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Mechanism of competitive grain growth in directional solidification of a nickel-base superalloy
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Acta Materialia 56 (2008) 2631–2637 www.elsevier.com/locate/actamat
Mechanism of competitive grain growth in directional solidification of a nickel-base superalloy Y.Z. Zhou a, A. Volek b, N.R. Green a,* a
School of Engineering, Metallurgy and Materials, The University of Birmingham, Edgbaston, Birmingham B15 2TT, UK b Diehl Stiftung & Co. KG, Stephanstrasse 49, 90478 Nu¨rnberg, Germany Received 22 May 2007; received in revised form 12 January 2008; accepted 2 February 2008 Available online 17 March 2008
Abstract The structure evolution of bicrystal (BC) samples during directional solidification (DS) was explored in an attempt to understand the mechanism of competitive grain growth. It was found that in the case of diverging dendrites the favorably oriented grain overgrows the misaligned grain. However, in the case of converging dendrites the result differs from the prediction of the generally accepted model for competitive grain growth. First, the unfavorably oriented dendrites are able to overgrow the favorably oriented dendrites. Second, the misaligned grain overgrows the favorably oriented grain by blocking the dendrites of the favorably oriented grain at the grain boundary. Based on the experimental results, the process by which a favored h0 0 1i texture is developed during DS process of a nickel-base superalloy is illustrated. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Grain growth; Theory; Directional solidification; Nickel alloys
1. Introduction Directional solidification (DS) has been widely used to produce turbine blades of Ni-base superalloys. A preferred crystallographic orientation is produced in the DS casting due to the anisotropic growth rates of dendrites associated with grains of different orientations [1]. Previous studies [2– 5] on nickel-base superalloys have confirmed the fast-growing dendritic orientation to be h0 0 1i. The range of orientations produced in the DS process depends directly on the efficiency of the competitive grain overgrowth. The generally accepted model for competitive grain growth proposed by Walton and Chalmers [1] is based on the difference in undercooling of favorably and unfavorably oriented dendrites with respect to the thermal gradient. Rappaz et al. [6,7] schematically summarized the Walton and Chalmers model (Fig. 1). Grains A1 and A2 are *
Corresponding author. Tel.: +44 (0) 121 414 5207; fax: +44 (0) 121 414 5232. E-mail address: [email protected] (N.R. Green).
favorably oriented. Grain B is unfavorably oriented and the h0 0 1i direction has a misorientation, h, with respect to the heat flow direction. To keep up with the more favorably oriented neighbors, grain B grows at a greater undercooling. In the case of diverging dendrites (the two grains on the right of Fig. 1), development of new dendrites from grain A2 can lead to overgrowth of grain B and the GB is thus inclined. In the case of converging dendrites (the two grains on the left of Fig. 1), the dendrite tips in grain B impinge upon the side of grain A1 at the GB and are stopped. Since grain A1 does not develop new dendrites at the GB and the dendrites in grain B cannot overgrow the dendrites in grain A1, the GB lies parallel to the dendrites in grain A1. In situ observations of the dendritic solidification of transparent organic analogs in Ref. [8] had the same result as described by Fig. 1. Three video sequences from Ref. [8] were shown in Ref. [7]. The in situ experiment was carried out on the organic film with one primary dendrite arm spacing (k1) thickness so that the microstructure evolution could be observed easily. However, because the solidification
1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.02.022
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Fig. 1. Schematic illustration of the Walton and Chalmers model for competitive grain growth [6,7]. Grain A and B are favorably and unfavorably oriented, respectively.
conditions in the volume materials are different from those in the film materials, it is uncertain whether the microstructure evolution in the volume materials is the same as that in thin films of the material. In a recent study [9], bicrystal (BC) volume samples with diverging and converging dendrites were produced to study the mechanism of competitive grain growth. It was reported that the GB planes lay parallel to the h0 0 1i directions in the favorably oriented grains in the BC samples. Fig. 2 schematically summarizes the results in Ref. [9]. In the case of the diverging dendrites (Fig. 2a), the GB plane lying parallel to the h0 0 1i growth direction of grain A indicated new primary (tertiary) dendrites could not develop from grain A at the GB. The result differed from the Walton and Chalmers model. In the case of converging dendrites (Fig. 2b), the result in Ref. [9] was the same as the prediction of the Walton and Chalmers model. Grain seeding is often used in single-crystal (SC) casting, whereby a seed is partially melted-back during the thermal soaking period of the mold prior to casting. It was reported [10,11] that upon initiation of withdrawal there is copious nucleation of crystals with random orientation distributed Growth direction GB plane
GB plane 13˚
7˚
13˚
33˚
<001>
<001>
A
B
7˚
20˚
<001>
<001>
A
Fig. 3. Schematic diagram showing the structure evolution in the SC casting initiated by the SC seed in Refs. [10,11]. Nucleation of crystals with random orientation occurs uniformly around the perimeter of the seed at the start of the casting process (time t0). In the following growth process (time t1), the stray grains only survive and expand transversely on the side of the seed where the primary dendrites of the seed diverge from the mold wall.
uniformly around the perimeter of the seed at the meltback interface. In the following growth process [10,11], stray grains only survived and expanded transversely on one side of the seed. The side of the seed where the primary dendrites of the seed diverged from the mold wall was where stray grains grew; where the dendrites converged on the mold wall the stray grains were overgrown by the seed crystal irrespective of their orientation (Fig. 3). The Walton and Chalmers model can explain why the stray grains survive and expand transversely on the diverging side, but it cannot explain why stray grains better aligned to the withdrawal direction and thermal gradient were overgrown by the misaligned seed on the converging side. According to the Walton and Chalmers model, these well-aligned stray grains should not be overgrown by the misaligned seed crystal. Similar to the experiments in Ref. [9], BC volume samples were produced to study the mechanism of competitive grain growth in the present work. The correlation of the grain overgrowth with dendrite formation or dendrite blocking was shown here so that the present results could be critically compared with the Walton and Chalmers model. In the case of diverging dendrites, our results are well in accordance to the Walton and Chalmers model. However, in the case of converging dendrites, our results do not support it. Based on the experimental results in the present work, the formation of h0 0 1i texture during DS process of a nickel-base superalloy is illustrated.
B
Divergence
Convergence
a
b
Fig. 2. Schematic diagram showing the experimental results of the BC casting samples in Ref. [9]. The GB plane is parallel to the h0 0 1i direction of the favorably oriented grain A in both cases of diverging and converging dendrites.
