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Correlation between grain boundary misorientation and the discontinuous precipitation reaction in Mg–10 wt.% Al alloy
Materials Chemistry and Physics 78 (2002) 222–226
Correlation between grain boundary misorientation and the discontinuous precipitation reaction in Mg–10 wt.% Al alloy D. Bradai a , P. Zi˛eba b,∗ , E. Bischoff c , W. Gust c b
a Institut de Physique, USTHB, BP 32 El-Alia, Bab-Ezzouar, Alger, Algeria Institute of Metallurgy and Materials Science, Polish Academy of Sciences, Reymonta Street 25, 30-059 Cracow, Poland c Max-Planck-Institut für Metallforschung and Institut für Metallkunde, Heisenbergstr. 3, D-70569 Stuttgart, Germany
Received 22 January 2002; received in revised form 5 May 2002; accepted 6 June 2002
Abstract The correlation between the geometry of the grain boundaries (GBs) and the kinetics of the discontinuous precipitation (DP) reaction in a Mg–10 wt.% Al alloy has been studied. The GBs were categorized as special or random by using the electron back-scattered diffraction (EBSD) technique and theoretical tables of the coincidence site lattice. The analysis showed convincingly the absence of low-angle GBs and no distinguished maximum on the GB misorientation angle distribution in this hexagonal system. The DP cells appeared predominantly at nonspecial (random) orientations, confirming that the initiation and growth of the reaction products occur at high-angle GBs. Generally, some orientations which are inactive after 20 min became active after 40 min of ageing at 500 K. For each rotation axis, there were several misorientation angles (no special ones) for which a maximum growth distance of DP reaction was observed. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Discontinuous precipitation; Electron back-scattered diffraction; Mg–Al alloys; Coincidence site lattice; Grain boundary geometry
1. Introduction The discontinuous precipitation (DP) reaction has been examined in many binary metallic systems through different experimental procedures and always attempts have been made to use new techniques to study the influence of various factors on the morphology and kinetics of the reaction. One important factor is the misorientation of neighboring grains when the geometry and the crystallographic nature of the interface are evoked. Several studies have shown that the properties of grain boundaries (GBs) varied with their crystallographic nature and structure (see, for example, Ref. [1]). Thus, the main interest is to know how great the influence of geometry is on the occurrence of the DP reaction. The influence of the type of GB on the discontinuous dissolution reaction, which is the reverse reaction of the DP reaction, has been studied in the Ni–In system [2]. The misorientation parameters of 17 GBs were determined using a Laue X-ray diffraction technique. A strong dependence of the kinetics of the discontinuous dissolution reaction on the GB type was found when the GBs were categorized as ∗ Corresponding author. Fax: +48-12-637-2192. E-mail address: [email protected] (P. Zi˛eba).
special ones. It was also shown that the Brandon coincidence criterion [3] plays only a small role. Recently, Semenov et al. [4] have established a relation between the GB geometry and the kinetics of the discontinuous ordering reaction which microstructurally resembles the DP reaction but provides more fundamental informations about the GB properties. They used the results from precise measurements of the local lattice orientation facilitated by orientation imaging microscopy. The misorientation relationships between the individual grains were determined by scanning electron microscopy (SEM) with the help of an automated electron back-scattered diffraction (EBSD) technique. The obtained results indicated clearly a strong dependence of the progress of the discontinuous ordering reaction on the GB geometry. Semenov et al. [4] also identified a good proportion of closest special misorientations within the number of GBs studied with respect to the Brandon criterion. The misorientation effect on the occurrence of DP and the morphology changes were also investigated in a FeCrNi austenitic steel through EBSD and convergent beam electron diffraction analysis [5]. Twenty-five GB misorientations were determined, and it was shown that the cellular colonies grow faster and a better organized two-phase lamellar structure develops as the GB misorientation increases.
0254-0584/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 0 2 ) 0 0 2 2 7 - 4
D. Bradai et al. / Materials Chemistry and Physics 78 (2002) 222–226
223
More recently, Hirth and Gottstein [6] have studied the misorientation effect on DP in a ternary Al–Ag–Ga alloy. Microstructure measurements carried out using the EBSD technique have allowed to determine around 300 misorientation relationships between grains undergoing DP reaction. In the present paper, the same automated EBSD technique in a scanning electron microscope was used to study the effect of the GB geometry on the DP reaction in a supersaturated Mg–10 wt.% Al solid solution. For the first time, the EBSD technique was applied to a noncubic crystal to reveal the link between the growth of the DP colonies and the geometry (misorientation) of the original GBs.
