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Crystallographic orientations of Ni3Al-based aluminide
Materials Characterization 45 (2000) 227 ± 231
Crystallographic orientations of Ni3Al-based aluminide Srdjan TadicÂ*, Slavica Zec, Milan T. Jovanovic Institute of Nuclear Sciences, VincÏa, PO Box 522, 11001 Belgrade, Yugoslavia Received 10 January 2000; received in revised form 16 June 2000; accepted 16 June 2000
Abstract Inverse pole figures have been plotted to determine preferred crystallographic orientations in a powdercompacted Ni3Al aluminide prealloyed with Fe, Ti and B. The main textural components, although weak, were noticeably altered by cold deformation, recrystallization and high-temperature deformation. Cold uniaxial compression generated a pronounced (110) orientation and the less common (112) orientation. The existence of the latter orientation was ascribed to the cubic ! tetragonal structural transformation (L12 ! DO22). The beginning of recrystallization was characterized by a string of (113) + (112) + (111) orientations. However, after prolonged periods of annealing, the (113) orientation diminished, whereas the (111) and (112) orientations became stronger, perhaps due to preferred orientational growth. Deformation at high-temperature gave rise to strong (111) and (100) + (112) orientations. It was found that disordering and dynamic recrystallization simultaneously control high-temperature deformation. D 2000 Elsevier Science Inc. All rights reserved.
1. Introduction In recent years, Ni3Al aluminides, which have an ordered L12 structure, attracted much attention because of their good tensile and compressive properties and excellent resistance to oxidation and carburization up to 1100°C. Because mechanical properties are affected by preferred crystallographic orientations, it is important to understand the factors that control texture development during thermomechanical treatments. However, with a few exceptions [1 ± 4], the texture properties of Ni3Al have not been widely investigated. Although the deformation texture was found to be of the abrass type, the recrystallization texture of Ni3Al was reported to be quite different from that of other face-centered-cubic (FCC) metals and alloys. In addition, Ball and Gottstein [2] reported that
* Corresponding author. E-mail address: [email protected] (S. TadicÂ).
the recrystallization textures were very weak compared with the deformation textures. This paper deals with the characterization of textures developed during compression of a Ni3Al-based intermetallic compound produced by a powder metallurgy technique. 2. Experimental procedures The master alloy had the nominal composition (wt.%) 12Al ± 6Fe ± 1.6Ti ± 0.1B ± balance Ni, and was produced by melting and casting in a vacuum induction furnace. The ingot, in the form of an electrode for the rotating electrode process (REP), was atomized by the REP with the angular velocity of 730 rad ÿ1 in a helium atmosphere. This produced a uniformly spherical powder with the average diameter of 360 mm. In the next step, the powder was compacted in a hot vacuum press at 1250°C and 35 MPa, yielding 98% of theoretical density and an average grain size of 50 mm.
1044-5803/00/$ ± see front matter D 2000 Elsevier Science Inc. All rights reserved. PII: S 1 0 4 4 - 5 8 0 3 ( 0 0 ) 0 0 0 8 3 - 8
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S. Tadic et al. / Materials Characterization 45 (2000) 227±231
Fig. 1. Weighing areas for the measured (hkl ) reflections according to Ref. [5].
Fig. 3. Inverse pole figure of room-temperature-compressed specimen. SD = 1.14.
Mechanically machined cylindrical specimens with dimensions 6 mm (diameter) and 12 mm (height) were subjected to uniaxial compression at a strain rate of 1.310 ÿ 3 s ÿ 1. The room temperature test was interrupted at a strain just prior to failure (e = ÿ 0.35), and followed by recrystallization annealing at 950°C for 30 min and for 4 h. In another experiment, a specimen was compressed to a strain e = ÿ 0.8 at 800°C in a vacuum of 110 ÿ 2 Pa. At the end of the compression phase, the specimen was rapidly cooled in a stream of argon to preserve the high-temperature structure. About one half of the length of the deformed specimen was removed by a low-speed diamond saw, and the surface polished and slightly etched. Inverse pole figures were used for texture determination. X-ray diffraction with Cu ± Ka radiation was used to determine intensities from (hkl ) reflections. Intensities were calculated as integrated areas under the peaks with background corrections of 2° apart. Primary (111), (200), (220), (113), (133) and superlattice (112), (120) reflections were used for
texture measurements. REP powder was used for normalization. The inverse pole figures were normalized following the method described in the literature [5]. This method depends on the weighting areas over the stereographic triangle with measured (hkl ) reflections (Fig. 1). The applied normalization, reported to be consistent with a series expansion method [5], suffers some disadvantages because it is limited to measured pole figures only. However, in anticipation of finding a weak texture, this normalization seemed to be quite appropriate because a series truncation error can be avoided [5]. The error associated with the applied procedure has been reported to be within 10% [1]. Inverse pole figures were gridded as a 5050 net applying a Kriging algorithm, but the interior area should be regarded as less reliable because all measured reflections are located around the figure. The dispersion of pole densities around the random level, i. e. the standard deviation (SD), is an indicator of the texture sharpness, similarly to the J index [5].