2. Experiments 2.1. Materials and arrangement of seeds The compositions of the materials used in the present work are listed in Table 1.
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Table 1 Nominal compositions of alloys as used in the experiments (in wt.%) Alloy
Cr
Co
Mo
W
Al
Ti
Ta
B
Zr
C
Ni
IN792 PWA1483
12.5 12.2
8.8 9.0
1.8 1.9
4.0 3.8
3.4 3.6
3.9 4.2
3.9 5.0
0.014 0
0.017 0
0.08 0.07
Balance Balance
SC seeds from superalloy PWA1483 were used to initiate the structure development in the BC casting process. In previous work [12], it has been reported that PWA1483 seeds do not influence the nominal composition of IN792 after casting since PWA1483 is the SC equivalent of IN792, having almost the same composition except the minor elements B and Zr. To keep both h0 0 1i directions in the BC samples on the same plane, the SC seeds were cut from the same SC plate. Each seed was cut into two halves along the sample axis. Subsequently, the seeds were arranged in such a way that the samples with diverging or converging dendrites were produced. Seed A was always oriented with the h0 0 1i direction parallel to the macroscopic growth direction, while the h0 0 1i direction in seed B had a misorientation from the growth direction and the misorientation was varied in the experiments. hA and hB were used to describe the misorientation of h0 0 1i direction from the sample axis in seed A and B, respectively. The details of hA and hB in the experiments are listed in Table 2. 2.2. DS casting experiments DS experiments were carried out using conventional Bridgman high rate solidification (HRS) technique in a vacuum environment. A pure alumina tube mounted on a water-cooled copper chill plate was used as mold. The SC seeds with 2025 mm length were placed in the bottom of the mold to control the orientations of casting samples. The mold temperature was 1500 °C in the experiments. At this temperature, the seeds in the mold were partially molten and the solid/liquid interface was determined as the start of the DS process. The alloy of IN792 was heated to 1550 °C and kept at temperature for 5 min. Afterwards the temperature was dropped to the casting temperature (1500 °C) and the melt poured into the preheated mold. BC casting samples with 10 mm diameter and 150 mm length were directionally solidified at a withdrawal speed of 1.67 105 m s1 (i.e. 1 mm min1). Table 2 Structural characteristics and casting method of the BC samples Experiments
Seed disposition
hA (°)
hB (°)
Casting method
Exp. Exp. Exp. Exp. Exp. Exp. Exp. Exp. Exp.
Divergence Divergence Divergence Convergence Convergence Convergence Convergence Divergence Convergence
0 0 0 0 0 0 0 0 0
9 13 20 10 19 23 30 10 10
HRS HRS HRS HRS HRS HRS HRS LMC LMC
1 2 3 4 5 6 7 8 9
Quenched DS experiments were performed using the liquid metal cooling (LMC) technique. The alumina mold was mounted on a steel chill plate. As with the above HRS experiments, SC seeds were placed in the bottom of the mold to control the orientations of the castings produced. The BC samples with diameter 12 mm were directionally solidified into a tin bath for a height of 50 mm at a withdrawal speed of 1.67 105 m s1 (i.e. 1 mm min1) and then rapidly quenched into the tin bath at a withdrawal speed of 2 103 m s1 (i.e. 120 mm min1), thereby freezing the microstructure of solidification front. 2.3. Sample examination Macroetching was employed to determine the positions of the grain overgrowth and the start of the DS process (Fig. 4a). The misorientation of the GB plane from the sample axis (hGB) was determined by, tan hGB = R/L, where R is the sample radius and L is the distance from the start to the position of grain overgrowth (Fig. 4b). hGB is defined to be positive when the GB plane is inclined in such a way that the favorably oriented grain A overgrows the misaligned grain B. In contrast, hGB is defined to be negative when the GB plane is inclined in such a way that the misaligned grain B overgrows the favorably
(b)
Growth direction Cut
Cut Sample axis
Overgrowth
R
GB plane θ GB
L Grain B
Grain A Start Seed B
Seed A
tg θGB = R / L Fig. 4. Macroscopic image of a BC sample with converging dendrites after macroetching (a) and schematic diagram showing the determination of the misorientation (hGB) of the GB plane from the sample axis (b). The positions of the grain overgrowth and start of the DS process could be determined after macroetching. hGB is calculated from tan hGB = R/L, where R is the sample radius and L is the distance from the start to the position of grain overgrowth. Subsequently, the sample was cut along the sample axis to show the microstructure.
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oriented grain A. Subsequently, the BC samples were cut along the sample axis to show the microstructures. hA, hB and k1 were examined by optical metallography on etched samples, using an image analysis system with OPTIMAS 6.2 software. k1 was also determined on the etched samples cut perpendicular to the growth direction at a height 50 mm from the chill end. In the LMC samples quenched into tin, there is a transition in secondary dendrite arm spacing (k2) from the quenched liquid to the DS structure at the solidification front. The change of k2 along the dendrite trunk was determined on etched samples. 3. Results k1 is measured to be 265 lm in grain A (hA = 0°) and k1 is 238 lm in grain B with maximum misorientation (hB = 30°). 3.1. HRS BC samples with diverging dendrites Fig. 5a shows the optical metallographic microstructure of a HRS BC sample with diverging dendrites. The GB is inclined in such a way that grain A overgrows grain B. The overgrowth position is shown in the figure. New dendrites developed from grains A and B at the GB and the gap between the diverging grains was filled by these new dendrites. Depending on the development of new dendrites, grain A overgrew grain B. The dependence of hGB on (hB hA) in the case of diverging dendrites is summarized in Fig. 5b. The values
of hGB are positive, showing grain A always overgrew grain B in this geometric disposition. Furthermore, the rate at which grain A overgrew grain B increased in near linear proportion with increasing (hB hA). The result is in accordance to the Walton and Chalmers model and the experimental result as shown in Fig. 3, while it is different from the result as shown in Fig. 2a. As mentioned in the introduction, in Fig. 2a alignment of the GB plane parallel to the favorably oriented dendrites means that new dendrites are not able to develop from grain A at the GB. Subsequently, the gap between the diverging grains is filled by new dendrites developed from grain B only. This result can be attributed to the geometrical disposition of the dendrite trunks. In Fig. 2a, since the secondary dendrites in grain A are undeveloped towards the GB gap because their orientation is less aligned with the temperature gradient, new dendrites are hard to develop from grain A in the GB gap (note the dendrite morphology shown in Fig. 2). In contrast, the secondary dendrites in grain B are more developed towards the GB gap because their orientation is more aligned with the temperature gradient; new dendrites are therefore easy to develop from grain B in the GB gap. The result, as shown in Fig. 2a, may not be essentially contradictory to the present results and the Walton and Chalmers model, but favorably oriented dendrites with a certain misorientation appear to be necessary for such a result. Since the inclination of dendrite trunks is beyond such condition in the present work (hA = 0°) new dendrites are able to develop from grain A. Consequently, the GB plane is not parallel to the h0 0 1i direction in grain A here.
