Pergamoo Scripta Matenalia. Vol. 37, No. 1 I, pp. 1637-1642, 1997

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GRAIN GROWTH BEHAVIOR IN THE SYSTEM OF ANISOTROPIC GRAIN BOUNDARY MOBILITY

Nong M. Hwang Korea Research Institute of Standards and Science, P.O. Box 102,

Taedok Science Town, Taejon, 305-600, Republic of Korea

(Received April 22, 1997) (Accepted July 29, 1997)

Introduction

Solid-state grain growth is driven by the overall decrease of the interfacial free energy of the system. The grain growth behavior is affected by both energy and mobility of the grain boundary, which are anisotropic. The anisotropic aspect of the grain boundary might be related to the evolution of preferred orientation by grain growth. It was experimentally observed that the texture can be evolved purely by grain growth (l-3). In the previous paper (4), we showed by Monte Carlo (MC) simulation that the low energy grain boundary is stable with respect to the high energy grain boundary and that the latter tends to be replaced by the former with grain growth, which can result in preferred orientation. On the other hand, the grain boundary mobility, which depends on crystallographic orientation between the grains in contact, would have a similar effect.

The character of the grain boundary of the growing grain depends on orientations of the adjacent grains, which continues to change with grain growth. Therefore, it is improbable for the grains with a specific orientation to continue to have the high mobility boundary unless there exists a pre-existing texture. If there is a pre-existing texture and the grains with specific orientations continue to have the high mobility grain boundary, the grains will have an advantage in growth over the other grains. And the grains with such orientations will become dominant, leading to a texture. This type of grain growth would result in a texture change. Previously, Novikov (5) showed this type of texture change by com- puter simulation.

When grain growth takes place under the condition of anisotropic mobility, the fraction of the high or the low mobility boundary would change. For example, the high mobility boundary will move faster than the low mobility one. As a result the former would tend to disappear faster than the latter. In that case, the fraction of those grains with specific orientations, which make the low mobility boundary, will increase with grain growth and the preferred orientation can be developed from relatively ran- domly-oriented grains. In this case, the pre-existing texture would not be not essential for the devel- opment of texture by grain growth. In this paper, we will study this possibility by Monte Carlo (MC) simulation (6-8). The effect of mobiIity on oriented growth is also studied simultaneously with the effect of anisotropic grain boundary energy in textural evolution.

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Monte Carlo Simulation

The scheme for MC simulation is the same as that of the previous paper (4), which was based on the Potts model (6-8). The two dimensional triangular lattice of 150 by 150 sites was used. The orientation of each grain was represented by the integers from 1 to Q, which is 50 in this simulation. The grain boundary energy function is given by

E = -J C (Sss, - 1) ,I,,

(1)

where S,is one of the Q orientations on site i and CL is the Kronecker delta function. j is a positive constant which represents grain boundary energy. The sum is taken over all nearest neighbor sites. Re- orientation attempts of 150 by 150 are referred to 1 Monte Carlo step (MCS). The initial structure of simulation has 900 grains, which are of the uniform size and whose orientations are randomly chosen.

In order to implement the effect of anisotropic mobility, a parameter C was introduced to distinguish between type I and type II grains. If Si I C, the grain is type I whereas if Si > C, the grain is type II. In order to distinguish between type I and type II, the grains of type I will be shaded in the microstructure in the figures. We will use only two kinds of grain boundary mobility: low and high. The mobility of grain boundaries between type I grains is assumed to be either high or low compared with that of the other grain boundaries. In the first series, isotropic grain boundary energy is assumed in order to see the effect of anisotropic mobility separately while in the second series, the effect of anisotropic energy is also implemented.

In MC simulation, the mobility cannot be made higher than the normal mobility. Thus, the mobility anisotropy can be made by reducing the mobility of the specific grain boundary. Therefore, the overall growth rate in the simulated system of anisotropic mobility decreases compared with that of isotropic mobility. For example, in order to make the mobility of the grain boundary between type I grains 10 times lower than that of the other grain boundary, the mobility of the grain boundary between type I grains should be reduced by 10 times compared with the normal mobility. Reducing mobility by 10 times can be achieved by allowing only one out of 10 attempts when the randomly-selected site or the random atomic jump corresponds to the grain boundary between type I grains. The triple junction where two type I grains and one type II grain meet is also regarded as the grain boundary between type I grains.

Figures l(a) and l(b) show a microstructural evolution after 40 MCS and 100 MCS, respectively, for the condition that the mobility of the grain boundary between type I grains is a 10 times lower than that of the other grain boundaries. C is chosen to be 5, which means that 10% of the total grains were initially type I grains. The result shows that the fraction of type I grains increases with grain growth. The fraction increases from an initial 10% to 25%, 47%, 67%, 81% and 88% after 20 MCS, 40 MCS, 60 MCS, 80 MCS and 100 MCS, respectively.

