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Interfacial segregation, nucleation and texture development in 3% silicon steel
Acta Materialia 51 (2003) 4953–4964 www.actamat-journals.com
Interfacial segregation, nucleation and texture development in 3% silicon steel N.H. Heo ∗, S.B. Kim, Y.S. Choi, S.S. Cho, K.H. Chai Machinery and Materials Group, Korea Electric Power Research Institute, 103-16 Munji-dong, Yusung-ku, Taejon 305-380, South Korea Received 6 June 2002; accepted 4 May 2003
Abstract In inhibitor-free 3% Si–Fe alloys containing sulfur, the matter which the final main texture after annealing becomes among the {1 0 0}具u v w典, {1 1 0}具0 0 1典 and {1 1 0}具u v w典 components depends on the combination of various factors: final reduction, heating rate, flow rate of hydrogen and bulk content of sulfur. With increasing final reduction and heating rate, the final main texture after annealing tends to be transited from the {1 1 0}具u v w典 to the {1 1 0}具0 0 1典 and then followed by the {1 0 0}具u v w典 component. This is due to the active surface-energy-induced selective growth of the {1 0 0}具u v w典 grains that makes the survival and selective growth of the {1 1 0} grains difficult. On the viewpoints of the nucleation and the selective growth, a higher flow rate of hydrogen and a lower bulk content of sulfur may result in the transition in final main texture of the {1 0 0}具u v w典 to the {1 1 0}具0 0 1典 and subsequently to the {1 1 0}具u v w典 component after annealing. 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Iron; Segregation; Nucleation; Grain growth; Texture
1. Introduction There have been several theories [1–3] and models [4–8] related to the nucleation from a rolled matrix and the texture development. Recently, the nucleation mechanism has been reassessed and experimentally confirmed in previous research [9]. The nucleation from the rolled matrix is mainly governed by the diffusionless nucleation, while the
diffusional nucleation plays a minor role in the nucleation from the rolled matrix. On the other hand, it has been shown that in 3% Si–Fe alloys, the surface-segregated sulfur governs the surfaceenergy-induced selective growth of grains [10,11]. It is the purpose of this study to correlate the interfacial segregation of sulfur, the nucleation and the surface-energy-induced selective growth of grains in inhibitor-free 3% Si–Fe alloys. 2. Experimental
Corresponding author. Tel.: +82-42-865-5915; fax: +8242-865-5804. E-mail address: [email protected] (N.H. Heo). ∗
Forty or 100 µm thick strips of an inhibitor-free 3% silicon steel containing 90 ppm sulfur were
1359-6454/$30.00 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/S1359-6454(03)00258-1
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prepared through vacuum induction melting, hotand multi-stage cold-rolling processes including an intermediate annealing. The chemical composition of the 3% silicon steel is listed in Table 1. Effects of final reduction, heating rate, flow rate of hydrogen and strip thickness on nucleation and surface-energy-induced selective growth of grains were investigated. Strips were finally isothermalannealed at 1200 oC for a prolonged time. Pole figures, ODFs (orientation distribution functions) and an etch-pit method were used for texture analyses. The surface segregation behavior of solutes (especially, sulfur) was investigated with the method used in previous researches [10,11]. Magnetic induction B10(Tesla) of strips with a dimension of 5 (width) × 100 (length) × 0.04 or 0.1 (thickness) mm3 was measured with a DC-fluxmeter and an open circuit method under an external magnetic field of 1000 A/m.
3. Theoretical consideration 3.1. Diffusionless and diffusional nucleation in a rolled matrix A brief description of nucleation from a rolled matrix is given here, based on the shortcut theory [9]. From the total free energy change associated with the nucleation of a spherical embryo of radius r at a distance d from a dislocation core, the critical size and the activation free energy are as follows: r∗ ⫽
⫺2gg 16p g3g and ⌬G∗r ⫽ . ⌬Gv 3 ⌬G2v
(1)
⌬Gv is the bulk free energy change per unit volume ( = ⫺Gv) that is the same as the elastic strain energy change per unit volume at the distance d from the dislocation core and gg is the energy per unit area of the interface that is formed by the embryo and the matrix. Based on Eq. (1), at the Table 1 The chemical composition of the 3% Si–Fe alloy used in this study Elements Si wt% 2.94
C 0.0035
S 0.0091
Mn ⬍0.001
Fe Balanced
distance d from the dislocation core, an embryo of lower interface energy and thus smaller critical size is easier to form than that of higher interface and consequently larger critical size, due to the relatively smaller activation free energy. Therefore, the best way for forming of the embryo is to follow the diffusionless nucleation. That is, if the critical size of the rolled matrix releases simply the elastic strain energy, it is enough for forming of the embryo of the critical size without a diffusion step. During the diffusionless nucleation, the orientation of the embryo takes, therefore, after that of the rolled matrix. The orientation of the embryo forming at the rolled surface also takes after that of the surface. Even at the same critical size of the embryo, the activation free energy is smaller at the surface than within the bulk due to a factor related to the wetting angle, resulting in a higher nucleation rate at the surface. A representative example of the diffusional nucleation is the nucleation of the {1 1 0}具0 0 1典 embryo at an imperfect {1 1 1}具1 1 2典 surface with 具1 1 0典 line defects of a rolled b.c.c. matrix. Referring to the rolling direction of the 具1 1 2典 and the easy slip direction of the 具1 1 1典, the line defects of the 具1 1 0典 type that are perpendicular to the rolling direction are the easiest to form. Due to the relative ease in movement of the matrix atoms just near the line defects onto the surface and the shortcut movement characteristic of the matrix atoms for minimizing of the number of broken bonds, among the {1 1 0} embryos the {1 1 0}具0 0 1典 embryo is the easiest to form at the {1 1 1}具1 1 2典 surface of the rolled b.c.c. matrix through the diffusional nucleation. Due to the intrinsic characteristic of the diffusional nucleation, the orientation of an embryo forming through the diffusional nucleation is different from that of the rolled surface or matrix. The diffusional nucleation is easier at the surface than within the bulk, due to the relatively easier movement of matrix atoms onto the surface. During the nucleation from the rolled surface or matrix, the prevalent nucleation is, therefore, the diffusionless nucleation and the diffusional nucleation occupies a minor portion due to the additional diffusion step of matrix atoms.
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3.2. Annealing atmosphere, heating rate, flow rate of hydrogen and interfacial segregation kinetics of solutes The surface segregation behavior has mostly been interpreted by means of models in which a decrease in surface free energy is assumed to be the predominant driving force for the segregation process [12]. In contrast, the interpretation of grain boundary segregation has generally been based on the assumption that a decrease in lattice strain energy, associated with misfitting solute atoms, provides the driving force for the segregation [13]. However, the minimization of the total system free energy includes contributions from both the interfacial free energy and the lattice strain energy of an alloy. In a hypothetical, ideal A–B solid solution in which the pure component A possesses a lower surface energy than the pure component B, the minimization of the surface free energy would dictate a higher concentration of A at the surface than in the bulk of the alloy, for all bulk compositions of the alloy. In contrast, the lattice strain energy concept would predict a higher concentration of the solute at the surface than in the bulk. Thus, the two effects would tend to reinforce one another in the case of a B-rich alloy whereas they would tend to counteract one another in an A-rich alloy. Such a segregation phenomenon has been well described in some studies [14–16]. Fig. 1 shows schematic diagrams for explaining the surface segregation kinetics of sulfur in inhibitor-free 3% Si–Fe alloy strips during heating. Even
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though a repulsive segregation between sulfur and silicon [17,18] is considered, like the curve I the equilibrium surface segregation concentration of sulfur decreases with increasing temperature. Following curve II, the surface concentration of segregated sulfur increases to a point M during heating, after which the concentration is controlled by the equilibrium concentration. Because the surfacesegregated sulfur evaporates under a vacuum atmosphere or gasifies as H2S under a hydrogen atmosphere [11], the segregation kinetics of sulfur under such an atmosphere is shifted from the curve II to the curve III in which a maximum P in the surface-segregated sulfur is observed, as shown in Fig. 1(b). During isothermal annealing at a temperature, the surface segregation concentration is generally saturated to the equilibrium concentration at the temperature with annealing time, following the curve IV. Due to the evaporation of the segregated sulfur or the H2S reaction that forms a depleted zone of sulfur just below the strip surface, the segregation kinetics follows, however, the curve V in Fig. 1(c) that shows also a maximum P. In the concentration profiles, the same concentration of sulfur occurs on both sides of the profiles, but the concentration of the right side governs mainly the surface-energy-induced selective growth of grains and the final texture [10,11]. This is because the cases of Fig. 1(a) and (b) are due to the much higher grain boundary mobility within the higher temperature range and the case of Fig. 1(c) due to the longer time range for the selective growth. Additional schematic diagrams for more
Fig. 1. Schematic diagrams for explaining the surface segregation kinetics of sulfur in inhibitor-free 3% Si–Fe alloy strips during heating.
