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Correlation between interfacial segregation and surface-energy-induced selective grain growth in 3% silicon–iron alloy
Acta mater. 48 (2000) 2901±2910 www.elsevier.com/locate/actamat
CORRELATION BETWEEN INTERFACIAL SEGREGATION AND SURFACE-ENERGY-INDUCED SELECTIVE GRAIN GROWTH IN 3% SILICON±IRON ALLOY N. H. HEO 1{, K. H. CHAI 2 and J. G. NA 2 1
Machinery and Materials Group, Korea Electric Power Research Institute, Taejon 305-380, South Korea and 2Division of Metals, Korea Institute of Science and Technology, Seoul 136-791, South Korea (Received 1 February 2000; accepted 15 March 2000)
AbstractÐEects of ®nal reduction and interfacial segregation of sulfur on surface-energy-induced selective grain growth have been investigated in 3% silicon±iron alloy strips with various bulk content of sulfur. Interfacial segregation kinetics of sulfur varies with annealing atmosphere: a convex pro®le under vacuum or hydrogen and a gradual increase under argon. This is because the segregated sulfur evaporates or gasi®es to hydrogen sul®de during ®nal vacuum or hydrogen annealing, resulting in a sulfur-depleted zone just below the strip surface. The surface-energy-induced selective growth of a grain at time t is determined by the concentration of segregated sulfur. The selective growth rate depends on the combined eect of the segregated sulfur and the ®nal reduction that determines the average grain size. For obtaining 110001 Goss texture, the ®nal reduction should, therefore, be controlled, depending on the bulk content of sulfur which in¯uences directly the segregation kinetics of sulfur and thus the texture development. 7 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Auger electron microscopy; XRD; Iron; Grain growth; Segregation
1. INTRODUCTION
Most theoretical calculations of crystal surface energy are based on the principle that an atom at the surface is at higher energy than an atom in the interior of a crystal because the surface atom has a smaller number of nearest neighbors and hence, less chance for complete resonant bonding [1]. It is, therefore, expected that surface energy would be a function of the density of packing of the crystal plane. From this point of view, the surface energy of the (110) plane in b.c.c. crystal should be less than the (100) and followed by the (111) and other less densely packed planes. Discrepancies between theory and practice are, however, found in many cases [2±9]. During vacuum annealing, a high-purity 3% silicon±iron alloy secondarily recrystallized to cube texture which was followed by 110001 texture on further annealing. This phenomenon has been called tertiary recrystallization, the driving force for which
{ To whom all correspondence should be addressed.
is the dierence in surface energy between the growing grain and those consumed [2]. In a 3% silicon± iron alloy only consisting of large (110) and (100) grains, (110) grains grew at the expense of (100) grains during vacuum annealing. The situation was, however, reversed during argon annealing, resulting in the growth of (100) grains. The selectivity in grain growth was reversible with varying annealing atmosphere. Such a selective grain growth was explained in terms of the eect of oxygen which was to lower the surface energy of the (100) plane more than that of the (110) plane [3±5]. Through an annealing experiment under hydrogen atmosphere with an additive of H2S [9], it was proposed that (110) growth would occur under very clean surface condition and (100) growth under slightly sulfur-contaminated condition. If the surface is highly contaminated, no surface-energyinduced selective growth would occur. On the other hand, one of the most convincing experiments of the role of surface energy dierence in grain growth comes from the observation of boundary migration in a 3% silicon±iron bicrystal containing a {100} grain and a {110} grain [10±12].
1359-6454/00/$20.00 7 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 5 4 ( 0 0 ) 0 0 0 8 4 - 7
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The {110} grain grew at the expense of the other grain in a sulfur-free environment of hydrogen, but the {100} grain grew into the {110} grain in hydrogen containing H2S. The continual to and fro motion of the boundary was observed simply by cycling the environment. The surface-energy-induced selective growth of {100} grains in the 3% silicon±iron alloy in a controlled sulfur environment, and the lack of such growth without it, strongly indicate that some preferential adsorption of sulfur occurs on the {100} plane [12]. Oxygen might also be an active species in promoting this growth, as is suggested [3±5]. The evidence for this, however, is not strong. The tendency for this alloy to oxidize severely limits the level of oxygen that can be used in the environment. Thus, control of the environment is more dicult. As a result, there is no clear one-to-one correlation between oxygen in the environment and the growth process. As mentioned above, surface-energy-induced selective grain growth has so far been correlated to the annealing atmosphere without consideration of eects of impurities in the bulk interior on the selective growth. Recently, it has been suggested that in a 3% silicon±iron alloy the surface-energyinduced selective grain growth is governed by the evaporation-controlled interfacial segregation of sulfur which is contained in the bulk interior [13±15]. In this paper, changes in interfacial segregation kinetics and magnetic induction with bulk content of sulfur and annealing atmosphere are investigated in detail. Then, these are correlated with changes in texture with ®nal annealing time. It is ®nally shown that a critical cold-rolling condition depends on the bulk content of sulfur, favorable for 110001 Goss texture. 2. EXPERIMENTAL
From three 3% silicon±iron alloys containing 6, 30, and 300 p.p.m. sulfur, as shown in Table 1, thin-gauged strips of 0.1 mm thickness were prepared through the hot- and multi-stage cold-rolling process. Final reduction in thickness was ®xed at 60% in two 3% silicon±iron alloys containing relatively lower bulk content of sulfur. The alloy containing 300 p.p.m. sulfur was ®nally cold rolled to 40 or 60%. After each cold-rolling stage, an intermediate annealing was performed at 8008C for 1.8 ks under a vacuum of 6 10 ÿ6 Torr: Final
Table 1. Chemical compositions of the three 3% silicon±iron alloys (wt%) Si 2.92 2.98 2.96
C
S
N
Mn
0.0020 0.0048 0.0066
0.0006 0.0030 0.0300
0.0013 0.0005 0.0017
< 0.001 < 0.001 < 0.001
annealing was carried out at 12008C under various atmospheres (i.e. a vacuum of 6 10 ÿ6 Torr, ¯owing hydrogen of 6 l/min, and ¯owing argon of 1 l/ min). Surface segregation behavior on the strips was investigated with an ion-sputtering technique in an AES (Auger electron spectroscope) after ®nal annealing and then fast cooling. In order to minimize the contamination eect from air, all the dierential peak heights of S 150 eV were normalized with the peak height, 90, of Fe 703 eV which was obtained after ion sputtering for 4±8 min. The primary beam energy was 2 keV, and the sputtering rate corresponded to 4.2 nm of SiO2/min. Magnetic induction, B10(T), under a magnetic ®eld of 10 Oersted was measured with a d.c. ¯uxmeter and an open circuit method. Changes in texture with ®nal annealing time were investigated with pole ®gure, ODF (orientation distribution function), and an etch-pit method.
