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Solidification morphologies in directionally solidified superalloys
Materials Science and Engineering, 65 (1984) 171-180
171
Solidification Morphologies in Directionally Solidified Superalloys P. N. QUESTED and M. McLEAN Division of Materials Applications, National Physical Laboratory, Teddington, Middx. TW11 OLW (Gt. Britain) (Received August 1, 1983)
SUMMARY The microstructures of several nickel-base superalloys directionally solidified using a wide range of processing conditions have been examined. The conditions required for plane front solidification are compatible with the concepts o f constitutional supercooling. In the dendritic regime the variations in cell spacing hi with temperature gradient G and solidification rate V are well described by the ~.1 cc G-1/2V-ll 4 relationship predicted by two recent theories; the observed magnitudes of ~1 are in better agreement with the predictions o f Hunt's theory. The implications of directional solidification processing conditions to the distribution of precipitates in nickel-base superalloys are also considered with particular reference to the occurrence of discontinuous ~,' precipitation and to the morphologies if Mc carbides.
tility grain boundary fracture in cast superalloys. However, the process also influences other microstructural characteristics [5] (e.g. dendrite form and size, crystallographic texture, precipitate morphology and distribution, microporosity). The beneficial mechanical properties of directionally solidified materials are likely to result from a combination of these features; however, their relative importance is not yet fully understood. Current concepts of solidification are largely based on theoretical modelling validated by experiments on simple model alloys. By contrast, superalloys are extremely complex often consisting of ten or more atomic constituents which solidify to form several phases. In this paper the relevance of some established solidification models to such industrial alloys will be examined and their implications for control of microstructure and improvement in mechanical behaviour will be considered.
1. INTRODUCTION 2. SOLIDIFICATION MICROSTRUCTURES The evolution of directional solidification technology for the production of gas turbine blades, pioneered b y Versnyder [1] and Versnyder and Shank [2] in the late 1950s, has been achieved b y industrial exploitation of the fundamental concepts of solidification, established from many studies inspired by the paper of Tiller et al. [3]. The process has been applied successfully to the production of columnar and single-crystal turbine blades from superalloys; blades of in situ composites prepared b y directional solidification of eutectic alloys are also technically possible [ 4] although high processing costs have militated against their commercial implementation. The initial motivation for the development of directional solidification was to control the grain morphology in order to inhibit low duc0025-5416/84/$3.00
The microstructures of four nickel-base superalloys, with compositions listed in Table 1, have been examined after directional solidification in a range of conditions giving different values of the principal process parameters, temperature gradient G and solidification rate V. The experimental procedures for achieving these conditions ranged from current commercial practice to advanced laboratory techniques using liquid metal cooling; full details have been described elsewhere [5]. The solidification morphologies, indicated by the microstructures, are displayed as functions of G and V in Fig. 1. Similar information available in the literature for other nickel-base superalloys is included. The differ© Elsevier Sequoia/Printed in The Netherlands
172 TABLE 1 C o m p o s i t i o n s in w e i g h t per c e n t o f alloys c o n s i d e r e d in t h e p r e s e n t s t u d y Alloy
Ni
Co
Cr
Al
Ti
C
Ta
Mo
W
Nb
Zr
B
Hf
MAR-M 002 MAR-M 246 IN-738LC IN-939
Balance Balance Balance Balance
10.0 10.0 8.5 10.0
9.0 9.0 16.0 22.5
5.5 5.5 3.5 1.9
1.5 1.5 3.5 3.7
0.15 0.15 0.11 0.15
2.5 1.5 1.6 1.4
-2.5 1.75 --
10.0 10.0 2.5 2.0
--0.7 1.0
0.05 0.05 0.08 0.09
0.015 0.015 0.008 0.009
1.5 ----
I
10-3
i
m 10-4 E 0 t,_ C
e 0
10-s 0 U3
"~0"~0/. 10-6
10 z
\ 10 3
10 4
10 s
T e m p e r a t u r e g r a d i e n t (Km -I) Fig. 1. M o r p h o l o g i e s o f d i r e c t i o n a l l y solidified nickel-base s u p e r a l l o y s m a p p e d o n a plot o f log V vs. log G ( t h e lines d r a w n b e t w e e n various z o n e s are c o n t o u r s o f c o n s t a n t G / V ) : o, p l a n e f r o n t ; o, [], v , 0, 0, cellular; o, m, A, v, #, 0, c o l u m n a r d e n d r i t i c ; v , ~, ~, e q u i a x e d d e n d r i t i c ; o, o, o, I N - 7 1 3 C [ 7 ]; D, m, M AR-M 2 0 0 [ 6 ] ; A , IN-100; v , T, v , M A R - M 2 4 6 ; 0, #, ~, M A R - M 0 0 2 ; 0, 0, ~, I N - 7 3 8 L C .
ent types of solidification morphology fall into clear zones, corresponding to plane front, cellular, columnar dendritic and equiaxed dendritic freezing, in the logarithmic display of the (G, V) field. The observations are consistent with the fact that the occurrence of a particular morphology is determined by the magnitude of the ratio G/V relative to various critical values associated with transitions between the zones. The greatest difference
between the various alloys is shown in the cell-to-dendrite transitions. The reasons for this are not apparent from the present experiments but may reflect small changes in the solid-melt interfacial energies which govern the stabilities of secondary dendrite arms.
2.1. Plane front solidification Plane front solidification, first demonstrated for superalloys by Tien and Gamble
173 [6], can be approached at the slowest solidification rates (less than about 10 -3 mm s-i) with the highest temperature gradients (greater than about 20 K mm -i) used, although the presence of carbides often originating in the melt may make this difficult. An example of an alloy at the transition to cellular solidification is shown in Fig. 2(a). The processing conditions required to obtain plane front solidification in several nickel-base superalloys, both from the present study and from published data, are listed in Table 2 together with measurements of their melting ranges AT0. Using the constitutional supercooling condition iV!rit - AT° DL
(l)
for the plane-front:to-cellular transition developed by Tiller e t al. [3], values of the diffusion coefficient D L in the liquid have been calculated from these data. Provided that the difficulties in measuring G are borne in mind, these values are self-consistent and within the accepted range of liquid state diffusivities at the melting point. Consequently, the constitutional supercooling concept appears to apply to these quite complex engineering alloys which largely solidify as a single phase. There has been no significant commerical interest in plane front superalloys, probably because of the poor processing economics. 2.2. Cellular and d e n d r i t i c m i c r o s t r u c t u r e s
Cellular and dendritic microstructures were obtained over most of the processing conditions used in the present study as are obtained in all commercial directional solidification rigs. A quenched longitudinal interface of such a structure, shown in Fig. 2(b), confirms that the dendrites project into the melt. However, the primary cell or dendrite spacing ),1 is very sensitive to both G and V, spanning the approximate range of 20-300 pm in current commercial and laboratory practice. There have been two recent theoretical analyses of cellular and dendritic solidification during directional solidification which yield identical functional dependences of Xl on G and V. H u n t [8] has derived an approximate analytical solution to the diffusion equations for the extremum growth condition (i.e. that the system will adopt the m a x i m u m
Fig. 2. Longitudinal sections of the superalloy MARM 2 4 6 quenched from steady state solidification to freeze the solidifying interface: (a) V = 1.67 × 10 -3 rams -1, G = 1 3 K m m -1, near plane front; (b) V =
8.3 x 10-2 mm s-1, G = 13 K mm-1, columnar dendritic.