As mentioned earlier, the growth advantage of the grains with specific orientations will result in preferred orientation. Preferred growth will be achieved by allowing the grain boundary of specific grains to continue to have higher mobility than the other grain boundaries. In order to give such a growth advantage to type I grains, the grain boundary between type I and type II grains as well as between type I grains is made to have the mobility a 10 times higher than that between type II grains. C is chosen to be 5. It should be noted that the mobility of the grain boundary between type I grains is made higher, which is different from the condition of Fig. 1. The microstructures after 100 MCS and 500 MCS are shown in Fig. 2(a) and 2(b), respectively. The fraction of type I grams increases from an initial 10% to lo%, 28%, 51%, 69% and 82% after 100 MCS, 200 MCS, 300 MCS, 400 MCS and 500

Vol. 37, No. 11 GRAIN GROWTH BEHAVIOR IN THE SYSTEM 1639

Figure 1. Microstructural evolution after (a) 40 MCS and (b) 100 MCS with the condition that the grain boundary between type I (shaded) grains has the mobility a 10 times lower than that of the other grain boundary. The fractions of shaded grains are 47% and 88%, respectively.

MCS, respectively. Besides, type I grains are much larger than type II grains with bimodal size distri- bution, which is typical of abnormal grain growth.

In a real polycrystal, the grain boundary has anisotropy in energy as well as in mobility. For exam- ple, the low angle grain boundary or the Cl boundary has low mobility and low energy. Thus, it would be worth examining both effects simultaneously. Both effects are considered in Fig. 3 and Fig. 4. In Fig. 3, the grain boundary between type I grains is made to have mobility a 10 times lower than that of the other grain boundaries. At the same time, its energy is made to be two-thirds of that of the other grain boundaries. C is chosen to be 5. The microstructures after 40 MCS and 100 MCS are shown in Fig. 3(a) and 3(lb), respectively. The fraction of type I grains increases from an initial 10% to 25%, 47%, 68%, 81% and 88% after 20 MCS, 40 MCS, 60 MCS, 80 MCS and 100 MCS, respectively.

In Fig. 4, it is assumed that the gram boundary between type I grains has low energy but has high mobility. The energy of the grain boundary between type I grains is two-thirds of the other grain boundaries but its mobility is 10 times faster than that of the other ones. C is chosen to be 20, which corresponds to 40% of the initial fraction of type I grains. The microstructures after 100 MCS and 500 MCS are shown in Fig. 4(a) and 4(b), respectively. The fraction of type I grains decreases from an initial 40% to 20%, 17%, 14%, 12% and 10% after 100 MCS, 200 MCS, 300 MCS, 400 MCS and 500 MCS, respectively.

Figure 2. Microstructural evolution (a) after 100 MCS and (b) after 500 MCS with the condition that the grain boundary between type I (shaded) grains and between type I and type II grains have the mobility a 10 times higher than that of the grain boundary between type II grains. The fractions of shaded grains are 10% and 82%, respectively.

1640 GRAIN GROWTH BEHAVIOR IN THE SYSTEM Vol. 37, No. 11

Figure 3. Microstructural evolution (a) after 40 MCS and (b) 100 MCS. The grain boundary between type I (shaded) grains has the energy two-thirds of and the mobility 10 times lower than that of the other grain boundaries. The fractions of shaded grains are 47% and 88%, respectively.

Discussion

Figure 1 indicates a strong tendency that the high mobility grain boundary disappears and that the fraction of the grains with low mobility increases with grain growth. The result means that when the grain boundary migrates with a high rate, it tends to disappear with grain growth. And with its disap- pearance, the grains that make such high mobility boundaries also disappear. As a result, the grains which makes the low mobility grain boundary would dominate after grain growth. It should be noted that the grain size of type I grains is bigger than that of type II grains even though the mobility of the grain boundary between type I grains is 10 times lower than that between type 11 grains.

In Fig. 2, the fraction of type I grains increases with grain growth even when the mobility of the grain boundary between type I grains is made higher than that between type II grains. The result is quite in contrast with that of Fig. 1. The main difference is in mobility between type I and type II grains. As a result, the grain boundary of type I grains is made to continue to have high mobility com- pared with that of type II grains. Type I grains have a growth advantage over type II grains. It should be noted that not only the fraction of type I grains increases but also their size is much larger than that

Figure 4. Microstructural evolution (a) after 100 MCS and (b) after 500 MCS with the initial fraction of type I (shaded) grains of 40%. The grain boundary between type I grains has the energy two-thirds of and the mobility a 10 times faster than that of the other grain boundaries. The fractions of shaded grains are 20% and lO%, respectively.

