Materials Science Forum Online: 2004-10-15 ISSN: 1662-9752, Vols. 467-470, pp 745-750 doi:10.4028/www.scientific.net/msf.467-470.745 Citation & Copyright 2004 Trans (to be Tech inserted Publications, by the publisher Switzerland ) New Understanding of Abnormal Grain Growth Approached by Solid-State Wetting along Grain Boundary or Triple Junction Nong-Moon Hwang Center for Microstructure Science of Materials, School of Mater. Sci. and Eng., Seoul National University, Seoul 151-742, Korea Keywords: abnormal grain growth, solid-state wetting, grain boundary, triple junction Abstract. Although it has been generally believed that the advantage of the grain boundary mobility induces abnormal grain growth (AGG), it is suggested that the advantage of the low grain boundary energy, which favors the growth by solid-state wetting, induces AGG. Analyses based on Monte Carlo (MC) simulation show that the approach by solid-state wetting could explain AGG much better than that by grain boundary mobility. AGG by solid-state wetting is supported not only by MC simulations but also by the experimental observation of microstructure evolution near or at the growth front of abnormally growing grain. The microstructure shows island grains and solid-state wetting along grain boundary and triple junction. Introduction In spite of the long history and intensive efforts, abnormal grain growth (AGG) is still not clearly understood. AGG has been approached mainly by the advantage in grain boundary mobility although there is some disagreement as to how this mobility advantage is achieved [1-4]. The migration of a grain boundary is kinetically coupled with that of other grain boundaries through triple junctions in polycrystalline materials. This kinetic coupling imposes a strong constraint on the grain boundary migration. Even if a grain boundary has a very high mobility, it cannot migrate sufficiently fast unless triple junctions keep abreast with its migration. This kinetic coupling disappears if solid-state wetting takes place at the triple junction, i.e., if the energy sum of the two grain boundaries is smaller than the energy of the third grain boundary at the triple junction. Under this condition, the two low energy grain boundaries replace the high energy grain boundary and the grain with the low energy grain boundaries grows by penetrating into the high energy grain boundary. The growth behavior changes abruptly when a grain grows by solid-state wetting. The grain with the advantage of solid-state wetting can grow abnormally. The purpose of this paper is to review AGG by considering solid-state wetting based on the results of the related papers. Before introducing AGG by solid-state wetting, the constraining effect of the triple junction on the grain boundary migration will be analyzed. This case will be compared with the case of solid-state wetting, where the triple junction migrates freely without constraint. Role of Constraint Imposed by Triple Junction in Grain Growth In polycrystalline materials, grain growth is driven by the grain boundary curvature. If a grain has an inward grain boundary curvature, the grain grows in the direction to flatten the curvature. If a grain has an outward curvature, the grain shrinks in the direction to flatten the curvature. The grain boundary curvature is originated from the force balance of the grain boundary tension at the triple junction, which is the point where three grain boundaries meet. Figure 1 shows shrinking and growing grains in contact with each other. The triple junction appears as the point on the two-dimensional section. The direction of the grain boundary migration (indicated by the arrow) is determined by the grain boundary curvature, which is a consequence of the force balance at the triple junction. The maximum limit of the grain boundary migration is designated as the straight dashed line in Fig. 1. In this case, the grain boundary curvature disappears and there exists no driving force for further grain All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (#69807605, Pennsylvania State University, University Park, USA-18/09/16,04:01:42)
