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The role of grain boundary character distribution in secondary recrystallization of electrical steels
Pergamon PII: 1359-6454(96)00251-O
Acta mater. Vol. 45, No. 3, pp. 1285-1295, 1997 Copyright 0 1997 Acta Metallurgica Inc. Published by Elsevier Science Ltd Printed in Great Britain. All rights reserved 1359~6454/97 $17.00 + 0.00
THE ROLE OF GRAIN BOUNDARY CHARACTER DISTRIBUTION IN SECONDARY RECRYSTALLIZATION OF ELECTRICAL STEELS Y. HAYAKAWAtS and J. A. SZPUNAR Department
of Mining
and Metallurgical Engineering, McGill Canada, H3A 2T5
University,
Montreal,
Quebec,
(Received 7 November 1995; acceplad 6 February 1996)
Abstract-Grain Boundary Character Distributions (GBCD) in grain-oriented electrical steels were calculated from the Orientation Distribution Functions of the primary recrystallization texture. The probability of a grain boundary having a misorientation angle from 20” to 45” is highest around the Goss grain. The observed difference in GBCD implies that the Goss grain is surrounded by the highest number of high-energy boundaries. The high-energy boundary has more structural defects, and these are often linked to a high grain boundary migration rate and a high grain boundary diffusion rate. An explanation of Goss texture development in secondary recrystallization is proposed, based on the property of the high-energy boundary. The role of special Coincident Site Lattice boundaries is analysed, and we conclude that they do not play a significant role in the development of Goss texture. Copyright #Q 1997 Acta Metallurgica Inc.
1. INTRODUCTION Various mechanisms of the development of secondary recrystallization { 1 lo} < 001 > Goss texture have been already proposed. They can be roughly divided into two types: one theory assumes that Goss grains form colonies and, as a result of coalescence during the annealing treatment, they develop the size-advantage [ 1, 21. This interpretation is predominantly used to explain the texture development in conventional grain-oriented electrical steel for which the final cold rolling reduction is approximately 60%. Another theory claims that the Goss grains are surrounded by the highest number of Coincidence Site Lattice (CSL) boundaries [3-71, and CSL boundaries are believed to have both lower grain boundary energies and higher migration mobilities than other general boundaries [8]. This theory is predominantly used to describe the case of high permeability grain-oriented electrical steel, for which the final cold rolling reduction is approximately 85%. Both of the above theories have weak points which are listed below. The main argument against the former theory is that, using the result of Monte Carlo simulation [9, IO], the size-advantage itself cannot maintain the secondary recrystallization. It has already been argued [ 1 l] that the growth rate of an embedded large grain was so small that the grain _ .._.~ ton leave from Kawasaki Steel Corporation, l-Kawasakidouri, Mizushima, Kurashiki, $To whom all correspondence
Okayama, Japan. should be addressed.
would be absorbed by the matrix when boundary energies, and mobilities are uniform. It was also demonstrated that, in the case of high permeability steel, the Goss grains did not form colonies [4, 121. Our argument against the latter theory is that, the number of CSL boundaries, other than the low angle grain boundary (El), is too small at approximately 10% [3-51 to be responsible for a major change in texture. Some authors [3,4,7] have reported that there were more CSL boundaries around the Goss grain, and emphasized a role of some special boundaries X9 [5], C7 [13], Z5 [14]. The number of these boundaries is less than 2%. In addition, the reported relative abundance in the presence of the CSL boundaries was less than 20%, and such an abundance was smaller than the statistical error caused by the small number of analysed grains. Using computer simulation, we estimated that if, for example, 100 grains were measured [7], the estimated error is 60%; if 500 grains [3,4] were analysed, the error is about 40%. The type of important CSL boundaries differed from case to case (X9 [5], C7 [13], X5 [14]); however, no explanation of the selection mechanism was offered. This brief discussion demonstrates that there is no satisfactory explanation of the development of the Goss texture in grain-oriented electrical steels. The aim of our research is to investigate the Grain Boundary Character Distribution (GBCD) of both conventional and high permeability steels and to propose a consistent mechanism of the secondary recrystallization.
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2. EXPERIMENT
3. RESULTS
Two different types of primary recrystallized texture are investigated. One specimen is a high permeability steel (Specimen A). The other specimen is a conventional steel (Specimen B). In specimen A, there are MnSe and also AlN precipitates. In specimen B, MnS precipitates are used as an inhibitor. A comparison between these materials is made in Table 1. X-ray reflection pole figures (llO), (200), (211) were measured from the subsurface layer at approximately l/l0 of the specimen thickness. The Orientation Distribution Functions (ODF) were calculated using the discrete method [15], which is free from ghost peaks that may distort the results obtained using the series expansion method. To calculate GBCD, pairs of grains were generated in proportion to the value of the ODF (f(g)), using the method proposed by Morawiec et al. [16]. To investigate grain boundaries around the grain having a certain specific orientation, the orientation of the selected grain was fixed, and the orientation of a neighbouring grain was generated using the same method. 10’pairs of grains were generated from the ODF in order to calculate the GBCD, and the error of such analysis caused by the number of grains was less than 1%. Misorientation angles, which are the minimum angle among the equivalent 24 angles and rotation axis, were calculated by using the unit quaternion [17]. The CSL boundary was defined by comparing the quaternion of the grain misorientation with that of the CSL using Brandon criterion [18], which allows 15/~‘/* degrees of deviation from the ideal position. The validity of the statistical calculation of GBCD has been tested previously [19] by comparing the result obtained from direct measurement of misorientation of grains using the Electron Back Scattering Pattern (EBSP). The portion of CSL boundaries obtained from the measurement of 511 grains in specimen A shows good agreement with the calculation except for the xl boundary. The percentage of the El boundary is higher than the calculated value, and the main reason for such a difference is that xl boundaries tend to form colonies that cannot be predicted from the ODF analysis.
3.1, Misorientation angle distributions
The ODF of both specimens is shown in Fig. 1. The most important texture characteristic of specimen A is a strong so-called y fibre (ND// < 1 11 >), which has its maximum value in the vicinity of {ill}< 112~ (precisely, at Q1 = 90”, 4 = 60”, 02 = 45”,f(g) = 11.86) the value of ODF at the Goss orientation (0, = 90”, 4 = 90”, Qz = 45”) is rather weak (f(g) = 0.46). Specimen B has a weak y fibre texture, with its maximum value at { 111) < 011 > (@ = 60”, 4 = 55”, @ = 45”, f(g) = 7.52), and a strong q fibre texture (RD/< 100 >), the intensity of the Goss orientation is rather strong (f(g) = 3.81). The probability of boundaries having misorientation angle (w) between certain angles (A) and (B) for grain having a specific orientation (g) is defined here by the following expression. Probability
(A < w < B,g) (X) = {W
< w < W/N(g))
where N(A < o < B,g) is the number of boundaries that have misorientation angle (A < o < B) around the grain having a specific orientation (g), and N(g) is the number of total generated boundaries around the grain having a specific orientation (g). In Fig. 2, the probability of grains having misorientation angle (0) with respect to the Goss grain, the grain having average orientation, and the grain representing the main texture component, are shown. The main difference between these distributions is that the Goss grain has more intermediate misorientation high angle (20” < w < 45”) grain boundaries, and less low angle (15” > w) and large misorientation high angle (45” < o) grain boundaries than a grain having an average orientation or the grain of the main texture component. Figure 2 also shows that the main texture component grains have fewer intermediate misorientation high angle boundaries and more low or large misorientation high angle grain boundaries than grain having the average texture. This observation is true for both specimens. The type of analysis presented above can be now extended to grains having other orientations. The misorientation probability of an intermediate (20” < w < 45”) high angle grain boundary is calculated around grains of different orientations,
Table 1. Comparison of the investigated specimens Thickness (mm)
Main component
A High permeability
0.23
B Conventional
0.35
{111}<112> 11.86 {111}<110> 7.40
Specimen type
x 100 (1)
fk)
Goss
Induction after final annealing
Sk)
w-u
0.46
1.93
3.81
1.84
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3.2. CSL boundary distribution
The probability of CSL boundaries around the grain having specific orientation (g) is defined here by the following expression. (Cn, g) (%) = {N(Cn, g)/N(g)} x 100
where N(Cn, g) is the number of 2.n CSL boundaries around the grain having a specific orientation (g), and N(g) is the number of total generated boundaries around the grain having a specific orientation (g). The probabilities of CSL boundaries around grains
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of various orientations were calculated and are given in Table 2. The total probability of CSL boundaries from Cl to X51 has a maximum of 26% for specimen A, and 24% for specimen B, around the grains representing the main texture component. Around the Goss grain, the probability is low. In previous calculations [6, 201, Cl and C3 boundaries were excluded from the CSL statistics because the low mobilities of these boundaries were never questioned. Excluding these boundaries, the highest probability of CSL boundaries is around { 110) < 113 > ($ = 65 , C$= 90”, $ = 45) orientation. The probability of CSL boundaries around the Goss grains is higher than around the grain having average orientation, however, grains having other orientations such as {111}<011>, and {210}<001> (@=OU, 4=35, a2 = Ol-) have higher or similar probabilities. The most important observation is that the absolute difference in probability is, at best, only 3%. The CSL boundaries are often described by defining the rotation axis and the rotation angle [S, 61. For both specimens, none of these probabilities indicates that the Goss grain has the highest number
and is shown in Fig. 3 in the grain orientation space. For specimen A, the probability shows a sharp maximum, which is 76% at the Goss orientation, and a minimum, which is 37%, at the main texture component. It must be noted that the difference in the probability is very large at approximately 40%. For specimen B, the Goss grain has a higher probability of being surrounded by the intermediate misorientation high angle grain boundaries, however, the peak position is rotated by 20” from the Goss orientation the around the ND/< 110 > axis.