174 TABLE 2 Experimentally determined solidification parameters for plane front solidification of nickel-base superalloys Alloy
G (K m m -1 )
Ycrit ( m m s -1)
(G/V)crit (K s m m -2)
AT0 (K)
D L = ATo(G/Y)crit -1 (mm 2 s-1)
Reference
IN-738LC MAR-M 246 MAR-M 002 MAR-M 200 IN-713C
20 20 20 10 11
<1.67 < 1.67 <1.67 10 -3 0.83
1.20 x 104 1.20 x 104 1.20 X 104 104 1.3 x l 0 4
85 ~100 ~100 139 30
7.1 x 10 -3 ~8.3 × 10 -3 ~ 8 . 3 X 10 -3 13.9 x 10 -3 2 . 3 × 1 0 -3
This work This w o r k This work [6] [7]
X 10 -3 X 10 -3 X 10 -3 ×10 -3
G, t e m p e r a t u r e gradient; V, solidification front velocity; AT0, alloy freezing range; DL, solute diffusivity in the liquid alloy.
growth rate or minimum undercooling), showing that
i
i
31117
X1 = {64FDLmL(ko-- 1)Co/3}t/4G-1/2V -1/4 (2) where
20C
E
/3=1+
koD L
G rl
m L ( 1 - - ko)Co V
DL G =l+----
AT0 V
i100
(3)
m L is the liquidus slope, k0 is the partition coefficient, Co is the solute concentration, F ~ 7~AS, ~( is the solid-melt interfacial energy and AS is the entropy of fusion. Equation (2) is only determinate when G/V < ATo/DL, i.e. when the condition for constitutional supercooling is satisfied. When G/V ~ ATo/DL, then/3 ~ 1 and eqn. (2) reduces to X1 -~-/647DLmL~(1 -- k0 )Co}1/4G_1/2V_I/4
(4)
The measurements of dendrite arm spacing for three nickel-base superalloys are displayed as a function of the product G-112V-114in Fig. 3. When the materials have clearly established dendritic microstructures, the data are approximately described by a c o m m o n straight line, where reductions in G or V lead to a coarsening of the dendrites. However, as the conditions for plane front solidification are approached (i.e. 1 >/3 > 0) then )tl decreases with decreasing G or V. This deviation results from the melting-back of the dendrite tips to lower temperatures as/3 ~ 0, which affects the kinetics of solute partitioning in the melt in proportion to the local liquid diffusivity. Breakaway from the linear portion
,<
I
I I 0.1 V-1/4 G~112 (ml/4sl/4 K-IIz)
I 02
Fig. 3. Primary cell or dendrite spacing )~t as a function o f G-1/2V -114 for three directionally solidified nickel-base superalloys: A, e, - , well-formed dendritic structures; A, O, G, approach of plane front conditions; A, MARoM 246; e, MAR-M 0 0 2 ; I , IN738LC; ~-e--% ~-B--% commercially processed.
of the curve does n o t occur at a unique value of G - 1 / 2 V -114 but is determined by G/V. However, the data shown obtained under similar conditions are consistent with the deviation from linearity which correlates with the alloy melting range. The curve for MAR-M 002 shows a less abrupt drop than those for IN738LC and MAR-M 246; this is probably a consequence of the larger volume fraction of 7-7' eutectic in MAR-M 002. Identifying the slope of the linear portion of the curve with the bracketed term in eqn. (4) and taking DL = 5 X 10 -9 m 2 s-1, mL = 300 K (wt.fraction) -1, 1 -- k0 = 0.9, Co = 0.2 wt.fraction and AS = 106 J m -3 K -1 gives a value for the solid-melt interracial energy of 176 mJ m -2 which is compatible with previous measurements. Consequently the model satisfactorily
175 describes the behaviour of these complex alloys in b o th predicting the plane-front-tocellular transition and accounting for the dimensions of the dendrites as a function of the principal solidification parameters. Kurz and Fisher [9] have proposed a model involving p e r t u r b a t i o n analysis rather than the e x t r e m u m criterion, which gives the same functional d ep en de nc e of X1 on V and G but with a different constant of proportionality. The ratio of the values of )~1 predicted by the two theories is ()kl)Hunt __ ( k O 2 ] TM
()~0KF
18.5I
~ 0.56
However, because of the f o u r t h r o o t the value o f 7 calculated f r om the Kurz-Fisher equation (16.8 mJ m -2) is an order of magnitude less than th at obtained from Hunt's model and is m u ch smaller than measured values of the solid-liquid interfacial energy. Consequently, the present data are better described by the H u n t model. Both the H u n t and the Kurz-Fisher models describe solidification in a cylindrical element, parallel to G and V, and the full periodic structure is generated by s y m m e t r y . This implicitly assumes a regular array of dendrites. However, experimental measurements show a very wide distribution in the distances between neighbouring dendrites as shown in Fig. 4, although analysis of the mean values of
X1 is consistent with the theoretical models. This range of spacings is probabl y i m p o r t a n t in a c c o m m o d a t i n g the mean X1 to changing growth conditions. Certainly, X1 changes rapidly in response to variations in G a n d / o r V as indicated by the plot of ~1 along the length of directionally solidified IN-738LC produced by a commercial process where G progressively decreases (Fig. 5). Details of quenched dendritic interfaces in various superalloys, shown in Fig. 6, indicate that dendrite spacings (i) increase by a simple overgrowth mechanism where some dendrites lag behind their neighbours which e x t e n d radially and prevent the continuing growth of the trailing dendrite and (ii) decrease by the initiation of instabilities on existing dendrites and their subsequent growth, either through the conversion of an existing tertiary arm to form a new primary or by the branching of dendrites.