746 Recrystallization and Grain Growth 2 Title of Publication (to be inserted by the publisher) boundary migration. Therefore, the grain boundary cannot migrate ahead of its triple junction. In other words, the grain boundary migration is accompanied by the triple junction migration, which is again accompanied by the migration of the three grain boundaries in contact at the triple junction. In other words, the triple junction and the three grain boundaries in contact at the triple junction migrates concurrently. In addition, the migration of the three grain boundaries is accompanied by the migration of the other triple junctions. Therefore, the grain boundary migration is kinetically coupled with the triple junction migration in a complicated way. This kinetic coupling between grain boundaries and triple junctions prevents a grain boundary of exceptionally high mobility from migrating freely and sufficiently fast. Consider the simple system of four grains, namely A, B, C and D as shown in Fig. 1. The grain boundary formed by two grains A and B will be designated as AB. The triple junction formed by three grains A, B and C will be designated as ABC. Other grain boundaries and triple junctions will be designated in the same way. If the mobility of grain boundaries AD and CD is extremely low, the mobility of the triple junction ACD would be extremely low, too. In this case, grain D would act like the second phase, which pins the migration of the grain boundary AC. Then, even if the grain boundary AC has extremely high mobility, its migration is practically pinned by the low mobility boundaries and triple junction. In the real system, high and low mobility boundaries coexist, and the low mobility boundaries are expected to pin or retard the migration of the high mobility boundaries through triple junctions. Fig. 1. Schematic diagram showing the relation between triple junctions and grain boundary for the grains A, B, C and D. Grains A and C are shrinking and growing, respectively, as indicated by the arrow and the grain boundary curvature. Even though the kinetic coupling between grain boundaries and triple junction is complicated in a real polycrystalline system with numerous grains, its effect is naturally implemented in Monte Carlo (MC) simulation of grain growth using metropolis algorithm [5]. Therefore, the effect of low mobility boundaries on the migration of high mobility boundaries can be examined by MC simulation. Using MC simulation, Rollett et al. [6] showed that a grain grows abnormally under the simulation condition, where 100% of the grain boundaries shared by the chosen grain have high mobility and 100% of other grain boundaries have low mobility. Under such an ideal condition, the chosen grain would undergo AGG. In this case, the triple junction has no appreciable pinning effect for the grain boundary migration of the abnormal grain. Using MC simulation, Hwang [7] examined the effect of the fraction of the low mobility grain boundary fraction on AGG. When 80% of the grain boundaries shared by the chosen grain have high mobility and the other 20% have low mobility while 100% of other grain boundaries have low mobility, the chosen grain did not grow abnormally. The reason for this was due to the pinning effect of the 20% low mobility grain boundaries. It should be noted that this condition is not realistic and artificially provides the exclusive growth advantage for the chosen grain. It can be said that the low
Materials Science Forum Vols. 467-470 747 Journal Title and Volume Number (to be inserted by the publisher) 3 mobility boundary has a strong pinning effect on the high mobility boundary through the kinetic coupling at the triple junction. The realistic fraction of the high mobility grain boundary shared by abnormally growing grain would be much lower than 80%. These facts indicate that the mobility advantage alone cannot induce AGG. The constraint of the grain boundary migration imposed by the triple junction can disappear when the anisotropy of grain boundary energy is satisfied. For example, if the sum of the energy of grain boundaries AD and CD in Fig. 1 is smaller than the energy of grain boundary AC, grain C will penetrate along the grain boundary AD just as the liquid phase wets the grain boundary. Then, the grain boundary AC can migrate freely without the constraint imposed by the triple junction ACD. Therefore, the migration velocity of the triple junction changes abruptly, depending on whether it migrates by a wetting mode or by a non-wetting mode. The growth characteristics of the grain C by a wetting mode can be drastically different from that by a non-wetting mode. The growth aspect by solid-state wetting will be analyzed in more detail in the following sections. Grain Growth by Solid-State Wetting The grain growth behavior changes abruptly when the grain grows by solid-state wetting. Figure 2 is a simple example to show how a grain grows by solid-state wetting. In Fig. 2, an infinitesimally small grain is located at one of two triple junctions made by three large grains. This small grain is shaded for distinction. The grain boundary energy between the infinitesimally small grain and its three neighboring large grains is assumed to be 1 while the grain boundary energy between the three large grains is assumed to be 