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The effects of elastic interaction energy on the γ′ precipitate morphology of continuously cooled nickel-base alloys
Materials Science and Engineering, 74 (1985) 1 3 9 - 1 4 5
139
T h e E f f e c t s of E l a s t i c I n t e r a c t i o n E n e r g y o n t h e y ' P r e c i p i t a t e M o r p h o l o g y of Continuously Cooled Nickel-base Alloys MINORU DOI, TORU MIYAZAKI and TERUYUKI WAKATSUKI*
Department of Metallurgical Engineering, Nagoya Institute of Technology, Goklso-cho, Showa-ku, Nagoya 466 (Japan) (Received October 3, 1984; in revised form December 27, 1984)
ABSTRACT
The morphological change o f T ' precipitates in some nickel-base alloys continuously cooled across the 7' solvus line was investigated by means o f transmission electron microscopy. In slowly cooled (e.g. a cooling rate o f about 10 -2 K s-I ) Ni-Al, N i - S i and Nimonic 115 alloys a single 7' particle split into eight small cuboids (i.e. an ogdoad) and the unit assemblies o f particles, each o f which consisted o f eight cuboids, were closely distributed in the 7 matrix. For quickly cooled (e.g. a cooling rate o f about 10 K s-I ) alloys, splitting did not occur and a large number o f small 7' particles were closely aligned along (100) directions. In N i - A l alloys, 7' precipitate ogdoads were formed during slow continuous cooling, whereas 7' precipitate doublets were formed during the isothermal aging just below the 7' solvus line. Such morphologies were introduced by the strong influence o f the elastic interaction energies.
I. I N T R O D U C T I O N
It is well known that the 7' precipitate morphology is of paramount importance in improving the high temperature strength of nickel-base superalloys. Therefore, control of the precipitate morphology is one of the most important topics for developing new types of precipitation-strengthened alloys. When we examine the precipitate morphology, the individual shape and distribution of precipitate particles should be considered. *Present address: Nippon Steel Corporation, Sakai Works, Sakai 590, Japan. 0025-5416/85/$3.30
Recently, our group found the extraordinary phenomenon that, during the coarsening of coherent 7' precipitates,a single7' particle sometimes splitsinto a group of eight small cuboids (i.e.an ogdoad) or into a pair of paraUel plates (i.e.a doublet), as shown in Fig. 1 [1-3]. This type of splittingis a typical example which indicatesthe importance of the elasticinteraction energy in determining the shape of individual7' precipitates.tThe effectsof elasticinteractionenergy on the shape are described well by the parameter A*, the ratio of the 7-7' latticemisfit to the surface energy density of 7' particlesin the 7 matrix (A* -= ~/Ts)- The following three cases are observed according to the magnitude of A*: (I) when IA*I ~ 0.2 the single 7' precipitate particles remain spherical and never split into several small particles, (II) when 0.2 IA*I ~ 0.4 the single cuboidal 7' precipitate particles split into eight small cuboids (anogdoad) and (III) when 0.4 ~ IA*I the single cuboidal 7' precipitate particles split into pairs of parallel plates (doublets). Furthermore, we have also pointed out that the splitting phenomenon is observed only when the 7' precipitate particles are sparsely distributed in the 7 matrix [1-3]. The sparse distribution of 7' particles is obtained when precipitation starts immediately after furnace cooling from a homogenizing temperature to an aging temperature just below the 7' solvus line. Some superalloys strengthened by 7' precipitates are used as cast material. Therefore, t K n o w l e d g e o f the effects o f elastic interaction energy on the precipitate morphology has been advancing rapidly [ 4 - 7 ] and, hitherto, it has been recognized incorrectly that the elastic interaction energy does not affect the shape b u t does markedly affect the distribution. © Elsevier Sequoia/Printed in The Netherlands
140 into water. The cooling rate was between 10 -2 and 102 K s-1. Hereafter the fast cooling rate means 10-102 K s-i and the slow cooling rate means 10-i-10 -2 K s-1. Thin foil specimens for TEM were obtained by electropolishing the samples subjected to these heat treatments. The morphological changes of the 7' precipitates were observed with an electron microscope operated at 200 kV. The energetically stable shape of the 7' precipitates was calculated numerically with a computer on the basis of microelasticity theory.
3. E X P E R I M E N T A L
Fig. 1. Transmission electron microscopy (TEM) images of 7' precipitate morphologies in nickel-base alloys: (a) 7 ogdoads in Ni-12at.%Si alloy aged at 1103 K for 72 000 s immediately after it had been furnace cooled from 1473 K (the homogenizing temperature) to 1103 K; (b)7' precipitate doublets in Ni-12at.%Al alloy aged at 1133 K for 144 000 s immediately after it had been furnace cooled from 1473 K (the homogenizing temperature) to 1133 K.
whether or not the splitting of 7' precipitates occurs during casting is an important problem. In the present study the shape changes of 7' precipitates in nickel-base alloys cluring continuous cooling are investigated by means of transmission electron microscopy (TEM). This heat t r e a t m e n t simulates the real thermal history during casting. The shape changes are discussed on the basis of microelasticity theory.
