abnormal grain growth and grain boundary faceting in a model ni-base superalloy(hip.pdf

ABNORMAL GRAIN GROWTH AND GRAIN BOUNDARY

FACETING IN A MODEL Ni-BASE SUPERALLOY

S. B. LEE 1{, D. Y. YOON 1 and M. F. HENRY 2

1Department of Materials Science and Engineering, Korea Advanced Institute of Science andTechnology, Taejon 305-701, South Korea and 2General Electric Corporate Research and Development

Center, One Research Circle, Niskayuna, NY 12309, USA

(Received 3 January 2000; accepted 23 April 2000)

AbstractÐNormal or abnormal grain growth in a model Ni-base superalloy is observed to depend on thegrain boundary structure when heat-treated in a solid solution temperature range above the solvus tem-perature (11508C) of the g ' phase. When heat-treated at 12008C abnormal grain growth occurs and mostof the grain boundaries are observed to be faceted by optical microscopy, transmission electron mi-croscopy, and scanning electron microscopy at the intergranular fracture surface. Some of the grain bound-ary facet planes are expected to be singular corresponding to the cusps in the polar plot of the boundaryenergy against the inclination angle, and it is proposed that if these boundary segments move by a bound-ary step mechanism, the abnormal grain growth can occur. When heat-treated at 13008C normal graingrowth occurs, the grain boundaries are defaceted, and hence atomically rough. Normal growth is expectedif the migration rate of the rough grain boundaries increases linearly with the driving force arising fromthe grain size di�erence. The correlation between the grain boundary structural transition and the growthbehavior thus appears to be general in pure metals and solid solution alloys. 7 2000 Acta MetallurgicaInc. Published by Elsevier Science Ltd. All rights reserved.

Keywords: Nickel alloy; Abnormal grain growth; Grain boundary faceting

1. INTRODUCTION

At temperatures close to 0 K all crystals in equili-

brium with a surrounding vapor or liquid are pre-

dicted [1±7] and have indeed been observed [8±11]

to be polyhedral with atomically ¯at singular sur-

face planes. At high temperatures each singular sur-

face plane can undergo roughening transition as

predicted initially by Burton et al. [12]. At the

roughening temperature TR the planar surface is

predicted to become curved [13] and at high tem-

peratures some grains even become spherical [14±

19]. The curved surface shape thus manifests the

rough atomic structures which have been con®rmed

by di�raction methods [20, 21]. The growth beha-

vior of a single crystal from melt or solution was

found to depend critically on the surface structure

[22±24]. It was also proposed that both the coarsen-

ing of many grains dispersed in a liquid matrix [25,

26] and the growth of catalytic metal particles on a

substrate [27, 28] also depended critically on their

shape and hence on their surface structure.

In the early 1970s Hart [29, 30] proposed a

®rst order structural transition of a grain bound-

ary treating it as a two-dimensional phase. At

about the same time Gleiter [31] also proposed a

grain boundary phase transition based on the ob-

servation of apparently discontinuous change of

the energies of two grain boundaries in Pb at

about 0.73Tm and 0.76Tm, where Tm is the melting

point. (These were probably defaceting transitions

as pointed out by Cahn [32].) Simpson et al. [33]

also suggested that the observed slope changes of

the log of the grain boundary migration rates

against the reciprocal temperature were due to

grain boundary transitions. Later (in 1986)

Rottman [34] predicted the roughening transition of

low angle grain boundaries by making an analogy

with a stepped surface. Shvindlerman and Straumal

[35] showed a collection of numerous results in var-

ious metals and non-metals which indicated the

roughening transitions of grain boundaries with co-

incidence site lattice (CSL) orientations or near

CSL orientations at temperatures between about

0.6Tm and 0.9Tm. Recently, Westmacott and

Dahmen [36] observed that a small aluminum grain

embedded in another large one with a large misor-

ientation angle had a polyhedral shape at low tem-

peratures. At a high temperature the ¯at symmetric

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grain boundary segments became rounded indicat-ing the roughening transition. It was shown to be

reversible during temperature cycling. Although therounding of the planar grain boundaries in theequilibrium shape is a direct indication of the

roughening transition as for the crystal surface, nodirect in situ observation of a rough grain boundaryat atomic scale has yet been made.