3. ANNEALING ATMOSPHERE, INTERFACIAL SEGREGATION, FINAL REDUCTION, AND TEXTURE DEVELOPMENT
Figure 1 shows changes in magnetic induction of 3% silicon±iron alloy strips with ®nal vacuum annealing time at 12008C. The ®nal reduction was ®xed at 40% in the 3% silicon±iron alloy strips containing 300 p.p.m. sulfur. During ®nal annealing, magnetic induction decreased to a minimum, after which it increased to a high value. The trough in magnetic induction became wider with increasing bulk content of sulfur. In general, magnetic induction increases with increasing grain size [16]. From the concave pro®le of magnetic induction, it is, therefore, expected that grains, detrimental to magnetic induction, have selectively grown until the annealing time corresponding to the minimum in magnetic induction, and then have been replaced by other grains more favorable for magnetic induction with further annealing. Correlation between magnetic induction and surface segregation kinetics of sulfur during ®nal vacuum annealing is shown in Fig. 2. The concentration of segregated sulfur passed through a maximum, and then decreased to a low level with further annealing. The maximum in segregation concentration increased as the bulk content of sulfur increased. Here, a detectable segregation behavior of other impurities was not observed. Surprisingly, the segregation kinetics of sulfur corresponded inversely to the change in magnetic induction. This result implies that, during ®nal annealing, the surface-energy-induced selective grain growth may be governed by the segregated sulfur and, thus, the growth selectivity of grains with an orientation at time t be determined by the concentration of segregated sulfur. In fact, the surfaceenergy-induced selective grain growth has only been
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Fig. 1. Changes in magnetic induction with ®nal vacuum annealing time at 12008C in 3% silicon±iron alloy strips containing: (a) 6, (b) 30, and (c) 300 p.p.m. sulfur.
explained in terms of impurities (i.e. sulfur or oxygen) introduced from the annealing atmosphere. Before investigating changes in texture with annealing time, the convex form in segregation kinetics of sulfur shown in Fig. 2 needs to be explained. The segregation kinetics of nickel and manganese in an Fe±Ni±Mn alloy [17, 18] is similar to that in Fig. 2. This is attributed to a precipitation reaction of y-NiMn. At the present annealing temperature, there is no possibility of formation of sul®de in the three kinds of 3% silicon±iron alloys because the solubility of sulfur in the alloys amounts to about 0.12% at 12008C [19]. Other factors should, therefore, be considered. In the present study, such a convex pro®le in segregation kinetics can be attributed to sulfur evaporation that results in a depleted zone of sulfur just below the strip surface during vacuum annealing. In an Fe±Sn alloy system, Lea and Seah [20, 21] derived an evaporation-controlled surface segregation kinetics of tin given by
Xs t ÿ Xs 0 1 EDt exp ÿ 2 2 Xs 1 ÿ Xs 0 E1 a d " 1=2 E 1Dt Dt 1 ÿ exp erfc a 2d 2 a 2d 2 1=2 # EDt 1=2 ÿ E erf ÿ 2 2 a d
1
where Xs(0), Xs(t ), and Xs(1) are the surface-segregated concentration at time 0, t, and 1, E is the dimensionless parameter related to evaporation rate, D is the bulk solute diusivity, a is the enrichment ratio, and d is related to the atom sizes of the solute and matrix. The results show no divergence initially from McLean's result [22]. However, as the segregation builds up, the evaporation rate increases and the bulk material just below the strip surface begins to be depleted of solute. As a result, the segregation concentration goes through a maximum
Fig. 2. Correlation between magnetic induction and surface segregation kinetics of sulfur during ®nal vacuum annealing at 12008C: (a) 6, (b) 30, and (c) 300 p.p.m. sulfur.
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and eventually falls to a low value as the substrate surface puri®es. In order to con®rm the depleted zone of sulfur, two strips, containing 6 p.p.m. sulfur and annealed at 12008C for 7.2 ks, were re-annealed at 12008C under the same vacuum conditions, one of which was chemically surface removed. Figure 3 shows the surface segregation kinetics of sulfur with the surface condition. During re-annealing, the surfaceremoved strip showed again a similar segregation kinetics to that in Fig. 2, but the sulfur segregation was not observed in the other strip. This is evidence for the depleted zone formed just below the strip surface during ®nal annealing. Figure 4 shows changes in the (110) pole ®gure of the 3% silicon±iron alloy strips containing 30 p.p.m. sulfur with ®nal vacuum annealing time at 12008C. It is evident that the surface-energyinduced selective growth of a grain varies with concentration of segregated sulfur. Referring to Fig. 2, g-®ber was strong within the annealing time range of highly segregated sulfur. At 3.6 ks which corresponds to a relatively lower concentration of segregated sulfur, f100ghuvwi texture became strong, while g-®ber was drastically weakened. After 14.4 ks the segregated sulfur is extremely low, the strip was nearly composed of (110)[001] Goss grains. This can be expected from the high magnetic induction of Fig. 2 and was con®rmed by an etch-pit method. On the other hand, the pole ®gure after ®nal annealing for 0.06 ks showed a weak a- and g-®ber. It has, however, been reported that a strong (110)[001] Goss texture in a 3% silicon±iron alloy containing 6 p.p.m. sulfur is observed after ®nal annealing at 12008C for 0.03 ks [23]. Also, the initial texture is varied by the intermediate annealing time, temperature, and atmosphere that in¯uence the segregation kinetics of sulfur during subsequent ®nal annealing. The details are at present under further investigation.
Fig. 3. The surface segregation kinetics of sulfur during reannealing at 12008C [14].
The dierence in (110) pole ®gure with bulk content of sulfur is prominent, as shown in Fig. 5. After ®nal vacuum annealing for 3.6 ks, the concentration of segregated sulfur was relatively higher in the 3% silicon±iron alloy strip containing 300 p.p.m. sulfur and ®nally cold-rolled to 40% than in the other alloy containing 30 p.p.m. sulfur. As expected, the alloy with higher bulk content of sulfur still showed a strong g-®ber as well as f100ghuvwi texture, while the other alloy showed only a strong f100ghuvwi texture. It can be concluded from the observed results that during vacuum annealing the surface-energy-induced selective growth of {110}, {100}, and {111} grains occurs continuously with increasing segregation concentration of sulfur. Eects of ®nal reduction on magnetic induction and surface-energy-induced selective grain growth were investigated in the 3% silicon±iron alloy strips containing 300 p.p.m. sulfur. As shown in Fig. 6, the saturation in magnetic induction after ®nal vacuum annealing at 12008C was much higher in the case of 40% reduction. Figure 7 shows etch-pit shapes representative of texture of both cases. A quite dierent appearance of the ®nal texture was observed in both cases. The strip given 40% reduction was almost composed of 110001 Goss grains, but, the other case of 60% reduction showed mostly 100uvw orientation. On the other hand, ®nal annealing was also performed under hydrogen or argon. Figure 8 shows changes in concentration of segregated sulfur and magnetic induction of the alloy strips containing 30 p.p.m. sulfur with ®nal hydrogen annealing time at 12008C. High magnetic induction was obtained from the alloy strip after ®nal annealing for 7.2 ks. The convex pro®le of segregated sulfur was also observed under hydrogen. This can be attributed to the gasi®cation of segregated sulfur to H2S [24±26] rather than the evaporation, which forms a depleted zone of sulfur just below the strip surface. Therefore, the shifted location of the convex pro®le to the left side, relative to that under vacuum, may be due to the dierence in the kinetics of evaporation of segregated sulfur and gasi®cation to H2S. As in the case of vacuum annealing, the correspondence between texture development and segregation kinetics of sulfur was observed in this case. Changes in concentration of segregated sulfur and magnetic induction of the alloy strips containing 30 p.p.m. sulfur with ®nal argon annealing time at 12008C are shown in Fig. 9. Unlike the case of vacuum or hydrogen annealing, the concentration of segregated sulfur was saturated with annealing time, while the magnetic induction continued to decrease to a very low value. As shown in Fig. 10, the pole ®gure even after argon annealing for 7.2 ks still showed a strong g-®ber in addition to high index orientation, due to the continuous increase of segregated sulfur with increasing annealing time.
