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Anomalous overgrowth of converging dendrites during directional solidification
Journal of Crystal Growth 402 (2014) 210–214
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Anomalous overgrowth of converging dendrites during directional solidification Honglei Yu, Junjie Li, Xin Lin n, Lilin Wang, Weidong Huang State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, 543# Box, 127 Youyixi Road, Xi’an 710072, China
art ic l e i nf o
a b s t r a c t
Article history: Received 27 January 2014 Received in revised form 26 April 2014 Accepted 21 May 2014 Communicated by M. Rettenmayr Available online 11 June 2014
Competitive growth of converging dendrites in directional solidification was investigated by in situ observation in a succinonitrile–acetone alloy. The specific dendrite growth behavior was analyzed and compared with the results of phase field simulations. It is found that the growth of the well aligned grain boundary dendrite is retarded and the spacing between this dendrite and its immediate neighbors (λGB1) decreases continuously as the misaligned dendrites get to the grain boundary, one by one. The anomalous overgrowth only happens when the spacing λGB1 decreases to certain level. Under the same solidification condition, smaller initial primary spacing makes the anomalous overgrowth take place earlier and more frequently. & 2014 Elsevier B.V. All rights reserved.
Keywords: A1. Directional solidification A1. Crystal morphology A1. Dendrites A2. Growth from melt B1. Metals
1. Introduction Single crystal superalloy has excellent high temperature performance, which makes it the key material for the aero engine and gas turbine blades. In general, the single crystal structure results from the competitive growth of grains with dendrites in different crystallographic orientations during directional solidification. Walton and Chalmers [1] gave the first qualitative explanation for the competitive grain growth, and then Rappaz and Gandin [2] made a schematically summarization. Most of the previous theories are based on the difference in tip undercooling between the dendrites with different crystallographic orientations. It is pointed out that, the misaligned dendrite whose preferred crystallographic orientation 〈001〉 significantly deviates from the thermal gradient direction should have a larger tip undercooling than the well aligned one, which means that the tip position of misaligned dendrite should be lower than that of the well aligned one. Thus, for the converging growth, the well aligned dendrite will block the misaligned one and the grain boundary (GB) between the two converging grains will lie parallel to the well aligned one, since new dendrite arms cannot develop at the GB. While for the diverging growth, new dendrites developed from the well aligned grain will lead to the overgrowth of misaligned one. These explanations have been supported by some experiments [3,4]
n
Corresponding author. Tel.: þ 86 2988460510. E-mail address: [email protected] (X. Lin).
http://dx.doi.org/10.1016/j.jcrysgro.2014.05.016 0022-0248/& 2014 Elsevier B.V. All rights reserved.
and simulations [5,6], and have been accepted as the basic guide for single crystal preparation. However, some recent observations indicated that there are some different competition behaviors for the converging growth of dendrites. In nickel-based superalloy bicrystal experiments, Zhou et al. [7,8] found that the tip position of well aligned dendrite is not always higher than that of misaligned one, and the well aligned dendrite can also be blocked by the misaligned one. They hypothesized that solute interaction near the converging dendrite tips may be the proper reason for this anomalous overgrowth. In our previous work [9], by using phase field simulation, the effect of solute interaction on the growth behaviors of converging dendrites was clearly shown and a reasonable mechanism for the anomalous overgrowth was summarized. Solute interaction can induce a lag of well aligned GB dendrite and make the misaligned dendrite overgrow the well aligned one. However, there is no direct experimental evidence for solute interaction induced growth behavior found in simulations, e.g. the lag and recovery of the well aligned GB dendrite and the lateral motion of this dendrite towards its immediate neighbors. Previous experiments [7,8] were carried out using superalloy, in which only the final state of the competitive growth was found. The dynamic growth behavior and the details of anomalous overgrowth cannot be observed from these experiments. In present paper, an in situ observation of the converging dendritic growth has been carried out in a transparent alloy of succinonitrile–acetone (SCN–2 wt%Ace). The growth behavior of well aligned GB dendrite is compared with our previous phase field simulations. The mechanism and influence factor of anomalous overgrowth are further analyzed.