2. Experimental The Mg–10 wt.% Al alloy was prepared by vacuuminduction melting of Mg and Al of high purity (99.95 wt.%) and casting in an 11 mm diameter rod. It was then homogenized at 703 K for 48 days in an evacuated glass capsule and water-quenched. Samples of 6 mm thickness were cut-off from the rod by spark erosion and a final homogenization was applied at 703 K for 48 h followed by water-quenching. The resulting grain size was about 200 m. For the study of the DP reaction kinetics and the EBSD analysis the samples were aged at 500 K for 20 and 40 min and the regions containing a great density of GBs were chosen for the SEM and EBSD analyses in both samples. A standard metallographic technique was used for the sample preparation, including wet grinding, pre-polishing and “Minimet” polishing with 1 and 6 m diamond paste using a nylon polishing cloth. Prior to the light microscopy (LM) and SEM observations, the samples were etched with 3% nitric acid in ethanol. For the EBSD analysis the samples were electropolished with a standard mixture for Mg alloys in an automated apparatus to ensure that no surface deformation remains.
Fig. 1. Morphology of the DP cells. Mg–10 wt.% Al annealed at 500 K for 20 min (LM).
the measurement of the widths of 60 randomly chosen cells after several ageing times. The measured values were averaged and normalized by using the factor π /4 according to the method proposed by Lück [8]. Then from the slope of the relationship cell width vs. ageing time the average growth rate was extracted. In the present case, such a procedure could not be applied and the measurements were done separately after ageing at 500 K for 20 and 40 min, which obviously introduced some uncertainty. Most of the cells belong to the so-called single-seam morphology [9]. This means that the growth of the DP product occurs only on one side of the original GB [9]. The aging temperature of 500 K is in the vicinity of the C-curve nose determined for this alloy where the single-seam type of growth prevails. On the other hand, Duly et al. [10] reported that the nucleation rate of solute-rich lamellae in
3. Results and discussion As observed in a previous work [7], isothermal aging of Mg–10 wt.% Al alloy at 500 K produces a typical DP reaction microstructure characterized by the presence of multiple cells, spreading out from the original GB positions towards the adjacent grain areas (Fig. 1). At higher magnification the cells show a lamellar mixture of depleted (Mg) solid solution and intermetallic Al12 Mg17 compound (Fig. 2). The zone studied in the first sample is shown in Fig. 3. The average velocity was found to be around 40–50 nm s−1 irrespective of the ageing time. This is a different value than 14 nm s−1 determined in studies of the DP reaction in the Mg–Al system by optical metallography [7]. This discrepancy is associated with the various procedures applied for the growth rate determination in both cases. Bradai et al. [7] used a quantitative metallography technique for
Fig. 2. Lamellar structure within a DP cell Mg–10 wt.% Al annealed at 500 K for 40 min: RF, reaction front; α 0 , supersaturated solid solution (SEM).
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Fig. 5. Histogram of the measured misorientation angle distribution for Mg–10 wt.% Al annealed at 500 K for 20 and 40 min.
Fig. 3. Microstructure of Mg–10 wt.% Al annealed at 500 K for 20 min. CSL boundaries 1–3 (Table 1) are marked (LM).
Mg–Al alloys is likely to be inversely proportional to the square of the initial average grain size. This indicates that the initiation mechanism of the DP reaction at 500 K is probably that proposed by Fournelle and Clark [11] because the pinning effect and the bowing out of the GB between
GB allotriomorphs are clearly seen (Fig. 4). Without detailed studies in a transmission electron microscope it is difficult to explain why some GB allotriomorphs convert into lamellae and why they remain stable in other alloys. The EBSD measurement of the misorientation parameters was performed for 97 and 115 GBs after ageing at 500 K for 20 and 40 min, respectively (Table 1). What can be immediately noticed is the complete absence of low-angle GBs contrary to the observations in cubic systems [4–6]. The lowest misorientation angle detected is 18.5 which is 3◦ higher than the low-angle limit established by Randle [12]. The histogram of the misorientation angles is presented in Fig. 5. It is obvious that there is no definitive tendency
Fig. 4. Early stage of the DP reaction in Mg–10 wt.% Al annealed at 500 K for 20 min. The bowing out of the GB between two allotriomorphs is clearly seen (LM).