2. Under this condition of anisotropic grain boundary energy, the small grain grows against the three large grains by solid state wetting. Fig. 2, which is the microstructure evolution after 500 Monte Carlo steps (MCS), shows that the infinitely small shaded grain grows against the size difference. The shaded grain in Fig. 2 has an inward grain boundary curvature, which is determined by the force balance at the triple junction. Although the shaded grain is only three-sided, it grows against the neighboring large grains. Fig. 2. MC simulation showing the grain growth of the infinitesimally small shaded grain against the size difference by solid-state wetting. the initial state and after 500 MCS Using MC simulation, Rollett et al. [6] first showed that a grain grows abnormally when 100% of the grain boundaries shared by the chosen grain have low energy. In that case, the chosen grain may grow exclusively by solid-state wetting along the other grain boundaries, the chosen grain grows abnormally. Besides, the dominant growth by solid-state wetting tends to leave numerous other grains behind, thereby producing island grains, which represents the realistic microstructure evolution during AGG [6-9]. Using MC simulation, Hwang [7] examined the effect of the fraction of the low energy boundary on AGG. Under the condition that 40% of the grain boundaries shared by the chosen grain have low
748 Recrystallization and Grain Growth 4 Title of Publication (to be inserted by the publisher) energy and the other 60% have high energy while 100% of other grain boundaries have high energy, the chosen grain underwent AGG. This result indicates that the low energy advantage induces AGG under much more realistic conditions than the mobility advantage. However, 40% of the low energy boundary is still unrealistically high and the percentage should be decreased further, considering that AGG occurs quite commonly in real systems. Since this simulation was two-dimensional, it was limited to grain boundary wetting only. However, in a real three-dimensional polycrystalline structure, triple junction wetting would take place more actively than grain boundary wetting, under the given anisotropic grain boundary energy. The wetting behavior along triple junction and grain boundary can be compared with the second phase. The latter wets the triple junction or the grain boundary of the mother phase. In this case, it is well established that the second phase can penetrate completely along the triple junction when the dihedral angle is less than 60 o while it can penetrate completely along the grain boundary only when the dihedral angle is zero [10]. In order to consider the effect of solid-state wetting along the triple junction, Hwang et al. [11] performed three-dimensional MC simulation. They found that under when 15% of the grain boundaries shared by the chosen grain have low energy and the other 85% have high energy while 100% of other grain boundaries have high energy, the chosen grain underwent AGG as shown in Fig. 3. Therefore, the mechanism of solid-state wetting explains AGG in a much realistic way than the mechanism based on mobility. (c) Fig. 3. Microstructural evolution of a two dimensional section at the center after 100, 500 and (c) 1000 MCS of the three dimensional MC simulation [11]. Microstructural Evidences of Solid-State Wetting Island Grains. In many cases of AGG, the growth front migrates leaving behind numerous grains and grain clusters and are consequently trapped inside the abnormally growing grains. These trapped grains are called island grains. Messina et al. [9] observed numerous island grains and grain clusters inside the abnormally grown grain in the nickel-base superalloy. Based on misorientation measurements of island grains by electron backscattered diffraction (EBSD), they suggested that grain boundaries between the island grains and the abnormally-growing grain have low energy whereas that island grains and grain clusters are formed by solid-state wetting. It might be argued that the formation of island grains can be explained by mobility in the following way: the growth front of abnormally-growing grains migrates so fast that the low mobility grain boundaries of island grains are left behind and trapped inside. However, MC simulation shows that island grains are hardly formed by the mobility effect [7]. When a grain has a low mobility grain boundary, it acts like a second phase, which pins the migration of nearby grain boundaries. It would be very difficult for a grain (or a second phase) with its dimension equivalent to the grain boundary to break away from the grain boundary. Formation of so many island grains cannot be explained by mobility difference alone.