Fig. 2. Inverse pole figure of vacuum hot-presed specimen. SD = 1.13.
Fig. 4. Inverse pole figure of specimen annealed at 950°C for 0.5 h. SD = 1.16.
S. Tadic et al. / Materials Characterization 45 (2000) 227±231
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3. Results and discussion The inverse pole figures for the material in different conditions are given in Figs. 2 ± 6, with SD for each figure in the corresponding legend. Fig. 2 is the inverse pole figure of the vacuum hot-pressed specimen. Pole densities appear to be almost random. Weak, but distinct pole densities are concentrated at (111), (110) and (112). Such texture is comparable with the previously reported (111) fibre obtained by powder extrusion [1]. The addition of (110) and (112) in this work might be attributed to applied processing procedure, i.e. vacuum hot pressing. The inverse pole figure of the room temperature uniaxially compressed specimen is shown in Fig. 3. Pole densities still remain close to random. Despite the low texture sharpness, the main differences from Fig. 2 is a decrease in (111) but increases in (110) and (112). The increase in the (110) pole density was expected, that being the main component of the compression texture of FCC structures [6]. Such a behaviour is attributed to the (111)h110iactive slip system, which is common for FCC systems. In addition, the peak at (112) might be regarded as unexpected. It has been already reported that a structural transformation, from cubic L12 to tetragonal DO22, takes place during cold rolling of Ni3Al. As a consequence, (111) of L12 aligns with (112) of DO22 [3]. The (112) orientation persists after recrystallization annealing. Short time (0.5 h) recrystallization (Fig. 4) shows that together with (112), reflections (113) and (111) are relatively distinct, exhibiting the string running from (113) to (111). However, a large amount of randomness is retained in the matrix. According to earlier papers, the recrystallization texture of cold rolled sheet is characterized by a rotated cube orientation which, at a later stage,
Fig. 5. Inverse pole figure of specimen annealed at 950°C for 4 h. SD = 1.40.
Fig. 6. Inverse pole figure of specimen compressed at 800°C. SD = 1.193.
develops to (112)h113i [2], (110)h001i [3] or modest (112) + weak (100) [4]. During prolonged recrystallization annealing (Fig. 5), the intensity of the (113) orientation became weak, that of (111) showed a further increase, while minor augmentation occurred with (100) and (112). It should be pointed out that the texture sharpness after recrystallization (Fig. 5) is significantly higher than after cold deformation. This result is not in accordance with the previously reported weakening of recrystallization textures [2]. Such a behaviour might be ascribed to the effect of alloying elements (Fe and Ti) in changing the grain boundary mobility. The texture after high-temperature deformation is quite different from that after cold deformation (Fig. 6). The marked increase in the (111) pole density is accompanied by lower densities at the (100) and (113) orientations, while the (112) orientation has completely disappeared. Thus, the main components of the cold deformation texture, (110) and (112), were supplanted by a well-defined (111) and weak (100) + (113) orientations during the high-temperature deformation. The pole density distribution in Fig. 6 can be explained by taking into account several parameters such as: (i) disordering during deformation [7]; (ii) dynamic recrystallization [8]; (iii) activation of additional, nonoctahedral slip systems [9]; and (iv) formation of the B2 phase due to alloying with Fe [7]. Cold deformation induces disordering of L12 [7], therefore, it should be expected that the work hardening exponent of the stress ± strain curve, n = d(log s)/d(log e), will decrease [10]. Logarithmic plots of the stress ± strain curves for cold and high-temperature deformation are shown in Fig. 7. At the beginning of yielding, up to e = ÿ0.04, the flow stress during high-temperature deformation is slightly larger than that during cold deformation. However, at higher strains, the flow stress corresponding to the
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S. Tadic et al. / Materials Characterization 45 (2000) 227±231
Fig. 7. Logarithmic plot of stress ± strain curves for cold-deformed (CD) and high-temperature-deformed (HTD) specimen.