H. Yu et al. / Journal of Crystal Growth 402 (2014) 210–214
2. Experimental A bi-crystal thin sample was produced in the present work. The sample cell was made of two glass plates with the dimension of 100 30 0.17 mm3, which were glued together with a 100 μm gap between them. The inner dimension of the sample was approximately 80 20 0.1 mm3. It was filled with the transparent alloy SCN–2 wt%Ace. A capillary with cross section dimension of 1 0.05 mm 2 was used for the preparation of single-crystal seed. First, the capillary was filled with the same alloy as in the sample. Then, a single crystal was carefully selected in the capillary with the 〈001〉 direction exactly parallel to its axis. The orientation of the crystal is verified by examining its well-developed dendrite morphologies along the directions both parallel and perpendicular to the temperature gradient direction, while the latter is done by rotating the sample by 901. After this, two single-crystal seeds were cut from the capillary and were inserted into the bottom of the sample. The 〈001〉 direction of one seed was parallel to the sample axis, while the 〈001〉 direction of another seed deviated about 141 from the sample axis in a converging way. The bi-crystal structure was initiated from the two seeds. Directional solidification experiments were carried out on the Jackson–Hunt temperature gradient stage with the pulling velocity of V¼2 μm/s and V¼5 μm/s respectively. In each case, two repeated experiments were carried out, named Exp. I, Exp. II for V ¼2 μm/s and Exp. III, Exp. IV for V ¼5 μm/s respectively. The temperature gradient was kept constant (G ¼4 K/mm) for all the experiments. All solidification processes were carried out from planar solid–liquid interface at the same position in the sample, and the pulling distance L was set to be zero at the point where the first stable well aligned dendritic array formed after the initial dendritic competition from the planar interface. Optical microscope was used to get in situ images during the directional solidification process.
3. Results and discussion Typical microstructures at the late stage (t 4360 min) of Exp. I are shown in Fig. 1 (the video of Exp. I can be found in the supplementary materials). Supplementary material related to this article can be found online at http://dx.doi.org/10.1016/j.jcrysgro.2014.05.016. It can be seen that, the misaligned dendrite B1 is blocked by the well aligned dendrite A1 from t¼ 360 min to t ¼387 min. In the following the next misaligned dendrite B2 is also blocked, which is similar to the case of dendrite B1 and is not shown here. But the subsequent overgrowth behavior is opposite, i.e. the well aligned dendrite A1 is blocked by misaligned dendrite B3 from t¼ 420 min to t¼ 438 min. This is the first anomalous overgrowth occurred in this directional solidification process. Before this, all the misaligned dendrites are blocked by dendrite A1. However, dendrite B3 cannot overgrow dendrite A2 further and is finally blocked by dendrite A2, as shown in Fig. 1(g) (t¼447 min). And then, after a few times of regular overgrowth, the anomalous overgrowth occurs again just as the situation during t ¼420–438 min. In the other runs of experiments, the overall competition processes are similar to those described above. In the experiments of Zhou [7,8] and our previous phase field simulations [9], it was also found that the anomalous overgrowth occurs after several times of regular overgrowth. It can be found that, the anomalous overgrowth doesn’t occur suddenly, but is related with the growth behavior of GB dendrites. From Fig. 1, three points can be concluded. Firstly, the position of
211