2. EXPERIMENTAL PROCEDURES The nickel-base alloys used in the present study were selected to represent each o f t h e above-mentioned three groups, as follows: (I) Inconel 700 for alloys with small I A* I, (II) Ni-12at.%Si and Nimonic 115 for alloys with intermediate IA*I and (III) Ni-(12-17)at.%A1 for alloys with large IA*I. After being homogenized at high temperatures, each alloy was continuously cooled to temperatures lower than the 7' solvus line, followed by quenching
RESULTS
Figure 2 shows the shape change of 7' precipitates in Nimonic 115 superalloy continuously cooled at a rate of 10 -i K s-i from 1523 K (homogenizing temperature TH) to 1288 K (Fig. 2(a)), to 1283 K (Fig. 2(b)) or to 1278 K (Fig. 2(c)). The split of a single 7' particle into a group of eight small cuboids progresses more quickly as the temperature at which the continuous cooling is finished is decreased. At 1273 K the split is virtually complete, as shown in Fig. 3. It can also be seen that the unit assemblies of 7' particles, each of which consists of eight cuboids, are closely distributed in the 7 matrix. For Ni-12at.%Si alloy also, the split into an ogdoad is observed during continuous cooling at a rate of 10 -2 K s-1 from 1473 K (TH) to 873 K. Figure 4 shows the precipitate morphology of 7' particles in Nimonic 115 superalloy continuously cooled at a rate which is of t h e order of 10 K s-i from 1523 K (TH) to 1273 K. Rather small 7' particles o f a cuboidal or plate-like shape are aligned along (100). In contrast with slow cooling, this type of fast cooling does not give rise to splitting of the 7' particles. Figure 5(a) shows the morphology of 7' precipitates in the Ni-14at.%A1 alloy continuously cooled at a rate of 5.5 X 10 -2 K s-i from 1473 K (TH) to 1273 K. The split into an ogdoad is observed. According to our previous observations [ 1 - 3 ] , the 7' particles in the NiA1 alloy exhibit a split into a doublet during isothermal aging just below the 7' solvus line, as shown in Fig. 5(b). It should be noted that the split into an ogdoad really takes place in the Ni-A1 alloy with a large IA*I. The split into an ogdoad is also observed in the Ni-
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Fig. 3. TEM images of 7' precipitate ogdoads in Nimonic 115 superalloy continuously cooled at a rate of 10-1 K s-1 from 1523 to 1273 K. It should be noted that the groups of eight 7' cuboids are closely distributed in the 3' matrix.
Fig. 4. TEM image of 7' precipitate particles in Nimonic 115 superalloy continuously cooled at a rate of the order of 10 K s-1 from 1523 to 1273 K. A large number of small 7' particles of a cuboidal Fig. 2. TEM images of the 7' precipitate particles in Nimonic 115 superalloy continuously cooled at a rate of 10-1 K s-1 from 1523 K (the homogenizing temperature) (a) to 1288 K, (b) to 1283 K and (c) to 1278 K. The split of a single particle into an ogdoad progresses more with decreasing temperature. 1 7 a t . % A l alloy c o n t i n u o u s l y c o o l e d at a r a t e o f 10 -I K s-1 f r o m 1 4 7 3 K (TH) t o 1 3 7 3 K. Figure 6 shows t h e p r e c i p i t a t e m o r p h o l o g y o f 7 ' particles in I n c o n e l 7 0 0 s u p e r a l l o y cont i n u o u a l y c o o l e d at a rate o f 10 -2 K s-1 f r o m 1 5 2 3 K (TH) t o 9 2 3 K. A l t h o u g h s o m e 7' Particles a p p e a r t o coalesce i n t o a g o u r d shape, each particle r e m a i n s essentially spherical and n e v e r splits i n t o several small particles.
or plate-like shape are closely aligned along (100).
w h i c h t h e e n e r g y state a f t e r t h e split is l o w e r t h a n t h a t b e f o r e t h e split [2, 3]. I f t h e precipitate particle grows larger t h a n D*, t h e particle c o u l d p o t e n t i a l l y split i n t o several small particles. W h e t h e r o r n o t splitting o c c u r s dep e n d s o n t h e size t o w h i c h t h e particle can grow. H o w e v e r , it s h o u l d be n o t e d t h a t in f a c t splitting does n o t a p p e a r o n l y at t h e critical size D* w h i c h is calculated energetically as described later. Splitting p r o c e e d s b y a t o m i c diff u s i o n w h i c h requires b o t h t i m e and driving f o r c e . T h e r e f o r e , splitting really o c c u r s at a certain critical size D** w h i c h is larger t h a n D*.
4. DISCUSSION
4.1. Changes in the precipitate morphology due to different continuous cooling rates
O u r previous studies i n d i c a t e t h a t t h e r e is a certain critical size D* o f 7' particles a b o v e
When a h o m o g e n i z e d nickel-base solid solut i o n is c o n t i n u o u s l y c o o l e d across t h e 7' solvus
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Fig. 5. TEM images showing the changes in 7 ' precipitate morphology o f the Ni-A1 alloys due to the different heat treatments: (a) for continuous cooling at a rate of 5.5 × 10 -2 K s-1 from 1473 to 1273 K, single ~/' particles split into ogdoads; (b) for aging just below the 7' solvus line (1133 K for 144 000 s), splits into doublets occur.
