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Sub-boundaries in abnormally growing Goss grains in Fe–3% Si steel
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Scripta Materialia 62 (2010) 376–378 www.elsevier.com/locate/scriptamat
Sub-boundaries in abnormally growing Goss grains in Fe–3% Si steel Hyung-Ki Park,a Sung-Dae Kim,a Seung-Chul Park,a Jong-Tae Parkb and Nong-Moon Hwanga,* a
Department of Materials Science and Engineering and National Research Laboratory of Charged Nanoparticles, Seoul National University, Seoul 151-742, Republic of Korea b POSCO Technical Research Laboratories, POSCO, Pohang 790-360, Republic of Korea Received 15 October 2009; revised 17 November 2009; accepted 18 November 2009 Available online 22 November 2009
The initial stage of secondary recrystallization of Fe–3% Si steel was investigated using a transmission electron microscope with a focus on the existence of sub-boundaries in abnormally growing Goss grains. Ten randomly chosen abnormally growing Goss grains were observed to have sub-boundaries consisting of aligned edge dislocations. In contrast, no sub-boundaries were observed in the matrix grains. The misorientation angles of the observed sub-boundaries were in the range 0.1–0.5°, which was estimated based on the spacing between the dislocations. Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Abnormal grain growth; Secondary recrystallization; Transmission electron microscopy; Grain boundary wetting; Sub-boundary
Since abnormal grain growth (AGG) of Goss grains in silicon steel was first reported in 1935 [1], many efforts have been made to understand the mechanism of selective AGG of Goss grains. Although intensive efforts have been made to find out the origin of selective AGG, its underlying principle has not yet been clarified. The selective AGG of Goss grains has been approached mainly based on the high mobility of grain boundaries shared by Goss grains with other matrix grains [2–4]. However, Etter et al. [5] and Morawiec [6] analyzed a possible mobility advantage of Goss grain boundaries based on experimental results and concluded that the mobility advantage cannot properly explain the selective AGG of Goss grains. On the other hand, Hwang et al. [7–15] showed that AGG could be due to solid-state wetting, which is supported by a large amount of microstructural evidence, as well as by computer simulations. Hwang et al. [11,14] recently suggested a mechanism of sub-boundary enhanced solidstate wetting to explain the selective AGG of Goss grains in Fe–3% Si steel. According to the mechanism, if a grain contains sub-boundaries of very low energy the probability of the grain growing by solid-state wet-
* Corresponding author. Tel.: +82 2 880 8922; fax: +82 2 885 3292; e-mail: [email protected]
ting along triple junctions becomes so high that grains containing sub-boundaries undergo selective AGG. If this concept is applied to the selective AGG of Goss grains in Fe–3% Si steel, abnormally growing Goss grains would be expected to have exclusively sub-boundaries. In relation to this possibility, sub-boundaries with very low misorientation angles of 0.04° and 0.09° inside Goss grains in Fe–3% Si steel were observed by Ushigami et al. [16,17]. Also, Dorner et al. [18] reported that Goss grains exclusively contain sub-boundaries after primary recrystallization. Considering all this, it is worthwhile examining whether sub-boundaries really exist exclusively in abnormally growing Goss grains. Motivated by this background, in this paper we examine the existence of sub-boundaries in abnormally growing Goss grains by transmission electron microscopy (TEM) in the initial stage of secondary recrystallization of Fe–3% Si steel. The material used in this study was Fe–3% Si steel with AlN employed as an inhibitor of grain growth to produce highly grain oriented (HGO) electrical steel. The steel ingot was hot rolled to 2.3 mm and the thickness was further reduced to 0.3 mm by a one stage cold rolling method. After primary recrystallization at 850 °C the sheet samples were heated up to 1030 °C, held for 0 s and cooled to room temperature, which treatment was intended to produce a microstructure in the initial stage
1359-6462/$ - see front matter Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2009.11.025
H.-K. Park et al. / Scripta Materialia 62 (2010) 376–378