misaligned dendrite tip is only slightly lower than that of well aligned dendrite tip. Some misaligned dendrites, e.g. dendrite B2 of Fig. 1(b) (circled in the figure), nearly catch up with the well aligned dendrites. Similar result has also been found in our previous phase field simulations [9]. Secondly, the growth of dendrite A1 is retarded as the misaligned dendrites get close to it, which is characterized by HGB1, i.e. the vertical distance between the tip of A1 and its well aligned neighbors. Third, the spacing between GB dendrite A1 and its adjacent well aligned dendrite A2 (named λGB1) becomes smaller during the anomalous overgrowth process. That is, as the misaligned dendrites get close to dendrite A1, it will move towards dendrite A2 laterally. The variations of HGB1 and λGB1 with pulling distance L, are shown in Fig. 2(a) for both V ¼2 μm/s and V¼ 5 μm/s. It can be seen that the spacing λGB1 gradually decreases with the movement of the sample. The small oscillation in λGB1 corresponds to the continuous impinging of two adjacent GB dendrites. There is also a certain oscillation of HGB1 with time. At the early stage (small L), HGB1 increases to some extent and then decreases nearly to the initial value, which means the tip lag of dendrite A1 induced by the interaction with misaligned dendrite cannot be maintained in this stage. The tip of dendrite A1 will almost recover to the same height as other well aligned dendrites when the adjacent misaligned dendrite drops behind largely and the next misaligned dendrite is still far from dendrite A1. After a certain time (approximately L 430 for V¼ 2 μm/s and L4 40 for V¼ 5 μm/s), HGB1 begins to increase gradually, which indicates the tip lag of dendrite A1 can keep and become larger and larger. Finally, the tip position of dendrite A1 will be lower than the misaligned dendritic tip, and the anomalous overgrowth occurs. The variation of HGB1 and λGB1 obtained in our previous phase field simulation [9] is also shown in Fig. 2(b). The simulation results are very similar to the experimental results, especially for the oscillation behaviors of HGB1 and λGB1. It is interesting to note that the significant lag of well aligned GB dendrite occurring in the late stage is related with the continuous decreasing of primary spacing (λGB1) in the well aligned dendrite array at GB. Fig. 3 shows the variation of the spacing λGB1 with pulling distance during directional solidification with V¼ 2 μm/s (Exp. I and Exp. II) and V ¼5 μm/s (Exp. III and Exp. IV). The positions where the well aligned dendrites are blocked by the misaligned ones are also marked by arrows in Fig. 3. With each pulling velocity, two different groups of dendrite spacing are obtained. This is understandable because of the wide allowable range under certain solidification condition with the effect of solidification history and process randomicity [10,11]. From Fig. 3(a), it can be seen that the initial primary spacing λGB1 in Exp. I is apparently smaller than that in Exp. II, and the pulling distance where the first general overgrowth occurs in Exp. I (L ¼37 mm) is shorter than that in Exp. II (L¼ 43 mm). The frequency of anomalous overgrowth in Exp. I is also larger than that in Exp. II. Similar phenomena are also observed under the condition of V¼5 μm/s, just as shown in Fig. 3(b). Actually, in our previous simulation [9], it has also been found that if a smaller initial value of λGB1 is given, the well aligned GB dendrite will be blocked earlier. The above results indicate that the smaller primary spacing λGB1 can accelerate the anomalous overgrowth. Moreover, it can be found that the pulling distance for the second anomalous overgrowth is shorter than that for the first one. This is due to that the primary spacing between dendrite A2 and dendrite A3 is also gradually decreasing as the misaligned dendrites get close to dendrite A1. Besides, because the length of our sample is finite, when the secondary anomalous overgrowth occurs, the solidification interface front approaches nearly to the top of the sample. The solute enrichment in this region may also have a certain effect on the large frequency of anomalous overgrowth.
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H. Yu et al. / Journal of Crystal Growth 402 (2014) 210–214
Fig. 1. Typical converging competitive growth behaviors in Exp. I, V ¼2 μm/s, G ¼ 4 K/mm.
