.40 and 1.11 nm, respectively. In fact, the TEM observation revealed that the dislocations of ordered Ni3 Fe deformed at low temperature widely extended (or dissociated) [38]. This result is consistent well with the intensity of the observed rolling textures (Figs. 3 and 5). As mentioned above, the octahedral cross slips become more difficult with increasing width of the extended dislocation. As a result, the development of the -fiber texture is suppressed and alternatively the Bs orientation (the ␣-fiber texture) remains as a main component of rolling textures in the L12 ordered specimen. Strictly describing, the superlattice dislocation introduced in ordered Ni3 Fe shows a four-fold dissociation scheme [38], i.e., a1 0 1 → (a/6)2 1 1 + CSF + (a/6)1 1 2 + APB + (a/6)2 1 1 + CSF + (a/6)112 (where CSF is a complex stacking fault). Such a dissociation scheme may make the cross slip event hard and at the same time result in unusual (unexpected) crystal rotation, leading to the observed weak (undeveloped) rolling texture in the ordered Ni3 Fe (Figs. 3 and 5). 4.2. Recrystallized state The initially ordered alloy showed faster recrystallization kinetics than the initially disordered alloy, whether the annealing is performed at temperatures below or above Tc . The driving force for the primary recrystallization is the stored energy of cold work. The stored energy E for the ordered and disordered materials per unit volume is simply estimated as follows [5]: E = αρGbh2
(6)
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Here, ρ is the dislocation density, G the shear modulus, bh the Burgurs’ vector of the dislocation and α is a constant whose value is assumed to be approximately 0.5. During deformation, the dislocations of Burgers’ vector bh move an average distance L, and the dislocation density (ρ) is related to the shear strain (γ) by γ = ρbh L
(7)
From Eqs. (6) and (7), the stored energy is then given by γ E=α (8) Gbh L For the 90% cold-rolled alloys in the initially ordered and disordered states, the value of γ is the same between both states, and α, L and G are assumed not to change greatly. Therefore, the stored energy E simply depends on the magnitude of the Burgers’ vector bh . Using the lattice parameters described in the previous section, 0.249 and 0.145 nm as the length of bh in the ordered and disordered Ni3 Fe are obtained, respectively. Apparently, the stored energy of the ordered Ni3 Fe alloy is greater than that of the disordered Ni3 Fe alloy, and consequently results in the fast recrystallization in the initially ordered specimen. Also, it is suggested that such a high stored energy introduced in the ordered Ni3 Fe alloy results in the earlier reordering and hardness increase (shown in Figs. 7 and 8). It was shown that the annealing in the ordered structure decelerates the recrystallization kinetics whether the specimen is deformed in initially ordered or disordered state (Fig. 13). The discontinuous change in recrystallization kinetics is primarily attributed to either a sharp change in diffusivity or a change in recrystallization mechanism through the order to disorder transformation. For the former reason, it has been suggested that atomic diffusion in the ordered structure is generally retarded due to the feature that atom cannot migrate to its neighboring fair site position without migrating through wrong site positions [39,40]. The main component of the observed recrystallization texture for the Ni3 Fe alloy was a cube {0 0 1}1 0 0 orientation. The recrystallization texture of the initially ordered alloy was weak compared with those of the initially disordered alloy. Similarly weak recrystallization texture has also been observed in strongly ordered Ni3 Al [8–10], Co3 Ti [13] and Ni3 (Si,Ti) [14]. The weak recrystallization texture observed in the initially ordered specimens appears to be closely related to the deformation microstructure. The weak recrystallization texture may stem from the weak rolling texture and/or the inhomogeneous deformation microstructure including shear bands. It has been reported that the recrystallized grains formed in shear bands had a wide spread of grain orientations, resulting in a weak cube recrystallization texture for cold-rolled and annealed polycrystalline copper (fcc) [41]. Actually, the preferential nucleation in the shear bands accompanied by a wide spread of orientations was observed in the present Ni3 Fe alloy. It is likely that such a preferential nucleation in the inhomogeneously deformed regions is related to the fast recrystallization observed in the initially ordered speci-
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men. There may be the other origin affecting the recrystallization texture. During the early stage of annealing, reordering and recover simultaneously occur in the cold-rolled ordered alloy, and result in nucleation of grains with unusual orientations, i.e., different from orientations formed by cold rolling. In the ordered structure, the migration of grain boundary is retarded because the grain boundary in the ordered lattices has to migrate, keeping or restoring atomic ordering. In fact, the grain sizes after recrystallization of the initially ordered alloy was small compared with those of the initially disordered alloy (Fig. 14). Also, it is unlikely that the preferential growth of the specified grains (such as a cube orientated grains) or the specific grain boundaries occurs in the ordered structure, e.g., as understood from the distributions of grain boundary character (see Fig. 14). Furthermore, it is possible that the annealing twining affects the recrystallization texture. If the multiple twinning occurs, recrystallization texture will be weak. Consequently, the weak recrystallization texture developed in the initially ordered alloy was suggested to be associated with the nucleation of randomly orientated grains and the non-selected grain growth. To furthermore clarify the formation mechanism for deformation and recrystallization textures of ordered alloys, more and atomistic studies on microstructural evolution during deformation and particularly the early stage of recrystallization will be required.
5. Conclusion (1) The 90% cold rolling texture of both the initially ordered and disordered Ni3 Fe alloys was basically a copper (pure-metal) type. However, the rolling texture of the initially ordered Ni3 Fe alloy, the Bs {0 1 1}2 1 1 component was enhanced in comparison with the C {1 1 2}1 1 1 and S {1 2 3}6 3 4 components. The intensity of the rolling texture was lower in the initially ordered alloy than in the initially disordered alloy. (2) After the recrystallization, cube {0 0 1}1 0 0 texture was formed, in both the initially ordered and the initially disordered alloys. However, the intensity of the recrystallization texture was much more reduced in the initially ordered alloy than in the initially disordered alloy. (3) During annealing of the cold-rolled specimen, the hardness showed a broad peak and then decreased rapidly with increasing temperature, regardless of ordered or disordered state before cold rolling. The rapid decease of the hardness due to the recrystallization occurred at lower temperature or faster in the initially ordered alloy than in the initially disordered alloy. (4) The intensity of the observed rolling texture was interpreted by considering the difficulty of the cross slip of superlattice dislocations and ordinary dislocations. Also, the weak recrystallization texture developed in the initially ordered alloy was suggested to be associated with the nucleation of randomly orientated grains and the non-selected grain growth.
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