Fig. 6. TEM image of the 7 ' precipitate particles in Inconel 700 superalloy continuously cooled at a rate of 10 -2 K s-1 from 1523 to 923 K. The splitting phenomenon is never observed.
line, a large n u m b e r of ~' particles appear and grow because the total a m o u n t of V' which precipitates increases with decreasing temperature. When the continuous cooling is stopped at a given temperature well below the solvus line, different cooling rates cause markedly different precipitate morphologies. For slow
cooling the ~/' particles have sufficient time to grow larger and t h e y are able to exceed the critical size D**; hence each particle splits into eight small cuboids under the strong influence of elastic interaction energy. For fast cooling, however, each particle has only a shorter time to grow than for slow cooling. Therefore, the ~/' particles in quickly cooled alloys are much smaller and there are more of t h e m than in the slowly cooled alloy. When the cooling rate is sufficiently fast, the size o f each particle cannot exceed the critical value D** so that no splitting occurs during cooling, which results in the formation o f the morphology in Fig. 4. A new idea which has been developed by us [8] on the basis o f the so-called "bifurcation t h e o r y " [9, 10] indicates that, once the precipitate morphology is finely developed as in Fig. 4, the individual particles hardly coarsen because such a fine microstructure is itself energetically in an extremely stable state as a result of the strong elastic interaction between the particles, i.e. the particles do not need to coarsen or split in order to decrease their energy.
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Our previous studies also indicate that, for isothermal aging just below the 7' solvus line (e.g. aging at 1383 K for Nimonic 115 and at 1103 K for Ni-Si), splitting takes place only when the particles are sparsely distributed in the 7 matrix [ 1 - 3 ]. In such isothermal aging the volume fraction of 7' is very low because the aging temperature is close to the solvus line. When coarsening of 7' particles proceeds, competitive growth should take place and the n u m b e r of particles becomes smaller. Therefore, when the particles grow large enough to split, such isothermal aging results in the formation of a sparse distribution of particles (and hence, for example, the groups of eight cuboids f o r m e d by the split are also sparsely distributed as in Fig. l(a)). For sufficiently slow cooling, however, the total amount of 7' which can precipitate increases with decreasing temperature (e.g. for cooling to 1273 K for Nimonic 115 and to 873 K for Ni-Si) and the particles, of which there are more than for isothermal aging near the solvus line, are able to grow large. Therefore, when the particles grow large enough to split,such slow cooling resultsin the formation of a close distribution of particles (and hence the groups of eight cuboids formed by the split are also closely distributed as in Fig. 3).
4.2. Different modes of split in Ni-Al alloys due to the different heat treatments An interesting point is t h a t single 7' particles in the Ni-A1 alloys split into doublets in some cases and into ogdoads in others, depending on the heat treatment. The validity of such morphological separation is discussed here by calculating the energy states before and after the split on the basis of microelasticity theory. In calculating the energies, the following three cases are considered: (i) a 7' particle (of volume V and surface area S(P)) which is a single i n h o m o g e n e o u s ellipsoid of revolution (with an aspect ratio P) a n d exists in an infinite 7 matrix t h a t is elastically anisotropic, (ii) a single 7' particle which splits into t w o small ellipsoidal 7' particles (of volume V/2 and surface area S'(P)) and (iii) a single 7' Particle which splits into eight small ellipsoidal 7' particles (of volume V/8 and surface area
S"(P)).
E (1), E (2) and E (s), which are the total energies for the three cases (i), (ii) and (iii) respec-
tively, are expressed by the following equations: E (1) = VE~e~(P) + S(Phr, E (2) = 2
V --Eincl(P) + 2S'(P~Ts + E " ~ i n t ( P ) 2
and V E (s) = 8 --E~cl(P) + 8S"(P)~ + E(s)~(P) 8
where Emcl(P) is the elastic strain energy of the ellipsoid, ?s is the surface energy density of the ellipsoid, Ea~int(P ) is the elastic interaction energy between the t w o ellipsoids produced by the split into a doublet and E(S)mt(P) is the elastic interaction energy between the eight ellipsoids produced by the split into an ogdoad. The details of the procedure for calculating the energies have been given in our previous papers [1, 3]. Figure 7 illustrates the changes in the energy state of 7' precipitates before and after the splits calculated for the Ni-A1 alloy. The abscissa indicates the diameter of the single particle before the split. When the particle remains small in size, E (1) is the lowest and the particle can stably exist as a single particle. However, as the particle grows larger than
1.G
!i
E"' . . . . . . . .
o
o.5
E(21
1.0
particle Diameter D (pro)
Fig. 7. Comparison b e t w e e n the total energies of a ~/' particle in the Ni-AI alloy before and after the split into a d o u b l e t or i n t o an ogdoad calculated o n the basis o f microelasticity theory. E (1), E (2) a n d E (s) are the total energies in a single state, in a d o u b l e t state and in an ogdoad state respectively. The energetically stable shape changes from a single particle to a doublet to an ogdoad with increasing particle size during growth.
