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Analysis of the growth of individual grains during recrystallization in pure nickel
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Acta Materialia 57 (2009) 2631–2639 www.elsevier.com/locate/actamat
Analysis of the growth of individual grains during recrystallization in pure nickel Y.B. Zhang a, A. Godfrey a, Q. Liu b, W. Liu a, D. Juul Jensen c,* a
Laboratory of Advanced Materials, Department of Material Science and Engineering, Tsinghua University, Beijing 100084, People’s Republic of China b Department of Material Science and Engineering, Chongqing University, Chongqing 400444, People’s Republic of China c Center for Fundamental Research, Metal Structure in Four Dimension, Materials Research Division, Risø National Laboratory for Sustainable Energy, Technical University of Denmark, DK-4000 Roskilde, Denmark Received 18 November 2008; received in revised form 29 January 2009; accepted 29 January 2009 Available online 26 March 2009
Abstract The growth of individual grains during recrystallization in 96% cold-rolled pure nickel has been followed using electron backscatter pattern maps of the same surface area taken after each of several annealing steps. It was found that the growth is quite complex, with boundaries moving, stopping and moving again. The growth kinetics differ from grain to grain and, on average, cube-oriented grains grow the fastest. The growth of the grains has also been analyzed as a function of boundary misorientation. This analysis shows that there is no significant difference in misorientation distribution between boundaries that move and those that do not. This is contrary to the usual assumption that the boundary mobility and the migration rate depend on the misorientation across a boundary. This observation and the reasons for the faster growth of cube-oriented grains are discussed. Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Nickel; Electron backscattering patterns (EBSP); Recrystallization; Growth kinetics
1. Introduction During recrystallization almost defect-free nuclei develop in a deformed matrix and grow by means of a thermally activated grain boundary migration process driven by the greater stored energy of the deformed microstructure. Generally the migration rate v is expressed as: m ¼ MF
ð1Þ
where M is the grain boundary mobility and F is the driving force, which for recrystallization is the stored energy of the deformed structure. This means that as long as M and F are constant (e.g. not varying with time and space), the boundary will also move at a constant rate. Thus, for a nucleus growing in a deformed single crystal or within one original grain in a deformed polycrystal, both M and F *
Corresponding author. E-mail address: [email protected] (D. Juul Jensen).
should be almost constant and thus also v. A constant migration rate has been observed experimentally (for example, in one of the earliest detailed studies of recrystallization [1]). Many experiments on cold-deformed metals have, however, shown that the migration rate is not always constant but can decrease during recrystallization [2–8]. The reasons therefor and implications thereof are discussed in Ref. [9]. Nevertheless, even for such cases of a decreasing growth rate, it is generally assumed that all grains grow with the same rate at any given time t, i.e. the time dependency is the same for all grains. The experiments mentioned above are all based on static statistical measurements where the migration rate is determined using stereological methods, e.g. using either the Cahn–Hagel approach [10,11] or the extended Cahn–Hagel approach [12] from a series of partly recrystallized samples annealed for different times. Recently, however, newer experimental methods have allowed direct measurements of the growth of individual grains in situ during annealing.
1359-6454/$36.00 Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2009.01.039
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For recrystallization these direct observation methods include examination in a high-voltage transmission electron microscope (TEM) [13], backscattered electron diffraction imaging [14,15] in a scanning electron microscope (SEM) and three-dimensional X-ray diffraction (3-D XRD) [16–18]. All these in situ measurements of the growth of individual grains in both deformed single crystals and polycrystals show that the boundary migration seems to be much more complex than hitherto assumed; the migration rate is not constant but changes from grain to grain, and it varies with space and time in a non-simple fashion. Each grain has its own kinetics [16,17] and the shapes of the grains during growth can become quite odd (i.e. far from spherical), with large local protrusions [18]. The latter phenomenon was also observed in the classical static experiments [9,19,20] but has not, until recently, been discussed in much detail. Models have yet to be formulated that explain these in situ growth observations of individual grains during recrystallization. The aim of the present study was to investigate in detail how individual grains grow during recrystallization. We chose to do this using the electron backscattering pattern (EBSP) method in an SEM by mapping the evolution in the microstructure within a single large sample surface area after five sequential annealing times. Compared to the TEM method, this approach has the advantage that only one sample surface, rather than two, can potentially affect the results; in addition, the extra driving force for boundary migration given by a wedge-shaped TEM sample is avoided. Compared to the 3-D XRD measurements, the present measurements are limited by not being from an interior volume, so surface effects have to be considered. However, the EBSP method offers the advantage of being able to study the effect of impingement between recrystallizing grains directly – something that is not yet possible with the 3-D XRD method. Additionally, and of great importance for the present investigation, the EBSP method allows the direct investigation of the effects of boundary misorientation on recrystallization boundary migration rates, because the data contain a record of the orientation of pixels in the deformed matrix which are ‘‘consumed” by each specific recrystallizing grain during any given annealing step. To do this in three dimensions using 3-D XRD requires an improvement in the method to allow mapping of deformation microstructures on the micrometre scale, but such an improvement is not likely to be achieved in the next five years. 2. Experimental The sample material chosen for the investigation was 99.999% pure nickel, with an initial grain size of 30 lm. The material was cold-rolled by 96% reduction to a thickness of 250 lm. Samples were annealed at 320 °C in an air furnace. The reasons for choosing this material for the investigation were (i) a previous investigation [21] has shown that a strong cube texture component develops dur-
ing the recrystallization, so the competing growth of cubeoriented and other grains may be studied; (ii) the strain is high, and less is known about boundary migration at such high strains; and (iii) similar material is of practical importance as a substrate for superconducting wires. Annealing was carried out to give accumulated times of 5, 10, 20, 40, and 80 min. After the first annealing step (5 min), the rolling plane (defined by the rolling direction (RD) and the transverse direction) was ground to SiC4000 before final electropolishing in a 1:3:4 HClO4:CH3COOH:C2H5OH solution at 0 °C and 12 V for 45 s. A microhardness indent was made on the polished surface to facilitate reidentification of the mapped area after each annealing step. During all subsequent annealing steps, the sample was enclosed in a vacuum glass tube (106 Pa) with 0.3 atm Ar + H2 to protect the sample surface. The microstructure was examined after each annealing step at the same position on the sample using a LEO 1530 SEM equipped with a fully automated EBSP analysis system. Orientation maps were obtained using a step size of 2 lm over an area of 1200 1200 lm2. In this paper texture components are defined using a 15° deviation to various ideal orientations. To classify the grains, the following three orientation classes were used: cube {0 0 1}<1 0 0>; rolling (including f1 1 2gh1 1 1i ðcopperÞ, f1 2 3gh6 3 4i ðSÞ and f1 1 0gh1 1 2i ðbrassÞ); and other (consisting of everything not belonging to the cube and rolling orientations). In the fully recrystallized state the volume fractions of cube, rolling and other texture components were 52%, 16% and 32%, respectively. In all the EBSP orientation maps presented in this paper, cube, S, brass and copper orientations are shown in orange, blue, red and green, respectively. Other orientations are shown in white; black pixels are non-indexed points. Aqua (cyan) and black lines represent boundary misorientations of >2° and >15°, respectively. Red lines indicate R3 boundaries, defined according to the Brandon criterion [22]. It is clear that the chosen experimental method samples volumes at and near the sample surface. It is thus important to consider if (and how) the results may be influenced by surface effects. A detailed analysis hereof is presented in the appendix. An important argument that is worth repeating here is that similar behavior to the observations reported in this paper have also been observed from 3-D XRD experiments, where data are from the bulk and where surface effects are out of the question. We thus believe that the results to be presented are general and not just typical for the surface. 3. Results 3.1. Microstructure After cold rolling to a thickness reduction of 96%, the microstructure is heavily subdivided into a lamellar structure with the lamellar boundaries more or less parallel to
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Fig. 1. Example of a region of the microstructure after annealing for (a) 5 min and (b) 5 + 10 + 20 min. Cube, S, brass and copper oriented grains are shown in orange, blue, red and green, respectively. Other grains are shown in white; black pixels are non-indexed points. Aqua and black lines represent boundary misorientations of >2° and >15°, respectively.