We have also carried out experiments with higher pulling velocity (V ¼10 μm/s). However, the primary dendrite spacing decreases with the increasing pulling velocity, leading to the formation of two slices of dendrite array in perpendicular
direction of the sample cell. This results in a three dimensional dendrite competition and the introduction of the more complicate influent factors. Further investigation will be performed in detail in the near future. Nevertheless, the details during the competitive
H. Yu et al. / Journal of Crystal Growth 402 (2014) 210–214
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Fig. 2. Variations of the tip lag of well aligned GB dendrite (HGB1) and the primary spacing (λGB1) in the well aligned dendrite array at GB with pulling distance during the converging competitive growth, (a) experiment results, V ¼2 μm/s in Exp. I and V¼ 5 μm/s in Exp. III; (b) phase field simulation results, using a binary approximation to a nickel-based superalloy for G ¼ 60 K/mm, V ¼ 100 μm/s.
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Fig. 3. Variation of primary spacing λGB1 with pulling distance for different runs at (a) V ¼2 μm/s, and (b) V¼ 5 μm/s. The positions where anomalous overgrowth occurs are indicated by the arrows.
process of two dimensional converging dendrite arrays, including the lag and recovery of the well aligned GB dendrite, the oscillation and continuous decrease of spacing λGB1, also provide a further support to our previous phase field studies [9], i.e. solute interaction should be accounted for the anomalous overgrowth. In the schematic illustration of the Walton–Chalmers model for dendritic competitive growth [2,7], the lag of misaligned dendrite has been drawn significantly and is even comparable with the average primary dendrite spacing. The anomalous overgrowth seems to be impossible. The present results indicate that the lag of misaligned dendrite is not so large, which makes the misaligned dendrite be also able to overgrow the well aligned one. When two converging dendrites get close to each other, their solute fields will overlap. The solute interaction can retard the growth of well aligned GB dendrite. But the lag cannot persist when the spacing λGB1 is large, so the well aligned GB dendrite cannot be blocked in this stage. The solute interaction will also cause an asymmetric solute field on the two sides of well aligned GB dendrite, which results in a lateral motion of well aligned dendrite and a corresponding decease of λGB1. When the spacing λGB1 deceases to some extent, the lag of the well aligned GB dendrite will persist and then the anomalous overgrowth occurs.
solidification in a transparent alloy of SCN–2 wt%Ace. The detailed growth behaviors of well aligned GB dendrite is analyzed and compared with the results of phase field simulations. It is found that the solute interaction induced decrease of primary dendrite spacing is a key factor to the anomalous overgrowth. This can further induce a lag of well aligned GB dendrite and thus make the misaligned dendrite overgrow the well aligned one. With the smaller initial primary spacing, anomalous overgrowth occurs more frequently and earlier. These results show a reasonable consistent with our previous phase field simulations. The solute interaction between the adjacent dendrites at GB should be a main factor for the anomalous overgrowth of converging dendrites.
4. Conclusions
References
To sum up, the specific competition process of converging growth is clearly shown by the in situ observation of directional
Acknowledgments This work is supported by the National Basic Research Program of China (No. 2011CB610402), the National High Technology Research and Development Program of China (No. 2013AA031103), the National Natural Science Foundation of China (No. 51371151), China Postdoctoral Science Foundation (No. 013M542384) and the Doctoral Program of Higher Education (No. 20116102120018)
[1] D. Walton, B. Chalmers, The origin of the preferred orientation in the columnar zone of ingots, Trans. Metall. Soc. AIME 215 (1959) 447–456.
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[2] M. Rappaz, C.A. Gandin, Probabilistic modelling of microstructure formation in solidification processes, Acta Mater. 41 (1993) 345–360. [3] H. Esaka, Dendrite Growth and Spacing in Succinonitrile–acetone Alloys (Ph.D. thesis), EPFL, Lausanne, Switzerland, 1986. [4] N. D’Souza, M.G. Ardakani, A. Wagner, B.A. Shollock, M.J. Mclean, Morphological aspects of competitive grain growth during directional solidification of a nickel-base superalloy, Mater. Sci. 37 (2002) 481–487. [5] M.F. Zhu, C.P. Hong, A modified cellular automaton model for the simulation of dendritic growth in solidification of alloys, ISIJ Int. 41 (2011) 436–445. [6] H.B. Dong, P.D. Lee, Simulation of the columnar-to-equiaxed transition in directionally solidified Al–Cu alloys, Acta Mater. 53 (2005) 659–668.