144
D*2, E (2) becomes the lowest and the doublet is the energetically favourable shape, which suggests the possibility of splitting into a doublet. Furthermore, when the particle size becomes larger than the critical size D's, E ~s) becomes the lowest and the energetically favourable shape changes from a doublet to an ogdoad. Our previous experimental studies on Ni-A1 alloys indicate that the particle size at which the split into a doublet is realized is about 0.25-~m (= D**2) [2, 3]. ~simflarly, the present study indicates that the size at which the split into an ogdoad is realized is more than 0.5 pm (= D**s) at least. It is considered that the difference between the calculated D*2 (or D's) and the experimentally obtained D**2 (or D**8 ) arises from the kinetics of splitting. An energy difference between E C1) and E C2)at D**2 (i.e. A E in Fig. 7) is regarded as the driving force for splitting a single particle into a doublet, for example. This implies that the splitting phenomenon does not appear until a driving force of AE has arisen. For slow continuous cooling, the reason why the 7' particle can grow, as a single particle, to the critical size D** s for the split into an ogdoad can be explained as follows. During continuous cooling, the particles grow to such a size that the split into a doublet should take place (i.e. the particle size ranges from D*2 to D*s in Fig. 7) but each particle can easily and rapidly grow to sizes larger than D*s because the total number of particles which can be precipitated increases continuously with decreasing temperature. In other words, the time that a particle takes to grow from D*~ to D*s is so short that it allows no splitting into a doublet. Even for continuous cooling, however, the single 7' particle is only expected to split into a doublet if the cooling rate is extremely slow. In contrast, for isothermal aging just below the 7' solvus line, the volume fraction of 7' particles remains very low and the particles grow much more slowly than for continuous cooling. Therefore, during such isothermal aging, each particle has sufficient time to take the energetically most favourable shape at any time during growth (i.e. at any particle size) as long as the driving force is sufficient for the shape change, i.e. each particle actually splits into a doublet which is in the lowest energy state at the intermediate particle sizes, i.e. between D**2 and D*s in Fig. 7.
Here we discuss whether or not the transition from a doublet to an ogdoad, i.e. the further splitting, actually occurs. From Fig. 7, we may easily imagine that each of the paired 7' plates formed by the split into a doublet should split further into four small cuboids, which results in the shape change from a doublet to an ogdoad. However, we should also consider the fact that the elastic interaction energy results from the overlap of strain fields which accompany coherent particles. Once the particles lose their coherency, the splitting phenomenon does not take place because of the annihilation of elastic interaction energy. Further splitting is only realized when the energy difference between E C2)and E Cs) becomes large enough to split further before the doublet loses coherency. We have not yet obtained positive evidence that further splitting really takes place. This suggests that the energy accumulation of the order of AE' in Fig. 7 is insufficient for the further splitting of a doublet into an ogdoad.
5. CONCLUSIONS The important facts obtained in the present study are as follows. (1) The 7' precipitate cuboid splits into eight small cuboids during slow cooling but does not split during fast cooling. In the slow cooling case the 7' particles are able to grow larger with decreasing temperature and take the energetically stable state by splitting when their size exceeds a critical value D**. In the fast cooling case, however, a large number of small 7' particles (there are more particles and they are smaller than in the slow cooling case) are closely aligned along (100). Such a finely developed microstructure is extremely stable in itself and the particles do not need to grow or split in order to decrease their energy state. (2) The unit assemblies of 7' particles, each of which consists of eight cuboids formed by the split, are closely distributed in the alloys slowly cooled to the temperature well below the 7' solvus line. In the alloys aged just below the 7' solvus line, however, the unit assemblies are sparsely distributed in the matrix. The volume fraction of 7' in the slowly cooled alloys is much larger than that in the aged alloys. Therefore, when the individual particles grow to a critical size D**s, the number of particles
145
in the slowly cooled alloys becomes much larger than that in the aged alloys; this results in the difference in the density of the unit assemblies formed by the splits. (3) As regards the 7' precipitates in Ni-A1 alloys, a split into an ogdoad occurs during slow cooling whereas a split into a doublet takes place during isothermal aging just below the 7' solvus line. In the slowly cooled alloys, since the total a m o u n t of 7' which precipitates increases with decreasing temperature, the particle is able to grow rapidly up to D*s without sufficient time to split into a doublet. In the aged alloys, however, the particle gradually coarsens because of the low volume fraction of 7', and hence it has sufficient time to split into a doublet at intermediate particle sizes (i.e. between D * * 2 and D's). The formation of such precipitate morphologies as the above is a result of the elastic interaction energy. During both continuous cooling and isothermal aging just below the solvus line, the elastic interaction energy plays an essential role in determining n o t only the distribution but also the individual shape of the 7' precipitates of nickel-base alloys.
ACKNOWLEDGMENT
A part of this work was financially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan. REFERENCES 1 T. Miyazaki, H. Imamura and T. Kozakai, Mater. Sci. Eng., 54 (1982) 9. 2 M. Doi and T. Miyazaki, Proc. 5th Int. Symp. on Superalloys, Seven Springs, PA, October 1984, Metall. Soc. AIME, Warrendale, PA, p. 543. 3 M. Doi, T. Miyazaki and T. Wakatsuki, Meter. Sci. Eng., 67 (1984) 247. 4 A. J. Ardell, R. B. Nicholson and J. D. Eshelby, Acta Metall., 14 (1966) 1295. 5 E. Seitz and D. de Fontaine, Acta MetaU., 26 (1978)1671. 6 W. C. Johnson and J. K. Lee, Metall. Trans. A, 10 (1979) 1149. 7 T. Miyazaki, H. Imamura, H. Mori and T. Kozakai, J. Mater. Sci., 16 (1981) 1197. 8 T. Miyazaki, K. Seki, M. Doi and T. Kozakai, to be published. 9 W. C. Johnson and J. W. Cahn, Acta Metall., 32 (1984) 1925. 10 W. C. Johnson, Acta Metall., 32 (1984) 465.