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Table 1 Results of EBSD data, migrating reaction front velocity, closest special CSL misorientation and deviation from it for Mg–10 wt.% Al alloy annealed at 500 K for 20 min (sample 1) and 40 min (sample 2) Grain boundary
Velocity (nm s−1 )
EBSD data (◦ )
(u v i w)
21 28.1 32.7 20.2 23.6
(0 0 0 1) ¯ (0 0 0 1) (0 0 0 1) (0 0 0 1) ¯ (0 0 0 1)
θ 1 2 3 4 5
27 37 0 9 20
Closest CSL misorientation Σ
θ
(◦ )
(u v i w)
7 13 13 7 7
21.8 27.8 27.8 21.8 21.8
(0 0 0 1) ¯ (0 0 0 1) (0 0 0 1) (0 0 0 1) ¯ (0 0 0 1)
toward the existence of a maximum in the GB distribution but the GBs are more or less regularly distributed between 40◦ and 80◦ . This is not in contradiction with the predicted values of the CSL misorientation in hexagonal systems where the major part (70%) of the misorientation angles are higher than 40◦ . For a comparison Hirth and Gottstein [6] found in the Al–Ag–Ga system a maximum of the misorientations in the angular range between 25◦ and 40◦ with a maximum at 32◦ . The relative frequency of misorientations with rotation angles below 20◦ and above 85◦ is 1%. In particular, low-angle GBs did not undergo the DP reaction. Referring to the occurrence of the DP reaction one can note that the shorter time of ageing resulted in only 37 GBs covered with slabs of the DP reaction while an ageing of 40 min led to 105 GBs with the DP reaction. The misorientations (1 0 1), (1 1 0), (1 1 1), (2 3 2), (3 3 1) and with higher indexes like (4 4 1), (5 5 1) and more were generally inactive after 20 min of ageing. After 40 min of ageing only 10 GBs, among the 115 investigated GBs, were not covered with DP products. Further, all the misorientations promoted the DP reaction. Fig. 6 shows the transition from inactive to active behavior of the GBs for the 1 1 0 and 3 3 1 rotation axes. On the other hand, several maxima were found on the graph showing the relationship between the DP zone width and misorientation angle, providing that a sufficient number of data was collected. An example is presented in Fig. 7 for the 2 2 1 rotation axis. Three maxima can be distinguished which are located for the same misorientation angles regardless of the time of ageing. These maxima can be interpreted in terms of the highest velocity of the reaction front of the DP. Unfortunately, it is not possible to say something about the role of special misorientations because they do not appear for the 2 2 1 rotation axis. The grain boundary categorization was done by comparing the results given by EBSD analysis and those provided by theoretical prediction for hexagonal materials [13–19]. The angular deviation from the exact coincidence was calculated using the mathematical methods described by Randle [12] and compared, for each GB, with the commonly accepted Brandon criterion given by θm = 15◦ Σ 0.5 where 1/Σ is the coincidence site density in volume.
Deviation θ (◦ )
Ageing time (min)
0.8 0.3 4.0 1.3 1.8
20 20 20 40 40
Fig. 6. Relationship between the DP zone width and the misorientation angle for 1 1 0 (a) and 3 3 1 (b) rotation axes. Mg–10 wt.% Al annealed at 500 K for 20 and 40 min.
Fig. 7. Relationship between the DP zone width and the misorientation angle for the 2 2 1 rotation axis. Mg–10 wt.% Al annealed at 500 K for 20 and 40 min.
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Boundaries which have special properties have been found to have the following combination of Σ values and (h k i l) planes: 7(0 0 0 1) and 13(0 0 0 1). Only five GBs have a special CSL description which corresponds to a relative proportion of 2% of all the GBs studied. However, most of the special misorientations are totally absent including (1 0 1¯ 0) and (2 1 3¯ 0) where according to the theoretical prediction [13], the special GBs appeared very frequently. The small number of CSL grain boundaries do not allow any ultimate conclusion, but it is worth to note that the DP reaction occurred at four GBs out of five CSL boundaries. The small number of CSL boundaries is in agreement with previous theoretical predictions on the occurrence of CSL GBs in hexagonal materials [13–19]. According to Warrington [13] not more than 10% of the number of CSL GBs in cubic materials is predicted to be found in hexagonal materials. In grain-specific texture measurements in the Ni-based superalloy, Randle and Ralph [20] found in samples, aged and overaged, a proportion of the CSL boundaries (for Σ ≤ 49) equal to 27 and 47% of the whole GB population, respectively. For the discontinuous ordering reaction in an Fe–Co alloy this number was approximately 50% [4]. On the contrary, Hirth and Gottstein [6] found that the fraction of low-Σ coincidence GBs (special boundaries with Σ ≤ 29) was only 8%. The c/a ratio of the lattice parameters a and c introduces an irrational factor which considerably limits the dimension and the number of ideal CSL GBs [21]. It is also noticed that contrary to cubic materials, both odd and even values of Σ are possible to provide an odd a parameter [13]. The GBs with large Σ values (above 30) were not found. A different observation was also reported by Antonopoulos et al. [22] concerning the study of GBs in annealed zirconium. They found boundaries with Σ = 49 and 67. Moreover, Antonopoulos et al. [22] detected a high number of GBs with coincidence orientations in tungsten carbide/cobalt composites. The material preparation by liquid sintering develops low-energy facets (1 0 1¯ 0) and (0 0 0 1) in the tungsten carbide grains and a good proportion of tungsten carbide GBs parallel to these two planes of the highest density.