[7] Y.Z. Zhou, A. Volek, N. Green, Mechanism of competitive grain growth in directional solidification of a nickel-base superalloy, Acta Mater. 56 (2008) 2631–2637. [8] Y.Z. Zhou, T. Jin, X.F. Sun, Structure evolution in directionally solidified bicrystals of nickel base superalloys, Acta Metall. Sin. 46 (2010) 1327–1334. [9] J.J. Li, Z.J. Wang, Y.Q. Wang, J.C. Wang, Phase-field study of competitive dendritic growth of converging 155 grains during directional solidification, Acta Mater. 60 (2012) 1478–1493. [10] W.D. Huang, X.G. Geng, Y.H. Zhou, Primary spacing selection of constrained dendritic growth, J. Cryst. Growth 134 (1993) 105–115. [11] S.H. Han, R. Trivedi, Primary spacing selection in directionally solidified alloys, Acta Metall. Mater. 42 (1994) 25–41.
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Anomalous overgrowth of converging dendrites during directional solidification Honglei Yu, Junjie Li, Xin Lin n, Lilin Wang, Weidong Huang State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, 543# Box, 127 Youyixi Road, Xi’an 710072, China
art ic l e i nf o
a b s t r a c t
Article history: Received 27 January 2014 Received in revised form 26 April 2014 Accepted 21 May 2014 Communicated by M. Rettenmayr Available online 11 June 2014
Competitive growth of converging dendrites in directional solidification was investigated by in situ observation in a succinonitrile–acetone alloy. The specific dendrite growth behavior was analyzed and compared with the results of phase field simulations. It is found that the growth of the well aligned grain boundary dendrite is retarded and the spacing between this dendrite and its immediate neighbors (λGB1) decreases continuously as the misaligned dendrites get to the grain boundary, one by one. The anomalous overgrowth only happens when the spacing λGB1 decreases to certain level. Under the same solidification condition, smaller initial primary spacing makes the anomalous overgrowth take place earlier and more frequently. & 2014 Elsevier B.V. All rights reserved.
Keywords: A1. Directional solidification A1. Crystal morphology A1. Dendrites A2. Growth from melt B1. Metals
1. Introduction Single crystal superalloy has excellent high temperature performance, which makes it the key material for the aero engine and gas turbine blades. In general, the single crystal structure results from the competitive growth of grains with dendrites in different crystallographic orientations during directional solidification. Walton and Chalmers [1] gave the first qualitative explanation for the competitive grain growth, and then Rappaz and Gandin [2] made a schematically summarization. Most of the previous theories are based on the difference in tip undercooling between the dendrites with different crystallographic orientations. It is pointed out that, the misaligned dendrite whose preferred crystallographic orientation 〈001〉 significantly deviates from the thermal gradient direction should have a larger tip undercooling than the well aligned one, which means that the tip position of misaligned dendrite should be lower than that of the well aligned one. Thus, for the converging growth, the well aligned dendrite will block the misaligned one and the grain boundary (GB) between the two converging grains will lie parallel to the well aligned one, since new dendrite arms cannot develop at the GB. While for the diverging growth, new dendrites developed from the well aligned grain will lead to the overgrowth of misaligned one. These explanations have been supported by some experiments [3,4]
n
Corresponding author. Tel.: þ 86 2988460510. E-mail address: [email protected] (X. Lin).
http://dx.doi.org/10.1016/j.jcrysgro.2014.05.016 0022-0248/& 2014 Elsevier B.V. All rights reserved.