139
T h e E f f e c t s of E l a s t i c I n t e r a c t i o n E n e r g y o n t h e y ' P r e c i p i t a t e M o r p h o l o g y of Continuously Cooled Nickel-base Alloys MINORU DOI, TORU MIYAZAKI and TERUYUKI WAKATSUKI*
Department of Metallurgical Engineering, Nagoya Institute of Technology, Goklso-cho, Showa-ku, Nagoya 466 (Japan) (Received October 3, 1984; in revised form December 27, 1984)
ABSTRACT
The morphological change o f T ' precipitates in some nickel-base alloys continuously cooled across the 7' solvus line was investigated by means o f transmission electron microscopy. In slowly cooled (e.g. a cooling rate o f about 10 -2 K s-I ) Ni-Al, N i - S i and Nimonic 115 alloys a single 7' particle split into eight small cuboids (i.e. an ogdoad) and the unit assemblies o f particles, each o f which consisted o f eight cuboids, were closely distributed in the 7 matrix. For quickly cooled (e.g. a cooling rate o f about 10 K s-I ) alloys, splitting did not occur and a large number o f small 7' particles were closely aligned along (100) directions. In N i - A l alloys, 7' precipitate ogdoads were formed during slow continuous cooling, whereas 7' precipitate doublets were formed during the isothermal aging just below the 7' solvus line. Such morphologies were introduced by the strong influence o f the elastic interaction energies.
I. I N T R O D U C T I O N
It is well known that the 7' precipitate morphology is of paramount importance in improving the high temperature strength of nickel-base superalloys. Therefore, control of the precipitate morphology is one of the most important topics for developing new types of precipitation-strengthened alloys. When we examine the precipitate morphology, the individual shape and distribution of precipitate particles should be considered. *Present address: Nippon Steel Corporation, Sakai Works, Sakai 590, Japan. 0025-5416/85/$3.30
Recently, our group found the extraordinary phenomenon that, during the coarsening of coherent 7' precipitates,a single7' particle sometimes splitsinto a group of eight small cuboids (i.e.an ogdoad) or into a pair of paraUel plates (i.e.a doublet), as shown in Fig. 1 [1-3]. This type of splittingis a typical example which indicatesthe importance of the elasticinteraction energy in determining the shape of individual7' precipitates.tThe effectsof elasticinteractionenergy on the shape are described well by the parameter A*, the ratio of the 7-7' latticemisfit to the surface energy density of 7' particlesin the 7 matrix (A* -= ~/Ts)- The following three cases are observed according to the magnitude of A*: (I) when IA*I ~ 0.2 the single 7' precipitate particles remain spherical and never split into several small particles, (II) when 0.2 IA*I ~ 0.4 the single cuboidal 7' precipitate particles split into eight small cuboids (anogdoad) and (III) when 0.4 ~ IA*I the single cuboidal 7' precipitate particles split into pairs of parallel plates (doublets). Furthermore, we have also pointed out that the splitting phenomenon is observed only when the 7' precipitate particles are sparsely distributed in the 7 matrix [1-3]. The sparse distribution of 7' particles is obtained when precipitation starts immediately after furnace cooling from a homogenizing temperature to an aging temperature just below the 7' solvus line. Some superalloys strengthened by 7' precipitates are used as cast material. Therefore, t K n o w l e d g e o f the effects o f elastic interaction energy on the precipitate morphology has been advancing rapidly [ 4 - 7 ] and, hitherto, it has been recognized incorrectly that the elastic interaction energy does not affect the shape b u t does markedly affect the distribution. © Elsevier Sequoia/Printed in The Netherlands
140 into water. The cooling rate was between 10 -2 and 102 K s-1. Hereafter the fast cooling rate means 10-102 K s-i and the slow cooling rate means 10-i-10 -2 K s-1. Thin foil specimens for TEM were obtained by electropolishing the samples subjected to these heat treatments. The morphological changes of the 7' precipitates were observed with an electron microscope operated at 200 kV. The energetically stable shape of the 7' precipitates was calculated numerically with a computer on the basis of microelasticity theory.
3. E X P E R I M E N T A L
Fig. 1. Transmission electron microscopy (TEM) images of 7' precipitate morphologies in nickel-base alloys: (a) 7 ogdoads in Ni-12at.%Si alloy aged at 1103 K for 72 000 s immediately after it had been furnace cooled from 1473 K (the homogenizing temperature) to 1103 K; (b)7' precipitate doublets in Ni-12at.%Al alloy aged at 1133 K for 144 000 s immediately after it had been furnace cooled from 1473 K (the homogenizing temperature) to 1133 K.
whether or not the splitting of 7' precipitates occurs during casting is an important problem. In the present study the shape changes of 7' precipitates in nickel-base alloys cluring continuous cooling are investigated by means of transmission electron microscopy (TEM). This heat t r e a t m e n t simulates the real thermal history during casting. The shape changes are discussed on the basis of microelasticity theory.