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Fig. 4. Changes in (110) pole ®gure of the 3% silicon±iron alloy strips containing 30 p.p.m. sulfur with ®nal vacuum annealing time at 12008C: (a) 0.06, (b) 0.6, (c) 2.4, and (d) 3.6 ks. 4. SURFACE-ENERGY-INDUCED SELECTIVE GRAIN GROWTH KINETICS
Figure 11 shows the dierence in growth rate of the alloy strips containing 30 p.p.m. sulfur with annealing atmosphere during ®nal annealing at 12008C. The incubation periods of largest grain growth were nearly congruent with the annealing time range of surface-segregated sulfur, referring to Figs 2(b), 8, and 9. The strongest grain boundary pinning eect by the highly segregated sulfur was observed in the case of argon annealing. In general, the sulfur-depleted zone formed under vacuum or hydrogen annealing disappears during subsequent argon annealing, because the solute is
supplied by diusion from the bulk interior to the depleted zone. With further argon annealing, the surface-segregated concentration increases again to a saturation point. The formation and disappearance of the depleted zone is, therefore, quasi-reversible through the cyclic environment. This is because the thickness of the depleted zone is extremely thin, relative to the strip thickness, and the loss of solute is thus trivial. The grain growth phenomenon observed by many investigators [2±5, 10±12] can, therefore, be considered as a kind of surfaceenergy-induced selective grain growth which is governed by the formation and disappearance of the sulfur-depleted zone. In order to explain eects of bulk content of
Fig. 5. The dierence in (110) pole ®gure with bulk content of sulfur after ®nal vacuum annealing at 12008C for 3.6 ks: (a) 30 and (b) 300 p.p.m. sulfur.
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Fig. 6. Eects of ®nal reduction on magnetic induction of the 3% silicon±iron alloy strips containing 300 p.p.m. sulfur.
sulfur and ®nal reduction on surface-energyinduced selective grain growth kinetics, a simple equation needs to be introduced. The growth rate of a grain is essentially equal to the product of its grain boundary mobility and the driving force exerted on the boundary. A modi®ed relation of surface-energy-induced selective grain growth rate G(t ) at time t, which is based on other research [27±29], can be given by gG 2DgS G t M t C t 2 r t d where M(t ) is the grain boundary mobility, gG is the grain boundary free energy, r(t ) is the average grain size which means, strictly speaking, the average radius of grains excluding the selectively growing grains, DgS gfhkl g ÿ gf110g , gfhkl g ÿ gf100g , or gfhkl g ÿ gf111g , gfhkl g represents the average surface energy of grains which are consumed, d is the sheet thickness, and C(t ), Zener's term, acts as a negative driving force, which is generally related to inclusions at grain boundaries. In the present alloy system with no inclusion, C(t ) is related to the segregated sulfur which varies with ®nal annealing time and has a strong pinning eect on grain boundary movement [30±32]. Because the magnitude of DgS =gG is found to be equal to 0.03 [28, 29], the surface energy dierence is responsible for selecting the grain that will grow, and is not the main controlling factor in the growth rate. The kinetics of surface-energy-induced selective grain growth is, therefore, determined primarily by the combined eect of the average grain size and the negative driving force term: the growth rate decreases as the average grain size and the concentration of segregated sulfur increase. At a ®xed ®nal reduction, the average grain size at time t is relatively smaller in the alloy strips with higher bulk content of sulfur, because of the stronger grain
Fig. 7. Changes in etch-pit shape with ®nal reduction in the 3% silicon±iron alloy containing 300 p.p.m. sulfur after ®nal vacuum annealing at 12008C for 14.4 ks: (a) 40 and (b) 60%.
boundary pinning eect of segregated sulfur. At a ®xed bulk content of sulfur, the average grain size decreases with increasing ®nal reduction. The average grain size also increases with annealing time,
Fig. 8. Changes in concentration of segregated sulfur and magnetic induction of the alloy strips containing 30 p.p.m. sulfur with ®nal hydrogen annealing time at 12008C.
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Fig. 9. Changes in concentration of segregated sulfur and magnetic induction of the alloy strips containing 30 p.p.m. sulfur with ®nal argon annealing time at 12008C.
which results in the decrease in total energy of surface-energy-induced selective grain growth. Figure 12 shows the dierence in growth kinetics of the alloy strips containing 300 p.p.m. sulfur with ®nal reduction during ®nal vacuum annealing at 12008C. The concentration pro®le of segregated sulfur is, therefore, ®xed. Here, the growth rate is the time derivative of the largest grain size. The surface-energy-induced selective growth rate of the largest grain decreased with increasing annealing time due to the increasing average grain size and segregation concentration of sulfur. A minimum in growth rate was formed by the combined eect of average grain size and concentration of segregated sulfur which minimizes the magnitude of the driving force term in equation (2). With further annealing, the growth rate restored a moderate level after the minimum, due to a little increase in average grain size and the drastic decrease of segregated sulfur. When only the eect of average grain size is considered, the surface-energy-induced selective growth rate of the largest grain should continue to decrease as average grain size increases. However, a trough in growth rate was shown in both cases, and the minimum in growth rate corresponded to the maximum in concentration of segregated sulfur. This implies a strong grain boundary pinning eect of segregated sulfur, even though the eect cannot be quanti®ed. The growth rate was overall higher in the alloy strips given 60% reduction within all the annealing time range. This can be attributed to the relatively smaller average grain size that makes the driving force of the growth rate higher. As expected, the largest grain size was smaller in the strips given 60% reduction at the early stage of annealing, and a reversion in the largest grain size was observed with further annealing due to the higher growth rate in the strips given 60% reduction. Figure 13 shows the dierence in growth kinetics
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Fig. 10. (110) pole ®gure of the 3% silicon±iron alloy strip containing 30 p.p.m. sulfur after ®nal argon annealing at 12008C for 7.2 ks.
of the 3% silicon±iron alloy strips with bulk content of sulfur during ®nal vacuum annealing at 12008C. The ®nal reduction in thickness was ®xed at 60%. Due to the relatively weaker grain boundary pinning eect of segregated sulfur, the average grain size was larger in the alloy strips with 30 p.p.m. sulfur and the dierence in two alloy strips increased with annealing time. The minimum in growth rate of the largest grain was approximately congruent with the maximum in concentration of segregated sulfur. Although both alloys show a similar trough in growth rate of the largest grain, the relative growth rate in the alloy strips with 300 p.p.m. sulfur was lower at the early stage of annealing irrespective of smaller average grain size, but the situation was reversed with further annealing. Referring to Fig. 2, this may be attributed to the dominant eects on growth rate: the relatively higher concentration of segregated sulfur in the former half of ®nal annealing and the smaller
Fig. 11. The dierence in growth kinetics with annealing atmosphere during ®nal annealing at 12008C.