Probability
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Fig. 1. The ODF of the 3%Si-Fe specimens after decarburizing annealing. Arrows indicate Goss orientation: (a) specimen A, cross-section (D2= 0’; (b) specimen A, cross-section @I = 45”; (c) specimen B. cross-section, @2 = 0”; (d) specimen B, cross-section, QZ = 45”; (e) skeleton line along q fibre texture (Q, = O”, @2 = 0”); (f) skeleton line along y fibre texture (Q = 55”, (D2= 45”).
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over the Goss orientation. Since the (21 I)<011 > orientation is not observed in the secondary recrystallized specimen, assuming a positive role of the C9 boundary in the grain growth process is questionable. Around the Goss grain of specimen B, the probability of the X3 and C7 boundaries is the lowest, and of the X9 boundary is average. The probability of the X5 boundary is the highest; however, the absolute difference in probability of the X5 boundary between the Goss grain and the grain having an average orientation is only 1.5%. Such a small difference cannot support the special role of the CSL boundaries in the growth of Goss grains. To summarize, we claim that none of the present calculations support the CSL-based grain growth model. We do not observe a high percentage of CSL boundaries around the Goss grain. In fact, around the Goss grain, the total number of the CSL boundaries is low, and the percentage of the X3 boundary and CSL boundaries having rotation axis < Ill> , is the lowest. The most important finding of the GBCD analysis is presented in Fig. 3, where it is demonstrated that the Goss grain is surrounded by the highest number of intermediate misorientation
Fig. 1. Continued of CSL boundaries. In fact, the probability of the CSL boundary having < 111> rotation axis is the lowest. The probabilities of low numbers CSL boundaries (C3, X.5, X7, C9) around the grains having different orientations were also investigated. Around the Goss grain of specimen A, the probability of the X3 boundary is the lowest, and the probabilities of the X5 and X7 boundaries are very low. The number of E9 boundaries around the Goss grains is approximately 2%, which is near the maximum number, as mentioned by Harase et al. [5,6]. Around grains having other orientations, such as {211}<011>, {110}<111> and {113}<332> (@, = 0”, 4 = 25”, @ = 45”), the probability of the X.9 boundary is comparable to that obtained around the Goss grain. The product of the probability of X9 around a specified grain and the ODF value corresponding to this grain orientation (Pcnz9) was used to explain the advantage of the Goss grain in the growth process [6]. For specimen A, the PcnE9 value for the grain having (21 l} ~01 1> orientation is 2.03, and this value is higher than 0.97 for the Goss grain. This means that, according to the previous model [6], the {211}<011> orientation should be favoured
0
5
10 15 20 25 30 35 40 45 60 55 60
Misorientation angle (degree)
a
Misorientation angle (degree)
Fig. 2. The misorientation angle Goss grain (a) High permeability steel.
distribution around the steel. (b) Conventional
SECONDARY RECRYSTALLIZATION OF ELECTRICAL STEELS 1289
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high angle (20” < w < 45”) grain boundaries. makes the Goss grain unique.
This
4. DISCUSSION 4.1. CSL theory applied to the grain growth It is widely accepted [8,21,22] that the CSL boundary has lower energy than the general boundary. From a structural point of view, the CSL boundary has a periodic dislocation arrangement reducing the grain boundary energy. These periodic dislocations are lattice dislocations in the case of the low angle grain boundary, and Displacement Shift Complete (DSC) dislocations [23, 241 in the case of the CSL boundary. The special character of the CSL boundary always corresponds to a low grain boundary diffusivity, low segregation of solute impurity, low grain boundary sliding rate, and a high resistance to corrosion. All these phenomena demonstrate that the CSL boundary has similar properties to the low angle grain boundary, because both have similar structures. When the CSL theory is applied to the grain growth [5, 13, 141,it assumes that certain CSL boundaries have high mobilities. On the
(a) 0
other hand, it assumes that the low angle grain boundary (Cl), or the twin boundary (X3) and the general high-energy boundary have a low mobility. In general [8,21,22,25], the interfacial energy cusp is large for Xl and z3 boundaries, and that of other CSL boundaries is smaller, or sometimes undetectable. Thus, it is natural to assume that Cl and X3 boundaries are the most typical CSL boundaries. The exclusion of the Cl and X3 boundaries from the discussion of the grain growth is inconsistent with other applications of the CSL theory. We use the term low-energy boundary for these boundaries including Xl and X.3 and CSL boundaries. Please note that the high mobility of CSL boundaries was observed only in pure materials. Aust et al. [26] observed a high mobility of CSL boundaries in a zone melted Pb with a very small addition of Sn from 0.002 to 0.005%. Another experiment was conducted on 99.9992% pure Al% [27], less than 20 ppm addition to pure lead [28], less than 40 ppm Cu addition to aluminium [29], and 99.999% high purity tin [30]. The high mobility of CSL boundaries is not observed when more than 0.005% tin is added [26], and the purity of aluminium
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Fig. 3. The probability (%) of boundaries having misorientation angle from 20” to 45” around grains having various orientations: (a) specimen A, cross-section @Z= 0”; (b) specimen A, cross-section @2 = 45”; (c) specimen B, cross-section, @Z= 0”; (d) specimen B, cross-section, a2 = 45”. Arrows indicate the Goss orientation, and the contour line of the average value is indicated by “A”.
1290 HAYAKAWA and SZPUNAR:
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Table 2. The probabilities (%) of CSL boundaries around the grain having various orientations in the specimen A and B; (a) maximum probability which is observed around the grain having a specified orientation {hk[}; (b) around a Goss grain; (c) around a grain having average orientation. The expression of the orientation {hkl} allows five degrees of the deviation
Specimen A (%) {hkl}
CSL 112151 3 2<110> X1111> 23 x5 27 z9
26.2 {111}<112> 17.4 {111}<112> 15.4 {110}<113> 4.9 {110}<113> 5.9 {211}<011> 7.9 (111)<011 > 5.5 {111}<112> 4.0 {110}<113> 2.1 {lll} 2.1 12111<011>
(b) Specimen
(a) Specimen B (%) (hkl) 24.3 17.3 15.2 4.2 4.6 8.4 3.8 2.9 2.5 1.9
{lll} {111}<011> {110}<113> 1230) {211}<011> {111}<011> {111}<011> {110}<001> (111}<011> 11101<113>
(c) Specimen
(C)
(;)
(G,
($
16.3 14.9 14.6 2.4 4.2 2.0 0.3 1.7 0.8 2.0
19.6 14.7 14.1 3.7 2.8 2.1 0.6 2.7 0.5 1.1
19.6 15.2 13.0 1.7 3.2 4.6 2.2 0.9 1.0 1.0
19.0 15.5 13.6 2.0 3.2 4.2 1.9 1.2 1.1 1.0
X: X(5+ 13a+ 17a+25a+29a+37a) Z< lOO>: X(9 + 11 + 19~ + 27~ + 33~ + 33c + 410 + 41~ + 51a + 51b) 2<111>: 213 + 7 + 196 + 210 + 310 + 37~ + 39a + 43a + 49a)
is reduced to 99.995% [27]. The high mobility of the CSL boundaries was observed only at a low temperature [27,28]. This does not apply to grain-oriented electrical steel, which is a commercial product with a considerable amount of solute atoms, such as Si, Mn, Sn, Sb, P. In several papers [2630], it is assumed that the CSL boundaries migrate faster than high-energy boundaries because there is less segregation of solute atoms at CSL boundaries, and therefore the CSL boundaries are not dragged. However, it was also observed [31] that more S was found at the grain boundary between the growing (1 lO)[OOl] grain and its surrounding matrix, than at the boundaries between coarse grains, which are supposed to be less mobile; and no difference of S content was observed on different CSL boundaries. This fact suggests that the moving boundary may have more solute atoms, therefore the argument that low solubility makes the CSL boundaries more mobile may not be valid. Furthermore, the temperature needed to develop the secondary recrystallization texture is higher than that for normal grain growth [32]. It is, therefore, doubtful that the same mechanism explaining a high mobility of CSL [2630] boundaries in pure materials at low temperature, holds in the case of the grain-oriented electrical steels.