(b) 7 Exp. 3
6 Exp. 2
5
Slope 1:3
4
A overgrows B.
Exp. 1
3 8
10
12
14
16
18
20
θ B – θA (°)
Fig. 5. (a) Optical micrograph showing the microstructure in a HRS BC sample with diverging dendrites, and (b) dependence of hGB on (hB hA) in the HRS BC samples with diverging dendrites. hGB are positive in the figure, which means the favorably oriented grain A overgrows the misaligned grain B.
-1
GB misorientation, θGB (°)
GB misorientation, θGB (°)
8
(b) -2 -3
Exp. 7
Exp. 4
-4
Exp. 6 Exp. 5
-5 -6
B overgrows A. 10
15
20
25
30
θ B – θA (°)
Fig. 6. (a) Optical micrograph showing the microstructure in a HRS BC sample with converging dendrites, and (b) dependence of hGB on (hB hA) in the HRS BC samples with converging dendrites. hGB are negative in the figure, the negative value is employed to reflect the misaligned grain B overgrows the favorably oriented grain A.
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3.2. HRS BC samples with converging dendrites
3.3. LMC BC samples
Fig. 4a shows a macroscopic image of a HRS BC sample with converging dendrites. The detailed GB structure is shown in Fig. 6a. The result differs significantly from the predictions of the Walton and Chalmers model. Firstly, the favorably oriented grain A was overgrown by the unfavorably oriented grain B as shown in Figs. 4a and 6a. Secondly, the dendrites in grain A were blocked by the dendrites in grain B at the GB as marked by short white arrows in Fig. 6a. In line with the Walton and Chalmers model new dendrites were hard to develop from grains A or B at the GB in our experiments. It should be noted that the primary dendrites in grain B were also blocked at the GB by the dendrites in grain A, examples of which are marked by short black arrows in Fig. 6a, and more dendrites in grain B are blocked at the GB. The dependence of hGB on (hB hA) in the case of converging dendrites is presented in Fig. 6b. The values of hGB all are negative, which indicates that grain B always overgrew grain A in this geometric disposition. The present result does not agree with the Walton and Chalmers model and the result is as shown in Fig. 2b, while it is well in accordance to the result shown in Fig. 3. As pointed out in the introduction, the Walton and Chalmers model contains two conclusions: (a) new dendrites do not develop from grain A at the GB; and (b) the dendrites in grain A cannot be blocked by the dendrites of grain B. The former conclusion is in accordance with the present result, while the latter is in contradiction. However, to get the result as shown in Figs. 3 and 6, it is inevitable that the dendrites in grain A must be blocked by the dendrites of grain B.
The structure evolution in the LMC BC samples (Exp. 8 and 9) are the same as that in the HRS BC samples, i.e. in the sample with diverging dendrites (Exp. 8) the GB is inclined from grain A to grain B depending on the development of new dendrites from grain A, while the GB is inclined from grain B to grain A due to the blocking of the favorably oriented dendrites at the GB in the sample with converging dendrites (Exp. 9). The result indicates the casting method does not change the behavior of grain overgrowth. Fig. 7a shows the quenched liquidus interface. k2 varies from the quenched liquid to the DS structure at the solidification front. The approximate position of the liquidus interface is marked by dashed line according to the transition in k2. Grains A and B show a near horizontal interface with maximum slope at the mold wall of 4°. The detailed morphology of the converging dendrites in the mushy zone is presented in Fig. 7b. The dendrites in grain A are not able to develop longer secondary arms (Pk1) towards grain B in the whole mushy zone and there is no dendrite development at the GB. The same result was reported in Refs. [9,13]. The positions of the dendrite tips at the GB region in Exp. 9 were determined according to the transition in k2. Fig. 8 shows the dependence of k2 on solidified length at the solidification front. k2 rapidly increased from the quenched liquid to the DS structure and we assume the primary dendrite tips were located at the position where k2 began to increase. It is well known that the position of the development of the first secondary dendrite is behind the primary dendrite tip. The inferred positions of the pri-
Fig. 7. Optical micrographs showing the quenched liquidus interface (a) and the detailed morphology of the converging dendrites in the mushy zone (b) in Exp. 9. Grains A and B show a near horizontal interface with maximum slope at the mold wall of 4° in (a). The dendrites in grain A are not able to develop longer secondary arms (Pk1) towards grain B and no dendrite development can be observed at the GB in (b).
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behind dendrite b2, which means in Fig. 8a that dendrite b2 may be ahead of dendrite a1 after dendrite b1 is blocked by dendrite a1 (i.e. the structure as shown by Fig. 8b). A similar experiment as Exp. 9 was carried out in superalloy CMSX-4 in Ref. [13], i.e. CMSX-4 BC castings with converging dendrites (the unfavorably oriented dendrites with 5–7° h0 0 1i misorientation) were directionally solidified and quenched to reveal the dendrite morphology. Although not directly described, the same result as that shown in Fig. 8a can be obtained by determining the change in k2 from the figures presented in Ref. [13], i.e. the GB dendrites are behind their immediate neighbors. 4. Discussion 4.1. Overgrowth of diverging grains
Fig. 8. Dependence of k2 on the solidified length at the solidification front and schematic diagram showing the correlation of the determined dendrites in the position. k2 rapidly increases from the quenched liquid to the DS structure and the dendrite tips are assumed to be located at the positions where k2 begins to increase. Dendrites a1 and b1 are always behind dendrite a2 and b2; and dendrite a2 is always ahead of dendrite b2. Dendrite a1 is ahead of dendrite b1 in (a), while dendrite a1 is behind dendrite b1 in (b).