4. Conclusions 1. The electron back-scattered diffraction analysis of the GBs in Mg–10 wt.% Al alloy showed the absence of lowangle GBs and no distinguished maximum on the GB misorientation angle distribution in this hexagonal system.
2. The DP cells appeared predominantly at nonspecial (random) orientations, confirming that the initiation and growth of the reaction products occurs at high-angle GBs. 3. Some misorientations like (1 0 1), (1 1 0), (1 1 1) and especially with higher indexes (four and more) required a longer time of incubation to form DP cells but after 40 min of ageing almost all the GBs were covered with the slabs of discontinuous precipitates. 4. For each rotation axis, there are several misorientation angles (no special ones) for which a maximum growth distance of the DP reaction is observed. References [1] A.P. Sutton, V. Vitek, Phil. Trans. R. Soc. London A, Ser. A 309 (1983) 1. [2] T.H. Chuang, Ph.D. Thesis, University of Stuttgart, 1983, p. 153. [3] D.G. Brandon, Acta Metall. 14 (1966) 1479. [4] V. Semenov, E. Rabkin, E. Bischoff, W. Gust, Acta Mater. 46 (1998) 2289. [5] S. Matsuoka, M.A. Mangan, G.J. Shiflet, in: W.C. Johnson, J.W. Howe, D.E. Laughlin, W.A. Soffa (Eds.), Proceedings of the International Conference on Solid–Solid Phase Transformations, The Minerals, Metals and Materials Society, Warrendale, PA, 1994, p. 521. [6] S. Hirth, G. Gottstein, Acta Mater. 26 (1998) 3975. [7] D. Bradai, M. Kadi-Hanifi, P. Zi˛eba, W.M. Kuschke, W. Gust, J. Mater. Sci. 84 (1999) 5331. [8] K. Lück, Z. Metallkd. 59 (1968) 814. [9] W. Gust, T.H. Chuang, B. Predel, in: P. Haasen, et al. (Eds.), Decomposition of Alloys: The Early Stages, Pergamon Press, Oxford, 1984, p. 208. [10] D. Duly, Y. Brechet, B. Chenal, Acta Metall. Mater. 40 (1992) 2289. [11] R.A. Fournelle, J.B. Clark, Metall. Trans. 3 (1972) 2757. [12] V. Randle, in: B. Cantor, M.J. Goringe (Eds.), The Measurement of Grain Boundary Geometry, Institute of Physics Publishing, Bristol, 1993, p. 104. [13] D.H. Warrington, J. Phys. 36 (1975) 87. [14] M.A. Fortes, D.A. Smith, Scripta Metall. 10 (1976) 575. [15] R. Bonnet, E. Cousineau, D.H. Warrington, Acta Cryst. A 37 (1981) 184. [16] S. Hagege, G. Nouet, P. Delavignette, Phys. Stat. Sol. (a) 61 (1980) 97. [17] G.L. Bleris, G. Nouet, S. Hagege, P. Delavignette, Acta Cryst. A 38 (1982) 550. [18] P. Delavignette, J. Phys. 43 (1982) 1. [19] H. Grimmer, D.H. Warrington, Z. Krist. 162 (1983) 88. [20] V. Randle, B. Ralph, Textures Microstruct. 8/9 (1988) 531. [21] S. Hagege, P. Ayed, J. Vicens, J.L. Chermant, G. Nouet, Trans. Jpn. Inst. Met. Suppl. 27 (1986) 163. [22] J.G. Antonopoulos, P. Delavignette, Th. Karakostas, Ph. Kominou, E. Laurent-Pinson, S. Lay, G. Nouet, J. Vicens, Colloid Phys. C1 51 (1990) 61.