the rolling plane. The volume fractions of cube, rolling and other texture components are 0.5%, 85% and 14.5%, respectively. When the sample is annealed at 320 °C for 5 min, nucleation of recrystallization occurs and the nuclei start to grow. In the present work a nucleus is identified as an area with interior misorientations smaller than 0.75° and where further annealing confirms that the nucleus actually grows. As always when describing recrystallization, confusion exists as to when to call a recrystallizing area a nucleus or a grain. In the following we have chosen to refer to recrystallizing nuclei/grains as just grains. A part of the total mapped area is shown in Fig. 1 for annealing times (total) of 5 and 35 min. It can be seen that after two annealing steps (10 + 20 min), all the grains in Fig. 1a still can be identified in Fig. 1b. However, some new grains also appear, either from below the surface or as a result of twinning of existing grains.
The ability to trace the growth of each grain allows growth curves for individual grains to be plotted. This is done by overlaying as precisely as possible two consecutive images by comparing the orientations of the pixels. From that, it is straightforward to measure the size increase (i.e. increase in number of pixels) of each grain and thus obtain growth curves. Some examples are given in Fig. 2 for grains of each orientation class (cube, rolling and other) chosen at random within the mapped area. Inspection of the growth curves clearly reveals that each grain has its own kinetics: no growth curves are alike regardless of the grain orientation class. A similar conclusion was reached using 3-D XRD in Ref. [16]. At all annealing times, the cube-oriented grain sizes are on average significantly larger than those of both rolling and other oriented grains, which b) rolling
a) cube
2500
Free Growth Partially Impinged
Area of Grains (µm2)
Area of Grains (µm2)
10000
3.2. Growth kinetics
8000 6000 4000 2000
Free Growth Partially Impinged
2000 1500 1000 500 0
0 0
40
80
120
0
160
Annealing Time (minutes)
40
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Annealing Time (minutes)
c) other Area of Grains (µm2)
5000
Free Growth Partially Impinged
4000 3000 2000 1000 0 0
40
80
120
160
Annealing Time (minutes) Fig. 2. Growth curves for individual grains of different orientations: (a) cube; (b) rolling; and (c) other.
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Fig. 3. Determination of the misorientations between a recrystallizing grain and its surrounding deformed matrix during annealing. Microstructures after annealing for (a) 5 min and (b) 5 + 10 min. (c) A semi-transparent overlay of (b) on (a). Thick magenta lines show boundaries that do not move during annealing.
is also in agreement with earlier observations of the present material [21]. The present data also allow the effects of impingement between recrystallizing grains to be investigated. In Fig. 2, the red solid symbol points indicate grains that are partially impinged (defined as a recrystallizing grain with at least one neighboring recrystallizing grain). The black open symbol points indicate freely growing grains, i.e. those surrounded completely by the deformed matrix. It may be noted that most grains become impinged at the very early stages of recrystallization, although some grains remain unimpinged even after the final annealing step. Moreover, some recrystallized grains do not grow even when they are free to grow (unimpinged) while others grow quickly, even though they are partially impinged by other recrystallizing grains.
deformed matrix both for rolling and other oriented grains. For cube-oriented grains, the distribution spread is relatively narrow, in the range of 38–62°. It is worth noting that a near 40° h1 1 1i misorientation is only seen for very few boundaries (<0.5%) for all the orientation classes. This is consistent with previous results [21]. The misorientation distribution encountered during growth of the largest observed cube-oriented grain after the first annealing step is also shown in Fig. 4d (739 pixels are involved in this calculation). Note that data for this grain are not included in the aggregate data for cube-oriented grains shown in Fig. 4a. It can be seen that both the axes and the angular range of the misorientation distributions are very similar to those seen for the aggregate data, though the peak is shifted to a slightly lower misorientation angle.
3.3. Misorientation of moving boundaries
3.4. Misorientation of non-moving boundaries
The area consumed during the growth of a recrystallizing grain contains information about the misorientations encountered during the growth of the grain, and these data can be used to investigate the effects of misorientation on the boundary migration rates. The procedure is illustrated in Fig. 3. Here, after 5 min of annealing, grain A is shown in orange in Fig. 3a. After additional annealing for 10 min, grain A has grown, as shown in Fig. 3b. By overlaying the two maps (Fig. 3c), the pixels of the deformed matrix that have been ‘‘consumed” by grain A during the annealing step can be found. The misorientations between the orientation of grain A and each consumed pixel can then be calculated and expressed as angle/axis pairs. The data resulting from such an analysis are plotted in Fig. 4. These data are gathered from between the first and second annealing steps and between the second and third annealing steps for 10–12 grains of each orientation class (involving transformation of 1272, 703 and 846 deformed pixels into cube, rolling and other oriented grains, respectively). The results show that a very wide variety of misorientation relationships (in the range of 10–62°) can be found between growing grains and the neighboring
The misorientation distribution for non-migrating unimpinged boundaries was also investigated. Such boundaries are shown in Fig. 3c as thick magenta lines; note that here we only analyze boundaries between recrystallizing grains and the deformed matrix. The results measured from between the first and second annealing steps and between the second and third annealing steps are shown in Fig. 5 for 20–25 grains of each orientation class (involving transformation of 354, 276 and 382 deformed pixels into cube, rolling and other oriented grains, respectively). Comparison with Fig. 4 shows that the misorientation distributions for both migrating and non-migrating boundaries are similar for all orientation classes, although more boundaries near 60° are observed for the non-migrating boundaries for cube-oriented grains. It is also observed that the rotation axis is generally more clustered around h1 1 1i for moving than for non-moving boundaries. 4. Discussion In the present study the migration of individual boundaries surrounding recrystallizing grains through deformed
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Fig. 4. Misorientation axis/angle distributions between recrystallizing grains and the consumed deformed matrix from between the first and second and between the second and third annealing steps for (a) cube, (b) rolling, (c) other grains, and (d) the largest cube-oriented grain. Thick black lines show the expected uncorrelated misorientation distributions. The inverse pole figures marked 1 and 2 show experimental and expected uncorrelated rotation axis distributions, respectively.