The results in the samples with diverging dendrites are in accordance to the Walton and Chalmers model. As shown in Fig. 1 (the two grains on the right), the gap between diverging grains is filled by new dendrites developed from grain A2 and B. Since the new dendrites develop from the base of the gap, the development of new dendrites is independent of the undercooling difference of grain A2 and B. Grain A2 expands transversely when a new dendrite develops from it at the GB. However, grain B does not expand transversely when a new dendrite develops from it at the GB. Consequently, grain A2 overgrows grain B depending on the rate of development of new dendrites from grain A2 at the GB. Fig. 5b suggests a ratio of GB angle to misorientation of 1:3, i.e. hGB ¼ ðhB hA Þ=3 ¼ hB =3
Within unit length l, average frequency of dendrite development can be calculated by f ¼
mary dendrite tips determined from k2 are therefore behind the actual positions. However, there is no doubt that this method does not vary the correlation of the relative position of primary dendrite tips. The relative position of the primary dendrite tips is schematically illustrated on the right side of Fig. 8. Dendrites a1 and b1 are the GB dendrites; and dendrite a2 and b2 are immediate neighbors to dendrites a1 and b1, respectively. The dendrite tips are positioned according to the determined results. In Fig. 8a, dendrite a1 and b1 are behind dendrite a2 and b2; dendrite a2 is ahead of dendrite b2; and dendrite a1 is ahead of dendrite b1. When k2 was measured on different longitudinal sections, it was found that dendrites a1 and b1 were always behind dendrite a2 and b2 and dendrite a2 was always ahead of dendrite b2. However, dendrite a1 was not always ahead of dendrite b1 (see Fig. 8b). In this instance dendrite a1 is behind dendrite b1 in the figure. Dendrite a2 is always ahead of dendrite b2, which means grain A is more favorably oriented. Dendrite a1 is always
ðhA ¼ 0Þ
l tan hB =3 k1
4.2. Overgrowth of converging grains and dendrites As shown in Fig. 7, the liquidus front is a near horizontal interface in a BC sample with converging dendrites, indicating the thermal gradient of the casting system is not the reason why the misaligned grain overgrew the favorably oriented grain, i.e. the overgrowth process is not due to the inclination of the thermal gradient and liquidus with respect to the withdrawal direction. The mechanism by which the unfavorably oriented dendrites are able to overgrow the favorably oriented dendrites cannot be stated conclusively from the experimental data. However, solutal interaction of the converging dendrite tips is the most probable factor. From the deduced dendrite tip positions at the convergent GB it is evident that when such interactions occurred it was not always the case that the well-aligned dendrite tip is the most advanced at the GB. This was shown in Fig. 8b. The conditions which lead to this are likely to be similar to those shown in Fig. 8a,
Y.Z. Zhou et al. / Acta Materialia 56 (2008) 2631–2637
Fig. 9. Schematic diagram showing the development of grain structure in DS process with low solidification rate (1.67 105 m s1 withdrawal speed).
where although the impinging primary stem b1 failed to arrest the growth of the well-aligned stem a1, it retarded it relative to stem b2, thereby increasing the likelihood of overgrowth by dendrite b2. In the Walton and Chalmers model, because the unfavorably oriented dendrites are not able to overgrow the favorably oriented dendrites, the GB of converging grains lies parallel to the favorably oriented dendrites. Here, we found that the unfavorably oriented dendrites are able to overgrow the favorably oriented dendrites in the case of converging dendrites. Consequently, the misaligned grain is able to overgrow the well-aligned grain by blocking the dendrites of the favorably oriented grain.
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In the case of diverging grains, the favorably oriented grain overgrows the misaligned grain. The grain overgrowth process depends on the development of new dendrites from the favorably oriented grain at the GB. In the case of converging grains, the result differs from the prediction of the Walton and Chalmers model. Since new dendrites are hard to develop at the GB, the inclination of the GB plane depends on the blocking of dendrites only. The blocking of the unfavorably oriented dendrites at the GB does not lead to GB moving towards the misaligned grain, while the blocking of the favorably oriented dendrites at the GB leads to GB moving towards the favorably oriented grain. Consequently, the misaligned grain is able to overgrow the favorably oriented grain. Quenching experiments show that the GB dendrites are behind of other dendrites in the case of converging dendrites. Such result implicates that the growth of converging dendrite tips is slowed down as soon as the tips get within solutal interaction distance. Acknowledgements The authors would like to thank WTM Institute, Erlangen, for support in experiments. Professor Robert F. Singer of WTM Institute is specially acknowledged for valuable discussions. References
4.3. Formation of h0 0 1i texture in DS process The process by which a favored h0 0 1i texture is developed at low withdrawal speed is schematically illustrated in Fig. 9 according to the present experimental results. The formation of h0 0 1i texture depends completely on the overgrowth of unfavorably oriented diverging grains by their more favorably oriented neighbors at a rate that is greater than that of overgrowth of favorably oriented grains by unfavorably oriented converging grains, i.e. the boundary slope of diverging grains is greater than the one of converging grains. Thus grain B may be overgrown by grain A2 before grain B overgrows grain A1. In practice, the oriented h0 0 1i DS texture usually forms more quickly than the one reported here because of the three-dimensional nature of the process leading to interaction of an individual grain with several neighbors, and also because of higher withdrawal speeds, the effect of which will be shown in future papers. 5. Conclusions The overgrowth mechanisms of diverging and converging grains in DS castings are different:
[1] Walton D, Chalmers B. Trans Metall Soc AIME 1959;215:447. [2] Mclean M. In: Directionally solidified materials for high temperature service. London: Metals Society; 1983. p. 5. [3] D’Souza N, Ardakani MG, McLean M, Shollock BA. Metall Mater Trans 2000;31A:2877. [4] Ardakani MG, D’Souza N, Shollock BA, McLean M. Metall Mater Trans 2000;31A:2887. [5] Quested PN, Mclean M. Mater Sci Eng 1984;65:171. [6] Rappaz M, Gandin CA, Desbiolles JL, Thevoz P. Metall Mater Trans 1996;27A:695. [7] Rappaz M, Gandin CA. Acta Metall Mater 1994;42:2233. [8] Esaka H. Ph.D. thesis. No. 615, Ecole Polytechnique Federale de Lausanne, Switzerland; 1986. [9] Wagner A, Shollock BA, McLean M. Mater Sci Eng 2004;374A:270. [10] Stanford N, Djakovic A, Shollock BA, McLean M, D’Souza N. In: Green KA, Pollock TM, Harada H, Howson TE, Reed RC, Schirra JJ, Walston S, editors. Superalloys 2004. Warrendale, PA: TMS; 2004. p. 719. [11] D’Souza N, Jennings PA, Yang XL, Dong HB, McLean M. Metall Mater Trans 2005;36B:657. [12] Zhang J, Singer RF. Metall Mater Trans 2004;35A:939. [13] D’Souza N, Ardakani MG, Wagner A, Shollock BA, McLean M. J Mater Sci 2002;37:481.