and simulations [5,6], and have been accepted as the basic guide for single crystal preparation. However, some recent observations indicated that there are some different competition behaviors for the converging growth of dendrites. In nickel-based superalloy bicrystal experiments, Zhou et al. [7,8] found that the tip position of well aligned dendrite is not always higher than that of misaligned one, and the well aligned dendrite can also be blocked by the misaligned one. They hypothesized that solute interaction near the converging dendrite tips may be the proper reason for this anomalous overgrowth. In our previous work [9], by using phase field simulation, the effect of solute interaction on the growth behaviors of converging dendrites was clearly shown and a reasonable mechanism for the anomalous overgrowth was summarized. Solute interaction can induce a lag of well aligned GB dendrite and make the misaligned dendrite overgrow the well aligned one. However, there is no direct experimental evidence for solute interaction induced growth behavior found in simulations, e.g. the lag and recovery of the well aligned GB dendrite and the lateral motion of this dendrite towards its immediate neighbors. Previous experiments [7,8] were carried out using superalloy, in which only the final state of the competitive growth was found. The dynamic growth behavior and the details of anomalous overgrowth cannot be observed from these experiments. In present paper, an in situ observation of the converging dendritic growth has been carried out in a transparent alloy of succinonitrile–acetone (SCN–2 wt%Ace). The growth behavior of well aligned GB dendrite is compared with our previous phase field simulations. The mechanism and influence factor of anomalous overgrowth are further analyzed.
H. Yu et al. / Journal of Crystal Growth 402 (2014) 210–214
2. Experimental A bi-crystal thin sample was produced in the present work. The sample cell was made of two glass plates with the dimension of 100 30 0.17 mm3, which were glued together with a 100 μm gap between them. The inner dimension of the sample was approximately 80 20 0.1 mm3. It was filled with the transparent alloy SCN–2 wt%Ace. A capillary with cross section dimension of 1 0.05 mm 2 was used for the preparation of single-crystal seed. First, the capillary was filled with the same alloy as in the sample. Then, a single crystal was carefully selected in the capillary with the 〈001〉 direction exactly parallel to its axis. The orientation of the crystal is verified by examining its well-developed dendrite morphologies along the directions both parallel and perpendicular to the temperature gradient direction, while the latter is done by rotating the sample by 901. After this, two single-crystal seeds were cut from the capillary and were inserted into the bottom of the sample. The 〈001〉 direction of one seed was parallel to the sample axis, while the 〈001〉 direction of another seed deviated about 141 from the sample axis in a converging way. The bi-crystal structure was initiated from the two seeds. Directional solidification experiments were carried out on the Jackson–Hunt temperature gradient stage with the pulling velocity of V¼2 μm/s and V¼5 μm/s respectively. In each case, two repeated experiments were carried out, named Exp. I, Exp. II for V ¼2 μm/s and Exp. III, Exp. IV for V ¼5 μm/s respectively. The temperature gradient was kept constant (G ¼4 K/mm) for all the experiments. All solidification processes were carried out from planar solid–liquid interface at the same position in the sample, and the pulling distance L was set to be zero at the point where the first stable well aligned dendritic array formed after the initial dendritic competition from the planar interface. Optical microscope was used to get in situ images during the directional solidification process.