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understanding of the surface segregation kinetics of solutes and the formation of a depleted zone are given in Fig. 2. Fig. 3 shows schematic diagrams for explaining changes in surface segregation kinetics of sulfur and nucleation behavior with heating rate in the 3% Si–Fe alloy strips. From previous research [9], if the concentration of surface-segregated sulfur is very low, the orientation of embryos forming at the rolled surface also takes after the surface orientation. If the concentration is higher than a critical level, due to the bond strength of Fe–S molecule [19] three times higher than that of Fe–Fe molecule [20] the segregated sulfur may strongly influence the orientation of the embryos forming at the surface, especially the direction. Therefore, CN{1 1 0} is specified into CN{1 1 0}具0 0 1典 and CN{1 1 0}具u v w典. N C{1 1 0}具0 0 1典 means a concentration of the segregated sulfur below that among the {1 1 0}具u v w典 embryos the {1 1 0}具0 0 1典 embryos nucleate dominantly from the rolled {1 1 0}具0 0 1典 or {1 1 1}具1 1 2典 surface. CN{1 1 0}具u v w典 means a concentration of the segregated sulfur above that the dominant nucleation of {1 1 0}具u v w典⫽具0 0 1典 embryos is observed from the rolled surface. The concentration between the CN{1 1 0}具0 0 1典 and the N C{1 1 0}具u v w典 corresponds to the mixed nucleation of the {1 1 0}具0 0 1典 and {1 1 0}具u v w典⫽具0 0 1典 embryos. Here, TR is the recrystallization temperature corresponding to a final reduction and heating
rate. Referring to the other previous research [11], C{1 1 0} is a concentration below that the {1 1 0} grains grow selectively. C{1 1 1} corresponds to a concentration above that the high index grains containing {1 1 1} grains grow selectively. The concentration between C{1 1 0} and C{1 1 1} corresponds to the surface-energy-induced selective growth of {1 0 0} grains. In Fig. 3, the concentration profile is shifted to a higher temperature range with increasing heating rate. Without the evaporation of the segregated sulfur or the gasification to H2S, the maximum concentration of the segregated sulfur would decrease with increasing heating rate, due to the lower equilibrium concentration at the temperature corresponding to the maximum. The case of a high heating rate corresponds to that of direct isothermal annealing. As expected from Fig. 3 and previous study [9], at a given final reduction the {1 1 0}具0 0 1典 embryos rather than the {1 1 0}具u v w典⫽具0 0 1典 embryos form dominantly from the rolled {1 1 0}具0 0 1典 or {1 1 1}具1 1 2典 surface with increasing heating rate. Fig. 4 shows effects of heating rate on surface segregation kinetics of sulfur. As has been expected from Fig. 3, the concentration profile of segregated sulfur is shifted to a higher temperature range with increasing heating rate. Unlike the expectation of Fig. 3, the increase in maximum concentration with increasing heating rate can be mainly attributed to the H2S reaction that has
Fig. 2. The surface segregation kinetics of solutes during direct isothermal annealing: (a) equilibrium segregation of solutes and (b) nonequilibrium segregation of sulfur in the 3% Si–Fe alloy strips under a vacuum or hydrogen atmosphere.
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Fig. 4. The effect of heating rate on surface segregation kinetics of sulfur in the 100 µm thick 3% Si–Fe alloy strips under a flow rate of 3 l H2/min.
Fig. 3. Schematic diagrams for explaining changes in surface segregation kinetics of sulfur and nucleation behavior with heating rate in the 3% Si–Fe alloy strips.
occurred during the relatively shorter annealing time to the maximum. 3.3. Surface-energy-induced selective growth in 3% Si–Fe alloy strips On the other hand, the surface-energy-induced selective growth rate [11] in the 3% Si–Fe alloy strips, G(t), is given by G(t) ⫽ M(t)
冋
gG 2⌬gS ⫹ ⫹ C(t) r(t) d
册
(2)
in which gG is the grain boundary free energy, r(t) is the average radius of grains excluding the selec-
tively growing grains at time t, ⌬gS is the difference in surface energy between the growing grain and the grain that is consumed, d is the sheet thickness, C(t) is the grain boundary segregation concentration of sulfur that has a strong grain boundary pinning effect [21–23] as the negative driving force term and M(t) is the grain boundary mobility that is strongly influenced by the grain boundary segregation concentration of sulfur [13] and the annealing temperature. In Eq. (2), the growth rate depends mainly on the average grain size and the grain boundary concentration of segregated sulfur. The second term in the parenthesis is not the main controlling factor of the growth rate due to the small ⌬gS / gG ratio, 0.03 [24]. Generally, the surface energy of {1 1 0} plane in b.c.c. metals is less than the {1 0 0} and followed by the {1 1 1} and other less densely packed planes [25,26]. A transition in selective growth of the {1 1 0} grains to the {1 0 0} and subsequently to the high index grains containing {1 1 1} occurs at strip surfaces with increasing concentration of surface-segregated sulfur. The selective growth rate of the {1 1 1} or high index grains under a higher surface-segregated sulfur atmosphere is, however, very sluggish due to the strong pinning effect of segregated sulfur at grain boundaries. Therefore, such components are often difficult to
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be observed as the final main texture, because these grains are mostly consumed during the selective growth of the {1 0 0} or {1 1 0} grains within the later time range showing the relatively lower segregation concentration of sulfur. Fig. 5 shows a schematic diagram for explaining the correlation between the segregation kinetics of sulfur, the flow rate of hydrogen, the growth rate and the final texture in the 3% Si–Fe alloy strips during direct isothermal annealing. In this diagram, LF and HF each mean the lower and higher flow rates of hydrogen, and the meaning of other symbols follows one in previous research [11]. Under the higher flow rate of hydrogen, the nucleation of the {1 1 0}具0 0 1典 embryos is also more dominant at the same rolled {1 1 0}具0 0 1典 or {1 1 1}具1 1 2典 surface, due to the lower concentration of surfacesegregated sulfur. With increasing flow rate of hydrogen, the final main texture tends to be changed from the {1 0 0}具u v w典 to the {1 1 0}具0 0 1典 component. This is due to two reasons. The first one is the relatively larger average grain size that arises from the weaker grain boundary pinning effect of the lower segregated sulfur. The second one is the shortened time for the selective growth of the {1 0 0} or high index grains that is favorable for the subsequent selective growth of the {1 1 0}具0 0 1典 grains. However, a much higher flow rate of hydrogen may result in
Fig. 5. A schematic diagram for explaining the correlation between segregation kinetics of sulfur, flow rate of hydrogen, growth rate and final texture in the 3% Si–Fe alloy strips during direct isothermal annealing.
the transition in final main texture from the {1 1 0}具0 0 1典 to the {1 1 0}具u v w典 component that will be described below.
4. Nucleation, surface-energy-induced selective growth and directionality of {1 1 0} grains 4.1. Heating rate and final texture Fig. 6 shows the cold rolling texture at the surface (S = 1) of the 100 µm thick 3% Si–Fe alloy strips. A much stronger {1 1 0}具0 0 1典 Goss texture was observed from the strip surface with the final reduction of 60%, but the texture was transited from the Goss texture to a strong γ-fiber + a weak cube texture with increasing depth to the strip center. The dependence of final texture and magnetic induction on heating rate and final reduction was investigated with these strips, and the details are listed in Table 2. The probability that the {1 1 0} grains survive to grow selectively later is lower at the higher heating rate, referring to Figs. 3 and 4. This is mainly due to the higher grain boundary mobility for the selective growth of the {1 0 0} or high index grains within the equivalent segregation concentration range. This is also the reason why the final main texture is changed from the {1 1 0} to the {1 0 0} component with increasing heating rate, as shown in Table 2.