of secondary recrystallization. The sheet samples were etched with 50% water–50% HCl at 80 °C to identify abnormally growing grains. The microstructure was observed by optical microscopy (OM) (Eclipse L150, Nikon) and field-emission scanning electron microscopy (FE-SEM) (JSM-6500F, JEOL). The orientation of abnormally growing grains was determined by electron backscattered diffractometer attached to the scanning electron microscope. EDAX/TSL software was used for the analysis of the orientation. After identifying the orientation of abnormally growing grains the samples were polished mechanically and electrolytically with an electrolyte of 10% perchlolic acid–90% ethanol using a jet polisher (Tenupolo-3, Struers) for TEM observation. Contamination of the samples was eliminated by a surface ion miller (PIPS 691, Gatan). The samples were observed by TEM (JEM-3000F, JEOL). For clear identification of sub-boundaries high quality images were needed because the sub-boundaries, consisting of dislocation arrangements, were much more difficult to identify than general grain boundaries. Annular dark field scanning transmission electron microscopy (ADF-STEM) is known to provide a clear image for observation of dislocations by reducing artifacts such as thickness fringes, striped dislocation contrast and bend contours [19]. For this reason, ADFSTEM was used to observe sub-boundaries consisting of dislocations. The characteristics of sub-boundaries were analyzed in bright field mode to confirm the Burgers vector and the type of dislocations. In order to make a statistically reliable conclusion 10 abnormally growing Goss grains and 100 matrix grains were examined by TEM for their possession of sub-boundaries. After etching the sample abnormally growing grains could be identified even by the naked eye, having a grain size of 1–3 mm. After microstructural observation of the abnormally growing grains by OM and FE-SEM, electron backscattered diffraction (EBSD) was used to determine their orientations. All abnormally growing grains identified in the etched sample had a Goss texture that deviated by less than 3° from the exact Goss orientation, {1 1 0}<0 0 1>. Figure 1 shows the microstructure of an abnormally growing grain observed by EBSD. The diameter of the large grain on the two-dimensional section was
Figure 1. Microstructure showing the initial stage of secondary recrystallization in Fe–3% Si steel. The orientation of a large green colored grain is (0 1 1)[1 0 0], which corresponds to a Goss orientation. (For interpretation of color mentioned in this figure, the reader is referred to the web version of this article.)
377
1.7 mm. EBSD identified the orientation of the abnormally growing grain in Figure 1 as (0 1 1)[1 0 0], which corresponds to a Goss orientation. Figure 2a shows a bright field image of a sub-boundary inside an abnormally growing Goss grain shown in Figure 1. A sub-boundary formed by aligned dislocations was observed in the Goss grain. Long black lines in Figure 2a and b are bend contours, which might be caused by the large grain size of the abnormally growing Goss grain. Among 10 abnormally growing Goss grains and 100 matrix grains examined by TEM abnormally growing Goss grains had sub-boundaries whereas matrix grains did not, without exception. The correlation between the existence of sub-boundaries and the AGG of Goss grains was perfect, at least in the grains examined in this study. Therefore, it can be said that abnormally growing Goss grains have the unique feature of possessing sub-boundaries. In relation to such a feature of abnormally growing Goss grains, Ushigami et al. [17] reported sub-boundaries in abnormally growing Goss grains in in situ observations using synchrotron X-ray during secondary recrystallization of Fe–3% Si steel. Also, Dorner et al. [18] reported sub-boundaries with a misorientation of less than 1° only in Goss grains after primary recrystallization of a sheet sample reduced 89% by cold rolling of a Goss single crystal. In order to determine the Burger vector and the type of dislocations of the sub-boundaries the dot product of g b in bright field mode, where g and b are the reciprocal lattice and Burgers vector, respectively, was analyzed. When a sample was tilted to produce the g = [1 1 0] two beam condition, where the (1 1 0) diffracted beam and the direct beam are strong, as shown in Figure 2a, the aligned dislocations making up the sub-boundary could be observed, which means that g b is not equal to 0. At the same position, however, when the sample was tilted to produce the g = [1 1 2] two beam condition, no dislocations were observed, which means that g b is equal to 0. Based on the g b = 0 criterion, the sub-boundary in Figure 2a had a Burgers vector 1=2½1 1 1, which is perpendicular to the dislocation line direction. This means that the dislocations making up the sub-boundary in Figure 2a are edge dislocations with a Burgers vector of 1=2½1 1 1. Generally, the dislocations in Fe–3% Si steel have a Burgers vector of the 1/2<1 1 1> family, which is a principal slip direction of a body-centered cubic (bcc) system [20].