Correlation between grain boundary misorientation and the discontinuous precipitation reaction in Mg–10 wt.% Al alloy D. Bradai a , P. Zi˛eba b,∗ , E. Bischoff c , W. Gust c b
a Institut de Physique, USTHB, BP 32 El-Alia, Bab-Ezzouar, Alger, Algeria Institute of Metallurgy and Materials Science, Polish Academy of Sciences, Reymonta Street 25, 30-059 Cracow, Poland c Max-Planck-Institut für Metallforschung and Institut für Metallkunde, Heisenbergstr. 3, D-70569 Stuttgart, Germany
Received 22 January 2002; received in revised form 5 May 2002; accepted 6 June 2002
Abstract The correlation between the geometry of the grain boundaries (GBs) and the kinetics of the discontinuous precipitation (DP) reaction in a Mg–10 wt.% Al alloy has been studied. The GBs were categorized as special or random by using the electron back-scattered diffraction (EBSD) technique and theoretical tables of the coincidence site lattice. The analysis showed convincingly the absence of low-angle GBs and no distinguished maximum on the GB misorientation angle distribution in this hexagonal system. The DP cells appeared predominantly at nonspecial (random) orientations, confirming that the initiation and growth of the reaction products occur at high-angle GBs. Generally, some orientations which are inactive after 20 min became active after 40 min of ageing at 500 K. For each rotation axis, there were several misorientation angles (no special ones) for which a maximum growth distance of DP reaction was observed. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Discontinuous precipitation; Electron back-scattered diffraction; Mg–Al alloys; Coincidence site lattice; Grain boundary geometry
1. Introduction The discontinuous precipitation (DP) reaction has been examined in many binary metallic systems through different experimental procedures and always attempts have been made to use new techniques to study the influence of various factors on the morphology and kinetics of the reaction. One important factor is the misorientation of neighboring grains when the geometry and the crystallographic nature of the interface are evoked. Several studies have shown that the properties of grain boundaries (GBs) varied with their crystallographic nature and structure (see, for example, Ref. [1]). Thus, the main interest is to know how great the influence of geometry is on the occurrence of the DP reaction. The influence of the type of GB on the discontinuous dissolution reaction, which is the reverse reaction of the DP reaction, has been studied in the Ni–In system [2]. The misorientation parameters of 17 GBs were determined using a Laue X-ray diffraction technique. A strong dependence of the kinetics of the discontinuous dissolution reaction on the GB type was found when the GBs were categorized as ∗ Corresponding author. Fax: +48-12-637-2192. E-mail address: [email protected] (P. Zi˛eba).
special ones. It was also shown that the Brandon coincidence criterion [3] plays only a small role. Recently, Semenov et al. [4] have established a relation between the GB geometry and the kinetics of the discontinuous ordering reaction which microstructurally resembles the DP reaction but provides more fundamental informations about the GB properties. They used the results from precise measurements of the local lattice orientation facilitated by orientation imaging microscopy. The misorientation relationships between the individual grains were determined by scanning electron microscopy (SEM) with the help of an automated electron back-scattered diffraction (EBSD) technique. The obtained results indicated clearly a strong dependence of the progress of the discontinuous ordering reaction on the GB geometry. Semenov et al. [4] also identified a good proportion of closest special misorientations within the number of GBs studied with respect to the Brandon criterion. The misorientation effect on the occurrence of DP and the morphology changes were also investigated in a FeCrNi austenitic steel through EBSD and convergent beam electron diffraction analysis [5]. Twenty-five GB misorientations were determined, and it was shown that the cellular colonies grow faster and a better organized two-phase lamellar structure develops as the GB misorientation increases.
0254-0584/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 0 2 ) 0 0 2 2 7 - 4
D. Bradai et al. / Materials Chemistry and Physics 78 (2002) 222–226
223
More recently, Hirth and Gottstein [6] have studied the misorientation effect on DP in a ternary Al–Ag–Ga alloy. Microstructure measurements carried out using the EBSD technique have allowed to determine around 300 misorientation relationships between grains undergoing DP reaction. In the present paper, the same automated EBSD technique in a scanning electron microscope was used to study the effect of the GB geometry on the DP reaction in a supersaturated Mg–10 wt.% Al solid solution. For the first time, the EBSD technique was applied to a noncubic crystal to reveal the link between the growth of the DP colonies and the geometry (misorientation) of the original GBs.