Fig. 6. ODF results obtained from the rolled surface (S = 1) of the 100 µm thick 3% Si–Fe alloy strips with the final reduction of: (a) 30% and (b) 60%. j 2 = 45°.
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Table 2 The dependence of final texture and magnetic induction B10(Tesla) on heating rate and final reduction in the 100 µm thick 3% Si– Fe alloy strips under a flow rate of 3 l H2/min Final reduction Annealing condition and strip thickness
Final main texture
B10(Tesla) just B10(Tesla) after after heating final annealing to 1200 oC
{1 1 0}具0 0 1典 {1 1 0}具u v w典⫽具0 0 1典 {1 0 0}具u v w典 30% (100 µm)
60% (100 µm)
100 oC/h 400 oC/h Direct isothermal annealing 100 oC/h 400 oC/h Direct isothermal annealing
– – –
Very strong Strong –
– Very strong Very strong
1.58 1.57 –
1.62 (5 h) 1.57 (5 h) 1.60 (13.8 h)
Very strong – –
Weak – –
– Very strong Very strong
2.00 1.62 –
2.02 (5 h) 1.69 (13.8 h) 1.66 (10 h)
4.2. Nucleation, surface-energy-induced selective growth and directionality of {1 1 0} grains In previous research [27], the matter that the final main texture in the 3% Si–Fe strips becomes either the {1 1 0}具0 0 1典 or {1 1 0}具u v w典 component has been understood on the viewpoint of the intrinsic surface formation of the embryos that may be strongly influenced by the surface-segregated sulfur. As shown in Fig. 6, the cold rolling texture is generally composed of a contour enclosing a core component: the {1 1 0}具0 0 1典 core component and the {1 1 0}具u v w典⫽具0 0 1典 and high index components enclosing the core component. Due to the strongest intensity in the cold rolling texture and the diffusionless nucleation characteristic, the number of the {1 1 0}具0 0 1典 grains with low angle boundary just after the complete consumption of the deformed matrix might be the most among the {1 1 0} grains. Also, the average size of the colonies that consist of the {1 1 0}具0 0 1典 grains of low angle boundary is statistically the biggest. However, it is emphasized that the number of the {1 1 0}具0 0 1典 grains of low angle boundary is less than the total number of the {1 1 0}具u v w典⫽具0 0 1典 grains. In addition, the number of the {1 1 0}具0 0 1典 grains is expected to be more in the 60% case, due to the stronger core intensity. The overall average size of primary grains at the strip
surface is, however, smaller in the 60% case due to the higher elastic strain energy. Due to the cold rolling texture composed of a contour, the {1 1 0} grains show various angles deviating from the 具0 0 1典 direction, and the maximum deviation angle is larger in the case with the final reduction of 30%. The deviation angle of the {1 1 0} grains and the total number of the {1 1 0} surface grains increase with increasing concentration of surface-segregated sulfur, while the number of the {1 1 0}具0 0 1典 surface grains decreases. The dependence of deviation angle on surface-segregated sulfur is, therefore, less in the 60% case. This is because, as the final reduction increases, the recrystallization temperature decreases and thus the lower surface-segregated sulfur atmosphere is favorable for the nucleation of the {1 1 0}具0 0 1典 embryos. At this point, the formation mechanism of final main texture needs to be considered in the aspect of the surface-energy-induced selective growth as well as the nucleation. Now, even at the same heating rate of 100 oC/h, the prominent difference in the final main texture of Table 2 (i.e., the {1 1 0}具u v w典 component at the 30% and the {1 1 0}具0 0 1典 component at the 60%) is understood on the basis of Eq. (2). Provided that the surface concentration of segregated sulfur is little dependent on the present final reduction range, the concentration profile of segregated sulfur is fixed
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like Fig. 4 at the same heating rate. During heating, the surface-energy-induced selective growth of grains with the lowest surface energy occurs at each time, depending on the surface concentration of segregated sulfur. In the case with the final reduction of 60%, the more active consumption by the {1 0 0}, {1 1 1} or high index grains of the {1 1 0} grains with various directions proceeds with time, due to the overall smaller average grain size and the resultantly bigger driving force for the selective growth. Therefore, only the {1 1 0}具0 0 1典 grains and the {1 1 0} grains with the direction close to the 具0 0 1典 remain after the selective growth. The selective growth process in the case with the final reduction of 30% is contrary to that in the 60% case. The relatively larger average grain size and thus the sluggish selective growth kinetics increase the probability that the {1 1 0}具u v w典 grains with various directions survive through the selective growth process, as shown in Table 2. A high magnetic induction of 2.02 Tesla was obtained only from the strip that is mainly composed of the {1 1 0}具0 0 1典 Goss grains, while a low magnetic induction of 1.62 Tesla was obtained from the strip that shows the final main texture of the {1 1 0}具u v w典. As has been expected from Fig. 5, the final main texture was transited from the {1 1 0}具0 0 1典 component to the {1 1 0}具u v w典 component with increasing flow rate of hydrogen. Conclusively, considering only the final main texture consisting of the {1 1 0} grains, a higher final reduction and heating rate is advantageous for obtaining the final main texture of the {1 1 0}具0 0 1典 component on the viewpoints of the nucleation and the surface-energy-induced selective growth. The higher flow rate of hydrogen and the lower bulk content of sulfur that are favorable for a relatively lower surface concentration of sulfur may cause the transition in final main texture of the {1 1 0}具0 0 1典 to the {1 1 0}具u v w典 component, on the viewpoint of particularly the selective growth as well as the nucleation. Therefore, the matter that the final main texture becomes either the {1 1 0}具0 0 1典 or the {1 1 0}具u v w典 component depends on the combination of those factors. In addition, it is very difficult to quantify the effects of the segregated-sulfur-controlled surface
nucleation and the surface-energy-induced selective growth kinetics on the directionality of {1 1 0} grains, due to no decisive evidence of the sulfurcontrolled surface nucleation. However, it is at least suggested that, based on the present experimental results, the directionality of the {1 1 0} grains after final annealing is mainly determined by the selective growth kinetics rather than by the surface nucleation influenced by the segregated sulfur.
5. Effects of flow rate of hydrogen and strip thickness on surface-energy-induced selective growth 5.1. Flow rate of hydrogen, strip thickness and final main texture of {1 1 0}具0 0 1典 Table 3 shows the dependence of final main texture and magnetic induction on flow rate of hydrogen and strip thickness in the 3% Si–Fe alloy strips. Under the flow rate of 3 l H2/min, the strips consisted mainly of the {1 0 0}具u v w典 grains after direct isothermal annealing, regardless of the strip thickness and the final reduction. However, the final main texture was mostly composed of the {1 1 0}具0 0 1典 Goss component under the flow rate of 10 l H2/min. The {1 1 0}具u v w典⫽具0 0 1典 component that was frequently observed in the cases of moderate heating rates of Table 2 was not nearly detected in this case. The magnetic induction of the strips was directly related to the final main texture: a magnetic induction higher than 1.9 Tesla corresponded to the final main texture of the {1 1 0}具0 0 1典 Goss component and a lower magnetic induction the {1 0 0}具u v w典 component. On the other hand, the texture development at the surface (S = 1) of the 100 µm thick 3% Si–Fe alloy strips with the final reduction of 60% under the flow rate of 10 l H2/min is shown in Fig. 7. The annealing time of 60 s corresponds to the strip temperature of about 1010 oC and the time of 120 s the temperature of about 1130 oC. The initial texture also took after the cold rolling texture, but high index grains including the {1 1 1} grains that grew selectively at the strip surface or grew out from the strip interior to the surface were observed
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Table 3 The dependence of final main texture and final magnetic induction B10(Tesla) on flow rate of hydrogen and strip thickness in the 3% Si–Fe alloy strips after direct isothermal annealing at 1200 oC for a prolonged time Strip thickness and final Flow rate of reduction hydrogen
40 µm (30%, 60%) 100 µm (30%, 60%)
3 l H2/min 10 l H2/min 3 l H2/min 10 l H2/min
Final main texture
B10(Tesla)
{1 1 0}具0 0 1典
{1 1 0}具u v w典⫽具0 0 1典
{1 0 0}具u v w典
– Very strong – Very strong
– Weak – Weak
Very strong – Very strong –
(1.56, 1.76) (2.01, 1.90) (1.60, 1.66) (1.92, 1.90)
Fig. 7. The texture development at the surface (S = 1) of the 100 µm thick 3% Si–Fe alloy strips with the final reduction of 60% with annealing time at 1200 oC under the flow rate of 10 l H2/min: (a) as-rolled, (b) 60 and (c) 120 s. j 2 = 45°.