3. Results and discussion Typical microstructures at the late stage (t 4360 min) of Exp. I are shown in Fig. 1 (the video of Exp. I can be found in the supplementary materials). Supplementary material related to this article can be found online at http://dx.doi.org/10.1016/j.jcrysgro.2014.05.016. It can be seen that, the misaligned dendrite B1 is blocked by the well aligned dendrite A1 from t¼ 360 min to t ¼387 min. In the following the next misaligned dendrite B2 is also blocked, which is similar to the case of dendrite B1 and is not shown here. But the subsequent overgrowth behavior is opposite, i.e. the well aligned dendrite A1 is blocked by misaligned dendrite B3 from t¼ 420 min to t¼ 438 min. This is the first anomalous overgrowth occurred in this directional solidification process. Before this, all the misaligned dendrites are blocked by dendrite A1. However, dendrite B3 cannot overgrow dendrite A2 further and is finally blocked by dendrite A2, as shown in Fig. 1(g) (t¼447 min). And then, after a few times of regular overgrowth, the anomalous overgrowth occurs again just as the situation during t ¼420–438 min. In the other runs of experiments, the overall competition processes are similar to those described above. In the experiments of Zhou [7,8] and our previous phase field simulations [9], it was also found that the anomalous overgrowth occurs after several times of regular overgrowth. It can be found that, the anomalous overgrowth doesn’t occur suddenly, but is related with the growth behavior of GB dendrites. From Fig. 1, three points can be concluded. Firstly, the position of
211
misaligned dendrite tip is only slightly lower than that of well aligned dendrite tip. Some misaligned dendrites, e.g. dendrite B2 of Fig. 1(b) (circled in the figure), nearly catch up with the well aligned dendrites. Similar result has also been found in our previous phase field simulations [9]. Secondly, the growth of dendrite A1 is retarded as the misaligned dendrites get close to it, which is characterized by HGB1, i.e. the vertical distance between the tip of A1 and its well aligned neighbors. Third, the spacing between GB dendrite A1 and its adjacent well aligned dendrite A2 (named λGB1) becomes smaller during the anomalous overgrowth process. That is, as the misaligned dendrites get close to dendrite A1, it will move towards dendrite A2 laterally. The variations of HGB1 and λGB1 with pulling distance L, are shown in Fig. 2(a) for both V ¼2 μm/s and V¼ 5 μm/s. It can be seen that the spacing λGB1 gradually decreases with the movement of the sample. The small oscillation in λGB1 corresponds to the continuous impinging of two adjacent GB dendrites. There is also a certain oscillation of HGB1 with time. At the early stage (small L), HGB1 increases to some extent and then decreases nearly to the initial value, which means the tip lag of dendrite A1 induced by the interaction with misaligned dendrite cannot be maintained in this stage. The tip of dendrite A1 will almost recover to the same height as other well aligned dendrites when the adjacent misaligned dendrite drops behind largely and the next misaligned dendrite is still far from dendrite A1. After a certain time (approximately L 430 for V¼ 2 μm/s and L4 40 for V¼ 5 μm/s), HGB1 begins to increase gradually, which indicates the tip lag of dendrite A1 can keep and become larger and larger. Finally, the tip position of dendrite A1 will be lower than the misaligned dendritic tip, and the anomalous overgrowth occurs. The variation of HGB1 and λGB1 obtained in our previous phase field simulation [9] is also shown in Fig. 2(b). The simulation results are very similar to the experimental results, especially for the oscillation behaviors of HGB1 and λGB1. It is interesting to note that the significant lag of well aligned GB dendrite occurring in the late stage is related with the continuous decreasing of primary spacing (λGB1) in the well aligned dendrite array at GB. Fig. 3 shows the variation of the spacing λGB1 with pulling distance during directional solidification with V¼ 2 μm/s (Exp. I and Exp. II) and V ¼5 μm/s (Exp. III and Exp. IV). The positions where the well aligned dendrites are blocked by the misaligned ones are also marked by arrows in Fig. 3. With each pulling velocity, two different groups of dendrite spacing are obtained. This is understandable because of the wide allowable range under certain solidification condition with the effect of solidification history and process randomicity [10,11]. From Fig. 3(a), it can be seen that the initial primary spacing λGB1 in Exp. I is apparently smaller than that in Exp. II, and the pulling distance where the first general overgrowth occurs in Exp. I (L ¼37 mm) is shorter than that in Exp. II (L¼ 43 mm). The frequency of anomalous overgrowth in Exp. I is also larger than that in Exp. II. Similar phenomena are also observed under the condition of V¼5 μm/s, just as shown in Fig. 3(b). Actually, in our previous simulation [9], it has also been found that if a smaller initial value of λGB1 is given, the well aligned GB dendrite will be blocked earlier. The above results indicate that the smaller primary spacing λGB1 can accelerate the anomalous overgrowth. Moreover, it can be found that the pulling distance for the second anomalous overgrowth is shorter than that for the first one. This is due to that the primary spacing between dendrite A2 and dendrite A3 is also gradually decreasing as the misaligned dendrites get close to dendrite A1. Besides, because the length of our sample is finite, when the secondary anomalous overgrowth occurs, the solidification interface front approaches nearly to the top of the sample. The solute enrichment in this region may also have a certain effect on the large frequency of anomalous overgrowth.