2. EXPERIMENTAL PROCEDURES The nickel-base alloys used in the present study were selected to represent each o f t h e above-mentioned three groups, as follows: (I) Inconel 700 for alloys with small I A* I, (II) Ni-12at.%Si and Nimonic 115 for alloys with intermediate IA*I and (III) Ni-(12-17)at.%A1 for alloys with large IA*I. After being homogenized at high temperatures, each alloy was continuously cooled to temperatures lower than the 7' solvus line, followed by quenching
RESULTS
Figure 2 shows the shape change of 7' precipitates in Nimonic 115 superalloy continuously cooled at a rate of 10 -i K s-i from 1523 K (homogenizing temperature TH) to 1288 K (Fig. 2(a)), to 1283 K (Fig. 2(b)) or to 1278 K (Fig. 2(c)). The split of a single 7' particle into a group of eight small cuboids progresses more quickly as the temperature at which the continuous cooling is finished is decreased. At 1273 K the split is virtually complete, as shown in Fig. 3. It can also be seen that the unit assemblies of 7' particles, each of which consists of eight cuboids, are closely distributed in the 7 matrix. For Ni-12at.%Si alloy also, the split into an ogdoad is observed during continuous cooling at a rate of 10 -2 K s-1 from 1473 K (TH) to 873 K. Figure 4 shows the precipitate morphology of 7' particles in Nimonic 115 superalloy continuously cooled at a rate which is of t h e order of 10 K s-i from 1523 K (TH) to 1273 K. Rather small 7' particles o f a cuboidal or plate-like shape are aligned along (100). In contrast with slow cooling, this type of fast cooling does not give rise to splitting of the 7' particles. Figure 5(a) shows the morphology of 7' precipitates in the Ni-14at.%A1 alloy continuously cooled at a rate of 5.5 X 10 -2 K s-i from 1473 K (TH) to 1273 K. The split into an ogdoad is observed. According to our previous observations [ 1 - 3 ] , the 7' particles in the NiA1 alloy exhibit a split into a doublet during isothermal aging just below the 7' solvus line, as shown in Fig. 5(b). It should be noted that the split into an ogdoad really takes place in the Ni-A1 alloy with a large IA*I. The split into an ogdoad is also observed in the Ni-
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Fig. 3. TEM images of 7' precipitate ogdoads in Nimonic 115 superalloy continuously cooled at a rate of 10-1 K s-1 from 1523 to 1273 K. It should be noted that the groups of eight 7' cuboids are closely distributed in the 3' matrix.
Fig. 4. TEM image of 7' precipitate particles in Nimonic 115 superalloy continuously cooled at a rate of the order of 10 K s-1 from 1523 to 1273 K. A large number of small 7' particles of a cuboidal Fig. 2. TEM images of the 7' precipitate particles in Nimonic 115 superalloy continuously cooled at a rate of 10-1 K s-1 from 1523 K (the homogenizing temperature) (a) to 1288 K, (b) to 1283 K and (c) to 1278 K. The split of a single particle into an ogdoad progresses more with decreasing temperature. 1 7 a t . % A l alloy c o n t i n u o u s l y c o o l e d at a r a t e o f 10 -I K s-1 f r o m 1 4 7 3 K (TH) t o 1 3 7 3 K. Figure 6 shows t h e p r e c i p i t a t e m o r p h o l o g y o f 7 ' particles in I n c o n e l 7 0 0 s u p e r a l l o y cont i n u o u a l y c o o l e d at a rate o f 10 -2 K s-1 f r o m 1 5 2 3 K (TH) t o 9 2 3 K. A l t h o u g h s o m e 7' Particles a p p e a r t o coalesce i n t o a g o u r d shape, each particle r e m a i n s essentially spherical and n e v e r splits i n t o several small particles.
or plate-like shape are closely aligned along (100).
w h i c h t h e e n e r g y state a f t e r t h e split is l o w e r t h a n t h a t b e f o r e t h e split [2, 3]. I f t h e precipitate particle grows larger t h a n D*, t h e particle c o u l d p o t e n t i a l l y split i n t o several small particles. W h e t h e r o r n o t splitting o c c u r s dep e n d s o n t h e size t o w h i c h t h e particle can grow. H o w e v e r , it s h o u l d be n o t e d t h a t in f a c t splitting does n o t a p p e a r o n l y at t h e critical size D* w h i c h is calculated energetically as described later. Splitting p r o c e e d s b y a t o m i c diff u s i o n w h i c h requires b o t h t i m e and driving f o r c e . T h e r e f o r e , splitting really o c c u r s at a certain critical size D** w h i c h is larger t h a n D*.
4. DISCUSSION
4.1. Changes in the precipitate morphology due to different continuous cooling rates
O u r previous studies i n d i c a t e t h a t t h e r e is a certain critical size D* o f 7' particles a b o v e
When a h o m o g e n i z e d nickel-base solid solut i o n is c o n t i n u o u s l y c o o l e d across t h e 7' solvus
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Fig. 5. TEM images showing the changes in 7 ' precipitate morphology o f the Ni-A1 alloys due to the different heat treatments: (a) for continuous cooling at a rate of 5.5 × 10 -2 K s-1 from 1473 to 1273 K, single ~/' particles split into ogdoads; (b) for aging just below the 7' solvus line (1133 K for 144 000 s), splits into doublets occur.