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grain growth in the present 3% silicon±iron alloys. Figure 14 shows a schematic time±concentration diagram of surface-energy-induced selective grain growth in the case of ®nal vacuum or hydrogen annealing. CS(t ) is the concentration of segregated sulfur which varies with annealing time. Cf110g on the ordinate axis means a concentration of segregated sulfur below which the surface-energy-induced selective growth of {110} grains occurs. Cf111g is a concentration of segregated sulfur above which {111} grains grow selectively, consuming other grains. Therefore, {100} grains grow selectively within the concentration range between Cf110g and Cf111g : As a result, the abscissa axis is divided into ®ve regions with the amount of segregated sulfur: the selective growth regions, I and V, of {110} grains, the growth regions, II and IV, of {100}
Fig. 12. The dierence in growth kinetics of the alloy strips containing 300 p.p.m. sulfur with ®nal reduction during ®nal vacuum annealing at 12008C.
average grain size in the latter half. As a result, the largest grain size of the alloy strips with 300 p.p.m. sulfur exceeded that of the other alloy strips after a reversion point. The location of the minimum of growth rate was, therefore, shifted to the left side in comparison with that of the other alloy. In this way, a narrower grain boundary pinning region of the largest grain is, as shown in Fig. 13(c), formed in the alloy strips with higher bulk content of sulfur. 5. A SCHEMATIC TIME±CONCENTRATION DIAGRAM OF SURFACE-ENERGY-INDUCED SELECTIVE GRAIN GROWTH
On the basis of the results obtained above, a schematic diagram can be composed in order to understand the correlation between interfacial segregation of sulfur and surface-energy-induced selective
Fig. 13. The dierence in growth kinetics with bulk content of sulfur during ®nal vacuum annealing at 12008C.
HEO et al.: SELECTIVE GRAIN GROWTH
grains, and the growth region, III, of {111} grains. The selective growth of {110} grains in region I is based on previous research [23]. Of course, grains other than the selectively growing grains in each region (e.g. {110} grains in regions II and IV) can also grow together with {100} grains, consuming high-index grains including {111}. However, the surface-energy-induced selective growth of {100} grains should be dominant in the regions for decreasing eectively the total energy of the system. DWC t is representative of the largest grain size in the case of relatively weaker cold rolling, and DSC t corresponds to the case of severe cold rolling. The prominent dierence in texture with severity of ®nal reduction, as shown in Fig. 7, can be explained, using equation (2) and the time±concentration diagram of Fig. 14(a). For two conditions ®nally cold-rolled to 40 and 60%, the selective growth kinetics of the largest grain, in turn, corresponds to DWC t and DSC t: During ®nal vacuum annealing, {110} grains grow selectively in region I due to the relatively lower concentration of segregated sulfur. As the concentration of segregated sul-
Fig. 14. A schematic time±concentration diagram of surface-energy-induced selective grain growth in the 3% silicon±iron alloy strips: (a) the case that the ®nal reduction is varied at a ®xed bulk content of sulfur and (b) the other case that the bulk content of sulfur is varied at a ®xed ®nal reduction.
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fur increases, {100} grains have a chance for selective growth in region II, while the growth rate decreases mainly due to the increase in concentration of segregated sulfur. {111} grains grow selectively in region III. The growth rate is, however, very low due to the strong grain boundary pinning eect, especially at around the maximum of segregated sulfur. Because the average grain size is relatively smaller in the case of higher reduction while the concentration of segregated sulfur is the same, DSC t exceeds DWC t after a reversion point Pr. In region IV, the chance for surface-energyinduced selective growth is again given {100} grains. For obtaining ®nal 110001 texture in region V, {110} grains should, therefore, survive to grow selectively after region IV. Considering the log-time plot of Fig. 14, the annealing time of region I is actually quite short in comparison with that of regions II±IV. As a result, a relatively lower ®nal reduction, which results in the lower selective growth rate of {100} or {111} grains in regions II± IV, is preferred for obtaining ®nal 110001 texture. Changes in surface-energy-induced selective growth kinetics with bulk content of sulfur during ®nal vacuum annealing can also be explained with Fig. 14(b). Here, the ®nal reduction in thickness is ®xed. LC and HC mean the lower and higher bulk content of sulfur. The concentration of segregated sulfur increases as the bulk content of sulfur increases. This results in a smaller average grain size due to the relatively stronger grain boundary pinning eect of highly segregated sulfur, which acts as a main source of the relatively higher growth rate of {111} or {100} grains in the latter half of ®nal annealing. Regions III and IV for the selective growth of {111} and {100} grains are also extended with increasing bulk content of sulfur, as shown in Fig. 14(b). Consequently, the probability that surface-energy-induced selective growth of {110} grains can occur in region V becomes lower with increasing bulk content of sulfur. On the other hand, the reason that among the 110uvw orientations only the 110001 Goss texture is obtained after ®nal annealing has been explained by a maximum energy release theory of 110001 Goss texture [33, 34]. According to the theoretical calculation in b.c.c. crystal [1], 110 huvwi nuclei including 110001 can also be formed at the strip surface during the initial annealing stage, because the surface energy of (110) grains is the same, regardless of the orientation. The ®nal 110001 Goss texture may, therefore, be attributed to the more dominant eect of the maximum energy release than that of the surface energy, which results in the larger number of 110001 nuclei in comparison with that of the 110uvw nuclei except for the 110001 one.
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HEO et al.: SELECTIVE GRAIN GROWTH 6. CONCLUSIONS
Eects of ®nal reduction and sulfur segregation under various annealing atmospheres on surfaceenergy-induced selective grain growth and texture development have been delineated in 3% silicon± iron alloy strips. During ®nal vacuum or hydrogen annealing, the strips, irrespective of the bulk content of sulfur, showed a convex pro®le in segregation kinetics of sulfur that is directly related to evaporation of segregated sulfur or gasi®cation to hydrogen sul®de. Surface-energy-induced selective growth of {110} grains occurs at a low concentration of segregated sulfur. With increasing concentration of segregated sulfur, the selective growth of {110} grains is in turn followed by that of {100} and {111} grains. The growth rate at time t is determined by the combined eect of average grain size and concentration of segregated sulfur which has a strong pinning eect on grain boundary movement. Two processing conditions, the relatively lower ®nal reduction at a ®xed bulk content of sulfur and the relatively lower bulk content of sulfur at a ®xed ®nal reduction, are preferred for obtaining ®nal 110001 Goss texture. This is because such conditions increase the average grain size so that the surface-energy-induced selective growth rate of {100} and {111} grains can be relatively decreased and thus the probability of selective growth of 110001 grains becomes higher in the sulfur-free region after prolonged annealing. REFERENCES 1. Friedel, J., et al., Acta metall., 1953, 1, 79. 2. Walter, J. L. and Dunn, C. G., Trans. Am. Inst. Min. Engrs, 1959, 215, 465. 3. Walter, J. L. and Dunn, C. G., Acta metall., 1960, 8, 497.