with further annealing. However, this strip showed the final main texture of the {1 1 0}具0 0 1典 component after direct isothermal annealing for a prolonged time, as shown in Table 3. 5.2. Details of sulfur segregation kinetics and surface-energy-induced selective growth Such a great dependence of final texture on flow rate of hydrogen is shown in Fig. 8. During direct isothermal annealing, a trough in magnetic induction [11] was also observed in both cases of flow rate. After the trough, the magnetic induction increased with increasing annealing time. The concentration of surface-segregated sulfur was overall
much lower under the flow rate of 10 l H2/min. After annealing for a prolonged time, a high magnetic induction of 1.90 Tesla that corresponds to the final main Goss texture was obtained in the case of 10 l H2/min, but the other case showed a low magnetic induction of 1.76 Tesla that results from the final main texture of the {1 0 0}具u v w典 component. The final Goss texture under the higher flow rate is due to the faster elimination of surfacesegregated sulfur arising from the more active H2S reaction that makes the survival and selective growth of Goss grains possible within the further annealing time range. In general, the average grain size increases with increasing strip thickness [24] that is supported by
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Fig. 8. Changes in magnetic induction of the 40 µm thick 3% Si–Fe alloy strips with the final reduction of 60% and concentration of surface-segregated sulfur with direct isothermal annealing time at 1200 oC under the flow rates of: (a) 3 and (b) 10 l H2/min.
Fig. 9. If other conditions are fixed, the smaller average grain size in the thinner strip increases the selective growth rate of the {1 0 0} and high index grains. This lowers the probability that the {1 1 0}具0 0 1典 grains survive to grow selectively after the surface-energy-induced selective growth of the other grains. As shown in Table 3, the final main texture showed, however, a strong dependence on the flow rate of hydrogen rather than on the strip thickness. Here, the correlation between
Fig. 9. The dependence of average grain size on strip thickness in the 3% Si–Fe alloy strips with the final reduction of 60% during direct isothermal annealing at 1200 oC under the flow rate of 10 l H2/min.
the surface segregation kinetics of sulfur and the strip thickness can be detailed in Fig. 10. Due to the less total amount of sulfur in the bulk interior, the sulfur depletion rate at the surface was faster in the 40 µm thick strip and the maximum in concentration of surface-segregated sulfur was, therefore, lower in the thinner strip. That is, the little dependence of final main texture on strip thickness is probably because the lower surface-segregated sulfur effect in the thinner strip counteracts the smaller average grain size effect, resulting in shortening the time range for the selective growth of the {1 0 0} and high index grains. As shown in Fig. 11, changes in magnetic induction with annealing time also need to be checked, even though a final magnetic induction higher than 1.9 Tesla was obtainsed under the flow rate of 10 l H2/min, irrespective of the strip thickness. The changing behavior in magnetic induction with annealing time was strongly dependent on the strip thickness. The 40 µm thick strip showed the trough in magnetic induction at the earlier time. Referring to Figs. 9 and 10(b), this can be attributed to the smaller average grain size and the lower grain boundary concentration of segregated sulfur favorable for the selective growth of the {1 0 0} or high index grains. After the selective growth of the {1 0 0} grains within the prolonged annealing time range, the surviving {1 1 0}具0 0 1典 Goss grains
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Fig. 10. The dependence of segregation kinetics of sulfur on strip thickness in the 3% Si–Fe alloy strips with the final reduction of 60% during direct isothermal annealing at 1200 oC under the flow rates of: (a) 3 and (b) 10 l H2/min.
energy-induced selective growth process of grains, the number of surviving Goss grains is absolutely fewer in the thinner strip than in the thicker strip. Based on Fig. 9, the fewer number of Goss grains in the thinner strip is mainly due to the smaller average grain size which resulted in the more active decrease in the number of the {1 1 0}具0 0 1典 grains during the selective growth of the other grains.
6. Conclusions
Fig. 11. The dependence of magnetic induction change on strip thickness in the 3% Si–Fe alloy strips with the final reduction of 60% during direct isothermal annealing at 1200 oC under the flow rate of 10 l H2/min.
start to grow selectively at the expense of the other grains. In this case, the increasing rate in magnetic induction depends on the number of surviving Goss grains. On the other hand, the 40 µm thick strip showed a plateau within the time range of 0.5–8 ks in which the magnetic induction was little changed and after which a high magnetic induction of 1.9 Tesla was observed at the relatively delayed time. This means that, throughout the surface-
The correlation between interfacial segregation of sulfur, nucleation and texture development has been investigated in inhibitor-free 3% Si–Fe alloys containing sulfur. Considering only the final main texture consisting of {1 1 0} grains, a higher final reduction, heating rate and flow rate of hydrogen and a lower bulk content of sulfur are advantageous for obtaining the final main texture of the {1 1 0}具0 0 1典 component on the viewpoint of nucleation. Among these, the higher flow rate of hydrogen and the lower bulk content of sulfur may result in the transition in final main texture of the {1 1 0}具0 0 1典 to the {1 1 0}具u v w典 component, based on the surface-energy-induced selective growth. Therefore, the matter that the final main
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texture consists of either the {1 1 0}具0 0 1典 or the {1 1 0}具u v w典 component depends on the combination of those factors. With increasing heating rate, the concentration profile of surface-segregated sulfur is shifted to a higher temperature range, and the final main texture after annealing tends, as a result, to be changed from the {1 1 0}具u v w典 to the {1 1 0}具0 0 1典 and then followed by the {1 0 0}具u v w典 component. This is due to the higher grain boundary mobility at the selective growth stage of the {1 0 0}具u v w典 or high index grains that makes the survival and selective growth of the {1 1 0} grains difficult. Because the smaller average grain size effect in the thinner strip is diluted by the lower surface concentration effect of segregated sulfur under a flowing hydrogen atmosphere, the final main texture shows little dependence on the strip thickness. Acknowledgement This research was partially supported by a grant from the Center for Advanced Materials Processing (CAMP) of the 21st Century Frontier R& D Program funded by the Ministry of Science and Technology, Republic of Korea. References [1] Burgers WG, Louwerse PC. Zeitschrift fur Metall 1931;67:605.