2. Experimental The Mg–10 wt.% Al alloy was prepared by vacuuminduction melting of Mg and Al of high purity (99.95 wt.%) and casting in an 11 mm diameter rod. It was then homogenized at 703 K for 48 days in an evacuated glass capsule and water-quenched. Samples of 6 mm thickness were cut-off from the rod by spark erosion and a final homogenization was applied at 703 K for 48 h followed by water-quenching. The resulting grain size was about 200 m. For the study of the DP reaction kinetics and the EBSD analysis the samples were aged at 500 K for 20 and 40 min and the regions containing a great density of GBs were chosen for the SEM and EBSD analyses in both samples. A standard metallographic technique was used for the sample preparation, including wet grinding, pre-polishing and “Minimet” polishing with 1 and 6 m diamond paste using a nylon polishing cloth. Prior to the light microscopy (LM) and SEM observations, the samples were etched with 3% nitric acid in ethanol. For the EBSD analysis the samples were electropolished with a standard mixture for Mg alloys in an automated apparatus to ensure that no surface deformation remains.
Fig. 1. Morphology of the DP cells. Mg–10 wt.% Al annealed at 500 K for 20 min (LM).
the measurement of the widths of 60 randomly chosen cells after several ageing times. The measured values were averaged and normalized by using the factor π /4 according to the method proposed by Lück [8]. Then from the slope of the relationship cell width vs. ageing time the average growth rate was extracted. In the present case, such a procedure could not be applied and the measurements were done separately after ageing at 500 K for 20 and 40 min, which obviously introduced some uncertainty. Most of the cells belong to the so-called single-seam morphology [9]. This means that the growth of the DP product occurs only on one side of the original GB [9]. The aging temperature of 500 K is in the vicinity of the C-curve nose determined for this alloy where the single-seam type of growth prevails. On the other hand, Duly et al. [10] reported that the nucleation rate of solute-rich lamellae in
3. Results and discussion As observed in a previous work [7], isothermal aging of Mg–10 wt.% Al alloy at 500 K produces a typical DP reaction microstructure characterized by the presence of multiple cells, spreading out from the original GB positions towards the adjacent grain areas (Fig. 1). At higher magnification the cells show a lamellar mixture of depleted (Mg) solid solution and intermetallic Al12 Mg17 compound (Fig. 2). The zone studied in the first sample is shown in Fig. 3. The average velocity was found to be around 40–50 nm s−1 irrespective of the ageing time. This is a different value than 14 nm s−1 determined in studies of the DP reaction in the Mg–Al system by optical metallography [7]. This discrepancy is associated with the various procedures applied for the growth rate determination in both cases. Bradai et al. [7] used a quantitative metallography technique for
Fig. 2. Lamellar structure within a DP cell Mg–10 wt.% Al annealed at 500 K for 40 min: RF, reaction front; α 0 , supersaturated solid solution (SEM).
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Fig. 5. Histogram of the measured misorientation angle distribution for Mg–10 wt.% Al annealed at 500 K for 20 and 40 min.
Fig. 3. Microstructure of Mg–10 wt.% Al annealed at 500 K for 20 min. CSL boundaries 1–3 (Table 1) are marked (LM).
Mg–Al alloys is likely to be inversely proportional to the square of the initial average grain size. This indicates that the initiation mechanism of the DP reaction at 500 K is probably that proposed by Fournelle and Clark [11] because the pinning effect and the bowing out of the GB between
GB allotriomorphs are clearly seen (Fig. 4). Without detailed studies in a transmission electron microscope it is difficult to explain why some GB allotriomorphs convert into lamellae and why they remain stable in other alloys. The EBSD measurement of the misorientation parameters was performed for 97 and 115 GBs after ageing at 500 K for 20 and 40 min, respectively (Table 1). What can be immediately noticed is the complete absence of low-angle GBs contrary to the observations in cubic systems [4–6]. The lowest misorientation angle detected is 18.5 which is 3◦ higher than the low-angle limit established by Randle [12]. The histogram of the misorientation angles is presented in Fig. 5. It is obvious that there is no definitive tendency
Fig. 4. Early stage of the DP reaction in Mg–10 wt.% Al annealed at 500 K for 20 min. The bowing out of the GB between two allotriomorphs is clearly seen (LM).