4. Walter, J. L. and Dunn, C. G., Trans. Am. Inst. Min. Engrs, 1960, 218, 1033. 5. Walter, J. L. and Dunn, C. G., Trans. Am. Inst. Min. Engrs, 1960, 218, 914. 6. Detert, K., Acta metall., 1959, 7, 589. 7. Wiener, G. W., J. Metals, September 1958. 8. Walter, J. L., Acta metall., 1959, 7, 424. 9. Kohler, D., J. appl. Phys., 1960, 31, 408. 10. Wiener, G. W., J. appl. Phys., 1964, 35, 856. 11. Elban, W. L., Hebbar, M. A. and Kramer, J. J., Metall. Trans., 1975, 6A, 1929. 12. Kramer, J. J., Metall. Trans., 1992, 23A, 1987. 13. Heo, N. H., et al., J. appl. Phys., 1998, 83, 6480. 14. Heo, N. H., et al., J. appl. Phys., 1999, 85, 6025. 15. Heo, N. H., et al., J. appl. Phys., 1999, 85, 6022. 16. Walters, R. E. S., Acta metall., 1955, 3, 293. 17. Heo, N. H., Acta mater., 1996, 44, 3015. 18. Heo, N. H. and Lee, H. C., Metall. Trans., 1996, 27A, 1015. 19. Ainslie, N. G. and Seybolt, A. U., JISI, 1960, 182, 341. 20. Lea, C. and Seah, M. P., Phil. Mag., 1977, 35, 213. 21. Lea, C. and Seah, M. P., Metals Sci., 1984, 18, 521. 22. McLean, D., Grain Boundaries in Metals. Oxford University Press, London, 1957. 23. Chai, K. H., et al., J. Korean Phys. Soc., 1999, 35, 466. 24. Randall, M. and von Bichowsky, F. R., J. Am. chem. Soc., 1918, 40, 368. 25. Ainslie, N. G. and Seybolt, A. U., JISI, 1960, March, 341. 26. Mager, T. R., AIME Trans., 1964, 230, 773. 27. May, J. E. and Turnbull, D., AIME Trans., 1958, 212, 769. 28. Foster, K., Kramer, J. J. and Wiener, G. W., AIME Trans., 1963, 227, 185. 29. Mullins, W. W., Acta metall., 1958, 6, 414. 30. Lucke, K. and Detert, K., Acta metall., 1957, 5, 628. 31. Cahn, J. W., Acta metall., 1962, 10, 789. 32. Lucke, K. and Stuwe, H. P., in Recovery and Recrystallization of Metals, ed. L. Himmel. Wiley Interscience, New York, 1963. 33. Choi, C. H. and Lee, D. N., Metall. Trans., 1997, 28A, 2217. 34. Park, Y. B., Lee, D. N. and Gottstein, G., Acta mater., 1998, 46, 3371.
CORRELATION BETWEEN INTERFACIAL SEGREGATION AND SURFACE-ENERGY-INDUCED SELECTIVE GRAIN GROWTH IN 3% SILICON±IRON ALLOY N. H. HEO 1{, K. H. CHAI 2 and J. G. NA 2 1
Machinery and Materials Group, Korea Electric Power Research Institute, Taejon 305-380, South Korea and 2Division of Metals, Korea Institute of Science and Technology, Seoul 136-791, South Korea (Received 1 February 2000; accepted 15 March 2000)
AbstractÐEects of ®nal reduction and interfacial segregation of sulfur on surface-energy-induced selective grain growth have been investigated in 3% silicon±iron alloy strips with various bulk content of sulfur. Interfacial segregation kinetics of sulfur varies with annealing atmosphere: a convex pro®le under vacuum or hydrogen and a gradual increase under argon. This is because the segregated sulfur evaporates or gasi®es to hydrogen sul®de during ®nal vacuum or hydrogen annealing, resulting in a sulfur-depleted zone just below the strip surface. The surface-energy-induced selective growth of a grain at time t is determined by the concentration of segregated sulfur. The selective growth rate depends on the combined eect of the segregated sulfur and the ®nal reduction that determines the average grain size. For obtaining 110001 Goss texture, the ®nal reduction should, therefore, be controlled, depending on the bulk content of sulfur which in¯uences directly the segregation kinetics of sulfur and thus the texture development. 7 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Auger electron microscopy; XRD; Iron; Grain growth; Segregation
1. INTRODUCTION
Most theoretical calculations of crystal surface energy are based on the principle that an atom at the surface is at higher energy than an atom in the interior of a crystal because the surface atom has a smaller number of nearest neighbors and hence, less chance for complete resonant bonding [1]. It is, therefore, expected that surface energy would be a function of the density of packing of the crystal plane. From this point of view, the surface energy of the (110) plane in b.c.c. crystal should be less than the (100) and followed by the (111) and other less densely packed planes. Discrepancies between theory and practice are, however, found in many cases [2±9]. During vacuum annealing, a high-purity 3% silicon±iron alloy secondarily recrystallized to cube texture which was followed by 110001 texture on further annealing. This phenomenon has been called tertiary recrystallization, the driving force for which
{ To whom all correspondence should be addressed.
is the dierence in surface energy between the growing grain and those consumed [2]. In a 3% silicon± iron alloy only consisting of large (110) and (100) grains, (110) grains grew at the expense of (100) grains during vacuum annealing. The situation was, however, reversed during argon annealing, resulting in the growth of (100) grains. The selectivity in grain growth was reversible with varying annealing atmosphere. Such a selective grain growth was explained in terms of the eect of oxygen which was to lower the surface energy of the (100) plane more than that of the (110) plane [3±5]. Through an annealing experiment under hydrogen atmosphere with an additive of H2S [9], it was proposed that (110) growth would occur under very clean surface condition and (100) growth under slightly sulfur-contaminated condition. If the surface is highly contaminated, no surface-energyinduced selective growth would occur. On the other hand, one of the most convincing experiments of the role of surface energy dierence in grain growth comes from the observation of boundary migration in a 3% silicon±iron bicrystal containing a {100} grain and a {110} grain [10±12].
1359-6454/00/$20.00 7 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 5 4 ( 0 0 ) 0 0 0 8 4 - 7
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The {110} grain grew at the expense of the other grain in a sulfur-free environment of hydrogen, but the {100} grain grew into the {110} grain in hydrogen containing H2S. The continual to and fro motion of the boundary was observed simply by cycling the environment. The surface-energy-induced selective growth of {100} grains in the 3% silicon±iron alloy in a controlled sulfur environment, and the lack of such growth without it, strongly indicate that some preferential adsorption of sulfur occurs on the {100} plane [12]. Oxygen might also be an active species in promoting this growth, as is suggested [3±5]. The evidence for this, however, is not strong. The tendency for this alloy to oxidize severely limits the level of oxygen that can be used in the environment. Thus, control of the environment is more dicult. As a result, there is no clear one-to-one correlation between oxygen in the environment and the growth process. As mentioned above, surface-energy-induced selective grain growth has so far been correlated to the annealing atmosphere without consideration of eects of impurities in the bulk interior on the selective growth. Recently, it has been suggested that in a 3% silicon±iron alloy the surface-energyinduced selective grain growth is governed by the evaporation-controlled interfacial segregation of sulfur which is contained in the bulk interior [13±15]. In this paper, changes in interfacial segregation kinetics and magnetic induction with bulk content of sulfur and annealing atmosphere are investigated in detail. Then, these are correlated with changes in texture with ®nal annealing time. It is ®nally shown that a critical cold-rolling condition depends on the bulk content of sulfur, favorable for 110001 Goss texture. 2. EXPERIMENTAL
From three 3% silicon±iron alloys containing 6, 30, and 300 p.p.m. sulfur, as shown in Table 1, thin-gauged strips of 0.1 mm thickness were prepared through the hot- and multi-stage cold-rolling process. Final reduction in thickness was ®xed at 60% in two 3% silicon±iron alloys containing relatively lower bulk content of sulfur. The alloy containing 300 p.p.m. sulfur was ®nally cold rolled to 40 or 60%. After each cold-rolling stage, an intermediate annealing was performed at 8008C for 1.8 ks under a vacuum of 6 10 ÿ6 Torr: Final
Table 1. Chemical compositions of the three 3% silicon±iron alloys (wt%) Si 2.92 2.98 2.96
C
S
N
Mn
0.0020 0.0048 0.0066
0.0006 0.0030 0.0300
0.0013 0.0005 0.0017
< 0.001 < 0.001 < 0.001
annealing was carried out at 12008C under various atmospheres (i.e. a vacuum of 6 10 ÿ6 Torr, ¯owing hydrogen of 6 l/min, and ¯owing argon of 1 l/ min). Surface segregation behavior on the strips was investigated with an ion-sputtering technique in an AES (Auger electron spectroscope) after ®nal annealing and then fast cooling. In order to minimize the contamination eect from air, all the dierential peak heights of S 150 eV were normalized with the peak height, 90, of Fe 703 eV which was obtained after ion sputtering for 4±8 min. The primary beam energy was 2 keV, and the sputtering rate corresponded to 4.2 nm of SiO2/min. Magnetic induction, B10(T), under a magnetic ®eld of 10 Oersted was measured with a d.c. ¯uxmeter and an open circuit method. Changes in texture with ®nal annealing time were investigated with pole ®gure, ODF (orientation distribution function), and an etch-pit method.