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Fig. 1. Typical converging competitive growth behaviors in Exp. I, V ¼2 μm/s, G ¼ 4 K/mm.
We have also carried out experiments with higher pulling velocity (V ¼10 μm/s). However, the primary dendrite spacing decreases with the increasing pulling velocity, leading to the formation of two slices of dendrite array in perpendicular
direction of the sample cell. This results in a three dimensional dendrite competition and the introduction of the more complicate influent factors. Further investigation will be performed in detail in the near future. Nevertheless, the details during the competitive
H. Yu et al. / Journal of Crystal Growth 402 (2014) 210–214
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Fig. 2. Variations of the tip lag of well aligned GB dendrite (HGB1) and the primary spacing (λGB1) in the well aligned dendrite array at GB with pulling distance during the converging competitive growth, (a) experiment results, V ¼2 μm/s in Exp. I and V¼ 5 μm/s in Exp. III; (b) phase field simulation results, using a binary approximation to a nickel-based superalloy for G ¼ 60 K/mm, V ¼ 100 μm/s.
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Fig. 3. Variation of primary spacing λGB1 with pulling distance for different runs at (a) V ¼2 μm/s, and (b) V¼ 5 μm/s. The positions where anomalous overgrowth occurs are indicated by the arrows.
process of two dimensional converging dendrite arrays, including the lag and recovery of the well aligned GB dendrite, the oscillation and continuous decrease of spacing λGB1, also provide a further support to our previous phase field studies [9], i.e. solute interaction should be accounted for the anomalous overgrowth. In the schematic illustration of the Walton–Chalmers model for dendritic competitive growth [2,7], the lag of misaligned dendrite has been drawn significantly and is even comparable with the average primary dendrite spacing. The anomalous overgrowth seems to be impossible. The present results indicate that the lag of misaligned dendrite is not so large, which makes the misaligned dendrite be also able to overgrow the well aligned one. When two converging dendrites get close to each other, their solute fields will overlap. The solute interaction can retard the growth of well aligned GB dendrite. But the lag cannot persist when the spacing λGB1 is large, so the well aligned GB dendrite cannot be blocked in this stage. The solute interaction will also cause an asymmetric solute field on the two sides of well aligned GB dendrite, which results in a lateral motion of well aligned dendrite and a corresponding decease of λGB1. When the spacing λGB1 deceases to some extent, the lag of the well aligned GB dendrite will persist and then the anomalous overgrowth occurs.
solidification in a transparent alloy of SCN–2 wt%Ace. The detailed growth behaviors of well aligned GB dendrite is analyzed and compared with the results of phase field simulations. It is found that the solute interaction induced decrease of primary dendrite spacing is a key factor to the anomalous overgrowth. This can further induce a lag of well aligned GB dendrite and thus make the misaligned dendrite overgrow the well aligned one. With the smaller initial primary spacing, anomalous overgrowth occurs more frequently and earlier. These results show a reasonable consistent with our previous phase field simulations. The solute interaction between the adjacent dendrites at GB should be a main factor for the anomalous overgrowth of converging dendrites.
4. Conclusions
References
To sum up, the specific competition process of converging growth is clearly shown by the in situ observation of directional
Acknowledgments This work is supported by the National Basic Research Program of China (No. 2011CB610402), the National High Technology Research and Development Program of China (No. 2013AA031103), the National Natural Science Foundation of China (No. 51371151), China Postdoctoral Science Foundation (No. 013M542384) and the Doctoral Program of Higher Education (No. 20116102120018)
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