[2] Barrett CS. Trans AIME 1940;137:128. [3] Dunn CG. Acta Metall 1954;2:173. [4] Inokuti Y, Maeda C. Trans Iron Steel Inst Japan 1984;24:655. [5] Harase J, Shimizu R, Dingley DJ. Acta Metall 1991;39:763. [6] Hayakawa Y, Szpunar JA, Palumbo G, Lin PJ. MMM 1996;160:143. [7] Hayakawa Y, Szpunar JA. Acta Mater 1997;45:4713. [8] Hayakawa Y, Muraki M, Szpunar JA. Acta Mater 1998;46:1063. [9] Heo NH, Kim SB, Chai KH, Choi YS, Cho SS. Mater Sci Form 2002;408-412:857. [10] Heo NH et al. J Appl Phys 1999;85:6025. [11] Heo NH, Chai KH, Na JG. Acta Mater 2000;48:2901. [12] Gibbs JW. The scientific papers of J. Willard Gibbs, vol. 1. New York: Dover, 1961 p. 219. [13] McLean D. Grain boundaries in metals. London: Oxford University Press, 1957 [chapter 5]. [14] Seah MP, Hondros D. R Soc London A 1973;335:191. [15] Seah MP, Lea C. Phil Mag 1975;31:627. [16] Johnson WC, Blakely JM. Interfacial segregation. Ohio 44073: American Society for Metals, 1977. [17] Es-Souni M, Mosser A. Scripta Metall 1988;22:1469. [18] De Rugy H, Viefhaus H. Surf Sci 1986;173:418. [19] Drowart J, Pattoret A, Smoes S. Proc. Br. Ceramic Soc 1967;(8):67. [20] Lin S-S, Kant A. J Phys Chem 1969;73:2450. [21] Lu¨ cke K, Detert K. Acta Metall 1957;5:628. [22] Cahn JW. Acta Metall 1962;10:789. [23] Lu¨ cke K, Stuwe HP. Recovery and recrystallization of metals. In: Himmel L, editor. New York: Wiley Interscience; 1963. [24] Kramer JJ. Metall Trans A 1992;23:1987. [25] Friedel J et al. Acta Metall 1953;1:79. [26] Vitos L et al. Surf Sci 1998;411:186. [27] Heo NH, Kim SB, Cho SS, Choi YS, Chai KH, Oh JM et al. Mater Sci Form 2002;408-412:863.
Interfacial segregation, nucleation and texture development in 3% silicon steel N.H. Heo ∗, S.B. Kim, Y.S. Choi, S.S. Cho, K.H. Chai Machinery and Materials Group, Korea Electric Power Research Institute, 103-16 Munji-dong, Yusung-ku, Taejon 305-380, South Korea Received 6 June 2002; accepted 4 May 2003
Abstract In inhibitor-free 3% Si–Fe alloys containing sulfur, the matter which the final main texture after annealing becomes among the {1 0 0}具u v w典, {1 1 0}具0 0 1典 and {1 1 0}具u v w典 components depends on the combination of various factors: final reduction, heating rate, flow rate of hydrogen and bulk content of sulfur. With increasing final reduction and heating rate, the final main texture after annealing tends to be transited from the {1 1 0}具u v w典 to the {1 1 0}具0 0 1典 and then followed by the {1 0 0}具u v w典 component. This is due to the active surface-energy-induced selective growth of the {1 0 0}具u v w典 grains that makes the survival and selective growth of the {1 1 0} grains difficult. On the viewpoints of the nucleation and the selective growth, a higher flow rate of hydrogen and a lower bulk content of sulfur may result in the transition in final main texture of the {1 0 0}具u v w典 to the {1 1 0}具0 0 1典 and subsequently to the {1 1 0}具u v w典 component after annealing. 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Iron; Segregation; Nucleation; Grain growth; Texture
1. Introduction There have been several theories [1–3] and models [4–8] related to the nucleation from a rolled matrix and the texture development. Recently, the nucleation mechanism has been reassessed and experimentally confirmed in previous research [9]. The nucleation from the rolled matrix is mainly governed by the diffusionless nucleation, while the
diffusional nucleation plays a minor role in the nucleation from the rolled matrix. On the other hand, it has been shown that in 3% Si–Fe alloys, the surface-segregated sulfur governs the surfaceenergy-induced selective growth of grains [10,11]. It is the purpose of this study to correlate the interfacial segregation of sulfur, the nucleation and the surface-energy-induced selective growth of grains in inhibitor-free 3% Si–Fe alloys. 2. Experimental
Corresponding author. Tel.: +82-42-865-5915; fax: +8242-865-5804. E-mail address: [email protected] (N.H. Heo). ∗
Forty or 100 µm thick strips of an inhibitor-free 3% silicon steel containing 90 ppm sulfur were
1359-6454/$30.00 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/S1359-6454(03)00258-1
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prepared through vacuum induction melting, hotand multi-stage cold-rolling processes including an intermediate annealing. The chemical composition of the 3% silicon steel is listed in Table 1. Effects of final reduction, heating rate, flow rate of hydrogen and strip thickness on nucleation and surface-energy-induced selective growth of grains were investigated. Strips were finally isothermalannealed at 1200 oC for a prolonged time. Pole figures, ODFs (orientation distribution functions) and an etch-pit method were used for texture analyses. The surface segregation behavior of solutes (especially, sulfur) was investigated with the method used in previous researches [10,11]. Magnetic induction B10(Tesla) of strips with a dimension of 5 (width) × 100 (length) × 0.04 or 0.1 (thickness) mm3 was measured with a DC-fluxmeter and an open circuit method under an external magnetic field of 1000 A/m.
3. Theoretical consideration 3.1. Diffusionless and diffusional nucleation in a rolled matrix A brief description of nucleation from a rolled matrix is given here, based on the shortcut theory [9]. From the total free energy change associated with the nucleation of a spherical embryo of radius r at a distance d from a dislocation core, the critical size and the activation free energy are as follows: r∗ ⫽
⫺2gg 16p g3g and ⌬G∗r ⫽ . ⌬Gv 3 ⌬G2v
(1)
⌬Gv is the bulk free energy change per unit volume ( = ⫺Gv) that is the same as the elastic strain energy change per unit volume at the distance d from the dislocation core and gg is the energy per unit area of the interface that is formed by the embryo and the matrix. Based on Eq. (1), at the Table 1 The chemical composition of the 3% Si–Fe alloy used in this study Elements Si wt% 2.94
C 0.0035
S 0.0091
Mn ⬍0.001
Fe Balanced
distance d from the dislocation core, an embryo of lower interface energy and thus smaller critical size is easier to form than that of higher interface and consequently larger critical size, due to the relatively smaller activation free energy. Therefore, the best way for forming of the embryo is to follow the diffusionless nucleation. That is, if the critical size of the rolled matrix releases simply the elastic strain energy, it is enough for forming of the embryo of the critical size without a diffusion step. During the diffusionless nucleation, the orientation of the embryo takes, therefore, after that of the rolled matrix. The orientation of the embryo forming at the rolled surface also takes after that of the surface. Even at the same critical size of the embryo, the activation free energy is smaller at the surface than within the bulk due to a factor related to the wetting angle, resulting in a higher nucleation rate at the surface. A representative example of the diffusional nucleation is the nucleation of the {1 1 0}具0 0 1典 embryo at an imperfect {1 1 1}具1 1 2典 surface with 具1 1 0典 line defects of a rolled b.c.c. matrix. Referring to the rolling direction of the 具1 1 2典 and the easy slip direction of the 具1 1 1典, the line defects of the 具1 1 0典 type that are perpendicular to the rolling direction are the easiest to form. Due to the relative ease in movement of the matrix atoms just near the line defects onto the surface and the shortcut movement characteristic of the matrix atoms for minimizing of the number of broken bonds, among the {1 1 0} embryos the {1 1 0}具0 0 1典 embryo is the easiest to form at the {1 1 1}具1 1 2典 surface of the rolled b.c.c. matrix through the diffusional nucleation. Due to the intrinsic characteristic of the diffusional nucleation, the orientation of an embryo forming through the diffusional nucleation is different from that of the rolled surface or matrix. The diffusional nucleation is easier at the surface than within the bulk, due to the relatively easier movement of matrix atoms onto the surface. During the nucleation from the rolled surface or matrix, the prevalent nucleation is, therefore, the diffusionless nucleation and the diffusional nucleation occupies a minor portion due to the additional diffusion step of matrix atoms.