3. ANNEALING ATMOSPHERE, INTERFACIAL SEGREGATION, FINAL REDUCTION, AND TEXTURE DEVELOPMENT
Figure 1 shows changes in magnetic induction of 3% silicon±iron alloy strips with ®nal vacuum annealing time at 12008C. The ®nal reduction was ®xed at 40% in the 3% silicon±iron alloy strips containing 300 p.p.m. sulfur. During ®nal annealing, magnetic induction decreased to a minimum, after which it increased to a high value. The trough in magnetic induction became wider with increasing bulk content of sulfur. In general, magnetic induction increases with increasing grain size [16]. From the concave pro®le of magnetic induction, it is, therefore, expected that grains, detrimental to magnetic induction, have selectively grown until the annealing time corresponding to the minimum in magnetic induction, and then have been replaced by other grains more favorable for magnetic induction with further annealing. Correlation between magnetic induction and surface segregation kinetics of sulfur during ®nal vacuum annealing is shown in Fig. 2. The concentration of segregated sulfur passed through a maximum, and then decreased to a low level with further annealing. The maximum in segregation concentration increased as the bulk content of sulfur increased. Here, a detectable segregation behavior of other impurities was not observed. Surprisingly, the segregation kinetics of sulfur corresponded inversely to the change in magnetic induction. This result implies that, during ®nal annealing, the surface-energy-induced selective grain growth may be governed by the segregated sulfur and, thus, the growth selectivity of grains with an orientation at time t be determined by the concentration of segregated sulfur. In fact, the surfaceenergy-induced selective grain growth has only been
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Fig. 1. Changes in magnetic induction with ®nal vacuum annealing time at 12008C in 3% silicon±iron alloy strips containing: (a) 6, (b) 30, and (c) 300 p.p.m. sulfur.
explained in terms of impurities (i.e. sulfur or oxygen) introduced from the annealing atmosphere. Before investigating changes in texture with annealing time, the convex form in segregation kinetics of sulfur shown in Fig. 2 needs to be explained. The segregation kinetics of nickel and manganese in an Fe±Ni±Mn alloy [17, 18] is similar to that in Fig. 2. This is attributed to a precipitation reaction of y-NiMn. At the present annealing temperature, there is no possibility of formation of sul®de in the three kinds of 3% silicon±iron alloys because the solubility of sulfur in the alloys amounts to about 0.12% at 12008C [19]. Other factors should, therefore, be considered. In the present study, such a convex pro®le in segregation kinetics can be attributed to sulfur evaporation that results in a depleted zone of sulfur just below the strip surface during vacuum annealing. In an Fe±Sn alloy system, Lea and Seah [20, 21] derived an evaporation-controlled surface segregation kinetics of tin given by
Xs t ÿ Xs 0 1 EDt exp ÿ 2 2 Xs 1 ÿ Xs 0 E1 a d " 1=2 E 1Dt Dt 1 ÿ exp erfc a 2d 2 a 2d 2 1=2 # EDt 1=2 ÿ E erf ÿ 2 2 a d
1
where Xs(0), Xs(t ), and Xs(1) are the surface-segregated concentration at time 0, t, and 1, E is the dimensionless parameter related to evaporation rate, D is the bulk solute diusivity, a is the enrichment ratio, and d is related to the atom sizes of the solute and matrix. The results show no divergence initially from McLean's result [22]. However, as the segregation builds up, the evaporation rate increases and the bulk material just below the strip surface begins to be depleted of solute. As a result, the segregation concentration goes through a maximum
Fig. 2. Correlation between magnetic induction and surface segregation kinetics of sulfur during ®nal vacuum annealing at 12008C: (a) 6, (b) 30, and (c) 300 p.p.m. sulfur.
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and eventually falls to a low value as the substrate surface puri®es. In order to con®rm the depleted zone of sulfur, two strips, containing 6 p.p.m. sulfur and annealed at 12008C for 7.2 ks, were re-annealed at 12008C under the same vacuum conditions, one of which was chemically surface removed. Figure 3 shows the surface segregation kinetics of sulfur with the surface condition. During re-annealing, the surfaceremoved strip showed again a similar segregation kinetics to that in Fig. 2, but the sulfur segregation was not observed in the other strip. This is evidence for the depleted zone formed just below the strip surface during ®nal annealing. Figure 4 shows changes in the (110) pole ®gure of the 3% silicon±iron alloy strips containing 30 p.p.m. sulfur with ®nal vacuum annealing time at 12008C. It is evident that the surface-energyinduced selective growth of a grain varies with concentration of segregated sulfur. Referring to Fig. 2, g-®ber was strong within the annealing time range of highly segregated sulfur. At 3.6 ks which corresponds to a relatively lower concentration of segregated sulfur, f100ghuvwi texture became strong, while g-®ber was drastically weakened. After 14.4 ks the segregated sulfur is extremely low, the strip was nearly composed of (110)[001] Goss grains. This can be expected from the high magnetic induction of Fig. 2 and was con®rmed by an etch-pit method. On the other hand, the pole ®gure after ®nal annealing for 0.06 ks showed a weak a- and g-®ber. It has, however, been reported that a strong (110)[001] Goss texture in a 3% silicon±iron alloy containing 6 p.p.m. sulfur is observed after ®nal annealing at 12008C for 0.03 ks [23]. Also, the initial texture is varied by the intermediate annealing time, temperature, and atmosphere that in¯uence the segregation kinetics of sulfur during subsequent ®nal annealing. The details are at present under further investigation.
Fig. 3. The surface segregation kinetics of sulfur during reannealing at 12008C [14].
The dierence in (110) pole ®gure with bulk content of sulfur is prominent, as shown in Fig. 5. After ®nal vacuum annealing for 3.6 ks, the concentration of segregated sulfur was relatively higher in the 3% silicon±iron alloy strip containing 300 p.p.m. sulfur and ®nally cold-rolled to 40% than in the other alloy containing 30 p.p.m. sulfur. As expected, the alloy with higher bulk content of sulfur still showed a strong g-®ber as well as f100ghuvwi texture, while the other alloy showed only a strong f100ghuvwi texture. It can be concluded from the observed results that during vacuum annealing the surface-energy-induced selective growth of {110}, {100}, and {111} grains occurs continuously with increasing segregation concentration of sulfur. Eects of ®nal reduction on magnetic induction and surface-energy-induced selective grain growth were investigated in the 3% silicon±iron alloy strips containing 300 p.p.m. sulfur. As shown in Fig. 6, the saturation in magnetic induction after ®nal vacuum annealing at 12008C was much higher in the case of 40% reduction. Figure 7 shows etch-pit shapes representative of texture of both cases. A quite dierent appearance of the ®nal texture was observed in both cases. The strip given 40% reduction was almost composed of 110001 Goss grains, but, the other case of 60% reduction showed mostly 100uvw orientation. On the other hand, ®nal annealing was also performed under hydrogen or argon. Figure 8 shows changes in concentration of segregated sulfur and magnetic induction of the alloy strips containing 30 p.p.m. sulfur with ®nal hydrogen annealing time at 12008C. High magnetic induction was obtained from the alloy strip after ®nal annealing for 7.2 ks. The convex pro®le of segregated sulfur was also observed under hydrogen. This can be attributed to the gasi®cation of segregated sulfur to H2S [24±26] rather than the evaporation, which forms a depleted zone of sulfur just below the strip surface. Therefore, the shifted location of the convex pro®le to the left side, relative to that under vacuum, may be due to the dierence in the kinetics of evaporation of segregated sulfur and gasi®cation to H2S. As in the case of vacuum annealing, the correspondence between texture development and segregation kinetics of sulfur was observed in this case. Changes in concentration of segregated sulfur and magnetic induction of the alloy strips containing 30 p.p.m. sulfur with ®nal argon annealing time at 12008C are shown in Fig. 9. Unlike the case of vacuum or hydrogen annealing, the concentration of segregated sulfur was saturated with annealing time, while the magnetic induction continued to decrease to a very low value. As shown in Fig. 10, the pole ®gure even after argon annealing for 7.2 ks still showed a strong g-®ber in addition to high index orientation, due to the continuous increase of segregated sulfur with increasing annealing time.