Acta Materialia 56 (2008) 2631–2637 www.elsevier.com/locate/actamat
Mechanism of competitive grain growth in directional solidification of a nickel-base superalloy Y.Z. Zhou a, A. Volek b, N.R. Green a,* a
School of Engineering, Metallurgy and Materials, The University of Birmingham, Edgbaston, Birmingham B15 2TT, UK b Diehl Stiftung & Co. KG, Stephanstrasse 49, 90478 Nu¨rnberg, Germany Received 22 May 2007; received in revised form 12 January 2008; accepted 2 February 2008 Available online 17 March 2008
Abstract The structure evolution of bicrystal (BC) samples during directional solidification (DS) was explored in an attempt to understand the mechanism of competitive grain growth. It was found that in the case of diverging dendrites the favorably oriented grain overgrows the misaligned grain. However, in the case of converging dendrites the result differs from the prediction of the generally accepted model for competitive grain growth. First, the unfavorably oriented dendrites are able to overgrow the favorably oriented dendrites. Second, the misaligned grain overgrows the favorably oriented grain by blocking the dendrites of the favorably oriented grain at the grain boundary. Based on the experimental results, the process by which a favored h0 0 1i texture is developed during DS process of a nickel-base superalloy is illustrated. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Grain growth; Theory; Directional solidification; Nickel alloys
1. Introduction Directional solidification (DS) has been widely used to produce turbine blades of Ni-base superalloys. A preferred crystallographic orientation is produced in the DS casting due to the anisotropic growth rates of dendrites associated with grains of different orientations [1]. Previous studies [2– 5] on nickel-base superalloys have confirmed the fast-growing dendritic orientation to be h0 0 1i. The range of orientations produced in the DS process depends directly on the efficiency of the competitive grain overgrowth. The generally accepted model for competitive grain growth proposed by Walton and Chalmers [1] is based on the difference in undercooling of favorably and unfavorably oriented dendrites with respect to the thermal gradient. Rappaz et al. [6,7] schematically summarized the Walton and Chalmers model (Fig. 1). Grains A1 and A2 are *
Corresponding author. Tel.: +44 (0) 121 414 5207; fax: +44 (0) 121 414 5232. E-mail address: [email protected] (N.R. Green).
favorably oriented. Grain B is unfavorably oriented and the h0 0 1i direction has a misorientation, h, with respect to the heat flow direction. To keep up with the more favorably oriented neighbors, grain B grows at a greater undercooling. In the case of diverging dendrites (the two grains on the right of Fig. 1), development of new dendrites from grain A2 can lead to overgrowth of grain B and the GB is thus inclined. In the case of converging dendrites (the two grains on the left of Fig. 1), the dendrite tips in grain B impinge upon the side of grain A1 at the GB and are stopped. Since grain A1 does not develop new dendrites at the GB and the dendrites in grain B cannot overgrow the dendrites in grain A1, the GB lies parallel to the dendrites in grain A1. In situ observations of the dendritic solidification of transparent organic analogs in Ref. [8] had the same result as described by Fig. 1. Three video sequences from Ref. [8] were shown in Ref. [7]. The in situ experiment was carried out on the organic film with one primary dendrite arm spacing (k1) thickness so that the microstructure evolution could be observed easily. However, because the solidification
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Fig. 1. Schematic illustration of the Walton and Chalmers model for competitive grain growth [6,7]. Grain A and B are favorably and unfavorably oriented, respectively.
conditions in the volume materials are different from those in the film materials, it is uncertain whether the microstructure evolution in the volume materials is the same as that in thin films of the material. In a recent study [9], bicrystal (BC) volume samples with diverging and converging dendrites were produced to study the mechanism of competitive grain growth. It was reported that the GB planes lay parallel to the h0 0 1i directions in the favorably oriented grains in the BC samples. Fig. 2 schematically summarizes the results in Ref. [9]. In the case of the diverging dendrites (Fig. 2a), the GB plane lying parallel to the h0 0 1i growth direction of grain A indicated new primary (tertiary) dendrites could not develop from grain A at the GB. The result differed from the Walton and Chalmers model. In the case of converging dendrites (Fig. 2b), the result in Ref. [9] was the same as the prediction of the Walton and Chalmers model. Grain seeding is often used in single-crystal (SC) casting, whereby a seed is partially melted-back during the thermal soaking period of the mold prior to casting. It was reported [10,11] that upon initiation of withdrawal there is copious nucleation of crystals with random orientation distributed Growth direction GB plane
GB plane 13˚
7˚
13˚
33˚
<001>
<001>
A
B
7˚
20˚
<001>
<001>
A
Fig. 3. Schematic diagram showing the structure evolution in the SC casting initiated by the SC seed in Refs. [10,11]. Nucleation of crystals with random orientation occurs uniformly around the perimeter of the seed at the start of the casting process (time t0). In the following growth process (time t1), the stray grains only survive and expand transversely on the side of the seed where the primary dendrites of the seed diverge from the mold wall.
uniformly around the perimeter of the seed at the meltback interface. In the following growth process [10,11], stray grains only survived and expanded transversely on one side of the seed. The side of the seed where the primary dendrites of the seed diverged from the mold wall was where stray grains grew; where the dendrites converged on the mold wall the stray grains were overgrown by the seed crystal irrespective of their orientation (Fig. 3). The Walton and Chalmers model can explain why the stray grains survive and expand transversely on the diverging side, but it cannot explain why stray grains better aligned to the withdrawal direction and thermal gradient were overgrown by the misaligned seed on the converging side. According to the Walton and Chalmers model, these well-aligned stray grains should not be overgrown by the misaligned seed crystal. Similar to the experiments in Ref. [9], BC volume samples were produced to study the mechanism of competitive grain growth in the present work. The correlation of the grain overgrowth with dendrite formation or dendrite blocking was shown here so that the present results could be critically compared with the Walton and Chalmers model. In the case of diverging dendrites, our results are well in accordance to the Walton and Chalmers model. However, in the case of converging dendrites, our results do not support it. Based on the experimental results in the present work, the formation of h0 0 1i texture during DS process of a nickel-base superalloy is illustrated.
B
Divergence
Convergence
a
b
Fig. 2. Schematic diagram showing the experimental results of the BC casting samples in Ref. [9]. The GB plane is parallel to the h0 0 1i direction of the favorably oriented grain A in both cases of diverging and converging dendrites.