From the experimental data for the tilt boundary presented in Fig. 4, the constants used in this expression were determined [37]. For the < llO> axis, 6, was 26.6” and A was 0.234, and for the < lOO> axis, 8, was 29.8” and A was 0.35. In Fig. 4, the energy cusp of the CSL boundaries can be observed for the X.1 boundary and a certain energy drop is observed around the X3 (0 = 70” around < 110 > axis) boundary. In polycrystalline materials there are five degrees of freedom which define both misorientation between grains and the grain boundary plane. In our analysis, only the misorientation between grains was taken into account, but the orientation of the grain boundary plane remains uncertain. In discussing the energy of the tilt boundary [36], in determining the constants in the formula, the effect of boundary inclination was averaged. In the 3%Si-Fe specimen, the shape of the grain was virtually isotropic, and no apparent faceting of the grain boundary was observed. It was, therefore, justified to use an average value for the grain boundary inclination. For the twist boundary, we could not find any experimental data. From the dislocation theory of the grain boundary [37], it was
4.2. The relation between grain boundary energy and mobility It is generally accepted that the misorientation angle is related to the grain boundary energy. Read and Schockley [33] proposed a well-known formula which was verified by Dunn [34-361 for 3%Si-Fe. The following expression was used: E(B) = E&&4 - IriB)
(2)
where E is the grain boundary energy, 0 is the misorientation angle, and E0 and A are constant. E,, is defined by the following expression: E,,, = Eo9,
(3)
where E,,, is the energy at the maximum, and 0, is the angle for which the maximum is observed.
1.4
*I
21 P
g i
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1
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j 0.6 Q) .$ 0.4. 2
0.2.
*
01 3, 8 - * 8 8 “““1 10 20 30 40 50 60 0 Misorientationangle(degree)
c
70
Fig. 4. The experimental data of the grain boundary energy and the tilt angle for a tilt boundary in 3%Si-Fe steel.
HAYAKAWA and SZPUNAR:
SECONDARY RECRYSTALLIZATION
Boundary energy(Ec) Fig 5. The probability of grain boundaries having higher _ energy than the critical energy E, around the Goss gram, around the grain having average orientation, and around the main texture component grain in specimen A.
justified to express the energy versus the misorientation angle using the same formula as that for the tilt boundary, and Wolf [38] showed, by molecular
dynamics calculations, that the relation between the misorientation angle and the energy of the twist boundary is similar to the tilt boundary. In the first attempt at estimating grain boundary energy, we used the experimental data [33-361 in Fig. 4 obtained for the tilt grain boundary, with axes < 100 > and < 110 > The curve described by the Read-Schockley formula gives a good fit only up to 45”, and we used the linear approximation to express the energy at high angles. For the tilt axis < Ill> , the calculated energy is available [39]. These data show a large energy drop for C3 (60” rotation around
Fig. 6. Precipitates in 3%Si-Fe steel observed in specimen B, using SEM after annealing at 1173 K for ten minutes. The right-hand side grain is a growing large Goss grain.
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Boundary energy(Ec)
Fig. 7. The value of {P(Goss,E > EJ - P(average,E > EJ}.
the < 11 1 > axis), and the angle corresponding to the maximum energy is similar to other tilt axes. The maximum energy of an < ill> tilt boundary is similar to that of the < 110 > tilt boundaries. The tilt angle of 70” around the < 110 > axis corresponds to the misorientation angle of 60” around the < 111 > axis, choosing the minimum misorientation angle. Thus, we used a different line as indicated in Fig. 4 for the < 111 > rotation axis. For other axes, the energy formula was approximated according to the angular deviation from the < loo>, < 1 lO> and < 111> axes. Using these fitted curves, the grain boundary energy was calculated from the misorientation angle and axis distribution. Since there are no cusps observed for CSL boundaries, we do not consider them as “special” in the calculation of energy. Figure 5 illustrates the calculated probability of the grain boundaries having energy that is higher than EC, where EC is a certain value of the grain boundary energy, around the Goss grain, around the grain having average orientation, and the grain of the main texture component. The Goss grain is surrounded by the highest number of high-energy grain boundaries. Following this finding, in order to simulate the abnormal growth, we made assumptions that are contrary to those made by other authors [40,41]. The Goss grain is preferentially surrounded by high-energy boundaries and not by low-energy boundaries. According to the previous assumptions, the Goss grain, or a grain which grows abnormally, was surrounded by a large number of low-energy grain boundaries. These assumptions were derived from stressing too strongly the existence and importance of some selected CSL boundaries, and neglecting the fact that the energy cusp of the low angle grain boundary (Xl) is deep, and the energy drop of the twin boundary (C3) is large, and that the grain of the main texture component has the maximum probability of being surrounded by Z 1 and X3 boundaries. From our results, it is concluded that the grain of the main texture component is surrounded by the highest number of low-energy boundaries,
1292 HAYAKAWA
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We agree that the low-energy boundary is favoured in the grain growth process because the critical radius for growth for the low-energy boundary is small [32]. However, the experimental findings showed that the growing grains had a higher number of general boundaries, while the small grain had a low number of the general boundaries. This observation was true both for 3%Si-Fe [42] and for Ni alloy [43]. These facts suggest a high mobility of the general boundaries, and that the grain surrounded by highenergy boundaries is growing, despite the unfavourable growth condition related to a large critical radius. We would like to emphasize that the concept of boundary energy used by us here, is mainly for the interpretation of the boundary structure. It has been shown that the boundary energy is related to the free volume, and the free volume can be linked to physical properties such as grain boundary mobility and grain boundary diffusion. Furthermore, from simulation work [44], we learned that when the low-energy boundaries played an important role during the grain growth, wetting around the growing grain was expected. This wetting
(a) 0
is not observed in grain-oriented electrical steel, and this fact can be used to support the assumption that low energy grain boundaries do not play an important role in the development of the Goss texture in grain-orientated electrical steels. In addition, in a recent simulation of the grain growth in S%Si-Fe steel [IO], it was concluded that the assumption of a high mobility of low-energy boundaries cannot produce the Goss texture. The high mobility of the high-energy boundary and the low mobility of the low-energy boundary can be explained using the following arguments. One proposed advantage of the CSL boundary was its shorter distance of atomic jump [45]. The process of grain boundary migration does not take place through a jump of an atom from one grain to another grain, but through the exchange of vacancies [8,46,47]. The high-energy boundary is more capable of absorbing and emitting vacancies [48] and the number of vacancies is related to the disorder in the grain boundary structure. The high-energy boundary has a more disordered structure, therefore a high
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Fig. 8. The maximum value of {P(S,E > EC)- P(average,E > EC)}with respect to ECaround various grain orientations (S): (a) specimen A, cross-section (D2= 0”; (b) specimen A, cross-section @z= 45”; (c) specimen B, cross-section (P2= 0”; (d) specimen B, cross-section @Z= 45”. Arrows indicate the GOSS orientation.