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Table 1 Results of EBSD data, migrating reaction front velocity, closest special CSL misorientation and deviation from it for Mg–10 wt.% Al alloy annealed at 500 K for 20 min (sample 1) and 40 min (sample 2) Grain boundary
Velocity (nm s−1 )
EBSD data (◦ )
(u v i w)
21 28.1 32.7 20.2 23.6
(0 0 0 1) ¯ (0 0 0 1) (0 0 0 1) (0 0 0 1) ¯ (0 0 0 1)
θ 1 2 3 4 5
27 37 0 9 20
Closest CSL misorientation Σ
θ
(◦ )
(u v i w)
7 13 13 7 7
21.8 27.8 27.8 21.8 21.8
(0 0 0 1) ¯ (0 0 0 1) (0 0 0 1) (0 0 0 1) ¯ (0 0 0 1)
toward the existence of a maximum in the GB distribution but the GBs are more or less regularly distributed between 40◦ and 80◦ . This is not in contradiction with the predicted values of the CSL misorientation in hexagonal systems where the major part (70%) of the misorientation angles are higher than 40◦ . For a comparison Hirth and Gottstein [6] found in the Al–Ag–Ga system a maximum of the misorientations in the angular range between 25◦ and 40◦ with a maximum at 32◦ . The relative frequency of misorientations with rotation angles below 20◦ and above 85◦ is 1%. In particular, low-angle GBs did not undergo the DP reaction. Referring to the occurrence of the DP reaction one can note that the shorter time of ageing resulted in only 37 GBs covered with slabs of the DP reaction while an ageing of 40 min led to 105 GBs with the DP reaction. The misorientations (1 0 1), (1 1 0), (1 1 1), (2 3 2), (3 3 1) and with higher indexes like (4 4 1), (5 5 1) and more were generally inactive after 20 min of ageing. After 40 min of ageing only 10 GBs, among the 115 investigated GBs, were not covered with DP products. Further, all the misorientations promoted the DP reaction. Fig. 6 shows the transition from inactive to active behavior of the GBs for the 1 1 0 and 3 3 1 rotation axes. On the other hand, several maxima were found on the graph showing the relationship between the DP zone width and misorientation angle, providing that a sufficient number of data was collected. An example is presented in Fig. 7 for the 2 2 1 rotation axis. Three maxima can be distinguished which are located for the same misorientation angles regardless of the time of ageing. These maxima can be interpreted in terms of the highest velocity of the reaction front of the DP. Unfortunately, it is not possible to say something about the role of special misorientations because they do not appear for the 2 2 1 rotation axis. The grain boundary categorization was done by comparing the results given by EBSD analysis and those provided by theoretical prediction for hexagonal materials [13–19]. The angular deviation from the exact coincidence was calculated using the mathematical methods described by Randle [12] and compared, for each GB, with the commonly accepted Brandon criterion given by θm = 15◦ Σ 0.5 where 1/Σ is the coincidence site density in volume.
Deviation θ (◦ )
Ageing time (min)
0.8 0.3 4.0 1.3 1.8
20 20 20 40 40
Fig. 6. Relationship between the DP zone width and the misorientation angle for 1 1 0 (a) and 3 3 1 (b) rotation axes. Mg–10 wt.% Al annealed at 500 K for 20 and 40 min.
Fig. 7. Relationship between the DP zone width and the misorientation angle for the 2 2 1 rotation axis. Mg–10 wt.% Al annealed at 500 K for 20 and 40 min.
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Boundaries which have special properties have been found to have the following combination of Σ values and (h k i l) planes: 7(0 0 0 1) and 13(0 0 0 1). Only five GBs have a special CSL description which corresponds to a relative proportion of 2% of all the GBs studied. However, most of the special misorientations are totally absent including (1 0 1¯ 0) and (2 1 3¯ 0) where according to the theoretical prediction [13], the special GBs appeared very frequently. The small number of CSL grain boundaries do not allow any ultimate conclusion, but it is worth to note that the DP reaction occurred at four GBs out of five CSL boundaries. The small number of CSL boundaries is in agreement with previous theoretical predictions on the occurrence of CSL GBs in hexagonal materials [13–19]. According to Warrington [13] not more than 10% of the number of CSL GBs in cubic materials is predicted to be found in hexagonal materials. In grain-specific texture measurements in the Ni-based superalloy, Randle and Ralph [20] found in samples, aged and overaged, a proportion of the CSL boundaries (for Σ ≤ 49) equal to 27 and 47% of the whole GB population, respectively. For the discontinuous ordering reaction in an Fe–Co alloy this number was approximately 50% [4]. On the contrary, Hirth and Gottstein [6] found that the fraction of low-Σ coincidence GBs (special boundaries with Σ ≤ 29) was only 8%. The c/a ratio of the lattice parameters a and c introduces an irrational factor which considerably limits the dimension and the number of ideal CSL GBs [21]. It is also noticed that contrary to cubic materials, both odd and even values of Σ are possible to provide an odd a parameter [13]. The GBs with large Σ values (above 30) were not found. A different observation was also reported by Antonopoulos et al. [22] concerning the study of GBs in annealed zirconium. They found boundaries with Σ = 49 and 67. Moreover, Antonopoulos et al. [22] detected a high number of GBs with coincidence orientations in tungsten carbide/cobalt composites. The material preparation by liquid sintering develops low-energy facets (1 0 1¯ 0) and (0 0 0 1) in the tungsten carbide grains and a good proportion of tungsten carbide GBs parallel to these two planes of the highest density.