cold deformation curve becomes much the greater. It is obvious that the stress ± strain curves exhibit the so-called double-n behaviour. Of a particular interest for the current discussion is the second stage of hardening. During the high-temperature deformation, the n2 value, although relatively low, is definitely positive, implying that complete dynamic softening has not been reached. In addition, visible repeatable plateau in the first stage of hardening supports the idea of the existence of some critical strains for the onset of dynamic recrystallization on localized shear bands [2] and/or unpinning of cross-slipped partials [9]. On the other side, the decrease in n2 at the higher strains suggests that during the second stage of hardening disordering appears as one of the
parameters controlling deformation of Ni3Al-based aluminide. X-ray diffraction lines in Fig. 8 may be regarded as a confirmation of this consideration. Apart from the absence of the B2 phase, it may be seen that the integrated intensity ratio of (100)/ (200), or of (110)/(220), which is proportional to the long-range order parameter [11], is lowest during the high-temperature deformation. Cold deformation of nearly random texture orientations also lowers longrange order, but to a lesser extent, which may be attributed to the localized deformation. Taking into account these results, it is obvious that two mechanisms are involved in controlling hightemperature deformation, i.e. dynamic recrystallization and disordering. However, determining which of these mechanisms is dominant is not possible at present. 4. Conclusions
Fig. 8. X-ray diffraction lines of (a) vacuum hot-pressed, (b) cold-deformed, (c) recrystallized and (d) high-temperaturedeformed specimen.
The intensities of textural components of the Ni3Al-based aluminide are weak, but perceptible differences exist when recrystallization texture and the texture during high-temperature deformation are compared with cold deformation texture. The cold deformation texture is characterized by increased (110) and (112) pole densities, while during recrystallization, an increased rise of (111) orientation is accompanied with a minor rise of (100) and (112) orientations. In contrast to other literature data, the texture sharpness after recrystallization is significantly higher than after cold deformation, which is probably the result of the influence of Fe and Ti on grain boundary mobility.
S. Tadic et al. / Materials Characterization 45 (2000) 227±231
During high-temperature deformation, the main components were altered to (111) and (100) + (113) orientations. Dynamic recrystallization and disordering control the high-temperature deformation.
[3] [4]
Acknowledgments The authors are grateful to the Ministry of Science and Technology of the Republic of Serbia for the financial support of this work. Thanks are due to M. Mitkov, head of the research project, and D. Bozic and N.llic for material provision and compression tests. References [1] Khadkikar PS, Michal GM, Vedula K. Preferred orientations in extruded nickel and iron aluminides. Metall Trans A 1990;21:279 ± 88. [2] Ball J, Gottstein G. Deformation microstructure and evolution of recrystallization texture in nickel alumi-
[5] [6] [7] [8] [9] [10] [11]
231
nide (Ni3Al) + boron. Mater Sci Forum 1993;113 ± 115:569 ± 74. Chowdhury SG, Ray RK, Jena AK. Effect of ordering on the development of recrystallization texture in Ni76Al24(B). J Mater Sci Lett 1996;15:1710 ± 2. Lin H, Pope DP. Texture and grain boundary character distribution in recrystallized Ni3Al sheets. Scr Metall Mater 1994;30:1409 ± 12. Bunge HJ. Texture in Analysis in Materials Science. London: Butterworth, 1982. Barrett CS, Massalski TB. Structure of Metals. New York, NY: McGraw-Hill, 1966. Stoloff NS. Physical and mechanical metallurgy of Ni3Al and its alloys. Int Mater Rev 1989;34:153 ± 83. Baker I, Viens DV, Schulson EM. Metallographic observations of dynamic recrystallization on Ni3Al. Scr Metall 1984;18:237 ± 40. Paidar V, Pope DP, Vitek V. A theory of the anomalous yield behavior in L12 ordered alloys. Acta Metall 1984;32:435 ± 48. Smallman RE. Modern Physical Metallurgy. London: Butterworth, 1986. Chowdhury SG, Ray RK, Jena AK. Structural transformation in Ni3Al(B) due to cold rolling. Scr Metall Mater 1995;32:1501 ± 6.