$ 0
HAYAKAWA and SZPUNAR: number of vacancies and contribute to a high mobility. 4.3. Interaction precipitates
between
SECONDARY RECRYSTALLIZATION OF ELECTRICAL STEELS 1293
dislocations
should
the grain boundary and
The development of the secondary recrystallization texture is controlled by the precipitates and, without the precipitates, the Goss texture does not develop. Interaction between the precipitates and the grain boundaries, therefore, is more important than the inherent mobility differences between different grain boundaries. There is not enough knowledge about this interaction in Fe-3%Si steel; however, it was reported [49] that for an aluminium alloy, the interaction between the precipitates and the grain boundaries was stronger for the low-energy boundaries than for the high-energy boundaries. The conclusion was that the low-energy grain boundaries are more strongly pinned by the particles than the high-energy boundaries. There is a high probability that this is also true in the case of the grain-oriented electrical steels and the difference between mobility of the high-energy boundary and that of the low-energy boundary becomes more significant. Secondary recrystallization is often related to the coarsening and depletion of precipitates, and this process was explained by the diffusion controlled Ostwald ripening [50, 511. We assume that the coarsening of precipitates starts at the grain boundary because the grain boundary diffusion rate is higher than the bulk diffusion. The boundary diffusion rate is dependent on the misorientation angle, which is similar to the grain boundary energy: the higher the boundary energy the higher the diffusion rate [52]. Attempts have been made [53] to relate the grain boundary energy to the grain boundary diffusion. The formula describing this relationship was proposed, and this formula was tested in various materials [54]. In the diffusion process, the presence of the vacancies, or interstitial atoms, at the grain boundary is important because the higher the number of these defects the higher the diffusion. The same defects are also linked to the high mobility of the high-energy grain boundaries. To illustrate some of these phenomena we observed the precipitates between a growing large Goss grain and small grains, after annealing specimen B at 1173 K for ten minutes. The coarse precipitates (see Fig. 6) were frequently found inside large growing Goss grains, and seldom found inside small grains, These facts might be explained by a faster coarsening of precipitates at the boundary of the growing grain. We expect that the high-energy boundary has a high diffusion rate, leading to the acceleration of Ostwald ripening of the precipitates. 4.4. Mechanism of the abnormal grain growth of Goss grains In this chapter, we would like to propose a model of the development of the Goss texture in secondary
recrystallization, based on the pinning of the boundaries by precipitates. We assume that, at the beginning of the annealing, all the grain boundaries are pinned by precipitates. The rate of coarsening of precipitates is higher for high-energy boundaries, that have high grain boundary diffusion coefficients. Therefore, at the early stage of the annealing, only the high-energy boundary moves when the precipitates on this boundary coarsen to some critical size for the pinning. Taking these assumptions into account, it is possible that the boundary, having a higher energy than the certain critical value (E,), can move. Let us express the probability that the grain boundary has a higher energy than a certain critical energy (E,), around the grain of arbitrary orientation S, by P(S,E > E,). This value represents the probability of the existence of mobile boundaries, and the difference between two probabilities {P(S,E > E,) P(average,E > E,)} describes the growth advantage of the S orientation. Following this definition, the data presented in Fig. 7 were obtained. The of {P(Goss,E > EJ - P(average,E > calculation E,)j, illustrates the growth advantage of the Goss grain over the grain of average orientation in specimens A and B. This distribution shows the maximum value of 26% for specimen A, and 17% for B. At the early stage of the annealing, when the value of E, is high, the growth advantage {P(Goss,E > EE) - P(average,E > E,)} is small, thus we can expect a normal grain growth, which is usually observed before the onset of secondary recrystallization. According to the progress of annealing, the coarsening of precipitates continues such that the precipitates, which are situated on lower energy boundaries, also reach the critical size for the pinning and such a boundary begins to move. We can, therefore, assume that, during the annealing process, the value of EC decreases. As the value of EC decreases from the highest value in Fig. 7, the value of {P(Goss,E > EC)- P(average,E > EC)} increases, such that the Goss grain has the advantage of having more mobile boundaries than the grains which have the average orientation, and we can expect the abnormal growth of the Goss grain at this stage. If the decrease of E, is too fast, and this may happen when the annealing temperature is too high, {P(Goss,E > EC)- P(average,E > EC)}decreases too quickly and the advantage of the Goss grains is quickly lost. This explains the failure to develop the Goss texture when the annealing temperature is very high. In order to compare the growth advantage around various other grain orientations, we calculated the maximum value of {P(S,E > EC) P(average,E > EC)}with respect to ECaround various orientations, and it is represented in Fig. 8. This value corresponds to the maximum surplus of mobile boundaries during the annealing, for the grain having orientation S over the grain having average
1294 HAYAKAWA and SZPUNAR:
SECONDARY RECRYSTALLIZATION OF ELECTRICAL STEELS
orientation. The map in Fig. 8 shows how strongly favoured the growth of the Goss orientation is over any other texture component. In specimen A, there is a clear, strong maximum at the Goss orientation. In specimen B, there is also a similar maximum at the Goss orientation; however, it is wider and weaker than that of specimen A. The shapes of the probability maximum correspond well to the final orientation of secondary grains in both specimens. The number of secondary grains close to the Goss orientation is higher for specimen A than for specimen B, and the deviation from the Goss orientation is small along the TD/< 110 > axes and large along the ND//< 110 > axes [5]. According to our model, the grain having a surplus of mobile boundaries is able to grow during the secondary recrystallization process, and Fig. 8 indicates that the secondary grains in specimen A should have orientations closer to the Goss orientation than in specimen B. It is to be noted that the Goss texture development of two different electrical steels are explained consistently using our model. The analysis supports the conclusion that the mechanism of the secondary recrystallization in 3%Si-Fe grain-oriented electrical steel is related, not to the special (CSL) boundary, but to the high-energy boundary with a disordered structure.
I.
N. Rouag, G. Vigna and R. Penelle, Acta metall. 38, 1101 (1990).
8. G. Gottstein Forum 94-96,
and F. Schwarzer,
Materials
Science
187 (1992).
9. D. J. Srolovitz, M. P. Anderson, P. S. Sahni and G. S. Grest, Acta metall. 33, 2233 (1985). 10. D. Hinz and J. A. Szpunar, Phys Rev. B52,9900 (1995). 11. C. V. Thompson, H. J. Frost and F. Spaepen, Acta metall. 35, 887 (1987).
12. N. C. Pease, D. W. Jones, M. H. L. Wise and W. B. Hutchison, Met. Sci. 15, 203 (1981). 13. J. Harase, Materials Science Forum 94-96, 419 (1992). 14. Y. Yoshitomi, Y. Ushigami, J. Harase, T. Nakayama, H. Matsui and N. Takahashi, Materials Science Forum 113-115,
715 (1993).
15. K. Pawlik, Phys. stat. sol (b) 134, 477 (1986). 16. A. Morawiec, J. A. Szpunar and D. C. Hinz, Acta metall. 41, 2825 (1993). 11. H. Grimmer, Acta Cryst. A30, 685 (1974). 18. D. G. Brandon, Acta metall. 14, 1479 (1966). 19. Y. Hayakawa, J. A. Szpunar, G. Palumbo and P. Lin, J. Magnetism and Magnetic Materials 160, 143 (1996). 20. J. Harase and R. Shimizu, Materials Science Forum 94-96, 399 (1992). 21. H. Gleiter and B. Chalmers, Progress in Materials Science 16, 1 (1972).
22. R. Z. Valiev, V. Yu. Gertsman and 0. A. Kainyshev, Phys. stat. sol (a) 97, 11 (1986). 23. R. W. Balluffi, Y. Komem and T. Schober, Surface Science 31, 68 (1972). 24. T. Schober and R. W. Balluffi, Phil. Mag. 21, 109 (1970).
25. A. P. Sutton and R. W. Balluffi, Acta metall. 35, 2177 (1987).
5. CONCLUSIONS (1) The probability of the presence of a grain boundary having a misorientation angle between 20” to 45” is highest around the Goss grain. (2) There is no unique and special configuration of the CSL boundaries around the Goss grain. On the contrary, the total number of CSL boundaries from El to z51 is small, and the number of the C3 boundary or CSL boundaries having rotation axis < 111 > is the lowest. (3) The Goss grain is surrounded by the highest number of high-energy grain boundaries. (4) The mechanism of secondary recrystallization proposed in this paper links the development of Goss texture to a high concentration of the general high energy boundaries that have a disordered structure, and these are often linked to a high migration rate and a high grain boundary diffusion rate which facilitates coarsening of precipitates.
26. K. T. Aust and J. W. Rutter, AZME Trans. 215, 119 (1959). 21. G. Gottstein and L. S. Shvindlerman, Scripta Metall. 27, 1515 (1992).
28. K. T. Aust and J. W. Rutter, AZME Trans. 215, 820 (1959).
29. D. W. Demianczuk and K. T. Aust, Acta metall. 23, 1149 (1975).
30. D. A. Molodov, B. B. Straumal, L. S. Shvindlerman, Scripta Metall. 18, 207 (1984).
31. K. Tagashira and H. Nakae, J. Japan Inst. Metals 35, 683 (1971).
32. J. E. May and D. Turnbull, AZME Trans. 212, 769 (1958).
33. W. T. Read and W. Shockley, Phys. Rev. 78,275 (1950). 34. C. G. Dunn and F. Lionetti, AZME Trans. 185, 125 (1949).
35. C. G. Dunn, F. W. Daniels and M. J. Bolton, AZME Trans. 188, 368 (1950).
36 C. G. Dunn. F. W. Daniels and M. J. Bolton. AZME Trans. 188, i245 (1950). 31 H. Brooks in Me&l Interface, p. 42, American Society for Metals (1952). 38 D. Wolf, Phil. Mag. B59, 667 (1989). 39. D. Wolf. Phil. Map. A62. 447 (1990). 40. T. Nakayama and Y. Ushigami, Materials Science Forum 94-96, 413 (1992).