2.3. Non-aligned structures The aligned dendritic structure can break dow n in two ways. Firstly, there can be a true columnar-to-equiaxed dendrite transition where the axial diffusion flux in the
Shell mould
300
40
Solidificatior rate m m h-t) --
60 . . . . . 300
30
Primary dendrite arm spacing (tJm) Intercept Planimeter method measurement 170 105
165.5.~0.9 1073:0,7
v
o £
20 _~ 100
,I.
I
I
o
la
I
,I,
200
I
I
20
i 300 Dendrite arm spacing
100
, I,
I
,
I, 40
l, 60
L , k , 1 , 1 , l , i 80
Position
4~0
Fig. 4. Distribution of nearest dendrite-dendrite separations measured on a transverse section of directionally solidified IN-939.
1(30 of
120
1/-.0
160
180
, ) 200
section ( m m )
Fig. 5. Mean dendrite spacings measured on transverse sections cut at various points along the lengths of directionally solidified ingots of IN-738LC prepared commercially in moulds with different thermal characteristics.
176
liquid is not adequate to supply the advancing solidification front; this limits the size of components that can be produced by the static power-down technique where G progressively decreases as solidification proceeds [lo]. However, practical limitations of heat flow present another problem at high withdrawal rates [ 111 from dynamic directional solidification rigs. Since, at steady state, heat loss from the solidified material is largely by radiation (or by forced cooling, e.g. by liquid metals) from the ingot surface, axial heat flow at the solid-liquid interface which is required for directional solidification can only be achieved when the solidification front is remote from the cooling zone of the rig. At high withdrawal rates the solidification front can move into the cooling zone where the dendrites solidify radially.
3.
PRECIPITATE
MORPHOLOGIES
The high temperature strength of superalloys largely derives from the precipitated phases most of which are deposited from the solid state in y (nickel) dendrites. The solidification conditions considerably influence the nature and distribution of these phases by virtue of the different post-solidification cooling sequences that are associated with the processing parameters G and V. For volume diffusion control, isotropic coarsening is described by the LifshitzSlyozov-Wagner cubic equation (see for example ref. 5)
where r and r. are the present and initial radii of the feature, B is a kinetic constant, T is the absolute temperature and t is elapsed time. If coarsening takes place as the material is translated at a rate V through a temperature gradient G, then the coarsening in the space element x to x + dx is described by the expression
Fig. 6. Details of quenched solid-liquid interfaces in directionally solidified nickel-base superalloy: (a) overgrowth of dendrite to increase the mean spacing in IN-100; (b) branching of dendrite to decrease the mean spacing in MAR-M 246.
or
177
The kinetic constant is proportional to the product of solute concentration and diffusion coefficient and so can be written as B = Bo exp(-- Q~I
RT!
Since the temperature is determined by G, therefore
~x
Bo exp[--Q/R{T(O) Gx}] T(0) -- Gx -
-
(r3) - V
where T(0) is the temperature when x = 0. Integration of eqn. (5) gives r 3 = ro3 + B ~ ( G V ) -1
(6)
where oo
xp =
- exp(--u) du •
Fig. 7. D i s c o n t i n u o u s p r e c i p i t a t i o n o f 7 ' in I N - 7 3 8 L C d i r e c t i o n a l l y solidified at 1.67 x 10 -2 m m s -1 in a t e m p e r a t u r e g r a d i e n t o f 13 K r a m -1. ( A f t e r ref. 12.)
1A
Q/RT(O)
is a standard integral. Typically ~o ~ 0.1 for liquid state diffusion and ~ ~ 10 -6 for solid state diffusion [5]. This points to the importance of the cooling rate GV in determining the size of secondary dendrites and 7' precipitates by liquid and solid state diffusion respectively. The secondary dendrites appear to have relatively little effect on the mechanical behaviour of directionally solidified superalloys and most of the 7' precipitates can be manipulated by subsequent heat treatment. However, at least two features of precipitate morphology that are dependent on processing conditions appear to be irreversible.
3.1. Discontinuous ~,' precipitates In certain alloys a small volume fraction of the 7' is heterogeneously precipitated at grain boundaries in a form that provides little strengthening. Examination of IN-738LC directionally solidified in a wide range of conditions indicates that this discontinuous precipitate forms when dendritic segregation occurs in combination with relatively slow cooling rates. A typical example is shown in Fig. 7. Quenching experiments suggest that these ~/-7' islands either can nucleate spontaneously at grain boundaries or can grow on small ~/-7' eutectic nuclei that constitute the last fraction of melt to freeze during dendritic solidification of this alloy. In both cases the final dimensions of the zones of discontinuous )" are very sensitive to the cooling rate GV, as
1000
X
t
100 o
c
~5
"6 ~o
~oo
G V ( K s "f )
Fig. 8. Cross-sectional areas, m e a s u r e d o n t r a n s v e r s e sections, o f d i s c o n t i n u o u s 7 - 7 ' islands in d i r e c t i o n a l l y solidified I N - 7 3 8 L C as a f u n c t i o n of G V .
indicated in Fig. 8. The processing conditions also influence the volume fraction of discontinuous 7' largely by affecting the extent of segregation which changes the composition of the final liquid fraction. Thus, when plane front conditions are approached, both eutectic and discontinuous 7' are inhibited. The growth of the discontinuous 7' zones as the temperature gradient is traversed will be described by an expression of the form of eqn. (6):
r o: (GV)-I/3 which appears to fit the experimental data reasonably well.
178
N o t all alloys exhibit either eutectic or discontinuous 7' precipitation after directional solidification. A recent trend in tbe development of superalloys specifically for use in the single-crystal form has been to produce a wide temperature gap between the solidus and the 7' solvus temperatures in order to improve the heat treatment characteristics of the alloys [13]. Where this heat treatment window is too small, or non-existent as for IN-738LC, it is not possible to dissolve fully the 7' produced in the directional solidification sequence. 3.2. Carbides The morphologies and dimensions of MC carbides that are deposited interdendritically are both very sensitive to the processing conditions. For example, Fernandez et al. [14] have shown that, in IN-100, Chinese script and blocky carbide morphologies are preferred at low and high values of G / V respectively; however, the average size of both types of carbide scales as G V. Similar behaviour is observed in IN-738LC and MAR-M 246. It is interesting that a similar transition between Chinese script and blocky carbides has been observed between virgin and recycled cast superalloys [15]. This has been clearly identified with the accumulation of nitrogen in the recycled materials which forms an extremely stable titanium carbonitride dispersion in the melt, so leading to profuse nucleation of carbides which grow in a blocky form. By contrast, when the Ti2(CN) particles are absent, homogeneous nucleation of the carbide is difficult and extensive carbide growth along (111~ directions occurs on relatively few nuclei. Examination of the blocky carbides in directionally solidified IN-738LC has shown that they also have a duplex structure of a small titanium-rich core on which the blocky MC carbide is deposited (Fig. 9). No such cores are apparent in the Chinese script carbides. These results clearly indicate that the carbide morphology is not simply a function of the solidification conditions b u t is largely influenced by subtle chemical modification during processing. The conditions leading to blocky carbides involve low solidification rates, when the melt has a relatively long contact time with mould and atmosphere, and changes in alloy composition probably result
V- w lOpm I
I
Fig. 9. Micrograph of a blocky MC carbide in directionally solidified IN-738LC showing the aluminiumand titanium-rich core.