Materials Science Forum Vols. 467-470 749 Journal Title and Volume Number (to be inserted by the publisher) 5 On the other hand, MC simulation shows that island grains are easily formed by solid-state wetting [7]. Island grain formation is enhanced under the MC simulation condition where grain boundaries have low mobility as shown in Fig. 4. Figure 4 show the scanning electron microscopy (SEM) image for the initial stage of AGG in Fe-3%Si alloy, where many island grains and grain clusters are formed. Fig. 4. MC simulation and SEM microstructure of Fe-3%Si alloy showing that numerous island grains are formed inside the abnormally-growing grain. In MC simulation of, the mobility of grain boundaries is reduced by 10 times [7]. Grain Boundary Wetting. The microstructure showing the grain boundary wetting might be observed at the growth front of abnormally growing grains. Figures 5 and 5 show a schematic picture and a real SEM microstructure of grain boundary wetting, respectively. Figure 5 shows that the abnormally-growing Goss grain penetrates the grain boundary of two neighboring grains and 34 cases of the microstructure showing grain boundary wetting such as Fig. 5 were observed at the growth front of two abnormally-growing grains [12]. A Low energy GB High energy GB C B Low energy GB Fig. 5. Schematic diagram and SEM microstructure showing solid-state wetting [12]. Triple Junction Wetting. By calculating the probability of triple junction and grain boundary wetting for a given anisotropy of grain boundary energy, Hwang et al. [11] showed that triple junction wetting is much more probable than grain boundary wetting. When observed on a two-dimensional section, triple junction wetting would look like the shaded grain in Fig. 2. That is, triple junction wetting on a two-dimensional section would appear as three-sided or four-sided grains with inward grain boundary curvatures.
750 Recrystallization and Grain Growth 6 Title of Publication (to be inserted by the publisher) Fig. 6. MC simulation and SEM microstructure of Fe-3%Si alloy showing the two-dimensional section of triple junction wetting, which is indicated by three-sided or four-sided grains with inward grain boundary curvatures [13]. Figure 6 shows a two-dimensional cross section of a three-dimensional MC simulation [13]. Since the sectioning was done away from the center of a large shaded AGG grain, Fig. 6 is near the edge of the AGG grain. Although the four shaded grains in Fig. 6 look separated, they are the same grain, which means that they are three-dimensionally connected. Eventually, they will merge together, producing numerous island grains and grain clusters. Two shaded three-sided grains at the center have inward grain boundary curvatures, indicating that they are growing rather than shrinking. Figure 6 shows a SEM microstructure near the growth front of an abnormally growing grain of Fe-3%Si alloy. Three-sided and four-sided grains have inward grain boundary curvatures, indicating that they are growing and penetrating or wetting along the triple junction. Conclusions Although solid-state wetting might not be a familiar concept in grain growth, it appears to play an important role in grain growth of the system of anisotropic grain boundary energy. Especially when a grain has the orientation favorable to make low grain boundary energy with respect to other grains, the grain can grow abnormally by solid-state wetting. References [1] J. Harase, R. Shimizu and D.J. Dingley: Acta metall. mater. Vol. 39 (1991), p. 763 [2] Y. Ushigami, S. Nakamura, S.Takebayashi and S. Suzuki: Mater. Sci. Forum Vol. 408-412 (2002), p. 973 [3] Y. Hayakawa, M. Muraki and J.A. Szpunar: Acta mater. Vol. 46 (1998), p 1063 [4] N. Rajmohan, J.A. Szpunar and Y. Hayakawa: Acta mater. Vol. 47 (1999), p. 2999 [5] D.J. Srolovitz, G.S. Grest and M.P. Anderson: Acta metall. Vol. 33 (1985), p. 2233 [6] A.D. Rollett, D.J. Srolovitz and M.P. Anderson: Acta metall. Vol. 37 (1989), p. 1227 [7] N.M. Hwang: J. Mater. Sci. Vol. 33 (1998), p. 5625 [8] S.B. Lee, N.M. Hwang, C.H. Han and D.Y. Yoon: Scripta mater. Vol. 39 (1998), p. 825 [9] R. Messina, M. Soucail, T. Baudin and L.P. Kubin: J. Appl. Phys. Vol. 84 (1998), p. 6366 [10] R.E. Reed-Hill: Physical Metallurgy Principles, (D. Van Nostrand Company, New York 1973). [11] N.M. Hwang, S.B. Lee and D.Y. Kim: Scripta mater. Vol. 44 (2001), p. 1153 [12] H. Park, D.Y. Kim, N.M. Hwang, Y.C. Joo, C.H. Han and J.K. Kim: To be published in J. Appl. Phys. [13] N.M. Hwang, S.B. Lee, C.H. Han and D.Y. Yoon: Proc. Grain Growth in Polycrystalline Materials III, (1998), p. 327.