REFERENCES 1. Y. Inokuti and C. Maeda, Trans. Iron SteelZnst. Jpn 24, 657 (1984).
2. M. Matsuo, ZSZJ International 29, 809 (1989). 3. J. Harase and R. Shimizu, Trans. Zron Steel Inst. Jpn 29, 388 (1988).
4. R. Shimizu and J. Harase, Acta metall. 37, 1241 (1989). 5. R. Shimizu, J. Harase and D. J. Dingley, Acta metall. 38, 1101 (1990). 6. J. Harase, R. Shimizu and D. J. Dingley, Acta metall. 39, 763 (1991).
41. G. Abbruzzese,
S. Fortunati
and A. Campopiano,
Materials Science Forum 94-96, 405 (1992). 42. T. Watanabe, Scripta Metall. 21, 427 (1987). 43. V. Randle and B. Ralph, Proc. Roy. Sot. A415, 239
(1988). 44. A. D. Rollett, D. J. Srolovita and M. P. Anderson, Acta metall. 37, 1227 (1989). 45. M. L. Kronberg, F. H. Wilson, Trans. Met. Sot. AZME
185, 501 (1949). 46. B. Ralnh. K. B. Shim. Z. Huda, J. Forley and M. Ed&nghe, Materials Science Forum 94-96, 129 (1992).
HAYAKAWA and SZPUNAR:
SECONDARY RECRYSTALLIZATION
41. S. E. Babcock and R. W. Balluffi, Acta metall. 31, 2367 (1989). 48. W. Hahn and H. Gleiter, Acta metall. 29, 601 (1980). 49. C. J. Tweed, B. Ralph and N. Hansen, Acta metall. 32, 1407 (1984). 50. M. W. Swift, Met. Trans. 153 (1973).
OF ELECTRICAL
STEELS
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51. M. W. Swift, Met. Trans. 4, 841 (1973). 52. N. L. Peterson, International Metal Reoiews 28, 65 (1983). 53. V. T. Borisov, V. M. Golikov and G. V. Scherbedinskiy, Phys. Met. Metal/. 17, 80 (1964). 54. J. Pelleg, Phil. Msg. 14, 595 (1966).
Acta mater. Vol. 45, No. 3, pp. 1285-1295, 1997 Copyright 0 1997 Acta Metallurgica Inc. Published by Elsevier Science Ltd Printed in Great Britain. All rights reserved 1359~6454/97 $17.00 + 0.00
THE ROLE OF GRAIN BOUNDARY CHARACTER DISTRIBUTION IN SECONDARY RECRYSTALLIZATION OF ELECTRICAL STEELS Y. HAYAKAWAtS and J. A. SZPUNAR Department
of Mining
and Metallurgical Engineering, McGill Canada, H3A 2T5
University,
Montreal,
Quebec,
(Received 7 November 1995; acceplad 6 February 1996)
Abstract-Grain Boundary Character Distributions (GBCD) in grain-oriented electrical steels were calculated from the Orientation Distribution Functions of the primary recrystallization texture. The probability of a grain boundary having a misorientation angle from 20” to 45” is highest around the Goss grain. The observed difference in GBCD implies that the Goss grain is surrounded by the highest number of high-energy boundaries. The high-energy boundary has more structural defects, and these are often linked to a high grain boundary migration rate and a high grain boundary diffusion rate. An explanation of Goss texture development in secondary recrystallization is proposed, based on the property of the high-energy boundary. The role of special Coincident Site Lattice boundaries is analysed, and we conclude that they do not play a significant role in the development of Goss texture. Copyright #Q 1997 Acta Metallurgica Inc.
1. INTRODUCTION Various mechanisms of the development of secondary recrystallization { 1 lo} < 001 > Goss texture have been already proposed. They can be roughly divided into two types: one theory assumes that Goss grains form colonies and, as a result of coalescence during the annealing treatment, they develop the size-advantage [ 1, 21. This interpretation is predominantly used to explain the texture development in conventional grain-oriented electrical steel for which the final cold rolling reduction is approximately 60%. Another theory claims that the Goss grains are surrounded by the highest number of Coincidence Site Lattice (CSL) boundaries [3-71, and CSL boundaries are believed to have both lower grain boundary energies and higher migration mobilities than other general boundaries [8]. This theory is predominantly used to describe the case of high permeability grain-oriented electrical steel, for which the final cold rolling reduction is approximately 85%. Both of the above theories have weak points which are listed below. The main argument against the former theory is that, using the result of Monte Carlo simulation [9, IO], the size-advantage itself cannot maintain the secondary recrystallization. It has already been argued [ 1 l] that the growth rate of an embedded large grain was so small that the grain _ .._.~ ton leave from Kawasaki Steel Corporation, l-Kawasakidouri, Mizushima, Kurashiki, $To whom all correspondence
Okayama, Japan. should be addressed.
would be absorbed by the matrix when boundary energies, and mobilities are uniform. It was also demonstrated that, in the case of high permeability steel, the Goss grains did not form colonies [4, 121. Our argument against the latter theory is that, the number of CSL boundaries, other than the low angle grain boundary (El), is too small at approximately 10% [3-51 to be responsible for a major change in texture. Some authors [3,4,7] have reported that there were more CSL boundaries around the Goss grain, and emphasized a role of some special boundaries X9 [5], C7 [13], Z5 [14]. The number of these boundaries is less than 2%. In addition, the reported relative abundance in the presence of the CSL boundaries was less than 20%, and such an abundance was smaller than the statistical error caused by the small number of analysed grains. Using computer simulation, we estimated that if, for example, 100 grains were measured [7], the estimated error is 60%; if 500 grains [3,4] were analysed, the error is about 40%. The type of important CSL boundaries differed from case to case (X9 [5], C7 [13], X5 [14]); however, no explanation of the selection mechanism was offered. This brief discussion demonstrates that there is no satisfactory explanation of the development of the Goss texture in grain-oriented electrical steels. The aim of our research is to investigate the Grain Boundary Character Distribution (GBCD) of both conventional and high permeability steels and to propose a consistent mechanism of the secondary recrystallization.
1285
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HAYAKAWA
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SECONDARY RECRYSTALLIZATION OF ELECTRICAL STEELS
2. EXPERIMENT
3. RESULTS
Two different types of primary recrystallized texture are investigated. One specimen is a high permeability steel (Specimen A). The other specimen is a conventional steel (Specimen B). In specimen A, there are MnSe and also AlN precipitates. In specimen B, MnS precipitates are used as an inhibitor. A comparison between these materials is made in Table 1. X-ray reflection pole figures (llO), (200), (211) were measured from the subsurface layer at approximately l/l0 of the specimen thickness. The Orientation Distribution Functions (ODF) were calculated using the discrete method [15], which is free from ghost peaks that may distort the results obtained using the series expansion method. To calculate GBCD, pairs of grains were generated in proportion to the value of the ODF (f(g)), using the method proposed by Morawiec et al. [16]. To investigate grain boundaries around the grain having a certain specific orientation, the orientation of the selected grain was fixed, and the orientation of a neighbouring grain was generated using the same method. 10’pairs of grains were generated from the ODF in order to calculate the GBCD, and the error of such analysis caused by the number of grains was less than 1%. Misorientation angles, which are the minimum angle among the equivalent 24 angles and rotation axis, were calculated by using the unit quaternion [17]. The CSL boundary was defined by comparing the quaternion of the grain misorientation with that of the CSL using Brandon criterion [18], which allows 15/~‘/* degrees of deviation from the ideal position. The validity of the statistical calculation of GBCD has been tested previously [19] by comparing the result obtained from direct measurement of misorientation of grains using the Electron Back Scattering Pattern (EBSP). The portion of CSL boundaries obtained from the measurement of 511 grains in specimen A shows good agreement with the calculation except for the xl boundary. The percentage of the El boundary is higher than the calculated value, and the main reason for such a difference is that xl boundaries tend to form colonies that cannot be predicted from the ODF analysis.