from interactions with the environment or mould. This indicates the importance of avoiding contamination of the melt during processing which could lead to damaging changes in the solidification sequence. Certainly in conventional castings there is an empirical correlation between the density of blocky carbide and the occurrence of microporosity. Since microporosity can dramatically affect the stress rupture properties at intermediate temperatures, these considerations may partly explain the improvements in creep behaviour that can be obtained by increasing G and V.
4. IMPLICATIONS F O R PERFORMANCE
The mechanical behaviour of directionally solidified superalloys is quite sensitive to both the processing and the testing conditions although it is difficult to correlate the changes with specific microstructural features. For example, Fig. 10 compares creep curves of MAR-M 246 directionally solidified in a commercial and in a liquid-metal-cooled laboratory rig, showing that the high temperature gradient consistently leads to longer lives. Not all this difference is attributable to the finer 7' dispersion in the liquid-cooled material although that certainly makes a contribution. Perhaps more important factors are the association of damage nucleation with interdendritic features such as carbides, dis-
179 0.20
I
I
x
o.15
~1
//
o.,o
iii I
-
0.05
0
/~/.~ -/
500
Time (h)
-
1000
1500
Fig. 10. C o m p a r i s o n o f creep curves f o r M A R - M 2 4 6 d i r e c t i o n a l l y s o l i d i f i e d at 8.3 x 10 -2 m m s -1 i n a l o w t e m p e r a t u r e g r a d i e n t o f 4 K m m -1 ( - - - ) a n d a h i g h t e m p e r a t u r e g r a d i e n t o f 13 K m m -1 ( ). T h e t e s t s w e r e per-
f o r m e d in air a t 1 1 2 3 K a n d 2 5 0 MPa.
3
(b)
creep behaviour of IN-738LC tested at 850 °C with different stresses giving a wide range of lives. There is clearly an increased advantage in the directional solidification of this alloy in long-term tests; however, at higher stresses and in a similar study on IN-939, even this trend is reversed. It is inevitable that over such a wide range of conditions there will be changes in deformation and/or fracture mechanisms in either or both of the materials which will affect their relative performances. However, insufficient data are currently available to allow predictions to be made with confidence. There remains, therefore, considerable scope to take full advantage of solidification microstructures that can be controlled during directional solidification of superalloys.
Fig. 11. R a t i o s o f (a) r u p t u r e life a n d (b) m i n i m u m c r e e p r a t e o f d i r e c t i o n a l l y s o l i d i f i e d (ds) r e l a t i v e t o c o n v e n t i o n a l l y cast (cc) I N - 7 3 8 L C (G = 13 K m m - 1 ; V = 8 . 3 3 × 10 -2 m m s - l ) .
5. C O N C L U S I O N S
continuous 7' precipitate zones and transverse grain boundary segments and the relationship of crack propagation to the dendrite dimensions. The benefits of directional solidification over conventional casting are not uniform. Figure 11 shows such a comparison for the
(1) The conditions giving plane front solidification in directionally solidified superalloys are consistent with the predictions of the constitutional supercooling theory. (2) Primary cell or dendrite arm spacings as a function of solidification conditions are in good agreement with the theoretical model of Hunt.
~u
2
0 (a) 1.5 u
-o1~, ~ 1.0
u
~ 0.5 _E .c IE
o
180
(3) Precipitate morphology and composition are both sensitive to the solidification conditions. (4) The mechanical behaviour of directionally solidified superalloys, particularly in longterm creep testing, is sensitive to the solidification conditions.
REFERENCES 1 F. L. Versnyder, in R. F. Hehemann and G. Mervin Ault (eds.), High Temperature Materials, Wiley-Interscience, New York, 1959. 2 F. L. Versnyder and M. E. Shank, Mater. Sc£ Eng., 6 (1970) 213. 3 W. A. Tiller, K. A. Jackson, J. W. Rutter and B. Chalmers, Acta Metall., 1 (1953) 428. 4 J. L. Walter, M. F. Gigliotti, B. F. Oliver and H. Bibring (eds.), Proc. 3rd Conf. on In Situ Composites, Ginn, Lexington, MA, 1979. 5 M. McLean, Directionally Solidified Materials for High Temperature Service, Metals Society, London, 1983.
6 J. K. Tien and R. P. Gamble, Mater. Sci. Eng., 8 (1971) 152. 7 A. K. Bhambri, T. Z. Kattamis and J. E. Mortal, Metall. Trans. B, 6 (1975) 523. 8 J. D. Hunt, Proc. Conf. on Solidification and Casting of Metals, Sheffield, July 1977, Metals Society, London, 1979, p. 3. 9 W. Kurz and D. J. Fisher, Acta Metall., 29 (1981) 11. 10 J. W. Erikson, C. P. Sullivan and F. L. Versnyder, in P. R. Sahm and M. O. Speidel (eds.), High Temperature Materials for Gas Turbines, Elsevier, Amsterdam, 1974. 11 A. F. Giamei and J. G. Tschinkel, Metall. Trans. A, 7 (1976) 1427. 12 R. Rosenthal, Ph.D. Thesis, University of London, February 1983. 13 M. Gell, A. F. Giamei and D. N. Duhl, in J. K. Tien, S. T. Wlodek, H. Morrow III, M. Gell and G. E. Maurer (eds.), Superalloys 1980, Proc. 4th Int. Syrup. on Superalloys, Seven Springs, PA, September 21-25, 1980, American Society for Metals, Metals Park, OH, 1980. 14 R. Fernandez, J. C. Lecomte and T. E. Kattamls, Metall. Trans. A, 9 (1978) 1381. 15 G. Durber, P. N. Quested and S. Osgerby, Met. Teehnol., 11 (1984)129.