matrix material has been studied by EBSP mapping of a single large sample area after five consecutive annealing
steps with the aim of learning more about the growth of individual grains during recrystallization. The growth
Fig. 5. Misorientation axis/angle distributions between recrystallizing grains and the deformed matrix for non-moving boundary segments from between the first and second and between the second and third annealing steps for (a) cube, (b) rolling and (c) other oriented grains. Thick black lines show the expected uncorrelated misorientation distributions. The inverse pole figures marked 1 and 2 show experimental and expected uncorrelated rotation axis distributions.
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kinetics and the characteristics of the migrating boundaries are analyzed in more detail in the following. It cannot be excluded that, in addition to the aspects discussed below, the grain boundary plane (which cannot be determined from 2-D EBSP maps) may also affect the observed boundary migration rates. However, as the experimental method used in this study does not allow determination of this parameter, this shall not be discussed further here. 4.1. Growth kinetics of individual grains The present results show that each grain has its own growth kinetics (see Fig. 2). This is in agreement with previous 3-D XRD experiments [16,17]. The present investigation reveals that this is not just an effect of impingement – a possibility that could not be excluded based only on 3-D XRD experiments. Even grains which are free to grow with totally unimpinged boundaries may grow very slowly or not at all, and grains which are partially impinged may increase in size (i.e. grow) at a very fast rate. This is the case for grains in each of the three orientation classes studied: cube, rolling and other. On average, however, the cube-oriented grains grow to become the largest, in agreement with earlier observations [21] in which only the average behavior was determined. The present results (see Fig. 2) show that the average size advantage is strongly influenced by a few cube-oriented grains growing to very large sizes. The reasons why some cube-oriented grains grow so preferentially are not clear. This is not because they are closer to the exact cube orientation and, as shown in Fig. 4d, the misorientation distribution for the largest cube-oriented grain is very similar to the ensemble misorientation distribution for all the cube-oriented grains (Fig. 4a). When the misorientation distribution for the cube and rolling/other grains are compared (see Figs. 4 and 5), significant differences are obvious. The cube-oriented grains have more 40–60° boundaries close to h1 1 1i, whereas rolling/other grains encounter the whole range of misorientation angles from 10° to 60°. This is not surprising considering the texture of the deformed matrix, as can be seen from the uncorrelated misorientation distributions for recrystallizing grains to the deformed matrix, plotted in Figs. 4 and 5 as thick black lines. To calculate these uncorrelated distributions, 15 nucleus/grain orientations for each orientation class were randomly chosen, and the misorientations to the deformation texture as determined from the RD–normal direction (ND) section were calculated. It can be seen that for all the orientation classes the experimentally measured misorientation angle distributions are in reasonable agreement with the uncorrelated distributions, whereas the experimentally measured rotation axis distributions for migrating boundaries (see Fig. 4) are more clustered than the expected uncorrelated distributions. Moreover, the calculation shows that rolling oriented grains have a relatively higher chance of forming low-angle boundaries, while the cube-oriented grains have a very small chance of encountering low-angle boundaries.
When considering the misorientation distributions for both the experimentally measured and the expected uncorrelated cases, it seems that high misorientation angle boundaries with rotation axes around h1 1 1i are favorable for growth (experimentally measured distributions in Fig. 4). For the cube-oriented grains there is a larger probability of being surrounded by boundaries of this type than there is for the rolling and other oriented grains. In the work by Schmidt and Lu¨cke [23] it was found that texture evolution during recrystallization could be described by ‘‘compromise orientations” due to the preferential growth of boundaries with misorientations close to 40° h1 1 1i. This can be compared to the present observations for boundaries surrounding cube grains, where fast migration is observed for boundaries over the whole range of misorientations from 40° to 60° h1 1 1i. 4.2. Migration of boundaries during recrystallization The present results confirm that the misorientation is an important parameter for the overall growth of recrystallizing grains. However, when looking at the local scale, comparing the misorientation distributions for specific boundary segments which move during a given annealing time with those that do not move during that annealing, it is surprising to observe that the differences are not so large. This can be seen when comparing Figs. 4 and 5. The main difference is that boundaries near 60° h1 1 1i (including coherent twin boundaries) are significant in the distribution for non-moving boundaries of cube-oriented grains (Fig. 5a) but not for the moving ones (Fig. 4a). Furthermore, the rotation axis distributions for migrating boundaries are generally more clustered at the h1 1 1i corner than for non-migrating boundaries. Besides these well-known effects, the present data show that, for a given misorientation (a similar angle and rotation axis), a boundary segment may sometimes move and sometimes not. It should be underlined that this result refers to boundary segments and not the whole boundary surrounding the recrystallizing grain, i.e. parts of the boundary surrounding the grain in three dimensions may move while other parts may not. Grains would thus be expected to grow in size in spite of the fact that one or more boundary segments at a given time step are immobile. One reason why some boundary segments move during an annealing step while others do not could be a difference in the local stored energy in the deformed matrix in front of the boundary: a boundary segment that migrates may have a higher local driving force than a non-migrating one. This possibility was investigated in detail for the specific example shown in Fig. 6. Here two cube-oriented grains, A and B, meet similar orientations in the deformed matrix. The stored energies in the deformed matrix within the black rectangles in front of A and B were calculated using the method described in [24]. The stored energies in front of grains A and B were found to be 0.75 106 and 0.72 106 J m3, respectively. However, after an addi-
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Fig. 6. Example to show the difference in growth for grains of the same orientation and misorientation. Rectangles show the regions used for calculation of the stored energy. (a) 7.5 min; and (b) 7.5 + 7.5 min.