2. Experiments 2.1. Materials and arrangement of seeds The compositions of the materials used in the present work are listed in Table 1.
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Table 1 Nominal compositions of alloys as used in the experiments (in wt.%) Alloy
Cr
Co
Mo
W
Al
Ti
Ta
B
Zr
C
Ni
IN792 PWA1483
12.5 12.2
8.8 9.0
1.8 1.9
4.0 3.8
3.4 3.6
3.9 4.2
3.9 5.0
0.014 0
0.017 0
0.08 0.07
Balance Balance
SC seeds from superalloy PWA1483 were used to initiate the structure development in the BC casting process. In previous work [12], it has been reported that PWA1483 seeds do not influence the nominal composition of IN792 after casting since PWA1483 is the SC equivalent of IN792, having almost the same composition except the minor elements B and Zr. To keep both h0 0 1i directions in the BC samples on the same plane, the SC seeds were cut from the same SC plate. Each seed was cut into two halves along the sample axis. Subsequently, the seeds were arranged in such a way that the samples with diverging or converging dendrites were produced. Seed A was always oriented with the h0 0 1i direction parallel to the macroscopic growth direction, while the h0 0 1i direction in seed B had a misorientation from the growth direction and the misorientation was varied in the experiments. hA and hB were used to describe the misorientation of h0 0 1i direction from the sample axis in seed A and B, respectively. The details of hA and hB in the experiments are listed in Table 2. 2.2. DS casting experiments DS experiments were carried out using conventional Bridgman high rate solidification (HRS) technique in a vacuum environment. A pure alumina tube mounted on a water-cooled copper chill plate was used as mold. The SC seeds with 2025 mm length were placed in the bottom of the mold to control the orientations of casting samples. The mold temperature was 1500 °C in the experiments. At this temperature, the seeds in the mold were partially molten and the solid/liquid interface was determined as the start of the DS process. The alloy of IN792 was heated to 1550 °C and kept at temperature for 5 min. Afterwards the temperature was dropped to the casting temperature (1500 °C) and the melt poured into the preheated mold. BC casting samples with 10 mm diameter and 150 mm length were directionally solidified at a withdrawal speed of 1.67 105 m s1 (i.e. 1 mm min1). Table 2 Structural characteristics and casting method of the BC samples Experiments
Seed disposition
hA (°)
hB (°)
Casting method
Exp. Exp. Exp. Exp. Exp. Exp. Exp. Exp. Exp.
Divergence Divergence Divergence Convergence Convergence Convergence Convergence Divergence Convergence
0 0 0 0 0 0 0 0 0
9 13 20 10 19 23 30 10 10
HRS HRS HRS HRS HRS HRS HRS LMC LMC
1 2 3 4 5 6 7 8 9
Quenched DS experiments were performed using the liquid metal cooling (LMC) technique. The alumina mold was mounted on a steel chill plate. As with the above HRS experiments, SC seeds were placed in the bottom of the mold to control the orientations of the castings produced. The BC samples with diameter 12 mm were directionally solidified into a tin bath for a height of 50 mm at a withdrawal speed of 1.67 105 m s1 (i.e. 1 mm min1) and then rapidly quenched into the tin bath at a withdrawal speed of 2 103 m s1 (i.e. 120 mm min1), thereby freezing the microstructure of solidification front. 2.3. Sample examination Macroetching was employed to determine the positions of the grain overgrowth and the start of the DS process (Fig. 4a). The misorientation of the GB plane from the sample axis (hGB) was determined by, tan hGB = R/L, where R is the sample radius and L is the distance from the start to the position of grain overgrowth (Fig. 4b). hGB is defined to be positive when the GB plane is inclined in such a way that the favorably oriented grain A overgrows the misaligned grain B. In contrast, hGB is defined to be negative when the GB plane is inclined in such a way that the misaligned grain B overgrows the favorably
(b)
Growth direction Cut
Cut Sample axis
Overgrowth
R
GB plane θ GB
L Grain B
Grain A Start Seed B
Seed A
tg θGB = R / L Fig. 4. Macroscopic image of a BC sample with converging dendrites after macroetching (a) and schematic diagram showing the determination of the misorientation (hGB) of the GB plane from the sample axis (b). The positions of the grain overgrowth and start of the DS process could be determined after macroetching. hGB is calculated from tan hGB = R/L, where R is the sample radius and L is the distance from the start to the position of grain overgrowth. Subsequently, the sample was cut along the sample axis to show the microstructure.
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oriented grain A. Subsequently, the BC samples were cut along the sample axis to show the microstructures. hA, hB and k1 were examined by optical metallography on etched samples, using an image analysis system with OPTIMAS 6.2 software. k1 was also determined on the etched samples cut perpendicular to the growth direction at a height 50 mm from the chill end. In the LMC samples quenched into tin, there is a transition in secondary dendrite arm spacing (k2) from the quenched liquid to the DS structure at the solidification front. The change of k2 along the dendrite trunk was determined on etched samples. 3. Results k1 is measured to be 265 lm in grain A (hA = 0°) and k1 is 238 lm in grain B with maximum misorientation (hB = 30°). 3.1. HRS BC samples with diverging dendrites Fig. 5a shows the optical metallographic microstructure of a HRS BC sample with diverging dendrites. The GB is inclined in such a way that grain A overgrows grain B. The overgrowth position is shown in the figure. New dendrites developed from grains A and B at the GB and the gap between the diverging grains was filled by these new dendrites. Depending on the development of new dendrites, grain A overgrew grain B. The dependence of hGB on (hB hA) in the case of diverging dendrites is summarized in Fig. 5b. The values
of hGB are positive, showing grain A always overgrew grain B in this geometric disposition. Furthermore, the rate at which grain A overgrew grain B increased in near linear proportion with increasing (hB hA). The result is in accordance to the Walton and Chalmers model and the experimental result as shown in Fig. 3, while it is different from the result as shown in Fig. 2a. As mentioned in the introduction, in Fig. 2a alignment of the GB plane parallel to the favorably oriented dendrites means that new dendrites are not able to develop from grain A at the GB. Subsequently, the gap between the diverging grains is filled by new dendrites developed from grain B only. This result can be attributed to the geometrical disposition of the dendrite trunks. In Fig. 2a, since the secondary dendrites in grain A are undeveloped towards the GB gap because their orientation is less aligned with the temperature gradient, new dendrites are hard to develop from grain A in the GB gap (note the dendrite morphology shown in Fig. 2). In contrast, the secondary dendrites in grain B are more developed towards the GB gap because their orientation is more aligned with the temperature gradient; new dendrites are therefore easy to develop from grain B in the GB gap. The result, as shown in Fig. 2a, may not be essentially contradictory to the present results and the Walton and Chalmers model, but favorably oriented dendrites with a certain misorientation appear to be necessary for such a result. Since the inclination of dendrite trunks is beyond such condition in the present work (hA = 0°) new dendrites are able to develop from grain A. Consequently, the GB plane is not parallel to the h0 0 1i direction in grain A here.