171
Solidification Morphologies in Directionally Solidified Superalloys P. N. QUESTED and M. McLEAN Division of Materials Applications, National Physical Laboratory, Teddington, Middx. TW11 OLW (Gt. Britain) (Received August 1, 1983)
SUMMARY The microstructures of several nickel-base superalloys directionally solidified using a wide range of processing conditions have been examined. The conditions required for plane front solidification are compatible with the concepts o f constitutional supercooling. In the dendritic regime the variations in cell spacing hi with temperature gradient G and solidification rate V are well described by the ~.1 cc G-1/2V-ll 4 relationship predicted by two recent theories; the observed magnitudes of ~1 are in better agreement with the predictions o f Hunt's theory. The implications of directional solidification processing conditions to the distribution of precipitates in nickel-base superalloys are also considered with particular reference to the occurrence of discontinuous ~,' precipitation and to the morphologies if Mc carbides.
tility grain boundary fracture in cast superalloys. However, the process also influences other microstructural characteristics [5] (e.g. dendrite form and size, crystallographic texture, precipitate morphology and distribution, microporosity). The beneficial mechanical properties of directionally solidified materials are likely to result from a combination of these features; however, their relative importance is not yet fully understood. Current concepts of solidification are largely based on theoretical modelling validated by experiments on simple model alloys. By contrast, superalloys are extremely complex often consisting of ten or more atomic constituents which solidify to form several phases. In this paper the relevance of some established solidification models to such industrial alloys will be examined and their implications for control of microstructure and improvement in mechanical behaviour will be considered.
1. INTRODUCTION 2. SOLIDIFICATION MICROSTRUCTURES The evolution of directional solidification technology for the production of gas turbine blades, pioneered b y Versnyder [1] and Versnyder and Shank [2] in the late 1950s, has been achieved b y industrial exploitation of the fundamental concepts of solidification, established from many studies inspired by the paper of Tiller et al. [3]. The process has been applied successfully to the production of columnar and single-crystal turbine blades from superalloys; blades of in situ composites prepared b y directional solidification of eutectic alloys are also technically possible [ 4] although high processing costs have militated against their commercial implementation. The initial motivation for the development of directional solidification was to control the grain morphology in order to inhibit low duc0025-5416/84/$3.00
The microstructures of four nickel-base superalloys, with compositions listed in Table 1, have been examined after directional solidification in a range of conditions giving different values of the principal process parameters, temperature gradient G and solidification rate V. The experimental procedures for achieving these conditions ranged from current commercial practice to advanced laboratory techniques using liquid metal cooling; full details have been described elsewhere [5]. The solidification morphologies, indicated by the microstructures, are displayed as functions of G and V in Fig. 1. Similar information available in the literature for other nickel-base superalloys is included. The differ© Elsevier Sequoia/Printed in The Netherlands
172 TABLE 1 C o m p o s i t i o n s in w e i g h t per c e n t o f alloys c o n s i d e r e d in t h e p r e s e n t s t u d y Alloy
Ni
Co
Cr
Al
Ti
C
Ta
Mo
W
Nb
Zr
B
Hf
MAR-M 002 MAR-M 246 IN-738LC IN-939
Balance Balance Balance Balance
10.0 10.0 8.5 10.0
9.0 9.0 16.0 22.5
5.5 5.5 3.5 1.9
1.5 1.5 3.5 3.7
0.15 0.15 0.11 0.15
2.5 1.5 1.6 1.4
-2.5 1.75 --
10.0 10.0 2.5 2.0
--0.7 1.0
0.05 0.05 0.08 0.09
0.015 0.015 0.008 0.009
1.5 ----
I
10-3
i
m 10-4 E 0 t,_ C
e 0
10-s 0 U3
"~0"~0/. 10-6
10 z
\ 10 3
10 4
10 s
T e m p e r a t u r e g r a d i e n t (Km -I) Fig. 1. M o r p h o l o g i e s o f d i r e c t i o n a l l y solidified nickel-base s u p e r a l l o y s m a p p e d o n a plot o f log V vs. log G ( t h e lines d r a w n b e t w e e n various z o n e s are c o n t o u r s o f c o n s t a n t G / V ) : o, p l a n e f r o n t ; o, [], v , 0, 0, cellular; o, m, A, v, #, 0, c o l u m n a r d e n d r i t i c ; v , ~, ~, e q u i a x e d d e n d r i t i c ; o, o, o, I N - 7 1 3 C [ 7 ]; D, m, M AR-M 2 0 0 [ 6 ] ; A , IN-100; v , T, v , M A R - M 2 4 6 ; 0, #, ~, M A R - M 0 0 2 ; 0, 0, ~, I N - 7 3 8 L C .
ent types of solidification morphology fall into clear zones, corresponding to plane front, cellular, columnar dendritic and equiaxed dendritic freezing, in the logarithmic display of the (G, V) field. The observations are consistent with the fact that the occurrence of a particular morphology is determined by the magnitude of the ratio G/V relative to various critical values associated with transitions between the zones. The greatest difference
between the various alloys is shown in the cell-to-dendrite transitions. The reasons for this are not apparent from the present experiments but may reflect small changes in the solid-melt interfacial energies which govern the stabilities of secondary dendrite arms.
2.1. Plane front solidification Plane front solidification, first demonstrated for superalloys by Tien and Gamble
173 [6], can be approached at the slowest solidification rates (less than about 10 -3 mm s-i) with the highest temperature gradients (greater than about 20 K mm -i) used, although the presence of carbides often originating in the melt may make this difficult. An example of an alloy at the transition to cellular solidification is shown in Fig. 2(a). The processing conditions required to obtain plane front solidification in several nickel-base superalloys, both from the present study and from published data, are listed in Table 2 together with measurements of their melting ranges AT0. Using the constitutional supercooling condition iV!rit - AT° DL
(l)
for the plane-front:to-cellular transition developed by Tiller e t al. [3], values of the diffusion coefficient D L in the liquid have been calculated from these data. Provided that the difficulties in measuring G are borne in mind, these values are self-consistent and within the accepted range of liquid state diffusivities at the melting point. Consequently, the constitutional supercooling concept appears to apply to these quite complex engineering alloys which largely solidify as a single phase. There has been no significant commerical interest in plane front superalloys, probably because of the poor processing economics. 2.2. Cellular and d e n d r i t i c m i c r o s t r u c t u r e s
Cellular and dendritic microstructures were obtained over most of the processing conditions used in the present study as are obtained in all commercial directional solidification rigs. A quenched longitudinal interface of such a structure, shown in Fig. 2(b), confirms that the dendrites project into the melt. However, the primary cell or dendrite spacing ),1 is very sensitive to both G and V, spanning the approximate range of 20-300 pm in current commercial and laboratory practice. There have been two recent theoretical analyses of cellular and dendritic solidification during directional solidification which yield identical functional dependences of Xl on G and V. H u n t [8] has derived an approximate analytical solution to the diffusion equations for the extremum growth condition (i.e. that the system will adopt the m a x i m u m
Fig. 2. Longitudinal sections of the superalloy MARM 2 4 6 quenched from steady state solidification to freeze the solidifying interface: (a) V = 1.67 × 10 -3 rams -1, G = 1 3 K m m -1, near plane front; (b) V =
8.3 x 10-2 mm s-1, G = 13 K mm-1, columnar dendritic.