Figure 2. Bright field images of a sub-boundary inside the abnormally growing Goss grain of Figure 1. The sub-boundary, consisting of edge dislocations, has a Burgers vector of 1=2½1 1 1.
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H.-K. Park et al. / Scripta Materialia 62 (2010) 376–378
of having sub-boundaries of very low boundary angle. This feature might be related to the selective AGG of Goss grains in Fe–3% Si steel. This work was financially supported by POSCO Technical Research Laboratories and the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (no. M10600000 159-06J0000-15910).
Figure 3. Annular dark field STEM images of sub-boundaries with misorientation angles of (a) 0.15° and (b) 0.17°.
The sub-boundaries examined in all 10 samples also had a Burgers vector of the 1/2<1 1 1> family. Figure 3a and b show ADF-STEM images of subboundaries observed in abnormally growing Goss grains of other samples. The distances between the individual dislocations in Figure 3a and b were 93.2 and 84.3 nm, respectively. For a spacing h of dislocations with a Burgers vector b in the boundary the crystals on either side of the boundary are misoriented by a small angle h b/ h [21]. From this equation the boundary angles of the sub-boundaries in Figure 3a and b were determined to be 0.15° and 0.17°, respectively. The sub-boundary in Figure 2a also had very low boundary angle of 0.38°. The misorientations of other sub-boundaries were less than 0.5°. In conclusion, abnormally growing Goss grains in Fe–3% Si steel were shown to have the unique feature
[1] N.P. Goss, Trans. Am. Soc. Met. 23 (1935) 511. [2] J. Harase, R. Shimizu, D.J. Dingley, Acta Metall. Mater. 39 (1991) 763. [3] N. Rajmohan, J.A. Szpunar, Y. Hayakawa, Acta Mater. 47 (1999) 2999. [4] Y. Ushigami, T. Kumano, T. Haratani, S. Nakamura, S. Takebayashi, T. Kubota, Mater. Sci. Forum 467–470 (2004) 863. [5] A.L. Etter, T. Baudin, R. Pnelle, Scr. Mater. 47 (2002) 725. [6] A. Morawiec, Scr. Mater. 43 (2000) 275. [7] N.M. Hwang, J. Mater. Sci. 33 (1998) 5625. [8] N.M. Hwang, S.B. Lee, D.Y. Kim, Scr. Mater. 44 (2001) 1153. [9] K.J. Ko, P.R. Cha, J.T. Park, J.K. Kim, N.M. Hwang, Mater. Sci. Forum 558 (2007) 1101. [10] K.J. Ko, P.R. Cha, J.T. Park, J.K. Kim, N.M. Hwang, Adv. Mater. Res. 26 (2007) 65. [11] K.J. Ko, P.R. Cha, D. Srolovitz, N.M. Hwang, Acta Mater. 57 (2009) 838. [12] K.J. Ko, J.T. Park, J.K. Kim, N.M. Hwang, Scr. Mater. 59 (2008) 764. [13] S.B. Lee, N.M. Hwang, C.H. Han, D.Y. Yoon, Scr. Mater. 39 (1998) 825. [14] D.K. Lee, K.J. Ko, B.J. Lee, N.M. Hwang, Scr. Mater. 58 (2008) 683. [15] H. Park, D.Y. Kim, N.M. Hwang, Appl. Phys. 95 (2004) 5515. [16] S. Suzuki, Y. Ushigami, Y. Suga, N. Takashashi, Mater. Sci. Forum 204–205 (1996) 575. [17] Y. Ushigami, Y. Suga, N. Takashashi, K. Kwasaki, Y. Chikaura, H. Kii, J. Mater. Eng. 13 (1991) 113. [18] D. Dorner, L. Lahn, S. Zaefferer, Mater. Sci. Forum 467 (2004) 129. [19] J.H. Sharp, J.S. Barnard, K. Kaneko, K. Higashida, P.A. Midgley, J. Phys. 126 (2008) 012013. [20] D. Hull, D.J. Bacon, Introduction to Dislocations, fourth ed., Pergamon Press, Oxford, 2005. [21] F.J. Humphreys, M. Hatherly, Recrystallization and Related Annealing Phenomena, second ed., Pergamon Press, Oxford, 1994.