Fig. 7. RD–ND section of partially recrystallized sample. The color code is the same as for Fig. 1. The black areas of the top are above the free sample surface.
tional annealing of 7.5 min only grain B had grown (see Fig. 6b). Thus, in spite of very similar driving forces and local misorientations (angles and axes), one boundary segment migrated and the other did not. It should be noted that the microstructure was also examined in the RD– ND plane (Fig. 7). It can be seen from the figure that the recrystallizing grains typically extend only 5–20 lm below the sample surface. The observation of differences between growth rates for grains of similar orientation class cannot therefore be accounted for by the growth of some grains across the entire thickness of the sample (250 lm). This result suggests that, whereas Eq. (1) has proven to be valid for the average overall boundary migration during recrystallization [25–27], the movement locally of boundary segments may be more complex. An atomistic view of the boundary migration process envisages interfacial atoms in front of the boundary to move to sites belonging to the lattice of the growing grain, thus moving the boundary forward [9]. This is generally thought of as a process of the diffusion of single atoms or a shuffling mechanism involving more than one atom at a time [28–32]. Both these processes are considered to be steady-state phenomena and thus cannot explain the observed stop–go motion of boundary segments. Whereas these classic theories are for boundary migration through perfect or near-perfect crystals, it is clear that for recrystallization the process must be much more complex, as the boundary migrates through a deformed material containing many dislocations of different types arranged locally in many different ways. The
boundary migration during recrystallization will thus involve local interactions between dislocations (and the atoms around these) and the grain boundary: for example, individual dislocations moving into a boundary, as observed by Jones et al. [33], leading to a local recovery in front of the boundary [34], or boundary segments moving forward by absorbing local dislocations, as predicted by molecular dynamics simulations [35,36]. Both of these processes lead to smaller or larger reorientations locally ahead of the boundary [37] and it takes some time for them to occur. This could be at least part of the explanation why the migration of boundary segment occurs in steps (move, stop and move) during recrystallization and thus also why one can observe boundary segments with the same M and F that behave differently at a given time. 5. Summary and conclusions The growth of individual grains during recrystallization in 96% cold-rolled pure nickel was followed using EBSP maps of a single area taken after each of several annealing steps. The following were found. The growth kinetics differ from grain to grain, and the present experiment proves that this is not just an effect of impingement between recrystallizing grains. Cube-oriented grains have a higher probability than rolling and other oriented grains of being surrounded by high-angle boundaries with their rotation axis near
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h1 1 1i to the deformed matrix, which is favorable for growth. It should be noted, however, that the observed average cube growth advantage is dominated by a few very large cube grains. These superlarge cube grains do not achieve their size advantage because they are closer to the ideal cube orientation or have a different misorientation than the smaller cube grains. The growth of individual grains was observed to occur in steps, with some boundary segments moving forward while others remained stationary for a given annealing time, after which they may also move. This is not believed to be a surface effect as very similar observations are also seen in in situ bulk 3-D XRD experiments. The misorientation angles and axes, as well as the local driving force, can be very similar for boundary segments which move and those which do not move at a given annealing time step. This suggests that the local migration process is complex, requiring time for local interactions between dislocations and boundary and thus for ensembles of atoms to rearrange before being adopted into the recrystallizing grain, leading to the forward migration of that boundary segment.
Acknowledgments The research was supported by the Natural Science Foundation of China (NSFC) under Grant Nos. 50571041, 50620130096 and 50671052. The authors thank Prof. B. Ralph for helpful comments and discussions. Y.B.Z. and D.J.J. further acknowledge support from the Danish National Research Foundation through the Center for Fundamental Research: Metal Structures in Four Dimensions. Appendix A A.1. Analysis of possible surface grooving effects for the present experiment Thermal grooving is a surface effect which has to be considered for the present experiment. According to Gottstein and Shvindlerman [25], ‘‘It is a common experience that grain boundary motion appears jerky when observed by grain boundary displacement on a surface. This jerky motion, however, is not the genuine mode of grain boundary migration rather it is caused by thermal grooving on the surface.” Whereas the quoted work was on high-temperature grain growth, our work is on low-temperature recrystallization, where the driving force is orders of magnitude larger. However, we also see ‘‘jerky movement” in the sense that boundary segments may move, stop for a while and then move again. This could be an effect of thermal grooving. Arguments against this, however, are: (1) The specimens were examined in the RD–ND section to see if the surface layer appeared different from the subsurface region. An example is shown in Fig. 7. Neither indi-
cations of thermal grooving nor other surface peculiarities can be seen. (2) According to Mullins’s theory of thermal grooving [38], the depth of the groove from the top to the root measured in the direction normal to the surface is given by: d ¼ 0:973mðBtÞ
1=4
ð2Þ
where m2 = cb/2cs is the slope at the groove root and B ¼ Ds ckTs X t in which t denotes the number of atoms per m2 of surface, X denotes the atomic volume, kT has its usual meaning, Ds denotes the surface diffusivity, cb and cs are grain boundary free energy and surface free energy, respectively, and t is the heating time. For the present material and temperature, we used the values m = 0.17 X = 1.09 1029 m3/atom, [39], kT = 8.2 1021 J, 19 2 t = 2.03 10 atoms/m , Ds = 10-17 m2/s (here no values could be found in the literature for nickel, so instead the value for surface diffusion of copper has been used [40]; this is expected to lead to an overestimation of the groove size) and t = 600–9000 s (from the second to the last annealing steps). It is found that the depth of the groove d = 1.28– 2.52 nm. This means that even after the last annealing step the thermal groove is still not well developed. Normally thermal grooving is considered in the grain growth experiment, in which the thermal groove can be much more developed. According to Mullins’s calculation [41], thermal grooving is of importance when the driving force for boundaries is less than or of the order of 104 J/ m3 (105 ergs/cm3). For the present material the stored energy was measured by a differential scanning calorimetry to be 107 J/m3 [42], i.e. far exceeding the value given by Mullins. (3) A further concern could be that the present experiment is a heating–cooling annealing type experiment. However, in situ SEM experiments [14,15] also show similarly ‘jerky’ boundary migration. (4) Careful bulk measurements performed by 3-D XRD have also shown that boundaries do not always move forward at a constant rate. Even in deformed single crystals 3D XRD measurements have shown boundaries or boundary segments in the bulk stopping for a while and then migrating quickly forward [18]. Thus it is obvious that this type of boundary migration is not just a phenomenon occurring at the surface. References [1] [2] [3] [4]
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[25] Gottstein G, Shvindlerman SL. Scripta Metal 1992;27:1521. [26] Vandermeer RA, Juul Jensen D, Woldt E. Metall Mater Trans A 1997;28:749. [27] Vandermeer RA. Trans TMS-AIME 1965;233:265. [28] Babcock SE, Balluffi RW. Acta Metall 1989;37:2367. [29] Mott NF. Proc Phys Soc Lond 1948;60:391. [30] Turnbull D. Trans TMS-AIME 1951;191:661. [31] Sutton AP, Balluffi RW. Interfaces in crystalline materials. Oxford: Oxford University Press; 1995. [32] Merkle KL, Thompson LJ, Philipp F. Phys Rev Lett 2002;88:225501. [33] Jones AR, Howell PR, Ralph B. Philos Mag 1977;35:603. [34] Jones AR, Ralph B, Hansen N. Proc Roy Soc Lond A 1979;368:345. [35] Godiksen RB, Trautt ZT, Upmanyu M, Schiotz J, Juul Jensen D, Schmidt S. Acta Mater 2007;55:6383. [36] Godiksen RB, Schmidt S, Juul Jensen D. Model Simul Mater Sci Eng 2008;16:065002. [37] Wu GL, Juul Jensen D. Acta Mater 2007;55:4955. [38] Mullins WW. J Appl Phys 1957;28:333. [39] Murr LE, Horylev RJ, Wong GI. Surf Sci 1971:26. [40] Mullins WW, Shewmen PG. Acta Metall 1959;7:163. [41] Mullins WW. Acta Metall 1958;6:414. [42] Knudsen T, Cao WQ, Godfrey A, Liu Q, Hansen N. Metall Mater Trans A 2008;39:430.