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of type II grains. Such an aspect of bimodal distribution in size is not marked in Fig. 1. Fig. 2(b) shows the typical microstructure of secondary recrystallization or abnormal grain growth. Abnormal growth of type I grains could be expected because they have a growth advantage over type II grains, which were initially 90% of the total grains. The microstructural feature of Fig. 2 showing abnormal grain growth accompanied by texture resembles the microstructure evolved during secondary recrystalliza- tion of the Fe-3%Si alloy, where the Goss texture ( 1 lO}<OOl> is accompanied (9,lO). Abnormal grain growth by this type of anisotropic mobility was reported by Rollett et al. (8) based on MC simulation.

Previously, we studied the effect of anisotropic grain boundary energy on grain growth and reported that the high energy grain boundary tends to be replaced by the low energy one with grain growth. This fact should be considered in understanding the results of Fig. 3 and Fig. 4, together with the effect of anisotropic mobility in Fig. 1. The grain boundary with low mobility or low energy tends to survive over the one with high mobility or high energy.

In Fig. 3, the grain boundary between type I grains has low mobility and low energy, both of which are favorable for the increase in the fraction of type I grains. As expected, the fraction of type I grains increases markedly over that of type II grains. The condition of low mobility and low energy is satis- fied by the low angle or the Xl grain boundary in a real polycrystal. Therefore, the result of Fig. 3 implies that the frequency of the low angle grain boundary or the Cl grain boundary will increase with grain growth.

The result of Fig. 3 is in agreement with the previous experimental observation in Fe-3%Si alloy by Shimizu and Harase (9) that the frequency of the Xl grain boundary was highest after primary recrys- tallization. The result is also in agreement with the previous experimental observation by Sursaeva and Shvindlerman (11) that the frequency of the low mobility boundaries increased during grain growth. The high frequency of the low angle or the Cl grain boundary can lead to the high fraction of the grains with similar orientation, which is a texture. Therefore, it is highly probable that grain growth in the presence of such anisotropic mobility can induce a textural evolution.

In Fig. 4, grain boundaries between type I grains has high mobility and low energy. The high mobil- ity and the low energy would be, respectively, unfavorable and favorable for dominant growth of type I grains. The result of Fig. 4 indicates that for conditions chosen in simulation, the mobility is the more dominant factor in microstructural evolution than the energy.

The condition of high mobility and low energy chosen in the simulation of Fig. 4 is satisfied by the high angle CSL boundary in the appropriate impurity range (12,13). In relation to this, Sursaeva and Shvindlerman (11) observed that after annealing of the 2-D aluminum foils, there were the high frac- tion of the low angle grain boundary, the lower fraction of the large angle grain boundary and only the isolated CSL grain boundary. The result of Fig. 4 agrees with this experimental observation. In some other reports (9,10,14), however, the frequency of the CSL boundary was high after recrystallization, whose result does not agree with that of Fig. 4. Such contradicting reports on the effect of the fre- quency of the CSL boundary on grain growth seem to be related to the dependence of mobility of the CSL boundary on the impurity level. Gottstein and Shvindlerman (13) reported that the orientation dependence o-f grain boundary mobility could only be observed in a small window of the impurity level. In this impurity level, the CSL boundary would have high mobility and low energy, whose con- dition is implemented in Fig. 4. In the other impurity level, the CSL boundary tends to have the same mobility as the other high angle boundary. In this case, the CSL boundary has normal mobility and low energy, which would result in the high frequency of the CSL boundary. This aspect was confirmed by MC simulation in our previous paper (4).

1642 GRAIN GROWTH BEHAVIOR IN THE SYSTEM Vol. 37, No. 11

Conclusion

It is shown by Monte Carlo simulation that the high mobility grain boundary tends to disappear and that as a result the grains sharing the low mobility boundary tend to be dominant with grain growth for isotropic grain boundary energy. It is also shown that the low mobility and low energy boundary such as Cl tends to be dominant with grain growth, which will lead to a textural evolution. When the gram boundary has low energy and high mobility, the grain boundary tends to disappear. The present results indicate that grain growth in the presence of anisotropic mobility can lead to a textural evolution from randomly-oriented grains.

Acknowledgments

This work is supported by Pohang Steel Company and by the Korean Science and Engineering Foun- dation through the Center for Interface Science and Engineering of Materials. The help in the computer program by Prof. O.J. Kwon at KyungPook National University is greatly appreciated.

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