3.1, Misorientation angle distributions
The ODF of both specimens is shown in Fig. 1. The most important texture characteristic of specimen A is a strong so-called y fibre (ND// < 1 11 >), which has its maximum value in the vicinity of {ill}< 112~ (precisely, at Q1 = 90”, 4 = 60”, 02 = 45”,f(g) = 11.86) the value of ODF at the Goss orientation (0, = 90”, 4 = 90”, Qz = 45”) is rather weak (f(g) = 0.46). Specimen B has a weak y fibre texture, with its maximum value at { 111) < 011 > (@ = 60”, 4 = 55”, @ = 45”, f(g) = 7.52), and a strong q fibre texture (RD/< 100 >), the intensity of the Goss orientation is rather strong (f(g) = 3.81). The probability of boundaries having misorientation angle (w) between certain angles (A) and (B) for grain having a specific orientation (g) is defined here by the following expression. Probability
(A < w < B,g) (X) = {W
< w < W/N(g))
where N(A < o < B,g) is the number of boundaries that have misorientation angle (A < o < B) around the grain having a specific orientation (g), and N(g) is the number of total generated boundaries around the grain having a specific orientation (g). In Fig. 2, the probability of grains having misorientation angle (0) with respect to the Goss grain, the grain having average orientation, and the grain representing the main texture component, are shown. The main difference between these distributions is that the Goss grain has more intermediate misorientation high angle (20” < w < 45”) grain boundaries, and less low angle (15” > w) and large misorientation high angle (45” < o) grain boundaries than a grain having an average orientation or the grain of the main texture component. Figure 2 also shows that the main texture component grains have fewer intermediate misorientation high angle boundaries and more low or large misorientation high angle grain boundaries than grain having the average texture. This observation is true for both specimens. The type of analysis presented above can be now extended to grains having other orientations. The misorientation probability of an intermediate (20” < w < 45”) high angle grain boundary is calculated around grains of different orientations,
Table 1. Comparison of the investigated specimens Thickness (mm)
Main component
A High permeability
0.23
B Conventional
0.35
{111}<112> 11.86 {111}<110> 7.40
Specimen type
x 100 (1)
fk)
Goss
Induction after final annealing
Sk)
w-u
0.46
1.93
3.81
1.84
HAYAKAWA
and SZPUNAR:
SECONDARY
RECRYSTALLIZATION
3.2. CSL boundary distribution
The probability of CSL boundaries around the grain having specific orientation (g) is defined here by the following expression. (Cn, g) (%) = {N(Cn, g)/N(g)} x 100
where N(Cn, g) is the number of 2.n CSL boundaries around the grain having a specific orientation (g), and N(g) is the number of total generated boundaries around the grain having a specific orientation (g). The probabilities of CSL boundaries around grains
(4 o
IO
20
30
40
50
60
70
60
STEELS
1287
of various orientations were calculated and are given in Table 2. The total probability of CSL boundaries from Cl to X51 has a maximum of 26% for specimen A, and 24% for specimen B, around the grains representing the main texture component. Around the Goss grain, the probability is low. In previous calculations [6, 201, Cl and C3 boundaries were excluded from the CSL statistics because the low mobilities of these boundaries were never questioned. Excluding these boundaries, the highest probability of CSL boundaries is around { 110) < 113 > ($ = 65 , C$= 90”, $ = 45) orientation. The probability of CSL boundaries around the Goss grains is higher than around the grain having average orientation, however, grains having other orientations such as {111}<011>, and {210}<001> (@=OU, 4=35, a2 = Ol-) have higher or similar probabilities. The most important observation is that the absolute difference in probability is, at best, only 3%. The CSL boundaries are often described by defining the rotation axis and the rotation angle [S, 61. For both specimens, none of these probabilities indicates that the Goss grain has the highest number
and is shown in Fig. 3 in the grain orientation space. For specimen A, the probability shows a sharp maximum, which is 76% at the Goss orientation, and a minimum, which is 37%, at the main texture component. It must be noted that the difference in the probability is very large at approximately 40%. For specimen B, the Goss grain has a higher probability of being surrounded by the intermediate misorientation high angle grain boundaries, however, the peak position is rotated by 20” from the Goss orientation the around the ND/< 110 > axis.
Probability
OF ELECTRICAL
0
90
01 10
20
30
40
50
60
70
60
90 1
I
$gi$g?q
m
35 t
P'
40
4 50 60
1:: 0
10
60 -
20
30
40
50
60
70
60
90
90
0
10
20
30
40
50
60
70
60
Fig. 1. The ODF of the 3%Si-Fe specimens after decarburizing annealing. Arrows indicate Goss orientation: (a) specimen A, cross-section (D2= 0’; (b) specimen A, cross-section @I = 45”; (c) specimen B. cross-section, @2 = 0”; (d) specimen B, cross-section, QZ = 45”; (e) skeleton line along q fibre texture (Q, = O”, @2 = 0”); (f) skeleton line along y fibre texture (Q = 55”, (D2= 45”).
90
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HAYAKAWA
and SZPUNAR:
SECONDARY RECRYSTALLIZATION OF ELECTRICAL STEELS
@I
2.5 G 2.0 c= 1.5
0
0
5
pii&iq
10
15
20
25
30
+(degree)
pi&icy
(f) 10
7 8 y5
6
1 B
over the Goss orientation. Since the (21 I)<011 > orientation is not observed in the secondary recrystallized specimen, assuming a positive role of the C9 boundary in the grain growth process is questionable. Around the Goss grain of specimen B, the probability of the X3 and C7 boundaries is the lowest, and of the X9 boundary is average. The probability of the X5 boundary is the highest; however, the absolute difference in probability of the X5 boundary between the Goss grain and the grain having an average orientation is only 1.5%. Such a small difference cannot support the special role of the CSL boundaries in the growth of Goss grains. To summarize, we claim that none of the present calculations support the CSL-based grain growth model. We do not observe a high percentage of CSL boundaries around the Goss grain. In fact, around the Goss grain, the total number of the CSL boundaries is low, and the percentage of the X3 boundary and CSL boundaries having rotation axis < Ill> , is the lowest. The most important finding of the GBCD analysis is presented in Fig. 3, where it is demonstrated that the Goss grain is surrounded by the highest number of intermediate misorientation
Fig. 1. Continued of CSL boundaries. In fact, the probability of the CSL boundary having < 111> rotation axis is the lowest. The probabilities of low numbers CSL boundaries (C3, X.5, X7, C9) around the grains having different orientations were also investigated. Around the Goss grain of specimen A, the probability of the X3 boundary is the lowest, and the probabilities of the X5 and X7 boundaries are very low. The number of E9 boundaries around the Goss grains is approximately 2%, which is near the maximum number, as mentioned by Harase et al. [5,6]. Around grains having other orientations, such as {211}<011>, {110}<111> and {113}<332> (@, = 0”, 4 = 25”, @ = 45”), the probability of the X.9 boundary is comparable to that obtained around the Goss grain. The product of the probability of X9 around a specified grain and the ODF value corresponding to this grain orientation (Pcnz9) was used to explain the advantage of the Goss grain in the growth process [6]. For specimen A, the PcnE9 value for the grain having (21 l} ~01 1> orientation is 2.03, and this value is higher than 0.97 for the Goss grain. This means that, according to the previous model [6], the {211}<011> orientation should be favoured
0
5
10 15 20 25 30 35 40 45 60 55 60
Misorientation angle (degree)
a
Misorientation angle (degree)
Fig. 2. The misorientation angle Goss grain (a) High permeability steel.
distribution around the steel. (b) Conventional
SECONDARY RECRYSTALLIZATION OF ELECTRICAL STEELS 1289
and SZPUNAR:
HAYAKAWA
high angle (20” < w < 45”) grain boundaries. makes the Goss grain unique.
This
4. DISCUSSION 4.1. CSL theory applied to the grain growth It is widely accepted [8,21,22] that the CSL boundary has lower energy than the general boundary. From a structural point of view, the CSL boundary has a periodic dislocation arrangement reducing the grain boundary energy. These periodic dislocations are lattice dislocations in the case of the low angle grain boundary, and Displacement Shift Complete (DSC) dislocations [23, 241 in the case of the CSL boundary. The special character of the CSL boundary always corresponds to a low grain boundary diffusivity, low segregation of solute impurity, low grain boundary sliding rate, and a high resistance to corrosion. All these phenomena demonstrate that the CSL boundary has similar properties to the low angle grain boundary, because both have similar structures. When the CSL theory is applied to the grain growth [5, 13, 141,it assumes that certain CSL boundaries have high mobilities. On the
(a) 0
other hand, it assumes that the low angle grain boundary (Cl), or the twin boundary (X3) and the general high-energy boundary have a low mobility. In general [8,21,22,25], the interfacial energy cusp is large for Xl and z3 boundaries, and that of other CSL boundaries is smaller, or sometimes undetectable. Thus, it is natural to assume that Cl and X3 boundaries are the most typical CSL boundaries. The exclusion of the Cl and X3 boundaries from the discussion of the grain growth is inconsistent with other applications of the CSL theory. We use the term low-energy boundary for these boundaries including Xl and X.3 and CSL boundaries. Please note that the high mobility of CSL boundaries was observed only in pure materials. Aust et al. [26] observed a high mobility of CSL boundaries in a zone melted Pb with a very small addition of Sn from 0.002 to 0.005%. Another experiment was conducted on 99.9992% pure Al% [27], less than 20 ppm addition to pure lead [28], less than 40 ppm Cu addition to aluminium [29], and 99.999% high purity tin [30]. The high mobility of CSL boundaries is not observed when more than 0.005% tin is added [26], and the purity of aluminium
(c)
@, 10
20
30
40
50
60
70
60
0
90
@I IO
20
30
40
50
60
70
80
90
10
20
30
40
50
60
70
80
90
A
5 15
15
+
+
25
25
35 45
lb)
(4
A
n
60
60
80
80
0
10
20
30
40
50
60
70
80
90
0
Fig. 3. The probability (%) of boundaries having misorientation angle from 20” to 45” around grains having various orientations: (a) specimen A, cross-section @Z= 0”; (b) specimen A, cross-section @2 = 45”; (c) specimen B, cross-section, @Z= 0”; (d) specimen B, cross-section, a2 = 45”. Arrows indicate the Goss orientation, and the contour line of the average value is indicated by “A”.