Crystallographic orientations of Ni3Al-based aluminide Srdjan TadicÂ*, Slavica Zec, Milan T. Jovanovic Institute of Nuclear Sciences, VincÏa, PO Box 522, 11001 Belgrade, Yugoslavia Received 10 January 2000; received in revised form 16 June 2000; accepted 16 June 2000
Abstract Inverse pole figures have been plotted to determine preferred crystallographic orientations in a powdercompacted Ni3Al aluminide prealloyed with Fe, Ti and B. The main textural components, although weak, were noticeably altered by cold deformation, recrystallization and high-temperature deformation. Cold uniaxial compression generated a pronounced (110) orientation and the less common (112) orientation. The existence of the latter orientation was ascribed to the cubic ! tetragonal structural transformation (L12 ! DO22). The beginning of recrystallization was characterized by a string of (113) + (112) + (111) orientations. However, after prolonged periods of annealing, the (113) orientation diminished, whereas the (111) and (112) orientations became stronger, perhaps due to preferred orientational growth. Deformation at high-temperature gave rise to strong (111) and (100) + (112) orientations. It was found that disordering and dynamic recrystallization simultaneously control high-temperature deformation. D 2000 Elsevier Science Inc. All rights reserved.
1. Introduction In recent years, Ni3Al aluminides, which have an ordered L12 structure, attracted much attention because of their good tensile and compressive properties and excellent resistance to oxidation and carburization up to 1100°C. Because mechanical properties are affected by preferred crystallographic orientations, it is important to understand the factors that control texture development during thermomechanical treatments. However, with a few exceptions [1 ± 4], the texture properties of Ni3Al have not been widely investigated. Although the deformation texture was found to be of the abrass type, the recrystallization texture of Ni3Al was reported to be quite different from that of other face-centered-cubic (FCC) metals and alloys. In addition, Ball and Gottstein [2] reported that
* Corresponding author. E-mail address: [email protected] (S. TadicÂ).
the recrystallization textures were very weak compared with the deformation textures. This paper deals with the characterization of textures developed during compression of a Ni3Al-based intermetallic compound produced by a powder metallurgy technique. 2. Experimental procedures The master alloy had the nominal composition (wt.%) 12Al ± 6Fe ± 1.6Ti ± 0.1B ± balance Ni, and was produced by melting and casting in a vacuum induction furnace. The ingot, in the form of an electrode for the rotating electrode process (REP), was atomized by the REP with the angular velocity of 730 rad ÿ1 in a helium atmosphere. This produced a uniformly spherical powder with the average diameter of 360 mm. In the next step, the powder was compacted in a hot vacuum press at 1250°C and 35 MPa, yielding 98% of theoretical density and an average grain size of 50 mm.
1044-5803/00/$ ± see front matter D 2000 Elsevier Science Inc. All rights reserved. PII: S 1 0 4 4 - 5 8 0 3 ( 0 0 ) 0 0 0 8 3 - 8
228
S. Tadic et al. / Materials Characterization 45 (2000) 227±231
Fig. 1. Weighing areas for the measured (hkl ) reflections according to Ref. [5].
Fig. 3. Inverse pole figure of room-temperature-compressed specimen. SD = 1.14.
Mechanically machined cylindrical specimens with dimensions 6 mm (diameter) and 12 mm (height) were subjected to uniaxial compression at a strain rate of 1.310 ÿ 3 s ÿ 1. The room temperature test was interrupted at a strain just prior to failure (e = ÿ 0.35), and followed by recrystallization annealing at 950°C for 30 min and for 4 h. In another experiment, a specimen was compressed to a strain e = ÿ 0.8 at 800°C in a vacuum of 110 ÿ 2 Pa. At the end of the compression phase, the specimen was rapidly cooled in a stream of argon to preserve the high-temperature structure. About one half of the length of the deformed specimen was removed by a low-speed diamond saw, and the surface polished and slightly etched. Inverse pole figures were used for texture determination. X-ray diffraction with Cu ± Ka radiation was used to determine intensities from (hkl ) reflections. Intensities were calculated as integrated areas under the peaks with background corrections of 2° apart. Primary (111), (200), (220), (113), (133) and superlattice (112), (120) reflections were used for
texture measurements. REP powder was used for normalization. The inverse pole figures were normalized following the method described in the literature [5]. This method depends on the weighting areas over the stereographic triangle with measured (hkl ) reflections (Fig. 1). The applied normalization, reported to be consistent with a series expansion method [5], suffers some disadvantages because it is limited to measured pole figures only. However, in anticipation of finding a weak texture, this normalization seemed to be quite appropriate because a series truncation error can be avoided [5]. The error associated with the applied procedure has been reported to be within 10% [1]. Inverse pole figures were gridded as a 5050 net applying a Kriging algorithm, but the interior area should be regarded as less reliable because all measured reflections are located around the figure. The dispersion of pole densities around the random level, i. e. the standard deviation (SD), is an indicator of the texture sharpness, similarly to the J index [5].