Fig. 6. TEM image of the 7 ' precipitate particles in Inconel 700 superalloy continuously cooled at a rate of 10 -2 K s-1 from 1523 to 923 K. The splitting phenomenon is never observed.
line, a large n u m b e r of ~' particles appear and grow because the total a m o u n t of V' which precipitates increases with decreasing temperature. When the continuous cooling is stopped at a given temperature well below the solvus line, different cooling rates cause markedly different precipitate morphologies. For slow
cooling the ~/' particles have sufficient time to grow larger and t h e y are able to exceed the critical size D**; hence each particle splits into eight small cuboids under the strong influence of elastic interaction energy. For fast cooling, however, each particle has only a shorter time to grow than for slow cooling. Therefore, the ~/' particles in quickly cooled alloys are much smaller and there are more of t h e m than in the slowly cooled alloy. When the cooling rate is sufficiently fast, the size o f each particle cannot exceed the critical value D** so that no splitting occurs during cooling, which results in the formation o f the morphology in Fig. 4. A new idea which has been developed by us [8] on the basis o f the so-called "bifurcation t h e o r y " [9, 10] indicates that, once the precipitate morphology is finely developed as in Fig. 4, the individual particles hardly coarsen because such a fine microstructure is itself energetically in an extremely stable state as a result of the strong elastic interaction between the particles, i.e. the particles do not need to coarsen or split in order to decrease their energy.
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Our previous studies also indicate that, for isothermal aging just below the 7' solvus line (e.g. aging at 1383 K for Nimonic 115 and at 1103 K for Ni-Si), splitting takes place only when the particles are sparsely distributed in the 7 matrix [ 1 - 3 ]. In such isothermal aging the volume fraction of 7' is very low because the aging temperature is close to the solvus line. When coarsening of 7' particles proceeds, competitive growth should take place and the n u m b e r of particles becomes smaller. Therefore, when the particles grow large enough to split, such isothermal aging results in the formation of a sparse distribution of particles (and hence, for example, the groups of eight cuboids f o r m e d by the split are also sparsely distributed as in Fig. l(a)). For sufficiently slow cooling, however, the total amount of 7' which can precipitate increases with decreasing temperature (e.g. for cooling to 1273 K for Nimonic 115 and to 873 K for Ni-Si) and the particles, of which there are more than for isothermal aging near the solvus line, are able to grow large. Therefore, when the particles grow large enough to split,such slow cooling resultsin the formation of a close distribution of particles (and hence the groups of eight cuboids formed by the split are also closely distributed as in Fig. 3).
4.2. Different modes of split in Ni-Al alloys due to the different heat treatments An interesting point is t h a t single 7' particles in the Ni-A1 alloys split into doublets in some cases and into ogdoads in others, depending on the heat treatment. The validity of such morphological separation is discussed here by calculating the energy states before and after the split on the basis of microelasticity theory. In calculating the energies, the following three cases are considered: (i) a 7' particle (of volume V and surface area S(P)) which is a single i n h o m o g e n e o u s ellipsoid of revolution (with an aspect ratio P) a n d exists in an infinite 7 matrix t h a t is elastically anisotropic, (ii) a single 7' particle which splits into t w o small ellipsoidal 7' particles (of volume V/2 and surface area S'(P)) and (iii) a single 7' Particle which splits into eight small ellipsoidal 7' particles (of volume V/8 and surface area
S"(P)).
E (1), E (2) and E (s), which are the total energies for the three cases (i), (ii) and (iii) respec-
tively, are expressed by the following equations: E (1) = VE~e~(P) + S(Phr, E (2) = 2
V --Eincl(P) + 2S'(P~Ts + E " ~ i n t ( P ) 2
and V E (s) = 8 --E~cl(P) + 8S"(P)~ + E(s)~(P) 8
where Emcl(P) is the elastic strain energy of the ellipsoid, ?s is the surface energy density of the ellipsoid, Ea~int(P ) is the elastic interaction energy between the t w o ellipsoids produced by the split into a doublet and E(S)mt(P) is the elastic interaction energy between the eight ellipsoids produced by the split into an ogdoad. The details of the procedure for calculating the energies have been given in our previous papers [1, 3]. Figure 7 illustrates the changes in the energy state of 7' precipitates before and after the splits calculated for the Ni-A1 alloy. The abscissa indicates the diameter of the single particle before the split. When the particle remains small in size, E (1) is the lowest and the particle can stably exist as a single particle. However, as the particle grows larger than
1.G
!i
E"' . . . . . . . .
o
o.5
E(21
1.0
particle Diameter D (pro)
Fig. 7. Comparison b e t w e e n the total energies of a ~/' particle in the Ni-AI alloy before and after the split into a d o u b l e t or i n t o an ogdoad calculated o n the basis o f microelasticity theory. E (1), E (2) a n d E (s) are the total energies in a single state, in a d o u b l e t state and in an ogdoad state respectively. The energetically stable shape changes from a single particle to a doublet to an ogdoad with increasing particle size during growth.