1290 HAYAKAWA and SZPUNAR:
SECONDARY RECRYSTALLIZATION OF ELECTRICAL STEELS
Table 2. The probabilities (%) of CSL boundaries around the grain having various orientations in the specimen A and B; (a) maximum probability which is observed around the grain having a specified orientation {hk[}
Specimen A (%) {hkl}
CSL 112151 3
26.2 {111}<112> 17.4 {111}<112> 15.4 {110}<113> 4.9 {110}<113> 5.9 {211}<011> 7.9 (111)<011 > 5.5 {111}<112> 4.0 {110}<113> 2.1 {lll}
(b) Specimen
(a) Specimen B (%) (hkl)
{lll}
(c) Specimen
(C)
(;)
(G,
($
16.3 14.9 14.6 2.4 4.2 2.0 0.3 1.7 0.8 2.0
19.6 14.7 14.1 3.7 2.8 2.1 0.6 2.7 0.5 1.1
19.6 15.2 13.0 1.7 3.2 4.6 2.2 0.9 1.0 1.0
19.0 15.5 13.6 2.0 3.2 4.2 1.9 1.2 1.1 1.0
X
is reduced to 99.995% [27]. The high mobility of the CSL boundaries was observed only at a low temperature [27,28]. This does not apply to grain-oriented electrical steel, which is a commercial product with a considerable amount of solute atoms, such as Si, Mn, Sn, Sb, P. In several papers [2630], it is assumed that the CSL boundaries migrate faster than high-energy boundaries because there is less segregation of solute atoms at CSL boundaries, and therefore the CSL boundaries are not dragged. However, it was also observed [31] that more S was found at the grain boundary between the growing (1 lO)[OOl] grain and its surrounding matrix, than at the boundaries between coarse grains, which are supposed to be less mobile; and no difference of S content was observed on different CSL boundaries. This fact suggests that the moving boundary may have more solute atoms, therefore the argument that low solubility makes the CSL boundaries more mobile may not be valid. Furthermore, the temperature needed to develop the secondary recrystallization texture is higher than that for normal grain growth [32]. It is, therefore, doubtful that the same mechanism explaining a high mobility of CSL [2630] boundaries in pure materials at low temperature, holds in the case of the grain-oriented electrical steels.
From the experimental data for the tilt boundary presented in Fig. 4, the constants used in this expression were determined [37]. For the < llO> axis, 6, was 26.6” and A was 0.234, and for the < lOO> axis, 8, was 29.8” and A was 0.35. In Fig. 4, the energy cusp of the CSL boundaries can be observed for the X.1 boundary and a certain energy drop is observed around the X3 (0 = 70” around < 110 > axis) boundary. In polycrystalline materials there are five degrees of freedom which define both misorientation between grains and the grain boundary plane. In our analysis, only the misorientation between grains was taken into account, but the orientation of the grain boundary plane remains uncertain. In discussing the energy of the tilt boundary [36], in determining the constants in the formula, the effect of boundary inclination was averaged. In the 3%Si-Fe specimen, the shape of the grain was virtually isotropic, and no apparent faceting of the grain boundary was observed. It was, therefore, justified to use an average value for the grain boundary inclination. For the twist boundary, we could not find any experimental data. From the dislocation theory of the grain boundary [37], it was
4.2. The relation between grain boundary energy and mobility It is generally accepted that the misorientation angle is related to the grain boundary energy. Read and Schockley [33] proposed a well-known formula which was verified by Dunn [34-361 for 3%Si-Fe. The following expression was used: E(B) = E&&4 - IriB)
(2)
where E is the grain boundary energy, 0 is the misorientation angle, and E0 and A are constant. E,, is defined by the following expression: E,,, = Eo9,
(3)
where E,,, is the energy at the maximum, and 0, is the angle for which the maximum is observed.
1.4
*I
21 P
g i
1.2 0
1
+
0.8
j 0.6 Q) .$ 0.4. 2
0.2.
*
01 3, 8 - * 8 8 “““1 10 20 30 40 50 60 0 Misorientationangle(degree)
c
70
Fig. 4. The experimental data of the grain boundary energy and the tilt angle for a tilt boundary in 3%Si-Fe steel.
HAYAKAWA and SZPUNAR:
SECONDARY RECRYSTALLIZATION
Boundary energy(Ec) Fig 5. The probability of grain boundaries having higher _ energy than the critical energy E, around the Goss gram, around the grain having average orientation, and around the main texture component grain in specimen A.
justified to express the energy versus the misorientation angle using the same formula as that for the tilt boundary, and Wolf [38] showed, by molecular
dynamics calculations, that the relation between the misorientation angle and the energy of the twist boundary is similar to the tilt boundary. In the first attempt at estimating grain boundary energy, we used the experimental data [33-361 in Fig. 4 obtained for the tilt grain boundary, with axes < 100 > and < 110 > The curve described by the Read-Schockley formula gives a good fit only up to 45”, and we used the linear approximation to express the energy at high angles. For the tilt axis < Ill> , the calculated energy is available [39]. These data show a large energy drop for C3 (60” rotation around
Fig. 6. Precipitates in 3%Si-Fe steel observed in specimen B, using SEM after annealing at 1173 K for ten minutes. The right-hand side grain is a growing large Goss grain.
OF ELECTRICAL STEELS
1291
Boundary energy(Ec)
Fig. 7. The value of {P(Goss,E > EJ - P(average,E > EJ}.
the < 11 1 > axis), and the angle corresponding to the maximum energy is similar to other tilt axes. The maximum energy of an < ill> tilt boundary is similar to that of the < 110 > tilt boundaries. The tilt angle of 70” around the < 110 > axis corresponds to the misorientation angle of 60” around the < 111 > axis, choosing the minimum misorientation angle. Thus, we used a different line as indicated in Fig. 4 for the < 111 > rotation axis. For other axes, the energy formula was approximated according to the angular deviation from the < loo>, < 1 lO> and < 111> axes. Using these fitted curves, the grain boundary energy was calculated from the misorientation angle and axis distribution. Since there are no cusps observed for CSL boundaries, we do not consider them as “special” in the calculation of energy. Figure 5 illustrates the calculated probability of the grain boundaries having energy that is higher than EC, where EC is a certain value of the grain boundary energy, around the Goss grain, around the grain having average orientation, and the grain of the main texture component. The Goss grain is surrounded by the highest number of high-energy grain boundaries. Following this finding, in order to simulate the abnormal growth, we made assumptions that are contrary to those made by other authors [40,41]. The Goss grain is preferentially surrounded by high-energy boundaries and not by low-energy boundaries. According to the previous assumptions, the Goss grain, or a grain which grows abnormally, was surrounded by a large number of low-energy grain boundaries. These assumptions were derived from stressing too strongly the existence and importance of some selected CSL boundaries, and neglecting the fact that the energy cusp of the low angle grain boundary (Xl) is deep, and the energy drop of the twin boundary (C3) is large, and that the grain of the main texture component has the maximum probability of being surrounded by Z 1 and X3 boundaries. From our results, it is concluded that the grain of the main texture component is surrounded by the highest number of low-energy boundaries,
1292 HAYAKAWA
and SZPUNAR:
SECONDARY RECRYSTALLIZATION OF ELECTRICAL STEELS
We agree that the low-energy boundary is favoured in the grain growth process because the critical radius for growth for the low-energy boundary is small [32]. However, the experimental findings showed that the growing grains had a higher number of general boundaries, while the small grain had a low number of the general boundaries. This observation was true both for 3%Si-Fe [42] and for Ni alloy [43]. These facts suggest a high mobility of the general boundaries, and that the grain surrounded by highenergy boundaries is growing, despite the unfavourable growth condition related to a large critical radius. We would like to emphasize that the concept of boundary energy used by us here, is mainly for the interpretation of the boundary structure. It has been shown that the boundary energy is related to the free volume, and the free volume can be linked to physical properties such as grain boundary mobility and grain boundary diffusion. Furthermore, from simulation work [44], we learned that when the low-energy boundaries played an important role during the grain growth, wetting around the growing grain was expected. This wetting
(a) 0
is not observed in grain-oriented electrical steel, and this fact can be used to support the assumption that low energy grain boundaries do not play an important role in the development of the Goss texture in grain-orientated electrical steels. In addition, in a recent simulation of the grain growth in S%Si-Fe steel [IO], it was concluded that the assumption of a high mobility of low-energy boundaries cannot produce the Goss texture. The high mobility of the high-energy boundary and the low mobility of the low-energy boundary can be explained using the following arguments. One proposed advantage of the CSL boundary was its shorter distance of atomic jump [45]. The process of grain boundary migration does not take place through a jump of an atom from one grain to another grain, but through the exchange of vacancies [8,46,47]. The high-energy boundary is more capable of absorbing and emitting vacancies [48] and the number of vacancies is related to the disorder in the grain boundary structure. The high-energy boundary has a more disordered structure, therefore a high
(4
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20
30
40
50
60
70
60
0
90
@I IO
20
30
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60
70
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h NJ)
(b) 0
”
I\
1
10
10
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60
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20
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70
60
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,
10
20
,& 30
40
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Fig. 8. The maximum value of {P(S,E > EC)- P(average,E > EC)}with respect to ECaround various grain orientations (S): (a) specimen A, cross-section (D2= 0”; (b) specimen A, cross-section @z= 45”; (c) specimen B, cross-section (P2= 0”; (d) specimen B, cross-section @Z= 45”. Arrows indicate the GOSS orientation.