Acta Materialia 57 (2009) 2631–2639 www.elsevier.com/locate/actamat
Analysis of the growth of individual grains during recrystallization in pure nickel Y.B. Zhang a, A. Godfrey a, Q. Liu b, W. Liu a, D. Juul Jensen c,* a
Laboratory of Advanced Materials, Department of Material Science and Engineering, Tsinghua University, Beijing 100084, People’s Republic of China b Department of Material Science and Engineering, Chongqing University, Chongqing 400444, People’s Republic of China c Center for Fundamental Research, Metal Structure in Four Dimension, Materials Research Division, Risø National Laboratory for Sustainable Energy, Technical University of Denmark, DK-4000 Roskilde, Denmark Received 18 November 2008; received in revised form 29 January 2009; accepted 29 January 2009 Available online 26 March 2009
Abstract The growth of individual grains during recrystallization in 96% cold-rolled pure nickel has been followed using electron backscatter pattern maps of the same surface area taken after each of several annealing steps. It was found that the growth is quite complex, with boundaries moving, stopping and moving again. The growth kinetics differ from grain to grain and, on average, cube-oriented grains grow the fastest. The growth of the grains has also been analyzed as a function of boundary misorientation. This analysis shows that there is no significant difference in misorientation distribution between boundaries that move and those that do not. This is contrary to the usual assumption that the boundary mobility and the migration rate depend on the misorientation across a boundary. This observation and the reasons for the faster growth of cube-oriented grains are discussed. Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Nickel; Electron backscattering patterns (EBSP); Recrystallization; Growth kinetics
1. Introduction During recrystallization almost defect-free nuclei develop in a deformed matrix and grow by means of a thermally activated grain boundary migration process driven by the greater stored energy of the deformed microstructure. Generally the migration rate v is expressed as: m ¼ MF
ð1Þ
where M is the grain boundary mobility and F is the driving force, which for recrystallization is the stored energy of the deformed structure. This means that as long as M and F are constant (e.g. not varying with time and space), the boundary will also move at a constant rate. Thus, for a nucleus growing in a deformed single crystal or within one original grain in a deformed polycrystal, both M and F *
Corresponding author. E-mail address: [email protected] (D. Juul Jensen).
should be almost constant and thus also v. A constant migration rate has been observed experimentally (for example, in one of the earliest detailed studies of recrystallization [1]). Many experiments on cold-deformed metals have, however, shown that the migration rate is not always constant but can decrease during recrystallization [2–8]. The reasons therefor and implications thereof are discussed in Ref. [9]. Nevertheless, even for such cases of a decreasing growth rate, it is generally assumed that all grains grow with the same rate at any given time t, i.e. the time dependency is the same for all grains. The experiments mentioned above are all based on static statistical measurements where the migration rate is determined using stereological methods, e.g. using either the Cahn–Hagel approach [10,11] or the extended Cahn–Hagel approach [12] from a series of partly recrystallized samples annealed for different times. Recently, however, newer experimental methods have allowed direct measurements of the growth of individual grains in situ during annealing.
1359-6454/$36.00 Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2009.01.039
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For recrystallization these direct observation methods include examination in a high-voltage transmission electron microscope (TEM) [13], backscattered electron diffraction imaging [14,15] in a scanning electron microscope (SEM) and three-dimensional X-ray diffraction (3-D XRD) [16–18]. All these in situ measurements of the growth of individual grains in both deformed single crystals and polycrystals show that the boundary migration seems to be much more complex than hitherto assumed; the migration rate is not constant but changes from grain to grain, and it varies with space and time in a non-simple fashion. Each grain has its own kinetics [16,17] and the shapes of the grains during growth can become quite odd (i.e. far from spherical), with large local protrusions [18]. The latter phenomenon was also observed in the classical static experiments [9,19,20] but has not, until recently, been discussed in much detail. Models have yet to be formulated that explain these in situ growth observations of individual grains during recrystallization. The aim of the present study was to investigate in detail how individual grains grow during recrystallization. We chose to do this using the electron backscattering pattern (EBSP) method in an SEM by mapping the evolution in the microstructure within a single large sample surface area after five sequential annealing times. Compared to the TEM method, this approach has the advantage that only one sample surface, rather than two, can potentially affect the results; in addition, the extra driving force for boundary migration given by a wedge-shaped TEM sample is avoided. Compared to the 3-D XRD measurements, the present measurements are limited by not being from an interior volume, so surface effects have to be considered. However, the EBSP method offers the advantage of being able to study the effect of impingement between recrystallizing grains directly – something that is not yet possible with the 3-D XRD method. Additionally, and of great importance for the present investigation, the EBSP method allows the direct investigation of the effects of boundary misorientation on recrystallization boundary migration rates, because the data contain a record of the orientation of pixels in the deformed matrix which are ‘‘consumed” by each specific recrystallizing grain during any given annealing step. To do this in three dimensions using 3-D XRD requires an improvement in the method to allow mapping of deformation microstructures on the micrometre scale, but such an improvement is not likely to be achieved in the next five years. 2. Experimental The sample material chosen for the investigation was 99.999% pure nickel, with an initial grain size of 30 lm. The material was cold-rolled by 96% reduction to a thickness of 250 lm. Samples were annealed at 320 °C in an air furnace. The reasons for choosing this material for the investigation were (i) a previous investigation [21] has shown that a strong cube texture component develops dur-