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3.2. Annealing atmosphere, heating rate, flow rate of hydrogen and interfacial segregation kinetics of solutes The surface segregation behavior has mostly been interpreted by means of models in which a decrease in surface free energy is assumed to be the predominant driving force for the segregation process [12]. In contrast, the interpretation of grain boundary segregation has generally been based on the assumption that a decrease in lattice strain energy, associated with misfitting solute atoms, provides the driving force for the segregation [13]. However, the minimization of the total system free energy includes contributions from both the interfacial free energy and the lattice strain energy of an alloy. In a hypothetical, ideal A–B solid solution in which the pure component A possesses a lower surface energy than the pure component B, the minimization of the surface free energy would dictate a higher concentration of A at the surface than in the bulk of the alloy, for all bulk compositions of the alloy. In contrast, the lattice strain energy concept would predict a higher concentration of the solute at the surface than in the bulk. Thus, the two effects would tend to reinforce one another in the case of a B-rich alloy whereas they would tend to counteract one another in an A-rich alloy. Such a segregation phenomenon has been well described in some studies [14–16]. Fig. 1 shows schematic diagrams for explaining the surface segregation kinetics of sulfur in inhibitor-free 3% Si–Fe alloy strips during heating. Even
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though a repulsive segregation between sulfur and silicon [17,18] is considered, like the curve I the equilibrium surface segregation concentration of sulfur decreases with increasing temperature. Following curve II, the surface concentration of segregated sulfur increases to a point M during heating, after which the concentration is controlled by the equilibrium concentration. Because the surfacesegregated sulfur evaporates under a vacuum atmosphere or gasifies as H2S under a hydrogen atmosphere [11], the segregation kinetics of sulfur under such an atmosphere is shifted from the curve II to the curve III in which a maximum P in the surface-segregated sulfur is observed, as shown in Fig. 1(b). During isothermal annealing at a temperature, the surface segregation concentration is generally saturated to the equilibrium concentration at the temperature with annealing time, following the curve IV. Due to the evaporation of the segregated sulfur or the H2S reaction that forms a depleted zone of sulfur just below the strip surface, the segregation kinetics follows, however, the curve V in Fig. 1(c) that shows also a maximum P. In the concentration profiles, the same concentration of sulfur occurs on both sides of the profiles, but the concentration of the right side governs mainly the surface-energy-induced selective growth of grains and the final texture [10,11]. This is because the cases of Fig. 1(a) and (b) are due to the much higher grain boundary mobility within the higher temperature range and the case of Fig. 1(c) due to the longer time range for the selective growth. Additional schematic diagrams for more
Fig. 1. Schematic diagrams for explaining the surface segregation kinetics of sulfur in inhibitor-free 3% Si–Fe alloy strips during heating.
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understanding of the surface segregation kinetics of solutes and the formation of a depleted zone are given in Fig. 2. Fig. 3 shows schematic diagrams for explaining changes in surface segregation kinetics of sulfur and nucleation behavior with heating rate in the 3% Si–Fe alloy strips. From previous research [9], if the concentration of surface-segregated sulfur is very low, the orientation of embryos forming at the rolled surface also takes after the surface orientation. If the concentration is higher than a critical level, due to the bond strength of Fe–S molecule [19] three times higher than that of Fe–Fe molecule [20] the segregated sulfur may strongly influence the orientation of the embryos forming at the surface, especially the direction. Therefore, CN{1 1 0} is specified into CN{1 1 0}具0 0 1典 and CN{1 1 0}具u v w典. N C{1 1 0}具0 0 1典 means a concentration of the segregated sulfur below that among the {1 1 0}具u v w典 embryos the {1 1 0}具0 0 1典 embryos nucleate dominantly from the rolled {1 1 0}具0 0 1典 or {1 1 1}具1 1 2典 surface. CN{1 1 0}具u v w典 means a concentration of the segregated sulfur above that the dominant nucleation of {1 1 0}具u v w典⫽具0 0 1典 embryos is observed from the rolled surface. The concentration between the CN{1 1 0}具0 0 1典 and the N C{1 1 0}具u v w典 corresponds to the mixed nucleation of the {1 1 0}具0 0 1典 and {1 1 0}具u v w典⫽具0 0 1典 embryos. Here, TR is the recrystallization temperature corresponding to a final reduction and heating
rate. Referring to the other previous research [11], C{1 1 0} is a concentration below that the {1 1 0} grains grow selectively. C{1 1 1} corresponds to a concentration above that the high index grains containing {1 1 1} grains grow selectively. The concentration between C{1 1 0} and C{1 1 1} corresponds to the surface-energy-induced selective growth of {1 0 0} grains. In Fig. 3, the concentration profile is shifted to a higher temperature range with increasing heating rate. Without the evaporation of the segregated sulfur or the gasification to H2S, the maximum concentration of the segregated sulfur would decrease with increasing heating rate, due to the lower equilibrium concentration at the temperature corresponding to the maximum. The case of a high heating rate corresponds to that of direct isothermal annealing. As expected from Fig. 3 and previous study [9], at a given final reduction the {1 1 0}具0 0 1典 embryos rather than the {1 1 0}具u v w典⫽具0 0 1典 embryos form dominantly from the rolled {1 1 0}具0 0 1典 or {1 1 1}具1 1 2典 surface with increasing heating rate. Fig. 4 shows effects of heating rate on surface segregation kinetics of sulfur. As has been expected from Fig. 3, the concentration profile of segregated sulfur is shifted to a higher temperature range with increasing heating rate. Unlike the expectation of Fig. 3, the increase in maximum concentration with increasing heating rate can be mainly attributed to the H2S reaction that has
Fig. 2. The surface segregation kinetics of solutes during direct isothermal annealing: (a) equilibrium segregation of solutes and (b) nonequilibrium segregation of sulfur in the 3% Si–Fe alloy strips under a vacuum or hydrogen atmosphere.
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Fig. 4. The effect of heating rate on surface segregation kinetics of sulfur in the 100 µm thick 3% Si–Fe alloy strips under a flow rate of 3 l H2/min.
Fig. 3. Schematic diagrams for explaining changes in surface segregation kinetics of sulfur and nucleation behavior with heating rate in the 3% Si–Fe alloy strips.
occurred during the relatively shorter annealing time to the maximum. 3.3. Surface-energy-induced selective growth in 3% Si–Fe alloy strips On the other hand, the surface-energy-induced selective growth rate [11] in the 3% Si–Fe alloy strips, G(t), is given by G(t) ⫽ M(t)
冋
gG 2⌬gS ⫹ ⫹ C(t) r(t) d
册
(2)
in which gG is the grain boundary free energy, r(t) is the average radius of grains excluding the selec-
tively growing grains at time t, ⌬gS is the difference in surface energy between the growing grain and the grain that is consumed, d is the sheet thickness, C(t) is the grain boundary segregation concentration of sulfur that has a strong grain boundary pinning effect [21–23] as the negative driving force term and M(t) is the grain boundary mobility that is strongly influenced by the grain boundary segregation concentration of sulfur [13] and the annealing temperature. In Eq. (2), the growth rate depends mainly on the average grain size and the grain boundary concentration of segregated sulfur. The second term in the parenthesis is not the main controlling factor of the growth rate due to the small ⌬gS / gG ratio, 0.03 [24]. Generally, the surface energy of {1 1 0} plane in b.c.c. metals is less than the {1 0 0} and followed by the {1 1 1} and other less densely packed planes [25,26]. A transition in selective growth of the {1 1 0} grains to the {1 0 0} and subsequently to the high index grains containing {1 1 1} occurs at strip surfaces with increasing concentration of surface-segregated sulfur. The selective growth rate of the {1 1 1} or high index grains under a higher surface-segregated sulfur atmosphere is, however, very sluggish due to the strong pinning effect of segregated sulfur at grain boundaries. Therefore, such components are often difficult to
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be observed as the final main texture, because these grains are mostly consumed during the selective growth of the {1 0 0} or {1 1 0} grains within the later time range showing the relatively lower segregation concentration of sulfur. Fig. 5 shows a schematic diagram for explaining the correlation between the segregation kinetics of sulfur, the flow rate of hydrogen, the growth rate and the final texture in the 3% Si–Fe alloy strips during direct isothermal annealing. In this diagram, LF and HF each mean the lower and higher flow rates of hydrogen, and the meaning of other symbols follows one in previous research [11]. Under the higher flow rate of hydrogen, the nucleation of the {1 1 0}具0 0 1典 embryos is also more dominant at the same rolled {1 1 0}具0 0 1典 or {1 1 1}具1 1 2典 surface, due to the lower concentration of surfacesegregated sulfur. With increasing flow rate of hydrogen, the final main texture tends to be changed from the {1 0 0}具u v w典 to the {1 1 0}具0 0 1典 component. This is due to two reasons. The first one is the relatively larger average grain size that arises from the weaker grain boundary pinning effect of the lower segregated sulfur. The second one is the shortened time for the selective growth of the {1 0 0} or high index grains that is favorable for the subsequent selective growth of the {1 1 0}具0 0 1典 grains. However, a much higher flow rate of hydrogen may result in
Fig. 5. A schematic diagram for explaining the correlation between segregation kinetics of sulfur, flow rate of hydrogen, growth rate and final texture in the 3% Si–Fe alloy strips during direct isothermal annealing.
the transition in final main texture from the {1 1 0}具0 0 1典 to the {1 1 0}具u v w典 component that will be described below.