$ 0
HAYAKAWA and SZPUNAR: number of vacancies and contribute to a high mobility. 4.3. Interaction precipitates
between
SECONDARY RECRYSTALLIZATION OF ELECTRICAL STEELS 1293
dislocations
should
the grain boundary and
The development of the secondary recrystallization texture is controlled by the precipitates and, without the precipitates, the Goss texture does not develop. Interaction between the precipitates and the grain boundaries, therefore, is more important than the inherent mobility differences between different grain boundaries. There is not enough knowledge about this interaction in Fe-3%Si steel; however, it was reported [49] that for an aluminium alloy, the interaction between the precipitates and the grain boundaries was stronger for the low-energy boundaries than for the high-energy boundaries. The conclusion was that the low-energy grain boundaries are more strongly pinned by the particles than the high-energy boundaries. There is a high probability that this is also true in the case of the grain-oriented electrical steels and the difference between mobility of the high-energy boundary and that of the low-energy boundary becomes more significant. Secondary recrystallization is often related to the coarsening and depletion of precipitates, and this process was explained by the diffusion controlled Ostwald ripening [50, 511. We assume that the coarsening of precipitates starts at the grain boundary because the grain boundary diffusion rate is higher than the bulk diffusion. The boundary diffusion rate is dependent on the misorientation angle, which is similar to the grain boundary energy: the higher the boundary energy the higher the diffusion rate [52]. Attempts have been made [53] to relate the grain boundary energy to the grain boundary diffusion. The formula describing this relationship was proposed, and this formula was tested in various materials [54]. In the diffusion process, the presence of the vacancies, or interstitial atoms, at the grain boundary is important because the higher the number of these defects the higher the diffusion. The same defects are also linked to the high mobility of the high-energy grain boundaries. To illustrate some of these phenomena we observed the precipitates between a growing large Goss grain and small grains, after annealing specimen B at 1173 K for ten minutes. The coarse precipitates (see Fig. 6) were frequently found inside large growing Goss grains, and seldom found inside small grains, These facts might be explained by a faster coarsening of precipitates at the boundary of the growing grain. We expect that the high-energy boundary has a high diffusion rate, leading to the acceleration of Ostwald ripening of the precipitates. 4.4. Mechanism of the abnormal grain growth of Goss grains In this chapter, we would like to propose a model of the development of the Goss texture in secondary
recrystallization, based on the pinning of the boundaries by precipitates. We assume that, at the beginning of the annealing, all the grain boundaries are pinned by precipitates. The rate of coarsening of precipitates is higher for high-energy boundaries, that have high grain boundary diffusion coefficients. Therefore, at the early stage of the annealing, only the high-energy boundary moves when the precipitates on this boundary coarsen to some critical size for the pinning. Taking these assumptions into account, it is possible that the boundary, having a higher energy than the certain critical value (E,), can move. Let us express the probability that the grain boundary has a higher energy than a certain critical energy (E,), around the grain of arbitrary orientation S, by P(S,E > E,). This value represents the probability of the existence of mobile boundaries, and the difference between two probabilities {P(S,E > E,) P(average,E > E,)} describes the growth advantage of the S orientation. Following this definition, the data presented in Fig. 7 were obtained. The of {P(Goss,E > EJ - P(average,E > calculation E,)j, illustrates the growth advantage of the Goss grain over the grain of average orientation in specimens A and B. This distribution shows the maximum value of 26% for specimen A, and 17% for B. At the early stage of the annealing, when the value of E, is high, the growth advantage {P(Goss,E > EE) - P(average,E > E,)} is small, thus we can expect a normal grain growth, which is usually observed before the onset of secondary recrystallization. According to the progress of annealing, the coarsening of precipitates continues such that the precipitates, which are situated on lower energy boundaries, also reach the critical size for the pinning and such a boundary begins to move. We can, therefore, assume that, during the annealing process, the value of EC decreases. As the value of EC decreases from the highest value in Fig. 7, the value of {P(Goss,E > EC)- P(average,E > EC)} increases, such that the Goss grain has the advantage of having more mobile boundaries than the grains which have the average orientation, and we can expect the abnormal growth of the Goss grain at this stage. If the decrease of E, is too fast, and this may happen when the annealing temperature is too high, {P(Goss,E > EC)- P(average,E > EC)}decreases too quickly and the advantage of the Goss grains is quickly lost. This explains the failure to develop the Goss texture when the annealing temperature is very high. In order to compare the growth advantage around various other grain orientations, we calculated the maximum value of {P(S,E > EC) P(average,E > EC)}with respect to ECaround various orientations, and it is represented in Fig. 8. This value corresponds to the maximum surplus of mobile boundaries during the annealing, for the grain having orientation S over the grain having average
1294 HAYAKAWA and SZPUNAR:
SECONDARY RECRYSTALLIZATION OF ELECTRICAL STEELS
orientation. The map in Fig. 8 shows how strongly favoured the growth of the Goss orientation is over any other texture component. In specimen A, there is a clear, strong maximum at the Goss orientation. In specimen B, there is also a similar maximum at the Goss orientation; however, it is wider and weaker than that of specimen A. The shapes of the probability maximum correspond well to the final orientation of secondary grains in both specimens. The number of secondary grains close to the Goss orientation is higher for specimen A than for specimen B, and the deviation from the Goss orientation is small along the TD/< 110 > axes and large along the ND//< 110 > axes [5]. According to our model, the grain having a surplus of mobile boundaries is able to grow during the secondary recrystallization process, and Fig. 8 indicates that the secondary grains in specimen A should have orientations closer to the Goss orientation than in specimen B. It is to be noted that the Goss texture development of two different electrical steels are explained consistently using our model. The analysis supports the conclusion that the mechanism of the secondary recrystallization in 3%Si-Fe grain-oriented electrical steel is related, not to the special (CSL) boundary, but to the high-energy boundary with a disordered structure.
I.
N. Rouag, G. Vigna and R. Penelle, Acta metall. 38, 1101 (1990).
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5. CONCLUSIONS (1) The probability of the presence of a grain boundary having a misorientation angle between 20” to 45” is highest around the Goss grain. (2) There is no unique and special configuration of the CSL boundaries around the Goss grain. On the contrary, the total number of CSL boundaries from El to z51 is small, and the number of the C3 boundary or CSL boundaries having rotation axis < 111 > is the lowest. (3) The Goss grain is surrounded by the highest number of high-energy grain boundaries. (4) The mechanism of secondary recrystallization proposed in this paper links the development of Goss texture to a high concentration of the general high energy boundaries that have a disordered structure, and these are often linked to a high migration rate and a high grain boundary diffusion rate which facilitates coarsening of precipitates.
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