4. Conclusions 1. The electron back-scattered diffraction analysis of the GBs in Mg–10 wt.% Al alloy showed the absence of lowangle GBs and no distinguished maximum on the GB misorientation angle distribution in this hexagonal system.
2. The DP cells appeared predominantly at nonspecial (random) orientations, confirming that the initiation and growth of the reaction products occurs at high-angle GBs. 3. Some misorientations like (1 0 1), (1 1 0), (1 1 1) and especially with higher indexes (four and more) required a longer time of incubation to form DP cells but after 40 min of ageing almost all the GBs were covered with the slabs of discontinuous precipitates. 4. For each rotation axis, there are several misorientation angles (no special ones) for which a maximum growth distance of the DP reaction is observed. References [1] A.P. Sutton, V. Vitek, Phil. Trans. R. Soc. London A, Ser. A 309 (1983) 1. [2] T.H. Chuang, Ph.D. Thesis, University of Stuttgart, 1983, p. 153. [3] D.G. Brandon, Acta Metall. 14 (1966) 1479. [4] V. Semenov, E. Rabkin, E. Bischoff, W. Gust, Acta Mater. 46 (1998) 2289. [5] S. Matsuoka, M.A. Mangan, G.J. Shiflet, in: W.C. Johnson, J.W. Howe, D.E. Laughlin, W.A. Soffa (Eds.), Proceedings of the International Conference on Solid–Solid Phase Transformations, The Minerals, Metals and Materials Society, Warrendale, PA, 1994, p. 521. [6] S. Hirth, G. Gottstein, Acta Mater. 26 (1998) 3975. [7] D. Bradai, M. Kadi-Hanifi, P. Zi˛eba, W.M. Kuschke, W. Gust, J. Mater. Sci. 84 (1999) 5331. [8] K. Lück, Z. Metallkd. 59 (1968) 814. [9] W. Gust, T.H. Chuang, B. Predel, in: P. Haasen, et al. (Eds.), Decomposition of Alloys: The Early Stages, Pergamon Press, Oxford, 1984, p. 208. [10] D. Duly, Y. Brechet, B. Chenal, Acta Metall. Mater. 40 (1992) 2289. [11] R.A. Fournelle, J.B. Clark, Metall. Trans. 3 (1972) 2757. [12] V. Randle, in: B. Cantor, M.J. Goringe (Eds.), The Measurement of Grain Boundary Geometry, Institute of Physics Publishing, Bristol, 1993, p. 104. [13] D.H. Warrington, J. Phys. 36 (1975) 87. [14] M.A. Fortes, D.A. Smith, Scripta Metall. 10 (1976) 575. [15] R. Bonnet, E. Cousineau, D.H. Warrington, Acta Cryst. A 37 (1981) 184. [16] S. Hagege, G. Nouet, P. Delavignette, Phys. Stat. Sol. (a) 61 (1980) 97. [17] G.L. Bleris, G. Nouet, S. Hagege, P. Delavignette, Acta Cryst. A 38 (1982) 550. [18] P. Delavignette, J. Phys. 43 (1982) 1. [19] H. Grimmer, D.H. Warrington, Z. Krist. 162 (1983) 88. [20] V. Randle, B. Ralph, Textures Microstruct. 8/9 (1988) 531. [21] S. Hagege, P. Ayed, J. Vicens, J.L. Chermant, G. Nouet, Trans. Jpn. Inst. Met. Suppl. 27 (1986) 163. [22] J.G. Antonopoulos, P. Delavignette, Th. Karakostas, Ph. Kominou, E. Laurent-Pinson, S. Lay, G. Nouet, J. Vicens, Colloid Phys. C1 51 (1990) 61.