ing the recrystallization, so the competing growth of cubeoriented and other grains may be studied; (ii) the strain is high, and less is known about boundary migration at such high strains; and (iii) similar material is of practical importance as a substrate for superconducting wires. Annealing was carried out to give accumulated times of 5, 10, 20, 40, and 80 min. After the first annealing step (5 min), the rolling plane (defined by the rolling direction (RD) and the transverse direction) was ground to SiC4000 before final electropolishing in a 1:3:4 HClO4:CH3COOH:C2H5OH solution at 0 °C and 12 V for 45 s. A microhardness indent was made on the polished surface to facilitate reidentification of the mapped area after each annealing step. During all subsequent annealing steps, the sample was enclosed in a vacuum glass tube (106 Pa) with 0.3 atm Ar + H2 to protect the sample surface. The microstructure was examined after each annealing step at the same position on the sample using a LEO 1530 SEM equipped with a fully automated EBSP analysis system. Orientation maps were obtained using a step size of 2 lm over an area of 1200 1200 lm2. In this paper texture components are defined using a 15° deviation to various ideal orientations. To classify the grains, the following three orientation classes were used: cube {0 0 1}<1 0 0>; rolling (including f1 1 2gh1 1 1i ðcopperÞ, f1 2 3gh6 3 4i ðSÞ and f1 1 0gh1 1 2i ðbrassÞ); and other (consisting of everything not belonging to the cube and rolling orientations). In the fully recrystallized state the volume fractions of cube, rolling and other texture components were 52%, 16% and 32%, respectively. In all the EBSP orientation maps presented in this paper, cube, S, brass and copper orientations are shown in orange, blue, red and green, respectively. Other orientations are shown in white; black pixels are non-indexed points. Aqua (cyan) and black lines represent boundary misorientations of >2° and >15°, respectively. Red lines indicate R3 boundaries, defined according to the Brandon criterion [22]. It is clear that the chosen experimental method samples volumes at and near the sample surface. It is thus important to consider if (and how) the results may be influenced by surface effects. A detailed analysis hereof is presented in the appendix. An important argument that is worth repeating here is that similar behavior to the observations reported in this paper have also been observed from 3-D XRD experiments, where data are from the bulk and where surface effects are out of the question. We thus believe that the results to be presented are general and not just typical for the surface. 3. Results 3.1. Microstructure After cold rolling to a thickness reduction of 96%, the microstructure is heavily subdivided into a lamellar structure with the lamellar boundaries more or less parallel to
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Fig. 1. Example of a region of the microstructure after annealing for (a) 5 min and (b) 5 + 10 + 20 min. Cube, S, brass and copper oriented grains are shown in orange, blue, red and green, respectively. Other grains are shown in white; black pixels are non-indexed points. Aqua and black lines represent boundary misorientations of >2° and >15°, respectively.
the rolling plane. The volume fractions of cube, rolling and other texture components are 0.5%, 85% and 14.5%, respectively. When the sample is annealed at 320 °C for 5 min, nucleation of recrystallization occurs and the nuclei start to grow. In the present work a nucleus is identified as an area with interior misorientations smaller than 0.75° and where further annealing confirms that the nucleus actually grows. As always when describing recrystallization, confusion exists as to when to call a recrystallizing area a nucleus or a grain. In the following we have chosen to refer to recrystallizing nuclei/grains as just grains. A part of the total mapped area is shown in Fig. 1 for annealing times (total) of 5 and 35 min. It can be seen that after two annealing steps (10 + 20 min), all the grains in Fig. 1a still can be identified in Fig. 1b. However, some new grains also appear, either from below the surface or as a result of twinning of existing grains.
The ability to trace the growth of each grain allows growth curves for individual grains to be plotted. This is done by overlaying as precisely as possible two consecutive images by comparing the orientations of the pixels. From that, it is straightforward to measure the size increase (i.e. increase in number of pixels) of each grain and thus obtain growth curves. Some examples are given in Fig. 2 for grains of each orientation class (cube, rolling and other) chosen at random within the mapped area. Inspection of the growth curves clearly reveals that each grain has its own kinetics: no growth curves are alike regardless of the grain orientation class. A similar conclusion was reached using 3-D XRD in Ref. [16]. At all annealing times, the cube-oriented grain sizes are on average significantly larger than those of both rolling and other oriented grains, which b) rolling
a) cube
2500
Free Growth Partially Impinged
Area of Grains (µm2)
Area of Grains (µm2)
10000
3.2. Growth kinetics
8000 6000 4000 2000
Free Growth Partially Impinged
2000 1500 1000 500 0
0 0
40
80
120
0
160
Annealing Time (minutes)
40
80
120
160
Annealing Time (minutes)
c) other Area of Grains (µm2)
5000
Free Growth Partially Impinged
4000 3000 2000 1000 0 0
40
80
120
160
Annealing Time (minutes) Fig. 2. Growth curves for individual grains of different orientations: (a) cube; (b) rolling; and (c) other.
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Fig. 3. Determination of the misorientations between a recrystallizing grain and its surrounding deformed matrix during annealing. Microstructures after annealing for (a) 5 min and (b) 5 + 10 min. (c) A semi-transparent overlay of (b) on (a). Thick magenta lines show boundaries that do not move during annealing.
is also in agreement with earlier observations of the present material [21]. The present data also allow the effects of impingement between recrystallizing grains to be investigated. In Fig. 2, the red solid symbol points indicate grains that are partially impinged (defined as a recrystallizing grain with at least one neighboring recrystallizing grain). The black open symbol points indicate freely growing grains, i.e. those surrounded completely by the deformed matrix. It may be noted that most grains become impinged at the very early stages of recrystallization, although some grains remain unimpinged even after the final annealing step. Moreover, some recrystallized grains do not grow even when they are free to grow (unimpinged) while others grow quickly, even though they are partially impinged by other recrystallizing grains.
deformed matrix both for rolling and other oriented grains. For cube-oriented grains, the distribution spread is relatively narrow, in the range of 38–62°. It is worth noting that a near 40° h1 1 1i misorientation is only seen for very few boundaries (<0.5%) for all the orientation classes. This is consistent with previous results [21]. The misorientation distribution encountered during growth of the largest observed cube-oriented grain after the first annealing step is also shown in Fig. 4d (739 pixels are involved in this calculation). Note that data for this grain are not included in the aggregate data for cube-oriented grains shown in Fig. 4a. It can be seen that both the axes and the angular range of the misorientation distributions are very similar to those seen for the aggregate data, though the peak is shifted to a slightly lower misorientation angle.