174 TABLE 2 Experimentally determined solidification parameters for plane front solidification of nickel-base superalloys Alloy
G (K m m -1 )
Ycrit ( m m s -1)
(G/V)crit (K s m m -2)
AT0 (K)
D L = ATo(G/Y)crit -1 (mm 2 s-1)
Reference
IN-738LC MAR-M 246 MAR-M 002 MAR-M 200 IN-713C
20 20 20 10 11
<1.67 < 1.67 <1.67 10 -3 0.83
1.20 x 104 1.20 x 104 1.20 X 104 104 1.3 x l 0 4
85 ~100 ~100 139 30
7.1 x 10 -3 ~8.3 × 10 -3 ~ 8 . 3 X 10 -3 13.9 x 10 -3 2 . 3 × 1 0 -3
This work This w o r k This work [6] [7]
X 10 -3 X 10 -3 X 10 -3 ×10 -3
G, t e m p e r a t u r e gradient; V, solidification front velocity; AT0, alloy freezing range; DL, solute diffusivity in the liquid alloy.
growth rate or minimum undercooling), showing that
i
i
31117
X1 = {64FDLmL(ko-- 1)Co/3}t/4G-1/2V -1/4 (2) where
20C
E
/3=1+
koD L
G rl
m L ( 1 - - ko)Co V
DL G =l+----
AT0 V
i100
(3)
m L is the liquidus slope, k0 is the partition coefficient, Co is the solute concentration, F ~ 7~AS, ~( is the solid-melt interfacial energy and AS is the entropy of fusion. Equation (2) is only determinate when G/V < ATo/DL, i.e. when the condition for constitutional supercooling is satisfied. When G/V ~ ATo/DL, then/3 ~ 1 and eqn. (2) reduces to X1 -~-/647DLmL~(1 -- k0 )Co}1/4G_1/2V_I/4
(4)
The measurements of dendrite arm spacing for three nickel-base superalloys are displayed as a function of the product G-112V-114in Fig. 3. When the materials have clearly established dendritic microstructures, the data are approximately described by a c o m m o n straight line, where reductions in G or V lead to a coarsening of the dendrites. However, as the conditions for plane front solidification are approached (i.e. 1 >/3 > 0) then )tl decreases with decreasing G or V. This deviation results from the melting-back of the dendrite tips to lower temperatures as/3 ~ 0, which affects the kinetics of solute partitioning in the melt in proportion to the local liquid diffusivity. Breakaway from the linear portion
,<
I
I I 0.1 V-1/4 G~112 (ml/4sl/4 K-IIz)
I 02
Fig. 3. Primary cell or dendrite spacing )~t as a function o f G-1/2V -114 for three directionally solidified nickel-base superalloys: A, e, - , well-formed dendritic structures; A, O, G, approach of plane front conditions; A, MARoM 246; e, MAR-M 0 0 2 ; I , IN738LC; ~-e--% ~-B--% commercially processed.
of the curve does n o t occur at a unique value of G - 1 / 2 V -114 but is determined by G/V. However, the data shown obtained under similar conditions are consistent with the deviation from linearity which correlates with the alloy melting range. The curve for MAR-M 002 shows a less abrupt drop than those for IN738LC and MAR-M 246; this is probably a consequence of the larger volume fraction of 7-7' eutectic in MAR-M 002. Identifying the slope of the linear portion of the curve with the bracketed term in eqn. (4) and taking DL = 5 X 10 -9 m 2 s-1, mL = 300 K (wt.fraction) -1, 1 -- k0 = 0.9, Co = 0.2 wt.fraction and AS = 106 J m -3 K -1 gives a value for the solid-melt interracial energy of 176 mJ m -2 which is compatible with previous measurements. Consequently the model satisfactorily
175 describes the behaviour of these complex alloys in b o th predicting the plane-front-tocellular transition and accounting for the dimensions of the dendrites as a function of the principal solidification parameters. Kurz and Fisher [9] have proposed a model involving p e r t u r b a t i o n analysis rather than the e x t r e m u m criterion, which gives the same functional d ep en de nc e of X1 on V and G but with a different constant of proportionality. The ratio of the values of )~1 predicted by the two theories is ()kl)Hunt __ ( k O 2 ] TM
()~0KF
18.5I
~ 0.56
However, because of the f o u r t h r o o t the value o f 7 calculated f r om the Kurz-Fisher equation (16.8 mJ m -2) is an order of magnitude less than th at obtained from Hunt's model and is m u ch smaller than measured values of the solid-liquid interfacial energy. Consequently, the present data are better described by the H u n t model. Both the H u n t and the Kurz-Fisher models describe solidification in a cylindrical element, parallel to G and V, and the full periodic structure is generated by s y m m e t r y . This implicitly assumes a regular array of dendrites. However, experimental measurements show a very wide distribution in the distances between neighbouring dendrites as shown in Fig. 4, although analysis of the mean values of
X1 is consistent with the theoretical models. This range of spacings is probabl y i m p o r t a n t in a c c o m m o d a t i n g the mean X1 to changing growth conditions. Certainly, X1 changes rapidly in response to variations in G a n d / o r V as indicated by the plot of ~1 along the length of directionally solidified IN-738LC produced by a commercial process where G progressively decreases (Fig. 5). Details of quenched dendritic interfaces in various superalloys, shown in Fig. 6, indicate that dendrite spacings (i) increase by a simple overgrowth mechanism where some dendrites lag behind their neighbours which e x t e n d radially and prevent the continuing growth of the trailing dendrite and (ii) decrease by the initiation of instabilities on existing dendrites and their subsequent growth, either through the conversion of an existing tertiary arm to form a new primary or by the branching of dendrites.