4. Nucleation, surface-energy-induced selective growth and directionality of {1 1 0} grains 4.1. Heating rate and final texture Fig. 6 shows the cold rolling texture at the surface (S = 1) of the 100 µm thick 3% Si–Fe alloy strips. A much stronger {1 1 0}具0 0 1典 Goss texture was observed from the strip surface with the final reduction of 60%, but the texture was transited from the Goss texture to a strong γ-fiber + a weak cube texture with increasing depth to the strip center. The dependence of final texture and magnetic induction on heating rate and final reduction was investigated with these strips, and the details are listed in Table 2. The probability that the {1 1 0} grains survive to grow selectively later is lower at the higher heating rate, referring to Figs. 3 and 4. This is mainly due to the higher grain boundary mobility for the selective growth of the {1 0 0} or high index grains within the equivalent segregation concentration range. This is also the reason why the final main texture is changed from the {1 1 0} to the {1 0 0} component with increasing heating rate, as shown in Table 2.
Fig. 6. ODF results obtained from the rolled surface (S = 1) of the 100 µm thick 3% Si–Fe alloy strips with the final reduction of: (a) 30% and (b) 60%. j 2 = 45°.
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Table 2 The dependence of final texture and magnetic induction B10(Tesla) on heating rate and final reduction in the 100 µm thick 3% Si– Fe alloy strips under a flow rate of 3 l H2/min Final reduction Annealing condition and strip thickness
Final main texture
B10(Tesla) just B10(Tesla) after after heating final annealing to 1200 oC
{1 1 0}具0 0 1典 {1 1 0}具u v w典⫽具0 0 1典 {1 0 0}具u v w典 30% (100 µm)
60% (100 µm)
100 oC/h 400 oC/h Direct isothermal annealing 100 oC/h 400 oC/h Direct isothermal annealing
– – –
Very strong Strong –
– Very strong Very strong
1.58 1.57 –
1.62 (5 h) 1.57 (5 h) 1.60 (13.8 h)
Very strong – –
Weak – –
– Very strong Very strong
2.00 1.62 –
2.02 (5 h) 1.69 (13.8 h) 1.66 (10 h)
4.2. Nucleation, surface-energy-induced selective growth and directionality of {1 1 0} grains In previous research [27], the matter that the final main texture in the 3% Si–Fe strips becomes either the {1 1 0}具0 0 1典 or {1 1 0}具u v w典 component has been understood on the viewpoint of the intrinsic surface formation of the embryos that may be strongly influenced by the surface-segregated sulfur. As shown in Fig. 6, the cold rolling texture is generally composed of a contour enclosing a core component: the {1 1 0}具0 0 1典 core component and the {1 1 0}具u v w典⫽具0 0 1典 and high index components enclosing the core component. Due to the strongest intensity in the cold rolling texture and the diffusionless nucleation characteristic, the number of the {1 1 0}具0 0 1典 grains with low angle boundary just after the complete consumption of the deformed matrix might be the most among the {1 1 0} grains. Also, the average size of the colonies that consist of the {1 1 0}具0 0 1典 grains of low angle boundary is statistically the biggest. However, it is emphasized that the number of the {1 1 0}具0 0 1典 grains of low angle boundary is less than the total number of the {1 1 0}具u v w典⫽具0 0 1典 grains. In addition, the number of the {1 1 0}具0 0 1典 grains is expected to be more in the 60% case, due to the stronger core intensity. The overall average size of primary grains at the strip
surface is, however, smaller in the 60% case due to the higher elastic strain energy. Due to the cold rolling texture composed of a contour, the {1 1 0} grains show various angles deviating from the 具0 0 1典 direction, and the maximum deviation angle is larger in the case with the final reduction of 30%. The deviation angle of the {1 1 0} grains and the total number of the {1 1 0} surface grains increase with increasing concentration of surface-segregated sulfur, while the number of the {1 1 0}具0 0 1典 surface grains decreases. The dependence of deviation angle on surface-segregated sulfur is, therefore, less in the 60% case. This is because, as the final reduction increases, the recrystallization temperature decreases and thus the lower surface-segregated sulfur atmosphere is favorable for the nucleation of the {1 1 0}具0 0 1典 embryos. At this point, the formation mechanism of final main texture needs to be considered in the aspect of the surface-energy-induced selective growth as well as the nucleation. Now, even at the same heating rate of 100 oC/h, the prominent difference in the final main texture of Table 2 (i.e., the {1 1 0}具u v w典 component at the 30% and the {1 1 0}具0 0 1典 component at the 60%) is understood on the basis of Eq. (2). Provided that the surface concentration of segregated sulfur is little dependent on the present final reduction range, the concentration profile of segregated sulfur is fixed
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like Fig. 4 at the same heating rate. During heating, the surface-energy-induced selective growth of grains with the lowest surface energy occurs at each time, depending on the surface concentration of segregated sulfur. In the case with the final reduction of 60%, the more active consumption by the {1 0 0}, {1 1 1} or high index grains of the {1 1 0} grains with various directions proceeds with time, due to the overall smaller average grain size and the resultantly bigger driving force for the selective growth. Therefore, only the {1 1 0}具0 0 1典 grains and the {1 1 0} grains with the direction close to the 具0 0 1典 remain after the selective growth. The selective growth process in the case with the final reduction of 30% is contrary to that in the 60% case. The relatively larger average grain size and thus the sluggish selective growth kinetics increase the probability that the {1 1 0}具u v w典 grains with various directions survive through the selective growth process, as shown in Table 2. A high magnetic induction of 2.02 Tesla was obtained only from the strip that is mainly composed of the {1 1 0}具0 0 1典 Goss grains, while a low magnetic induction of 1.62 Tesla was obtained from the strip that shows the final main texture of the {1 1 0}具u v w典. As has been expected from Fig. 5, the final main texture was transited from the {1 1 0}具0 0 1典 component to the {1 1 0}具u v w典 component with increasing flow rate of hydrogen. Conclusively, considering only the final main texture consisting of the {1 1 0} grains, a higher final reduction and heating rate is advantageous for obtaining the final main texture of the {1 1 0}具0 0 1典 component on the viewpoints of the nucleation and the surface-energy-induced selective growth. The higher flow rate of hydrogen and the lower bulk content of sulfur that are favorable for a relatively lower surface concentration of sulfur may cause the transition in final main texture of the {1 1 0}具0 0 1典 to the {1 1 0}具u v w典 component, on the viewpoint of particularly the selective growth as well as the nucleation. Therefore, the matter that the final main texture becomes either the {1 1 0}具0 0 1典 or the {1 1 0}具u v w典 component depends on the combination of those factors. In addition, it is very difficult to quantify the effects of the segregated-sulfur-controlled surface
nucleation and the surface-energy-induced selective growth kinetics on the directionality of {1 1 0} grains, due to no decisive evidence of the sulfurcontrolled surface nucleation. However, it is at least suggested that, based on the present experimental results, the directionality of the {1 1 0} grains after final annealing is mainly determined by the selective growth kinetics rather than by the surface nucleation influenced by the segregated sulfur.