Scripta Materialia 62 (2010) 376–378 www.elsevier.com/locate/scriptamat
Sub-boundaries in abnormally growing Goss grains in Fe–3% Si steel Hyung-Ki Park,a Sung-Dae Kim,a Seung-Chul Park,a Jong-Tae Parkb and Nong-Moon Hwanga,* a
Department of Materials Science and Engineering and National Research Laboratory of Charged Nanoparticles, Seoul National University, Seoul 151-742, Republic of Korea b POSCO Technical Research Laboratories, POSCO, Pohang 790-360, Republic of Korea Received 15 October 2009; revised 17 November 2009; accepted 18 November 2009 Available online 22 November 2009
The initial stage of secondary recrystallization of Fe–3% Si steel was investigated using a transmission electron microscope with a focus on the existence of sub-boundaries in abnormally growing Goss grains. Ten randomly chosen abnormally growing Goss grains were observed to have sub-boundaries consisting of aligned edge dislocations. In contrast, no sub-boundaries were observed in the matrix grains. The misorientation angles of the observed sub-boundaries were in the range 0.1–0.5°, which was estimated based on the spacing between the dislocations. Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Abnormal grain growth; Secondary recrystallization; Transmission electron microscopy; Grain boundary wetting; Sub-boundary
Since abnormal grain growth (AGG) of Goss grains in silicon steel was first reported in 1935 [1], many efforts have been made to understand the mechanism of selective AGG of Goss grains. Although intensive efforts have been made to find out the origin of selective AGG, its underlying principle has not yet been clarified. The selective AGG of Goss grains has been approached mainly based on the high mobility of grain boundaries shared by Goss grains with other matrix grains [2–4]. However, Etter et al. [5] and Morawiec [6] analyzed a possible mobility advantage of Goss grain boundaries based on experimental results and concluded that the mobility advantage cannot properly explain the selective AGG of Goss grains. On the other hand, Hwang et al. [7–15] showed that AGG could be due to solid-state wetting, which is supported by a large amount of microstructural evidence, as well as by computer simulations. Hwang et al. [11,14] recently suggested a mechanism of sub-boundary enhanced solidstate wetting to explain the selective AGG of Goss grains in Fe–3% Si steel. According to the mechanism, if a grain contains sub-boundaries of very low energy the probability of the grain growing by solid-state wet-
* Corresponding author. Tel.: +82 2 880 8922; fax: +82 2 885 3292; e-mail: [email protected]
ting along triple junctions becomes so high that grains containing sub-boundaries undergo selective AGG. If this concept is applied to the selective AGG of Goss grains in Fe–3% Si steel, abnormally growing Goss grains would be expected to have exclusively sub-boundaries. In relation to this possibility, sub-boundaries with very low misorientation angles of 0.04° and 0.09° inside Goss grains in Fe–3% Si steel were observed by Ushigami et al. [16,17]. Also, Dorner et al. [18] reported that Goss grains exclusively contain sub-boundaries after primary recrystallization. Considering all this, it is worthwhile examining whether sub-boundaries really exist exclusively in abnormally growing Goss grains. Motivated by this background, in this paper we examine the existence of sub-boundaries in abnormally growing Goss grains by transmission electron microscopy (TEM) in the initial stage of secondary recrystallization of Fe–3% Si steel. The material used in this study was Fe–3% Si steel with AlN employed as an inhibitor of grain growth to produce highly grain oriented (HGO) electrical steel. The steel ingot was hot rolled to 2.3 mm and the thickness was further reduced to 0.3 mm by a one stage cold rolling method. After primary recrystallization at 850 °C the sheet samples were heated up to 1030 °C, held for 0 s and cooled to room temperature, which treatment was intended to produce a microstructure in the initial stage
1359-6462/$ - see front matter Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2009.11.025
H.-K. Park et al. / Scripta Materialia 62 (2010) 376–378