2.3. Non-aligned structures The aligned dendritic structure can break dow n in two ways. Firstly, there can be a true columnar-to-equiaxed dendrite transition where the axial diffusion flux in the
Shell mould
300
40
Solidificatior rate m m h-t) --
60 . . . . . 300
30
Primary dendrite arm spacing (tJm) Intercept Planimeter method measurement 170 105
165.5.~0.9 1073:0,7
v
o £
20 _~ 100
,I.
I
I
o
la
I
,I,
200
I
I
20
i 300 Dendrite arm spacing
100
, I,
I
,
I, 40
l, 60
L , k , 1 , 1 , l , i 80
Position
4~0
Fig. 4. Distribution of nearest dendrite-dendrite separations measured on a transverse section of directionally solidified IN-939.
1(30 of
120
1/-.0
160
180
, ) 200
section ( m m )
Fig. 5. Mean dendrite spacings measured on transverse sections cut at various points along the lengths of directionally solidified ingots of IN-738LC prepared commercially in moulds with different thermal characteristics.
176
liquid is not adequate to supply the advancing solidification front; this limits the size of components that can be produced by the static power-down technique where G progressively decreases as solidification proceeds [lo]. However, practical limitations of heat flow present another problem at high withdrawal rates [ 111 from dynamic directional solidification rigs. Since, at steady state, heat loss from the solidified material is largely by radiation (or by forced cooling, e.g. by liquid metals) from the ingot surface, axial heat flow at the solid-liquid interface which is required for directional solidification can only be achieved when the solidification front is remote from the cooling zone of the rig. At high withdrawal rates the solidification front can move into the cooling zone where the dendrites solidify radially.
3.
PRECIPITATE
MORPHOLOGIES
The high temperature strength of superalloys largely derives from the precipitated phases most of which are deposited from the solid state in y (nickel) dendrites. The solidification conditions considerably influence the nature and distribution of these phases by virtue of the different post-solidification cooling sequences that are associated with the processing parameters G and V. For volume diffusion control, isotropic coarsening is described by the LifshitzSlyozov-Wagner cubic equation (see for example ref. 5)
where r and r. are the present and initial radii of the feature, B is a kinetic constant, T is the absolute temperature and t is elapsed time. If coarsening takes place as the material is translated at a rate V through a temperature gradient G, then the coarsening in the space element x to x + dx is described by the expression
Fig. 6. Details of quenched solid-liquid interfaces in directionally solidified nickel-base superalloy: (a) overgrowth of dendrite to increase the mean spacing in IN-100; (b) branching of dendrite to decrease the mean spacing in MAR-M 246.
or
177
The kinetic constant is proportional to the product of solute concentration and diffusion coefficient and so can be written as B = Bo exp(-- Q~I
RT!
Since the temperature is determined by G, therefore
~x
Bo exp[--Q/R{T(O) Gx}] T(0) -- Gx -
-
(r3) - V
where T(0) is the temperature when x = 0. Integration of eqn. (5) gives r 3 = ro3 + B ~ ( G V ) -1
(6)
where oo
xp =
- exp(--u) du •
Fig. 7. D i s c o n t i n u o u s p r e c i p i t a t i o n o f 7 ' in I N - 7 3 8 L C d i r e c t i o n a l l y solidified at 1.67 x 10 -2 m m s -1 in a t e m p e r a t u r e g r a d i e n t o f 13 K r a m -1. ( A f t e r ref. 12.)
1A
Q/RT(O)
is a standard integral. Typically ~o ~ 0.1 for liquid state diffusion and ~ ~ 10 -6 for solid state diffusion [5]. This points to the importance of the cooling rate GV in determining the size of secondary dendrites and 7' precipitates by liquid and solid state diffusion respectively. The secondary dendrites appear to have relatively little effect on the mechanical behaviour of directionally solidified superalloys and most of the 7' precipitates can be manipulated by subsequent heat treatment. However, at least two features of precipitate morphology that are dependent on processing conditions appear to be irreversible.
3.1. Discontinuous ~,' precipitates In certain alloys a small volume fraction of the 7' is heterogeneously precipitated at grain boundaries in a form that provides little strengthening. Examination of IN-738LC directionally solidified in a wide range of conditions indicates that this discontinuous precipitate forms when dendritic segregation occurs in combination with relatively slow cooling rates. A typical example is shown in Fig. 7. Quenching experiments suggest that these ~/-7' islands either can nucleate spontaneously at grain boundaries or can grow on small ~/-7' eutectic nuclei that constitute the last fraction of melt to freeze during dendritic solidification of this alloy. In both cases the final dimensions of the zones of discontinuous )" are very sensitive to the cooling rate GV, as
1000
X
t
100 o
c
~5
"6 ~o
~oo
G V ( K s "f )
Fig. 8. Cross-sectional areas, m e a s u r e d o n t r a n s v e r s e sections, o f d i s c o n t i n u o u s 7 - 7 ' islands in d i r e c t i o n a l l y solidified I N - 7 3 8 L C as a f u n c t i o n of G V .
indicated in Fig. 8. The processing conditions also influence the volume fraction of discontinuous 7' largely by affecting the extent of segregation which changes the composition of the final liquid fraction. Thus, when plane front conditions are approached, both eutectic and discontinuous 7' are inhibited. The growth of the discontinuous 7' zones as the temperature gradient is traversed will be described by an expression of the form of eqn. (6):
r o: (GV)-I/3 which appears to fit the experimental data reasonably well.
178
N o t all alloys exhibit either eutectic or discontinuous 7' precipitation after directional solidification. A recent trend in tbe development of superalloys specifically for use in the single-crystal form has been to produce a wide temperature gap between the solidus and the 7' solvus temperatures in order to improve the heat treatment characteristics of the alloys [13]. Where this heat treatment window is too small, or non-existent as for IN-738LC, it is not possible to dissolve fully the 7' produced in the directional solidification sequence. 3.2. Carbides The morphologies and dimensions of MC carbides that are deposited interdendritically are both very sensitive to the processing conditions. For example, Fernandez et al. [14] have shown that, in IN-100, Chinese script and blocky carbide morphologies are preferred at low and high values of G / V respectively; however, the average size of both types of carbide scales as G V. Similar behaviour is observed in IN-738LC and MAR-M 246. It is interesting that a similar transition between Chinese script and blocky carbides has been observed between virgin and recycled cast superalloys [15]. This has been clearly identified with the accumulation of nitrogen in the recycled materials which forms an extremely stable titanium carbonitride dispersion in the melt, so leading to profuse nucleation of carbides which grow in a blocky form. By contrast, when the Ti2(CN) particles are absent, homogeneous nucleation of the carbide is difficult and extensive carbide growth along (111~ directions occurs on relatively few nuclei. Examination of the blocky carbides in directionally solidified IN-738LC has shown that they also have a duplex structure of a small titanium-rich core on which the blocky MC carbide is deposited (Fig. 9). No such cores are apparent in the Chinese script carbides. These results clearly indicate that the carbide morphology is not simply a function of the solidification conditions b u t is largely influenced by subtle chemical modification during processing. The conditions leading to blocky carbides involve low solidification rates, when the melt has a relatively long contact time with mould and atmosphere, and changes in alloy composition probably result
V- w lOpm I
I
Fig. 9. Micrograph of a blocky MC carbide in directionally solidified IN-738LC showing the aluminiumand titanium-rich core.