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D*2, E (2) becomes the lowest and the doublet is the energetically favourable shape, which suggests the possibility of splitting into a doublet. Furthermore, when the particle size becomes larger than the critical size D's, E ~s) becomes the lowest and the energetically favourable shape changes from a doublet to an ogdoad. Our previous experimental studies on Ni-A1 alloys indicate that the particle size at which the split into a doublet is realized is about 0.25-~m (= D**2) [2, 3]. ~simflarly, the present study indicates that the size at which the split into an ogdoad is realized is more than 0.5 pm (= D**s) at least. It is considered that the difference between the calculated D*2 (or D's) and the experimentally obtained D**2 (or D**8 ) arises from the kinetics of splitting. An energy difference between E C1) and E C2)at D**2 (i.e. A E in Fig. 7) is regarded as the driving force for splitting a single particle into a doublet, for example. This implies that the splitting phenomenon does not appear until a driving force of AE has arisen. For slow continuous cooling, the reason why the 7' particle can grow, as a single particle, to the critical size D** s for the split into an ogdoad can be explained as follows. During continuous cooling, the particles grow to such a size that the split into a doublet should take place (i.e. the particle size ranges from D*2 to D*s in Fig. 7) but each particle can easily and rapidly grow to sizes larger than D*s because the total number of particles which can be precipitated increases continuously with decreasing temperature. In other words, the time that a particle takes to grow from D*~ to D*s is so short that it allows no splitting into a doublet. Even for continuous cooling, however, the single 7' particle is only expected to split into a doublet if the cooling rate is extremely slow. In contrast, for isothermal aging just below the 7' solvus line, the volume fraction of 7' particles remains very low and the particles grow much more slowly than for continuous cooling. Therefore, during such isothermal aging, each particle has sufficient time to take the energetically most favourable shape at any time during growth (i.e. at any particle size) as long as the driving force is sufficient for the shape change, i.e. each particle actually splits into a doublet which is in the lowest energy state at the intermediate particle sizes, i.e. between D**2 and D*s in Fig. 7.
Here we discuss whether or not the transition from a doublet to an ogdoad, i.e. the further splitting, actually occurs. From Fig. 7, we may easily imagine that each of the paired 7' plates formed by the split into a doublet should split further into four small cuboids, which results in the shape change from a doublet to an ogdoad. However, we should also consider the fact that the elastic interaction energy results from the overlap of strain fields which accompany coherent particles. Once the particles lose their coherency, the splitting phenomenon does not take place because of the annihilation of elastic interaction energy. Further splitting is only realized when the energy difference between E C2)and E Cs) becomes large enough to split further before the doublet loses coherency. We have not yet obtained positive evidence that further splitting really takes place. This suggests that the energy accumulation of the order of AE' in Fig. 7 is insufficient for the further splitting of a doublet into an ogdoad.
5. CONCLUSIONS The important facts obtained in the present study are as follows. (1) The 7' precipitate cuboid splits into eight small cuboids during slow cooling but does not split during fast cooling. In the slow cooling case the 7' particles are able to grow larger with decreasing temperature and take the energetically stable state by splitting when their size exceeds a critical value D**. In the fast cooling case, however, a large number of small 7' particles (there are more particles and they are smaller than in the slow cooling case) are closely aligned along (100). Such a finely developed microstructure is extremely stable in itself and the particles do not need to grow or split in order to decrease their energy state. (2) The unit assemblies of 7' particles, each of which consists of eight cuboids formed by the split, are closely distributed in the alloys slowly cooled to the temperature well below the 7' solvus line. In the alloys aged just below the 7' solvus line, however, the unit assemblies are sparsely distributed in the matrix. The volume fraction of 7' in the slowly cooled alloys is much larger than that in the aged alloys. Therefore, when the individual particles grow to a critical size D**s, the number of particles
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in the slowly cooled alloys becomes much larger than that in the aged alloys; this results in the difference in the density of the unit assemblies formed by the splits. (3) As regards the 7' precipitates in Ni-A1 alloys, a split into an ogdoad occurs during slow cooling whereas a split into a doublet takes place during isothermal aging just below the 7' solvus line. In the slowly cooled alloys, since the total a m o u n t of 7' which precipitates increases with decreasing temperature, the particle is able to grow rapidly up to D*s without sufficient time to split into a doublet. In the aged alloys, however, the particle gradually coarsens because of the low volume fraction of 7', and hence it has sufficient time to split into a doublet at intermediate particle sizes (i.e. between D * * 2 and D's). The formation of such precipitate morphologies as the above is a result of the elastic interaction energy. During both continuous cooling and isothermal aging just below the solvus line, the elastic interaction energy plays an essential role in determining n o t only the distribution but also the individual shape of the 7' precipitates of nickel-base alloys.
ACKNOWLEDGMENT
A part of this work was financially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan. REFERENCES 1 T. Miyazaki, H. Imamura and T. Kozakai, Mater. Sci. Eng., 54 (1982) 9. 2 M. Doi and T. Miyazaki, Proc. 5th Int. Symp. on Superalloys, Seven Springs, PA, October 1984, Metall. Soc. AIME, Warrendale, PA, p. 543. 3 M. Doi, T. Miyazaki and T. Wakatsuki, Meter. Sci. Eng., 67 (1984) 247. 4 A. J. Ardell, R. B. Nicholson and J. D. Eshelby, Acta Metall., 14 (1966) 1295. 5 E. Seitz and D. de Fontaine, Acta MetaU., 26 (1978)1671. 6 W. C. Johnson and J. K. Lee, Metall. Trans. A, 10 (1979) 1149. 7 T. Miyazaki, H. Imamura, H. Mori and T. Kozakai, J. Mater. Sci., 16 (1981) 1197. 8 T. Miyazaki, K. Seki, M. Doi and T. Kozakai, to be published. 9 W. C. Johnson and J. W. Cahn, Acta Metall., 32 (1984) 1925. 10 W. C. Johnson, Acta Metall., 32 (1984) 465.