of secondary recrystallization. The sheet samples were etched with 50% water–50% HCl at 80 °C to identify abnormally growing grains. The microstructure was observed by optical microscopy (OM) (Eclipse L150, Nikon) and field-emission scanning electron microscopy (FE-SEM) (JSM-6500F, JEOL). The orientation of abnormally growing grains was determined by electron backscattered diffractometer attached to the scanning electron microscope. EDAX/TSL software was used for the analysis of the orientation. After identifying the orientation of abnormally growing grains the samples were polished mechanically and electrolytically with an electrolyte of 10% perchlolic acid–90% ethanol using a jet polisher (Tenupolo-3, Struers) for TEM observation. Contamination of the samples was eliminated by a surface ion miller (PIPS 691, Gatan). The samples were observed by TEM (JEM-3000F, JEOL). For clear identification of sub-boundaries high quality images were needed because the sub-boundaries, consisting of dislocation arrangements, were much more difficult to identify than general grain boundaries. Annular dark field scanning transmission electron microscopy (ADF-STEM) is known to provide a clear image for observation of dislocations by reducing artifacts such as thickness fringes, striped dislocation contrast and bend contours [19]. For this reason, ADFSTEM was used to observe sub-boundaries consisting of dislocations. The characteristics of sub-boundaries were analyzed in bright field mode to confirm the Burgers vector and the type of dislocations. In order to make a statistically reliable conclusion 10 abnormally growing Goss grains and 100 matrix grains were examined by TEM for their possession of sub-boundaries. After etching the sample abnormally growing grains could be identified even by the naked eye, having a grain size of 1–3 mm. After microstructural observation of the abnormally growing grains by OM and FE-SEM, electron backscattered diffraction (EBSD) was used to determine their orientations. All abnormally growing grains identified in the etched sample had a Goss texture that deviated by less than 3° from the exact Goss orientation, {1 1 0}<0 0 1>. Figure 1 shows the microstructure of an abnormally growing grain observed by EBSD. The diameter of the large grain on the two-dimensional section was
Figure 1. Microstructure showing the initial stage of secondary recrystallization in Fe–3% Si steel. The orientation of a large green colored grain is (0 1 1)[1 0 0], which corresponds to a Goss orientation. (For interpretation of color mentioned in this figure, the reader is referred to the web version of this article.)
377
1.7 mm. EBSD identified the orientation of the abnormally growing grain in Figure 1 as (0 1 1)[1 0 0], which corresponds to a Goss orientation. Figure 2a shows a bright field image of a sub-boundary inside an abnormally growing Goss grain shown in Figure 1. A sub-boundary formed by aligned dislocations was observed in the Goss grain. Long black lines in Figure 2a and b are bend contours, which might be caused by the large grain size of the abnormally growing Goss grain. Among 10 abnormally growing Goss grains and 100 matrix grains examined by TEM abnormally growing Goss grains had sub-boundaries whereas matrix grains did not, without exception. The correlation between the existence of sub-boundaries and the AGG of Goss grains was perfect, at least in the grains examined in this study. Therefore, it can be said that abnormally growing Goss grains have the unique feature of possessing sub-boundaries. In relation to such a feature of abnormally growing Goss grains, Ushigami et al. [17] reported sub-boundaries in abnormally growing Goss grains in in situ observations using synchrotron X-ray during secondary recrystallization of Fe–3% Si steel. Also, Dorner et al. [18] reported sub-boundaries with a misorientation of less than 1° only in Goss grains after primary recrystallization of a sheet sample reduced 89% by cold rolling of a Goss single crystal. In order to determine the Burger vector and the type of dislocations of the sub-boundaries the dot product of g b in bright field mode, where g and b are the reciprocal lattice and Burgers vector, respectively, was analyzed. When a sample was tilted to produce the g = [1 1 0] two beam condition, where the (1 1 0) diffracted beam and the direct beam are strong, as shown in Figure 2a, the aligned dislocations making up the sub-boundary could be observed, which means that g b is not equal to 0. At the same position, however, when the sample was tilted to produce the g = [1 1 2] two beam condition, no dislocations were observed, which means that g b is equal to 0. Based on the g b = 0 criterion, the sub-boundary in Figure 2a had a Burgers vector 1=2½1 1 1, which is perpendicular to the dislocation line direction. This means that the dislocations making up the sub-boundary in Figure 2a are edge dislocations with a Burgers vector of 1=2½1 1 1. Generally, the dislocations in Fe–3% Si steel have a Burgers vector of the 1/2<1 1 1> family, which is a principal slip direction of a body-centered cubic (bcc) system [20].