3.3. Misorientation of moving boundaries
3.4. Misorientation of non-moving boundaries
The area consumed during the growth of a recrystallizing grain contains information about the misorientations encountered during the growth of the grain, and these data can be used to investigate the effects of misorientation on the boundary migration rates. The procedure is illustrated in Fig. 3. Here, after 5 min of annealing, grain A is shown in orange in Fig. 3a. After additional annealing for 10 min, grain A has grown, as shown in Fig. 3b. By overlaying the two maps (Fig. 3c), the pixels of the deformed matrix that have been ‘‘consumed” by grain A during the annealing step can be found. The misorientations between the orientation of grain A and each consumed pixel can then be calculated and expressed as angle/axis pairs. The data resulting from such an analysis are plotted in Fig. 4. These data are gathered from between the first and second annealing steps and between the second and third annealing steps for 10–12 grains of each orientation class (involving transformation of 1272, 703 and 846 deformed pixels into cube, rolling and other oriented grains, respectively). The results show that a very wide variety of misorientation relationships (in the range of 10–62°) can be found between growing grains and the neighboring
The misorientation distribution for non-migrating unimpinged boundaries was also investigated. Such boundaries are shown in Fig. 3c as thick magenta lines; note that here we only analyze boundaries between recrystallizing grains and the deformed matrix. The results measured from between the first and second annealing steps and between the second and third annealing steps are shown in Fig. 5 for 20–25 grains of each orientation class (involving transformation of 354, 276 and 382 deformed pixels into cube, rolling and other oriented grains, respectively). Comparison with Fig. 4 shows that the misorientation distributions for both migrating and non-migrating boundaries are similar for all orientation classes, although more boundaries near 60° are observed for the non-migrating boundaries for cube-oriented grains. It is also observed that the rotation axis is generally more clustered around h1 1 1i for moving than for non-moving boundaries. 4. Discussion In the present study the migration of individual boundaries surrounding recrystallizing grains through deformed
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Fig. 4. Misorientation axis/angle distributions between recrystallizing grains and the consumed deformed matrix from between the first and second and between the second and third annealing steps for (a) cube, (b) rolling, (c) other grains, and (d) the largest cube-oriented grain. Thick black lines show the expected uncorrelated misorientation distributions. The inverse pole figures marked 1 and 2 show experimental and expected uncorrelated rotation axis distributions, respectively.
matrix material has been studied by EBSP mapping of a single large sample area after five consecutive annealing
steps with the aim of learning more about the growth of individual grains during recrystallization. The growth
Fig. 5. Misorientation axis/angle distributions between recrystallizing grains and the deformed matrix for non-moving boundary segments from between the first and second and between the second and third annealing steps for (a) cube, (b) rolling and (c) other oriented grains. Thick black lines show the expected uncorrelated misorientation distributions. The inverse pole figures marked 1 and 2 show experimental and expected uncorrelated rotation axis distributions.
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kinetics and the characteristics of the migrating boundaries are analyzed in more detail in the following. It cannot be excluded that, in addition to the aspects discussed below, the grain boundary plane (which cannot be determined from 2-D EBSP maps) may also affect the observed boundary migration rates. However, as the experimental method used in this study does not allow determination of this parameter, this shall not be discussed further here. 4.1. Growth kinetics of individual grains The present results show that each grain has its own growth kinetics (see Fig. 2). This is in agreement with previous 3-D XRD experiments [16,17]. The present investigation reveals that this is not just an effect of impingement – a possibility that could not be excluded based only on 3-D XRD experiments. Even grains which are free to grow with totally unimpinged boundaries may grow very slowly or not at all, and grains which are partially impinged may increase in size (i.e. grow) at a very fast rate. This is the case for grains in each of the three orientation classes studied: cube, rolling and other. On average, however, the cube-oriented grains grow to become the largest, in agreement with earlier observations [21] in which only the average behavior was determined. The present results (see Fig. 2) show that the average size advantage is strongly influenced by a few cube-oriented grains growing to very large sizes. The reasons why some cube-oriented grains grow so preferentially are not clear. This is not because they are closer to the exact cube orientation and, as shown in Fig. 4d, the misorientation distribution for the largest cube-oriented grain is very similar to the ensemble misorientation distribution for all the cube-oriented grains (Fig. 4a). When the misorientation distribution for the cube and rolling/other grains are compared (see Figs. 4 and 5), significant differences are obvious. The cube-oriented grains have more 40–60° boundaries close to h1 1 1i, whereas rolling/other grains encounter the whole range of misorientation angles from 10° to 60°. This is not surprising considering the texture of the deformed matrix, as can be seen from the uncorrelated misorientation distributions for recrystallizing grains to the deformed matrix, plotted in Figs. 4 and 5 as thick black lines. To calculate these uncorrelated distributions, 15 nucleus/grain orientations for each orientation class were randomly chosen, and the misorientations to the deformation texture as determined from the RD–normal direction (ND) section were calculated. It can be seen that for all the orientation classes the experimentally measured misorientation angle distributions are in reasonable agreement with the uncorrelated distributions, whereas the experimentally measured rotation axis distributions for migrating boundaries (see Fig. 4) are more clustered than the expected uncorrelated distributions. Moreover, the calculation shows that rolling oriented grains have a relatively higher chance of forming low-angle boundaries, while the cube-oriented grains have a very small chance of encountering low-angle boundaries.
When considering the misorientation distributions for both the experimentally measured and the expected uncorrelated cases, it seems that high misorientation angle boundaries with rotation axes around h1 1 1i are favorable for growth (experimentally measured distributions in Fig. 4). For the cube-oriented grains there is a larger probability of being surrounded by boundaries of this type than there is for the rolling and other oriented grains. In the work by Schmidt and Lu¨cke [23] it was found that texture evolution during recrystallization could be described by ‘‘compromise orientations” due to the preferential growth of boundaries with misorientations close to 40° h1 1 1i. This can be compared to the present observations for boundaries surrounding cube grains, where fast migration is observed for boundaries over the whole range of misorientations from 40° to 60° h1 1 1i. 4.2. Migration of boundaries during recrystallization The present results confirm that the misorientation is an important parameter for the overall growth of recrystallizing grains. However, when looking at the local scale, comparing the misorientation distributions for specific boundary segments which move during a given annealing time with those that do not move during that annealing, it is surprising to observe that the differences are not so large. This can be seen when comparing Figs. 4 and 5. The main difference is that boundaries near 60° h1 1 1i (including coherent twin boundaries) are significant in the distribution for non-moving boundaries of cube-oriented grains (Fig. 5a) but not for the moving ones (Fig. 4a). Furthermore, the rotation axis distributions for migrating boundaries are generally more clustered at the h1 1 1i corner than for non-migrating boundaries. Besides these well-known effects, the present data show that, for a given misorientation (a similar angle and rotation axis), a boundary segment may sometimes move and sometimes not. It should be underlined that this result refers to boundary segments and not the whole boundary surrounding the recrystallizing grain, i.e. parts of the boundary surrounding the grain in three dimensions may move while other parts may not. Grains would thus be expected to grow in size in spite of the fact that one or more boundary segments at a given time step are immobile. One reason why some boundary segments move during an annealing step while others do not could be a difference in the local stored energy in the deformed matrix in front of the boundary: a boundary segment that migrates may have a higher local driving force than a non-migrating one. This possibility was investigated in detail for the specific example shown in Fig. 6. Here two cube-oriented grains, A and B, meet similar orientations in the deformed matrix. The stored energies in the deformed matrix within the black rectangles in front of A and B were calculated using the method described in [24]. The stored energies in front of grains A and B were found to be 0.75 106 and 0.72 106 J m3, respectively. However, after an addi-
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Fig. 6. Example to show the difference in growth for grains of the same orientation and misorientation. Rectangles show the regions used for calculation of the stored energy. (a) 7.5 min; and (b) 7.5 + 7.5 min.