from interactions with the environment or mould. This indicates the importance of avoiding contamination of the melt during processing which could lead to damaging changes in the solidification sequence. Certainly in conventional castings there is an empirical correlation between the density of blocky carbide and the occurrence of microporosity. Since microporosity can dramatically affect the stress rupture properties at intermediate temperatures, these considerations may partly explain the improvements in creep behaviour that can be obtained by increasing G and V.
4. IMPLICATIONS F O R PERFORMANCE
The mechanical behaviour of directionally solidified superalloys is quite sensitive to both the processing and the testing conditions although it is difficult to correlate the changes with specific microstructural features. For example, Fig. 10 compares creep curves of MAR-M 246 directionally solidified in a commercial and in a liquid-metal-cooled laboratory rig, showing that the high temperature gradient consistently leads to longer lives. Not all this difference is attributable to the finer 7' dispersion in the liquid-cooled material although that certainly makes a contribution. Perhaps more important factors are the association of damage nucleation with interdendritic features such as carbides, dis-
179 0.20
I
I
x
o.15
~1
//
o.,o
iii I
-
0.05
0
/~/.~ -/
500
Time (h)
-
1000
1500
Fig. 10. C o m p a r i s o n o f creep curves f o r M A R - M 2 4 6 d i r e c t i o n a l l y s o l i d i f i e d at 8.3 x 10 -2 m m s -1 i n a l o w t e m p e r a t u r e g r a d i e n t o f 4 K m m -1 ( - - - ) a n d a h i g h t e m p e r a t u r e g r a d i e n t o f 13 K m m -1 ( ). T h e t e s t s w e r e per-
f o r m e d in air a t 1 1 2 3 K a n d 2 5 0 MPa.
3
(b)
creep behaviour of IN-738LC tested at 850 °C with different stresses giving a wide range of lives. There is clearly an increased advantage in the directional solidification of this alloy in long-term tests; however, at higher stresses and in a similar study on IN-939, even this trend is reversed. It is inevitable that over such a wide range of conditions there will be changes in deformation and/or fracture mechanisms in either or both of the materials which will affect their relative performances. However, insufficient data are currently available to allow predictions to be made with confidence. There remains, therefore, considerable scope to take full advantage of solidification microstructures that can be controlled during directional solidification of superalloys.
Fig. 11. R a t i o s o f (a) r u p t u r e life a n d (b) m i n i m u m c r e e p r a t e o f d i r e c t i o n a l l y s o l i d i f i e d (ds) r e l a t i v e t o c o n v e n t i o n a l l y cast (cc) I N - 7 3 8 L C (G = 13 K m m - 1 ; V = 8 . 3 3 × 10 -2 m m s - l ) .
5. C O N C L U S I O N S
continuous 7' precipitate zones and transverse grain boundary segments and the relationship of crack propagation to the dendrite dimensions. The benefits of directional solidification over conventional casting are not uniform. Figure 11 shows such a comparison for the
(1) The conditions giving plane front solidification in directionally solidified superalloys are consistent with the predictions of the constitutional supercooling theory. (2) Primary cell or dendrite arm spacings as a function of solidification conditions are in good agreement with the theoretical model of Hunt.
~u
2
0 (a) 1.5 u
-o1~, ~ 1.0
u
~ 0.5 _E .c IE
o
180
(3) Precipitate morphology and composition are both sensitive to the solidification conditions. (4) The mechanical behaviour of directionally solidified superalloys, particularly in longterm creep testing, is sensitive to the solidification conditions.
REFERENCES 1 F. L. Versnyder, in R. F. Hehemann and G. Mervin Ault (eds.), High Temperature Materials, Wiley-Interscience, New York, 1959. 2 F. L. Versnyder and M. E. Shank, Mater. Sc£ Eng., 6 (1970) 213. 3 W. A. Tiller, K. A. Jackson, J. W. Rutter and B. Chalmers, Acta Metall., 1 (1953) 428. 4 J. L. Walter, M. F. Gigliotti, B. F. Oliver and H. Bibring (eds.), Proc. 3rd Conf. on In Situ Composites, Ginn, Lexington, MA, 1979. 5 M. McLean, Directionally Solidified Materials for High Temperature Service, Metals Society, London, 1983.
6 J. K. Tien and R. P. Gamble, Mater. Sci. Eng., 8 (1971) 152. 7 A. K. Bhambri, T. Z. Kattamis and J. E. Mortal, Metall. Trans. B, 6 (1975) 523. 8 J. D. Hunt, Proc. Conf. on Solidification and Casting of Metals, Sheffield, July 1977, Metals Society, London, 1979, p. 3. 9 W. Kurz and D. J. Fisher, Acta Metall., 29 (1981) 11. 10 J. W. Erikson, C. P. Sullivan and F. L. Versnyder, in P. R. Sahm and M. O. Speidel (eds.), High Temperature Materials for Gas Turbines, Elsevier, Amsterdam, 1974. 11 A. F. Giamei and J. G. Tschinkel, Metall. Trans. A, 7 (1976) 1427. 12 R. Rosenthal, Ph.D. Thesis, University of London, February 1983. 13 M. Gell, A. F. Giamei and D. N. Duhl, in J. K. Tien, S. T. Wlodek, H. Morrow III, M. Gell and G. E. Maurer (eds.), Superalloys 1980, Proc. 4th Int. Syrup. on Superalloys, Seven Springs, PA, September 21-25, 1980, American Society for Metals, Metals Park, OH, 1980. 14 R. Fernandez, J. C. Lecomte and T. E. Kattamls, Metall. Trans. A, 9 (1978) 1381. 15 G. Durber, P. N. Quested and S. Osgerby, Met. Teehnol., 11 (1984)129.