5. Effects of flow rate of hydrogen and strip thickness on surface-energy-induced selective growth 5.1. Flow rate of hydrogen, strip thickness and final main texture of {1 1 0}具0 0 1典 Table 3 shows the dependence of final main texture and magnetic induction on flow rate of hydrogen and strip thickness in the 3% Si–Fe alloy strips. Under the flow rate of 3 l H2/min, the strips consisted mainly of the {1 0 0}具u v w典 grains after direct isothermal annealing, regardless of the strip thickness and the final reduction. However, the final main texture was mostly composed of the {1 1 0}具0 0 1典 Goss component under the flow rate of 10 l H2/min. The {1 1 0}具u v w典⫽具0 0 1典 component that was frequently observed in the cases of moderate heating rates of Table 2 was not nearly detected in this case. The magnetic induction of the strips was directly related to the final main texture: a magnetic induction higher than 1.9 Tesla corresponded to the final main texture of the {1 1 0}具0 0 1典 Goss component and a lower magnetic induction the {1 0 0}具u v w典 component. On the other hand, the texture development at the surface (S = 1) of the 100 µm thick 3% Si–Fe alloy strips with the final reduction of 60% under the flow rate of 10 l H2/min is shown in Fig. 7. The annealing time of 60 s corresponds to the strip temperature of about 1010 oC and the time of 120 s the temperature of about 1130 oC. The initial texture also took after the cold rolling texture, but high index grains including the {1 1 1} grains that grew selectively at the strip surface or grew out from the strip interior to the surface were observed
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Table 3 The dependence of final main texture and final magnetic induction B10(Tesla) on flow rate of hydrogen and strip thickness in the 3% Si–Fe alloy strips after direct isothermal annealing at 1200 oC for a prolonged time Strip thickness and final Flow rate of reduction hydrogen
40 µm (30%, 60%) 100 µm (30%, 60%)
3 l H2/min 10 l H2/min 3 l H2/min 10 l H2/min
Final main texture
B10(Tesla)
{1 1 0}具0 0 1典
{1 1 0}具u v w典⫽具0 0 1典
{1 0 0}具u v w典
– Very strong – Very strong
– Weak – Weak
Very strong – Very strong –
(1.56, 1.76) (2.01, 1.90) (1.60, 1.66) (1.92, 1.90)
Fig. 7. The texture development at the surface (S = 1) of the 100 µm thick 3% Si–Fe alloy strips with the final reduction of 60% with annealing time at 1200 oC under the flow rate of 10 l H2/min: (a) as-rolled, (b) 60 and (c) 120 s. j 2 = 45°.
with further annealing. However, this strip showed the final main texture of the {1 1 0}具0 0 1典 component after direct isothermal annealing for a prolonged time, as shown in Table 3. 5.2. Details of sulfur segregation kinetics and surface-energy-induced selective growth Such a great dependence of final texture on flow rate of hydrogen is shown in Fig. 8. During direct isothermal annealing, a trough in magnetic induction [11] was also observed in both cases of flow rate. After the trough, the magnetic induction increased with increasing annealing time. The concentration of surface-segregated sulfur was overall
much lower under the flow rate of 10 l H2/min. After annealing for a prolonged time, a high magnetic induction of 1.90 Tesla that corresponds to the final main Goss texture was obtained in the case of 10 l H2/min, but the other case showed a low magnetic induction of 1.76 Tesla that results from the final main texture of the {1 0 0}具u v w典 component. The final Goss texture under the higher flow rate is due to the faster elimination of surfacesegregated sulfur arising from the more active H2S reaction that makes the survival and selective growth of Goss grains possible within the further annealing time range. In general, the average grain size increases with increasing strip thickness [24] that is supported by
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Fig. 8. Changes in magnetic induction of the 40 µm thick 3% Si–Fe alloy strips with the final reduction of 60% and concentration of surface-segregated sulfur with direct isothermal annealing time at 1200 oC under the flow rates of: (a) 3 and (b) 10 l H2/min.
Fig. 9. If other conditions are fixed, the smaller average grain size in the thinner strip increases the selective growth rate of the {1 0 0} and high index grains. This lowers the probability that the {1 1 0}具0 0 1典 grains survive to grow selectively after the surface-energy-induced selective growth of the other grains. As shown in Table 3, the final main texture showed, however, a strong dependence on the flow rate of hydrogen rather than on the strip thickness. Here, the correlation between
Fig. 9. The dependence of average grain size on strip thickness in the 3% Si–Fe alloy strips with the final reduction of 60% during direct isothermal annealing at 1200 oC under the flow rate of 10 l H2/min.
the surface segregation kinetics of sulfur and the strip thickness can be detailed in Fig. 10. Due to the less total amount of sulfur in the bulk interior, the sulfur depletion rate at the surface was faster in the 40 µm thick strip and the maximum in concentration of surface-segregated sulfur was, therefore, lower in the thinner strip. That is, the little dependence of final main texture on strip thickness is probably because the lower surface-segregated sulfur effect in the thinner strip counteracts the smaller average grain size effect, resulting in shortening the time range for the selective growth of the {1 0 0} and high index grains. As shown in Fig. 11, changes in magnetic induction with annealing time also need to be checked, even though a final magnetic induction higher than 1.9 Tesla was obtainsed under the flow rate of 10 l H2/min, irrespective of the strip thickness. The changing behavior in magnetic induction with annealing time was strongly dependent on the strip thickness. The 40 µm thick strip showed the trough in magnetic induction at the earlier time. Referring to Figs. 9 and 10(b), this can be attributed to the smaller average grain size and the lower grain boundary concentration of segregated sulfur favorable for the selective growth of the {1 0 0} or high index grains. After the selective growth of the {1 0 0} grains within the prolonged annealing time range, the surviving {1 1 0}具0 0 1典 Goss grains
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Fig. 10. The dependence of segregation kinetics of sulfur on strip thickness in the 3% Si–Fe alloy strips with the final reduction of 60% during direct isothermal annealing at 1200 oC under the flow rates of: (a) 3 and (b) 10 l H2/min.
energy-induced selective growth process of grains, the number of surviving Goss grains is absolutely fewer in the thinner strip than in the thicker strip. Based on Fig. 9, the fewer number of Goss grains in the thinner strip is mainly due to the smaller average grain size which resulted in the more active decrease in the number of the {1 1 0}具0 0 1典 grains during the selective growth of the other grains.
6. Conclusions
Fig. 11. The dependence of magnetic induction change on strip thickness in the 3% Si–Fe alloy strips with the final reduction of 60% during direct isothermal annealing at 1200 oC under the flow rate of 10 l H2/min.
start to grow selectively at the expense of the other grains. In this case, the increasing rate in magnetic induction depends on the number of surviving Goss grains. On the other hand, the 40 µm thick strip showed a plateau within the time range of 0.5–8 ks in which the magnetic induction was little changed and after which a high magnetic induction of 1.9 Tesla was observed at the relatively delayed time. This means that, throughout the surface-
The correlation between interfacial segregation of sulfur, nucleation and texture development has been investigated in inhibitor-free 3% Si–Fe alloys containing sulfur. Considering only the final main texture consisting of {1 1 0} grains, a higher final reduction, heating rate and flow rate of hydrogen and a lower bulk content of sulfur are advantageous for obtaining the final main texture of the {1 1 0}具0 0 1典 component on the viewpoint of nucleation. Among these, the higher flow rate of hydrogen and the lower bulk content of sulfur may result in the transition in final main texture of the {1 1 0}具0 0 1典 to the {1 1 0}具u v w典 component, based on the surface-energy-induced selective growth. Therefore, the matter that the final main
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texture consists of either the {1 1 0}具0 0 1典 or the {1 1 0}具u v w典 component depends on the combination of those factors. With increasing heating rate, the concentration profile of surface-segregated sulfur is shifted to a higher temperature range, and the final main texture after annealing tends, as a result, to be changed from the {1 1 0}具u v w典 to the {1 1 0}具0 0 1典 and then followed by the {1 0 0}具u v w典 component. This is due to the higher grain boundary mobility at the selective growth stage of the {1 0 0}具u v w典 or high index grains that makes the survival and selective growth of the {1 1 0} grains difficult. Because the smaller average grain size effect in the thinner strip is diluted by the lower surface concentration effect of segregated sulfur under a flowing hydrogen atmosphere, the final main texture shows little dependence on the strip thickness. Acknowledgement This research was partially supported by a grant from the Center for Advanced Materials Processing (CAMP) of the 21st Century Frontier R& D Program funded by the Ministry of Science and Technology, Republic of Korea. References [1] Burgers WG, Louwerse PC. Zeitschrift fur Metall 1931;67:605.
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