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Fig. 4. Changes in (110) pole ®gure of the 3% silicon±iron alloy strips containing 30 p.p.m. sulfur with ®nal vacuum annealing time at 12008C: (a) 0.06, (b) 0.6, (c) 2.4, and (d) 3.6 ks. 4. SURFACE-ENERGY-INDUCED SELECTIVE GRAIN GROWTH KINETICS
Figure 11 shows the dierence in growth rate of the alloy strips containing 30 p.p.m. sulfur with annealing atmosphere during ®nal annealing at 12008C. The incubation periods of largest grain growth were nearly congruent with the annealing time range of surface-segregated sulfur, referring to Figs 2(b), 8, and 9. The strongest grain boundary pinning eect by the highly segregated sulfur was observed in the case of argon annealing. In general, the sulfur-depleted zone formed under vacuum or hydrogen annealing disappears during subsequent argon annealing, because the solute is
supplied by diusion from the bulk interior to the depleted zone. With further argon annealing, the surface-segregated concentration increases again to a saturation point. The formation and disappearance of the depleted zone is, therefore, quasi-reversible through the cyclic environment. This is because the thickness of the depleted zone is extremely thin, relative to the strip thickness, and the loss of solute is thus trivial. The grain growth phenomenon observed by many investigators [2±5, 10±12] can, therefore, be considered as a kind of surfaceenergy-induced selective grain growth which is governed by the formation and disappearance of the sulfur-depleted zone. In order to explain eects of bulk content of
Fig. 5. The dierence in (110) pole ®gure with bulk content of sulfur after ®nal vacuum annealing at 12008C for 3.6 ks: (a) 30 and (b) 300 p.p.m. sulfur.
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Fig. 6. Eects of ®nal reduction on magnetic induction of the 3% silicon±iron alloy strips containing 300 p.p.m. sulfur.
sulfur and ®nal reduction on surface-energyinduced selective grain growth kinetics, a simple equation needs to be introduced. The growth rate of a grain is essentially equal to the product of its grain boundary mobility and the driving force exerted on the boundary. A modi®ed relation of surface-energy-induced selective grain growth rate G(t ) at time t, which is based on other research [27±29], can be given by gG 2DgS G t M t C t 2 r t d where M(t ) is the grain boundary mobility, gG is the grain boundary free energy, r(t ) is the average grain size which means, strictly speaking, the average radius of grains excluding the selectively growing grains, DgS gfhkl g ÿ gf110g , gfhkl g ÿ gf100g , or gfhkl g ÿ gf111g , gfhkl g represents the average surface energy of grains which are consumed, d is the sheet thickness, and C(t ), Zener's term, acts as a negative driving force, which is generally related to inclusions at grain boundaries. In the present alloy system with no inclusion, C(t ) is related to the segregated sulfur which varies with ®nal annealing time and has a strong pinning eect on grain boundary movement [30±32]. Because the magnitude of DgS =gG is found to be equal to 0.03 [28, 29], the surface energy dierence is responsible for selecting the grain that will grow, and is not the main controlling factor in the growth rate. The kinetics of surface-energy-induced selective grain growth is, therefore, determined primarily by the combined eect of the average grain size and the negative driving force term: the growth rate decreases as the average grain size and the concentration of segregated sulfur increase. At a ®xed ®nal reduction, the average grain size at time t is relatively smaller in the alloy strips with higher bulk content of sulfur, because of the stronger grain
Fig. 7. Changes in etch-pit shape with ®nal reduction in the 3% silicon±iron alloy containing 300 p.p.m. sulfur after ®nal vacuum annealing at 12008C for 14.4 ks: (a) 40 and (b) 60%.
boundary pinning eect of segregated sulfur. At a ®xed bulk content of sulfur, the average grain size decreases with increasing ®nal reduction. The average grain size also increases with annealing time,
Fig. 8. Changes in concentration of segregated sulfur and magnetic induction of the alloy strips containing 30 p.p.m. sulfur with ®nal hydrogen annealing time at 12008C.
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Fig. 9. Changes in concentration of segregated sulfur and magnetic induction of the alloy strips containing 30 p.p.m. sulfur with ®nal argon annealing time at 12008C.
which results in the decrease in total energy of surface-energy-induced selective grain growth. Figure 12 shows the dierence in growth kinetics of the alloy strips containing 300 p.p.m. sulfur with ®nal reduction during ®nal vacuum annealing at 12008C. The concentration pro®le of segregated sulfur is, therefore, ®xed. Here, the growth rate is the time derivative of the largest grain size. The surface-energy-induced selective growth rate of the largest grain decreased with increasing annealing time due to the increasing average grain size and segregation concentration of sulfur. A minimum in growth rate was formed by the combined eect of average grain size and concentration of segregated sulfur which minimizes the magnitude of the driving force term in equation (2). With further annealing, the growth rate restored a moderate level after the minimum, due to a little increase in average grain size and the drastic decrease of segregated sulfur. When only the eect of average grain size is considered, the surface-energy-induced selective growth rate of the largest grain should continue to decrease as average grain size increases. However, a trough in growth rate was shown in both cases, and the minimum in growth rate corresponded to the maximum in concentration of segregated sulfur. This implies a strong grain boundary pinning eect of segregated sulfur, even though the eect cannot be quanti®ed. The growth rate was overall higher in the alloy strips given 60% reduction within all the annealing time range. This can be attributed to the relatively smaller average grain size that makes the driving force of the growth rate higher. As expected, the largest grain size was smaller in the strips given 60% reduction at the early stage of annealing, and a reversion in the largest grain size was observed with further annealing due to the higher growth rate in the strips given 60% reduction. Figure 13 shows the dierence in growth kinetics
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Fig. 10. (110) pole ®gure of the 3% silicon±iron alloy strip containing 30 p.p.m. sulfur after ®nal argon annealing at 12008C for 7.2 ks.
of the 3% silicon±iron alloy strips with bulk content of sulfur during ®nal vacuum annealing at 12008C. The ®nal reduction in thickness was ®xed at 60%. Due to the relatively weaker grain boundary pinning eect of segregated sulfur, the average grain size was larger in the alloy strips with 30 p.p.m. sulfur and the dierence in two alloy strips increased with annealing time. The minimum in growth rate of the largest grain was approximately congruent with the maximum in concentration of segregated sulfur. Although both alloys show a similar trough in growth rate of the largest grain, the relative growth rate in the alloy strips with 300 p.p.m. sulfur was lower at the early stage of annealing irrespective of smaller average grain size, but the situation was reversed with further annealing. Referring to Fig. 2, this may be attributed to the dominant eects on growth rate: the relatively higher concentration of segregated sulfur in the former half of ®nal annealing and the smaller
Fig. 11. The dierence in growth kinetics with annealing atmosphere during ®nal annealing at 12008C.