Figure 2. Bright field images of a sub-boundary inside the abnormally growing Goss grain of Figure 1. The sub-boundary, consisting of edge dislocations, has a Burgers vector of 1=2½1 1 1.
378
H.-K. Park et al. / Scripta Materialia 62 (2010) 376–378
of having sub-boundaries of very low boundary angle. This feature might be related to the selective AGG of Goss grains in Fe–3% Si steel. This work was financially supported by POSCO Technical Research Laboratories and the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (no. M10600000 159-06J0000-15910).
Figure 3. Annular dark field STEM images of sub-boundaries with misorientation angles of (a) 0.15° and (b) 0.17°.
The sub-boundaries examined in all 10 samples also had a Burgers vector of the 1/2<1 1 1> family. Figure 3a and b show ADF-STEM images of subboundaries observed in abnormally growing Goss grains of other samples. The distances between the individual dislocations in Figure 3a and b were 93.2 and 84.3 nm, respectively. For a spacing h of dislocations with a Burgers vector b in the boundary the crystals on either side of the boundary are misoriented by a small angle h b/ h [21]. From this equation the boundary angles of the sub-boundaries in Figure 3a and b were determined to be 0.15° and 0.17°, respectively. The sub-boundary in Figure 2a also had very low boundary angle of 0.38°. The misorientations of other sub-boundaries were less than 0.5°. In conclusion, abnormally growing Goss grains in Fe–3% Si steel were shown to have the unique feature
[1] N.P. Goss, Trans. Am. Soc. Met. 23 (1935) 511. [2] J. Harase, R. Shimizu, D.J. Dingley, Acta Metall. Mater. 39 (1991) 763. [3] N. Rajmohan, J.A. Szpunar, Y. Hayakawa, Acta Mater. 47 (1999) 2999. [4] Y. Ushigami, T. Kumano, T. Haratani, S. Nakamura, S. Takebayashi, T. Kubota, Mater. Sci. Forum 467–470 (2004) 863. [5] A.L. Etter, T. Baudin, R. Pnelle, Scr. Mater. 47 (2002) 725. [6] A. Morawiec, Scr. Mater. 43 (2000) 275. [7] N.M. Hwang, J. Mater. Sci. 33 (1998) 5625. [8] N.M. Hwang, S.B. Lee, D.Y. Kim, Scr. Mater. 44 (2001) 1153. [9] K.J. Ko, P.R. Cha, J.T. Park, J.K. Kim, N.M. Hwang, Mater. Sci. Forum 558 (2007) 1101. [10] K.J. Ko, P.R. Cha, J.T. Park, J.K. Kim, N.M. Hwang, Adv. Mater. Res. 26 (2007) 65. [11] K.J. Ko, P.R. Cha, D. Srolovitz, N.M. Hwang, Acta Mater. 57 (2009) 838. [12] K.J. Ko, J.T. Park, J.K. Kim, N.M. Hwang, Scr. Mater. 59 (2008) 764. [13] S.B. Lee, N.M. Hwang, C.H. Han, D.Y. Yoon, Scr. Mater. 39 (1998) 825. [14] D.K. Lee, K.J. Ko, B.J. Lee, N.M. Hwang, Scr. Mater. 58 (2008) 683. [15] H. Park, D.Y. Kim, N.M. Hwang, Appl. Phys. 95 (2004) 5515. [16] S. Suzuki, Y. Ushigami, Y. Suga, N. Takashashi, Mater. Sci. Forum 204–205 (1996) 575. [17] Y. Ushigami, Y. Suga, N. Takashashi, K. Kwasaki, Y. Chikaura, H. Kii, J. Mater. Eng. 13 (1991) 113. [18] D. Dorner, L. Lahn, S. Zaefferer, Mater. Sci. Forum 467 (2004) 129. [19] J.H. Sharp, J.S. Barnard, K. Kaneko, K. Higashida, P.A. Midgley, J. Phys. 126 (2008) 012013. [20] D. Hull, D.J. Bacon, Introduction to Dislocations, fourth ed., Pergamon Press, Oxford, 2005. [21] F.J. Humphreys, M. Hatherly, Recrystallization and Related Annealing Phenomena, second ed., Pergamon Press, Oxford, 1994.