(b) 7 Exp. 3
6 Exp. 2
5
Slope 1:3
4
A overgrows B.
Exp. 1
3 8
10
12
14
16
18
20
θ B – θA (°)
Fig. 5. (a) Optical micrograph showing the microstructure in a HRS BC sample with diverging dendrites, and (b) dependence of hGB on (hB hA) in the HRS BC samples with diverging dendrites. hGB are positive in the figure, which means the favorably oriented grain A overgrows the misaligned grain B.
-1
GB misorientation, θGB (°)
GB misorientation, θGB (°)
8
(b) -2 -3
Exp. 7
Exp. 4
-4
Exp. 6 Exp. 5
-5 -6
B overgrows A. 10
15
20
25
30
θ B – θA (°)
Fig. 6. (a) Optical micrograph showing the microstructure in a HRS BC sample with converging dendrites, and (b) dependence of hGB on (hB hA) in the HRS BC samples with converging dendrites. hGB are negative in the figure, the negative value is employed to reflect the misaligned grain B overgrows the favorably oriented grain A.
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3.2. HRS BC samples with converging dendrites
3.3. LMC BC samples
Fig. 4a shows a macroscopic image of a HRS BC sample with converging dendrites. The detailed GB structure is shown in Fig. 6a. The result differs significantly from the predictions of the Walton and Chalmers model. Firstly, the favorably oriented grain A was overgrown by the unfavorably oriented grain B as shown in Figs. 4a and 6a. Secondly, the dendrites in grain A were blocked by the dendrites in grain B at the GB as marked by short white arrows in Fig. 6a. In line with the Walton and Chalmers model new dendrites were hard to develop from grains A or B at the GB in our experiments. It should be noted that the primary dendrites in grain B were also blocked at the GB by the dendrites in grain A, examples of which are marked by short black arrows in Fig. 6a, and more dendrites in grain B are blocked at the GB. The dependence of hGB on (hB hA) in the case of converging dendrites is presented in Fig. 6b. The values of hGB all are negative, which indicates that grain B always overgrew grain A in this geometric disposition. The present result does not agree with the Walton and Chalmers model and the result is as shown in Fig. 2b, while it is well in accordance to the result shown in Fig. 3. As pointed out in the introduction, the Walton and Chalmers model contains two conclusions: (a) new dendrites do not develop from grain A at the GB; and (b) the dendrites in grain A cannot be blocked by the dendrites of grain B. The former conclusion is in accordance with the present result, while the latter is in contradiction. However, to get the result as shown in Figs. 3 and 6, it is inevitable that the dendrites in grain A must be blocked by the dendrites of grain B.
The structure evolution in the LMC BC samples (Exp. 8 and 9) are the same as that in the HRS BC samples, i.e. in the sample with diverging dendrites (Exp. 8) the GB is inclined from grain A to grain B depending on the development of new dendrites from grain A, while the GB is inclined from grain B to grain A due to the blocking of the favorably oriented dendrites at the GB in the sample with converging dendrites (Exp. 9). The result indicates the casting method does not change the behavior of grain overgrowth. Fig. 7a shows the quenched liquidus interface. k2 varies from the quenched liquid to the DS structure at the solidification front. The approximate position of the liquidus interface is marked by dashed line according to the transition in k2. Grains A and B show a near horizontal interface with maximum slope at the mold wall of 4°. The detailed morphology of the converging dendrites in the mushy zone is presented in Fig. 7b. The dendrites in grain A are not able to develop longer secondary arms (Pk1) towards grain B in the whole mushy zone and there is no dendrite development at the GB. The same result was reported in Refs. [9,13]. The positions of the dendrite tips at the GB region in Exp. 9 were determined according to the transition in k2. Fig. 8 shows the dependence of k2 on solidified length at the solidification front. k2 rapidly increased from the quenched liquid to the DS structure and we assume the primary dendrite tips were located at the position where k2 began to increase. It is well known that the position of the development of the first secondary dendrite is behind the primary dendrite tip. The inferred positions of the pri-
Fig. 7. Optical micrographs showing the quenched liquidus interface (a) and the detailed morphology of the converging dendrites in the mushy zone (b) in Exp. 9. Grains A and B show a near horizontal interface with maximum slope at the mold wall of 4° in (a). The dendrites in grain A are not able to develop longer secondary arms (Pk1) towards grain B and no dendrite development can be observed at the GB in (b).
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behind dendrite b2, which means in Fig. 8a that dendrite b2 may be ahead of dendrite a1 after dendrite b1 is blocked by dendrite a1 (i.e. the structure as shown by Fig. 8b). A similar experiment as Exp. 9 was carried out in superalloy CMSX-4 in Ref. [13], i.e. CMSX-4 BC castings with converging dendrites (the unfavorably oriented dendrites with 5–7° h0 0 1i misorientation) were directionally solidified and quenched to reveal the dendrite morphology. Although not directly described, the same result as that shown in Fig. 8a can be obtained by determining the change in k2 from the figures presented in Ref. [13], i.e. the GB dendrites are behind their immediate neighbors. 4. Discussion 4.1. Overgrowth of diverging grains
Fig. 8. Dependence of k2 on the solidified length at the solidification front and schematic diagram showing the correlation of the determined dendrites in the position. k2 rapidly increases from the quenched liquid to the DS structure and the dendrite tips are assumed to be located at the positions where k2 begins to increase. Dendrites a1 and b1 are always behind dendrite a2 and b2; and dendrite a2 is always ahead of dendrite b2. Dendrite a1 is ahead of dendrite b1 in (a), while dendrite a1 is behind dendrite b1 in (b).