Fig. 2. Inverse pole figure of vacuum hot-presed specimen. SD = 1.13.
Fig. 4. Inverse pole figure of specimen annealed at 950°C for 0.5 h. SD = 1.16.
S. Tadic et al. / Materials Characterization 45 (2000) 227±231
229
3. Results and discussion The inverse pole figures for the material in different conditions are given in Figs. 2 ± 6, with SD for each figure in the corresponding legend. Fig. 2 is the inverse pole figure of the vacuum hot-pressed specimen. Pole densities appear to be almost random. Weak, but distinct pole densities are concentrated at (111), (110) and (112). Such texture is comparable with the previously reported (111) fibre obtained by powder extrusion [1]. The addition of (110) and (112) in this work might be attributed to applied processing procedure, i.e. vacuum hot pressing. The inverse pole figure of the room temperature uniaxially compressed specimen is shown in Fig. 3. Pole densities still remain close to random. Despite the low texture sharpness, the main differences from Fig. 2 is a decrease in (111) but increases in (110) and (112). The increase in the (110) pole density was expected, that being the main component of the compression texture of FCC structures [6]. Such a behaviour is attributed to the (111)h110iactive slip system, which is common for FCC systems. In addition, the peak at (112) might be regarded as unexpected. It has been already reported that a structural transformation, from cubic L12 to tetragonal DO22, takes place during cold rolling of Ni3Al. As a consequence, (111) of L12 aligns with (112) of DO22 [3]. The (112) orientation persists after recrystallization annealing. Short time (0.5 h) recrystallization (Fig. 4) shows that together with (112), reflections (113) and (111) are relatively distinct, exhibiting the string running from (113) to (111). However, a large amount of randomness is retained in the matrix. According to earlier papers, the recrystallization texture of cold rolled sheet is characterized by a rotated cube orientation which, at a later stage,
Fig. 5. Inverse pole figure of specimen annealed at 950°C for 4 h. SD = 1.40.
Fig. 6. Inverse pole figure of specimen compressed at 800°C. SD = 1.193.
develops to (112)h113i [2], (110)h001i [3] or modest (112) + weak (100) [4]. During prolonged recrystallization annealing (Fig. 5), the intensity of the (113) orientation became weak, that of (111) showed a further increase, while minor augmentation occurred with (100) and (112). It should be pointed out that the texture sharpness after recrystallization (Fig. 5) is significantly higher than after cold deformation. This result is not in accordance with the previously reported weakening of recrystallization textures [2]. Such a behaviour might be ascribed to the effect of alloying elements (Fe and Ti) in changing the grain boundary mobility. The texture after high-temperature deformation is quite different from that after cold deformation (Fig. 6). The marked increase in the (111) pole density is accompanied by lower densities at the (100) and (113) orientations, while the (112) orientation has completely disappeared. Thus, the main components of the cold deformation texture, (110) and (112), were supplanted by a well-defined (111) and weak (100) + (113) orientations during the high-temperature deformation. The pole density distribution in Fig. 6 can be explained by taking into account several parameters such as: (i) disordering during deformation [7]; (ii) dynamic recrystallization [8]; (iii) activation of additional, nonoctahedral slip systems [9]; and (iv) formation of the B2 phase due to alloying with Fe [7]. Cold deformation induces disordering of L12 [7], therefore, it should be expected that the work hardening exponent of the stress ± strain curve, n = d(log s)/d(log e), will decrease [10]. Logarithmic plots of the stress ± strain curves for cold and high-temperature deformation are shown in Fig. 7. At the beginning of yielding, up to e = ÿ0.04, the flow stress during high-temperature deformation is slightly larger than that during cold deformation. However, at higher strains, the flow stress corresponding to the
230
S. Tadic et al. / Materials Characterization 45 (2000) 227±231
Fig. 7. Logarithmic plot of stress ± strain curves for cold-deformed (CD) and high-temperature-deformed (HTD) specimen.