Fig. 7. RD–ND section of partially recrystallized sample. The color code is the same as for Fig. 1. The black areas of the top are above the free sample surface.
tional annealing of 7.5 min only grain B had grown (see Fig. 6b). Thus, in spite of very similar driving forces and local misorientations (angles and axes), one boundary segment migrated and the other did not. It should be noted that the microstructure was also examined in the RD– ND plane (Fig. 7). It can be seen from the figure that the recrystallizing grains typically extend only 5–20 lm below the sample surface. The observation of differences between growth rates for grains of similar orientation class cannot therefore be accounted for by the growth of some grains across the entire thickness of the sample (250 lm). This result suggests that, whereas Eq. (1) has proven to be valid for the average overall boundary migration during recrystallization [25–27], the movement locally of boundary segments may be more complex. An atomistic view of the boundary migration process envisages interfacial atoms in front of the boundary to move to sites belonging to the lattice of the growing grain, thus moving the boundary forward [9]. This is generally thought of as a process of the diffusion of single atoms or a shuffling mechanism involving more than one atom at a time [28–32]. Both these processes are considered to be steady-state phenomena and thus cannot explain the observed stop–go motion of boundary segments. Whereas these classic theories are for boundary migration through perfect or near-perfect crystals, it is clear that for recrystallization the process must be much more complex, as the boundary migrates through a deformed material containing many dislocations of different types arranged locally in many different ways. The
boundary migration during recrystallization will thus involve local interactions between dislocations (and the atoms around these) and the grain boundary: for example, individual dislocations moving into a boundary, as observed by Jones et al. [33], leading to a local recovery in front of the boundary [34], or boundary segments moving forward by absorbing local dislocations, as predicted by molecular dynamics simulations [35,36]. Both of these processes lead to smaller or larger reorientations locally ahead of the boundary [37] and it takes some time for them to occur. This could be at least part of the explanation why the migration of boundary segment occurs in steps (move, stop and move) during recrystallization and thus also why one can observe boundary segments with the same M and F that behave differently at a given time. 5. Summary and conclusions The growth of individual grains during recrystallization in 96% cold-rolled pure nickel was followed using EBSP maps of a single area taken after each of several annealing steps. The following were found. The growth kinetics differ from grain to grain, and the present experiment proves that this is not just an effect of impingement between recrystallizing grains. Cube-oriented grains have a higher probability than rolling and other oriented grains of being surrounded by high-angle boundaries with their rotation axis near
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h1 1 1i to the deformed matrix, which is favorable for growth. It should be noted, however, that the observed average cube growth advantage is dominated by a few very large cube grains. These superlarge cube grains do not achieve their size advantage because they are closer to the ideal cube orientation or have a different misorientation than the smaller cube grains. The growth of individual grains was observed to occur in steps, with some boundary segments moving forward while others remained stationary for a given annealing time, after which they may also move. This is not believed to be a surface effect as very similar observations are also seen in in situ bulk 3-D XRD experiments. The misorientation angles and axes, as well as the local driving force, can be very similar for boundary segments which move and those which do not move at a given annealing time step. This suggests that the local migration process is complex, requiring time for local interactions between dislocations and boundary and thus for ensembles of atoms to rearrange before being adopted into the recrystallizing grain, leading to the forward migration of that boundary segment.
Acknowledgments The research was supported by the Natural Science Foundation of China (NSFC) under Grant Nos. 50571041, 50620130096 and 50671052. The authors thank Prof. B. Ralph for helpful comments and discussions. Y.B.Z. and D.J.J. further acknowledge support from the Danish National Research Foundation through the Center for Fundamental Research: Metal Structures in Four Dimensions. Appendix A A.1. Analysis of possible surface grooving effects for the present experiment Thermal grooving is a surface effect which has to be considered for the present experiment. According to Gottstein and Shvindlerman [25], ‘‘It is a common experience that grain boundary motion appears jerky when observed by grain boundary displacement on a surface. This jerky motion, however, is not the genuine mode of grain boundary migration rather it is caused by thermal grooving on the surface.” Whereas the quoted work was on high-temperature grain growth, our work is on low-temperature recrystallization, where the driving force is orders of magnitude larger. However, we also see ‘‘jerky movement” in the sense that boundary segments may move, stop for a while and then move again. This could be an effect of thermal grooving. Arguments against this, however, are: (1) The specimens were examined in the RD–ND section to see if the surface layer appeared different from the subsurface region. An example is shown in Fig. 7. Neither indi-
cations of thermal grooving nor other surface peculiarities can be seen. (2) According to Mullins’s theory of thermal grooving [38], the depth of the groove from the top to the root measured in the direction normal to the surface is given by: d ¼ 0:973mðBtÞ
1=4
ð2Þ
where m2 = cb/2cs is the slope at the groove root and B ¼ Ds ckTs X t in which t denotes the number of atoms per m2 of surface, X denotes the atomic volume, kT has its usual meaning, Ds denotes the surface diffusivity, cb and cs are grain boundary free energy and surface free energy, respectively, and t is the heating time. For the present material and temperature, we used the values m = 0.17 X = 1.09 1029 m3/atom, [39], kT = 8.2 1021 J, 19 2 t = 2.03 10 atoms/m , Ds = 10-17 m2/s (here no values could be found in the literature for nickel, so instead the value for surface diffusion of copper has been used [40]; this is expected to lead to an overestimation of the groove size) and t = 600–9000 s (from the second to the last annealing steps). It is found that the depth of the groove d = 1.28– 2.52 nm. This means that even after the last annealing step the thermal groove is still not well developed. Normally thermal grooving is considered in the grain growth experiment, in which the thermal groove can be much more developed. According to Mullins’s calculation [41], thermal grooving is of importance when the driving force for boundaries is less than or of the order of 104 J/ m3 (105 ergs/cm3). For the present material the stored energy was measured by a differential scanning calorimetry to be 107 J/m3 [42], i.e. far exceeding the value given by Mullins. (3) A further concern could be that the present experiment is a heating–cooling annealing type experiment. However, in situ SEM experiments [14,15] also show similarly ‘jerky’ boundary migration. (4) Careful bulk measurements performed by 3-D XRD have also shown that boundaries do not always move forward at a constant rate. Even in deformed single crystals 3D XRD measurements have shown boundaries or boundary segments in the bulk stopping for a while and then migrating quickly forward [18]. Thus it is obvious that this type of boundary migration is not just a phenomenon occurring at the surface. References [1] [2] [3] [4]
[5] [6] [7] [8] [9]
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