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grain growth in the present 3% silicon±iron alloys. Figure 14 shows a schematic time±concentration diagram of surface-energy-induced selective grain growth in the case of ®nal vacuum or hydrogen annealing. CS(t ) is the concentration of segregated sulfur which varies with annealing time. Cf110g on the ordinate axis means a concentration of segregated sulfur below which the surface-energy-induced selective growth of {110} grains occurs. Cf111g is a concentration of segregated sulfur above which {111} grains grow selectively, consuming other grains. Therefore, {100} grains grow selectively within the concentration range between Cf110g and Cf111g : As a result, the abscissa axis is divided into ®ve regions with the amount of segregated sulfur: the selective growth regions, I and V, of {110} grains, the growth regions, II and IV, of {100}
Fig. 12. The dierence in growth kinetics of the alloy strips containing 300 p.p.m. sulfur with ®nal reduction during ®nal vacuum annealing at 12008C.
average grain size in the latter half. As a result, the largest grain size of the alloy strips with 300 p.p.m. sulfur exceeded that of the other alloy strips after a reversion point. The location of the minimum of growth rate was, therefore, shifted to the left side in comparison with that of the other alloy. In this way, a narrower grain boundary pinning region of the largest grain is, as shown in Fig. 13(c), formed in the alloy strips with higher bulk content of sulfur. 5. A SCHEMATIC TIME±CONCENTRATION DIAGRAM OF SURFACE-ENERGY-INDUCED SELECTIVE GRAIN GROWTH
On the basis of the results obtained above, a schematic diagram can be composed in order to understand the correlation between interfacial segregation of sulfur and surface-energy-induced selective
Fig. 13. The dierence in growth kinetics with bulk content of sulfur during ®nal vacuum annealing at 12008C.
HEO et al.: SELECTIVE GRAIN GROWTH
grains, and the growth region, III, of {111} grains. The selective growth of {110} grains in region I is based on previous research [23]. Of course, grains other than the selectively growing grains in each region (e.g. {110} grains in regions II and IV) can also grow together with {100} grains, consuming high-index grains including {111}. However, the surface-energy-induced selective growth of {100} grains should be dominant in the regions for decreasing eectively the total energy of the system. DWC t is representative of the largest grain size in the case of relatively weaker cold rolling, and DSC t corresponds to the case of severe cold rolling. The prominent dierence in texture with severity of ®nal reduction, as shown in Fig. 7, can be explained, using equation (2) and the time±concentration diagram of Fig. 14(a). For two conditions ®nally cold-rolled to 40 and 60%, the selective growth kinetics of the largest grain, in turn, corresponds to DWC t and DSC t: During ®nal vacuum annealing, {110} grains grow selectively in region I due to the relatively lower concentration of segregated sulfur. As the concentration of segregated sul-
Fig. 14. A schematic time±concentration diagram of surface-energy-induced selective grain growth in the 3% silicon±iron alloy strips: (a) the case that the ®nal reduction is varied at a ®xed bulk content of sulfur and (b) the other case that the bulk content of sulfur is varied at a ®xed ®nal reduction.
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fur increases, {100} grains have a chance for selective growth in region II, while the growth rate decreases mainly due to the increase in concentration of segregated sulfur. {111} grains grow selectively in region III. The growth rate is, however, very low due to the strong grain boundary pinning eect, especially at around the maximum of segregated sulfur. Because the average grain size is relatively smaller in the case of higher reduction while the concentration of segregated sulfur is the same, DSC t exceeds DWC t after a reversion point Pr. In region IV, the chance for surface-energyinduced selective growth is again given {100} grains. For obtaining ®nal 110001 texture in region V, {110} grains should, therefore, survive to grow selectively after region IV. Considering the log-time plot of Fig. 14, the annealing time of region I is actually quite short in comparison with that of regions II±IV. As a result, a relatively lower ®nal reduction, which results in the lower selective growth rate of {100} or {111} grains in regions II± IV, is preferred for obtaining ®nal 110001 texture. Changes in surface-energy-induced selective growth kinetics with bulk content of sulfur during ®nal vacuum annealing can also be explained with Fig. 14(b). Here, the ®nal reduction in thickness is ®xed. LC and HC mean the lower and higher bulk content of sulfur. The concentration of segregated sulfur increases as the bulk content of sulfur increases. This results in a smaller average grain size due to the relatively stronger grain boundary pinning eect of highly segregated sulfur, which acts as a main source of the relatively higher growth rate of {111} or {100} grains in the latter half of ®nal annealing. Regions III and IV for the selective growth of {111} and {100} grains are also extended with increasing bulk content of sulfur, as shown in Fig. 14(b). Consequently, the probability that surface-energy-induced selective growth of {110} grains can occur in region V becomes lower with increasing bulk content of sulfur. On the other hand, the reason that among the 110uvw orientations only the 110001 Goss texture is obtained after ®nal annealing has been explained by a maximum energy release theory of 110001 Goss texture [33, 34]. According to the theoretical calculation in b.c.c. crystal [1], 110 huvwi nuclei including 110001 can also be formed at the strip surface during the initial annealing stage, because the surface energy of (110) grains is the same, regardless of the orientation. The ®nal 110001 Goss texture may, therefore, be attributed to the more dominant eect of the maximum energy release than that of the surface energy, which results in the larger number of 110001 nuclei in comparison with that of the 110uvw nuclei except for the 110001 one.
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HEO et al.: SELECTIVE GRAIN GROWTH 6. CONCLUSIONS
Eects of ®nal reduction and sulfur segregation under various annealing atmospheres on surfaceenergy-induced selective grain growth and texture development have been delineated in 3% silicon± iron alloy strips. During ®nal vacuum or hydrogen annealing, the strips, irrespective of the bulk content of sulfur, showed a convex pro®le in segregation kinetics of sulfur that is directly related to evaporation of segregated sulfur or gasi®cation to hydrogen sul®de. Surface-energy-induced selective growth of {110} grains occurs at a low concentration of segregated sulfur. With increasing concentration of segregated sulfur, the selective growth of {110} grains is in turn followed by that of {100} and {111} grains. The growth rate at time t is determined by the combined eect of average grain size and concentration of segregated sulfur which has a strong pinning eect on grain boundary movement. Two processing conditions, the relatively lower ®nal reduction at a ®xed bulk content of sulfur and the relatively lower bulk content of sulfur at a ®xed ®nal reduction, are preferred for obtaining ®nal 110001 Goss texture. This is because such conditions increase the average grain size so that the surface-energy-induced selective growth rate of {100} and {111} grains can be relatively decreased and thus the probability of selective growth of 110001 grains becomes higher in the sulfur-free region after prolonged annealing. REFERENCES 1. Friedel, J., et al., Acta metall., 1953, 1, 79. 2. Walter, J. L. and Dunn, C. G., Trans. Am. Inst. Min. Engrs, 1959, 215, 465. 3. Walter, J. L. and Dunn, C. G., Acta metall., 1960, 8, 497.
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