cold deformation curve becomes much the greater. It is obvious that the stress ± strain curves exhibit the so-called double-n behaviour. Of a particular interest for the current discussion is the second stage of hardening. During the high-temperature deformation, the n2 value, although relatively low, is definitely positive, implying that complete dynamic softening has not been reached. In addition, visible repeatable plateau in the first stage of hardening supports the idea of the existence of some critical strains for the onset of dynamic recrystallization on localized shear bands [2] and/or unpinning of cross-slipped partials [9]. On the other side, the decrease in n2 at the higher strains suggests that during the second stage of hardening disordering appears as one of the
parameters controlling deformation of Ni3Al-based aluminide. X-ray diffraction lines in Fig. 8 may be regarded as a confirmation of this consideration. Apart from the absence of the B2 phase, it may be seen that the integrated intensity ratio of (100)/ (200), or of (110)/(220), which is proportional to the long-range order parameter [11], is lowest during the high-temperature deformation. Cold deformation of nearly random texture orientations also lowers longrange order, but to a lesser extent, which may be attributed to the localized deformation. Taking into account these results, it is obvious that two mechanisms are involved in controlling hightemperature deformation, i.e. dynamic recrystallization and disordering. However, determining which of these mechanisms is dominant is not possible at present. 4. Conclusions
Fig. 8. X-ray diffraction lines of (a) vacuum hot-pressed, (b) cold-deformed, (c) recrystallized and (d) high-temperaturedeformed specimen.
The intensities of textural components of the Ni3Al-based aluminide are weak, but perceptible differences exist when recrystallization texture and the texture during high-temperature deformation are compared with cold deformation texture. The cold deformation texture is characterized by increased (110) and (112) pole densities, while during recrystallization, an increased rise of (111) orientation is accompanied with a minor rise of (100) and (112) orientations. In contrast to other literature data, the texture sharpness after recrystallization is significantly higher than after cold deformation, which is probably the result of the influence of Fe and Ti on grain boundary mobility.
S. Tadic et al. / Materials Characterization 45 (2000) 227±231
During high-temperature deformation, the main components were altered to (111) and (100) + (113) orientations. Dynamic recrystallization and disordering control the high-temperature deformation.
[3] [4]
Acknowledgments The authors are grateful to the Ministry of Science and Technology of the Republic of Serbia for the financial support of this work. Thanks are due to M. Mitkov, head of the research project, and D. Bozic and N.llic for material provision and compression tests. References [1] Khadkikar PS, Michal GM, Vedula K. Preferred orientations in extruded nickel and iron aluminides. Metall Trans A 1990;21:279 ± 88. [2] Ball J, Gottstein G. Deformation microstructure and evolution of recrystallization texture in nickel alumi-
[5] [6] [7] [8] [9] [10] [11]
231
nide (Ni3Al) + boron. Mater Sci Forum 1993;113 ± 115:569 ± 74. Chowdhury SG, Ray RK, Jena AK. Effect of ordering on the development of recrystallization texture in Ni76Al24(B). J Mater Sci Lett 1996;15:1710 ± 2. Lin H, Pope DP. Texture and grain boundary character distribution in recrystallized Ni3Al sheets. Scr Metall Mater 1994;30:1409 ± 12. Bunge HJ. Texture in Analysis in Materials Science. London: Butterworth, 1982. Barrett CS, Massalski TB. Structure of Metals. New York, NY: McGraw-Hill, 1966. Stoloff NS. Physical and mechanical metallurgy of Ni3Al and its alloys. Int Mater Rev 1989;34:153 ± 83. Baker I, Viens DV, Schulson EM. Metallographic observations of dynamic recrystallization on Ni3Al. Scr Metall 1984;18:237 ± 40. Paidar V, Pope DP, Vitek V. A theory of the anomalous yield behavior in L12 ordered alloys. Acta Metall 1984;32:435 ± 48. Smallman RE. Modern Physical Metallurgy. London: Butterworth, 1986. Chowdhury SG, Ray RK, Jena AK. Structural transformation in Ni3Al(B) due to cold rolling. Scr Metall Mater 1995;32:1501 ± 6.