The results in the samples with diverging dendrites are in accordance to the Walton and Chalmers model. As shown in Fig. 1 (the two grains on the right), the gap between diverging grains is filled by new dendrites developed from grain A2 and B. Since the new dendrites develop from the base of the gap, the development of new dendrites is independent of the undercooling difference of grain A2 and B. Grain A2 expands transversely when a new dendrite develops from it at the GB. However, grain B does not expand transversely when a new dendrite develops from it at the GB. Consequently, grain A2 overgrows grain B depending on the rate of development of new dendrites from grain A2 at the GB. Fig. 5b suggests a ratio of GB angle to misorientation of 1:3, i.e. hGB ¼ ðhB hA Þ=3 ¼ hB =3
Within unit length l, average frequency of dendrite development can be calculated by f ¼
mary dendrite tips determined from k2 are therefore behind the actual positions. However, there is no doubt that this method does not vary the correlation of the relative position of primary dendrite tips. The relative position of the primary dendrite tips is schematically illustrated on the right side of Fig. 8. Dendrites a1 and b1 are the GB dendrites; and dendrite a2 and b2 are immediate neighbors to dendrites a1 and b1, respectively. The dendrite tips are positioned according to the determined results. In Fig. 8a, dendrite a1 and b1 are behind dendrite a2 and b2; dendrite a2 is ahead of dendrite b2; and dendrite a1 is ahead of dendrite b1. When k2 was measured on different longitudinal sections, it was found that dendrites a1 and b1 were always behind dendrite a2 and b2 and dendrite a2 was always ahead of dendrite b2. However, dendrite a1 was not always ahead of dendrite b1 (see Fig. 8b). In this instance dendrite a1 is behind dendrite b1 in the figure. Dendrite a2 is always ahead of dendrite b2, which means grain A is more favorably oriented. Dendrite a1 is always
ðhA ¼ 0Þ
l tan hB =3 k1
4.2. Overgrowth of converging grains and dendrites As shown in Fig. 7, the liquidus front is a near horizontal interface in a BC sample with converging dendrites, indicating the thermal gradient of the casting system is not the reason why the misaligned grain overgrew the favorably oriented grain, i.e. the overgrowth process is not due to the inclination of the thermal gradient and liquidus with respect to the withdrawal direction. The mechanism by which the unfavorably oriented dendrites are able to overgrow the favorably oriented dendrites cannot be stated conclusively from the experimental data. However, solutal interaction of the converging dendrite tips is the most probable factor. From the deduced dendrite tip positions at the convergent GB it is evident that when such interactions occurred it was not always the case that the well-aligned dendrite tip is the most advanced at the GB. This was shown in Fig. 8b. The conditions which lead to this are likely to be similar to those shown in Fig. 8a,
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Fig. 9. Schematic diagram showing the development of grain structure in DS process with low solidification rate (1.67 105 m s1 withdrawal speed).
where although the impinging primary stem b1 failed to arrest the growth of the well-aligned stem a1, it retarded it relative to stem b2, thereby increasing the likelihood of overgrowth by dendrite b2. In the Walton and Chalmers model, because the unfavorably oriented dendrites are not able to overgrow the favorably oriented dendrites, the GB of converging grains lies parallel to the favorably oriented dendrites. Here, we found that the unfavorably oriented dendrites are able to overgrow the favorably oriented dendrites in the case of converging dendrites. Consequently, the misaligned grain is able to overgrow the well-aligned grain by blocking the dendrites of the favorably oriented grain.
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In the case of diverging grains, the favorably oriented grain overgrows the misaligned grain. The grain overgrowth process depends on the development of new dendrites from the favorably oriented grain at the GB. In the case of converging grains, the result differs from the prediction of the Walton and Chalmers model. Since new dendrites are hard to develop at the GB, the inclination of the GB plane depends on the blocking of dendrites only. The blocking of the unfavorably oriented dendrites at the GB does not lead to GB moving towards the misaligned grain, while the blocking of the favorably oriented dendrites at the GB leads to GB moving towards the favorably oriented grain. Consequently, the misaligned grain is able to overgrow the favorably oriented grain. Quenching experiments show that the GB dendrites are behind of other dendrites in the case of converging dendrites. Such result implicates that the growth of converging dendrite tips is slowed down as soon as the tips get within solutal interaction distance. Acknowledgements The authors would like to thank WTM Institute, Erlangen, for support in experiments. Professor Robert F. Singer of WTM Institute is specially acknowledged for valuable discussions. References
4.3. Formation of h0 0 1i texture in DS process The process by which a favored h0 0 1i texture is developed at low withdrawal speed is schematically illustrated in Fig. 9 according to the present experimental results. The formation of h0 0 1i texture depends completely on the overgrowth of unfavorably oriented diverging grains by their more favorably oriented neighbors at a rate that is greater than that of overgrowth of favorably oriented grains by unfavorably oriented converging grains, i.e. the boundary slope of diverging grains is greater than the one of converging grains. Thus grain B may be overgrown by grain A2 before grain B overgrows grain A1. In practice, the oriented h0 0 1i DS texture usually forms more quickly than the one reported here because of the three-dimensional nature of the process leading to interaction of an individual grain with several neighbors, and also because of higher withdrawal speeds, the effect of which will be shown in future papers. 5. Conclusions The overgrowth mechanisms of diverging and converging grains in DS castings are different:
[1] Walton D, Chalmers B. Trans Metall Soc AIME 1959;215:447. [2] Mclean M. In: Directionally solidified materials for high temperature service. London: Metals Society; 1983. p. 5. [3] D’Souza N, Ardakani MG, McLean M, Shollock BA. Metall Mater Trans 2000;31A:2877. [4] Ardakani MG, D’Souza N, Shollock BA, McLean M. Metall Mater Trans 2000;31A:2887. [5] Quested PN, Mclean M. Mater Sci Eng 1984;65:171. [6] Rappaz M, Gandin CA, Desbiolles JL, Thevoz P. Metall Mater Trans 1996;27A:695. [7] Rappaz M, Gandin CA. Acta Metall Mater 1994;42:2233. [8] Esaka H. Ph.D. thesis. No. 615, Ecole Polytechnique Federale de Lausanne, Switzerland; 1986. [9] Wagner A, Shollock BA, McLean M. Mater Sci Eng 2004;374A:270. [10] Stanford N, Djakovic A, Shollock BA, McLean M, D’Souza N. In: Green KA, Pollock TM, Harada H, Howson TE, Reed RC, Schirra JJ, Walston S, editors. Superalloys 2004. Warrendale, PA: TMS; 2004. p. 719. [11] D’Souza N, Jennings PA, Yang XL, Dong HB, McLean M. Metall Mater Trans 2005;36B:657. [12] Zhang J, Singer RF. Metall Mater Trans 2004;35A:939. [13] D’Souza N, Ardakani MG, Wagner A, Shollock BA, McLean M. J Mater Sci 2002;37:481.