In polycrystals the grain boundary planes donot normally correspond to those which appearin the equilibrium shape. If the grain boundary

energy varies strongly with the grain boundarynormal (or the inclination angle) or particularlyif there are cusps in the polar plot of the grainboundary energy s against the normal direction,

the grain boundaries can be faceted [1, 2, 32]with zigzag shapes. The faceting of both generaland special grain boundaries have indeed been

observed in a number of metals [37±40] and ox-ides [41±43]. Such impurities and additives as Oin Ni [37, 38], Bi in Cu [44±47], Te in Fe [48,

49], and CaO or SiO2 in Al2O3 [50] have beenobserved to induce the grain boundary faceting. Athigh temperatures some of the grain boundary facet

planes are expected to be rough corresponding tothe edges of the curved boundary segments in theequilibrium shape [1, 2, 13, 32], and with tempera-ture increase the defaceting transition proceeds with

an increase of the rough facet plane area. This is a®rst order phase transition unlike the rougheningtransition of a singular grain boundary which can

be a higher order transition if the analogy to thesurface roughening transition holds [51±53]. If thedefaceting proceeds with temperature increase until

the average boundary orientation becomes equal toan orientation of a curved boundary segment in theequilibrium shape, the defaceting transition is com-plete with a rough structure for the entire boundary

and a macroscopically curved shape. Thus in defa-ceting transition the singular boundary segments

which coexist with the rough boundary segments

transform into the rough boundaries. As pointed

out by Cahn [32], this is equivalent to the dissol-

ution of an intermetallic compound into a solid sol-

ution. The defaceting transition arises from the

roughening of the edges and corners of an equili-

brium shape, while the roughening transition

usually refers to the change of a singular boundary

corresponding to a cusp in the s-plot and hence its

blunting.

As pointed out earlier, the grain boundary tran-

sition observed by Gleiter [31] in Pb was probably a

defaceting transition and many of the observations

collected by Shvindlerman and Straumal [35] may

also have been defaceting rather than roughening

transitions. The ®rst direct and deliberate obser-

vations of the defaceting transition were made by

Hsieh and Ballu� [39] for asymmetric tilt grain

boundaries with CSL orientations in Al and Au.

The defaceting±faceting transitions were observed

to be reversible, and the defaceting was complete in

Al at 0.54Tm and in Au at 0.96Tm [39].

The grain boundary properties are expected and

indeed have been observed to depend on the bound-

ary structural transition as cited by Shvindlerman

and Straumal [35]. We have recently observed [37]

that the grain coarsening behavior in pure polycrys-

talline Ni varied with the boundary structural

change. At high temperatures close to the melting

point in a carburizing atmosphere, the grain bound-

aries were defaceted with curved shapes and hence

had an atomically rough structure. Then normal

grain growth was observed. However, at low tem-

peratures the grain boundaries were faceted and

abnormal grain growth (AGG) occurred. In a low

vacuum some or all of the grain boundaries were

faceted at all temperatures tested and AGG

occurred. Such a correlation between the grain

boundary faceting and AGG was also observed in

pure Ag when heat-treated at di�erent temperatures

in either oxygen or vacuum [54]. It has been

suggested [25, 37] that AGG occurs with faceted

grain boundaries because they move by a boundary

step mechanism which has been proposed by

Gleiter [55, 56].

The purpose of this work is to test the correlation

between the grain boundary faceting and AGG in a

model Ni-base superalloy with most of the metallic

elements (Co, Al, Ti, Cr, and Mo) that are found in

the commercial alloys but without any C. Like in

commercial Ni-base superalloys coherent g '-precipi-tates form in this model alloy when heat-treated at

temperatures below the solvus temperature of

11508C [57]. The advantage of using this alloy is

that because the grain boundaries are strongly

pinned by the g '-precipitates the initial structures

with ®ne grains can be obtained by heat-treating

below the solvus temperature. The heat treatments

for grain growth were performed at 1200 andFig. 1. The initial optical microstructure of the specimen

before the heat treatments.

3072 LEE et al.: ABNORMAL GRAIN GROWTH

13008C above the g ' solvus temperature where thealloy existed as a single phase solid solution.

2. EXPERIMENTAL PROCEDURE

The alloy of Ni±24Co±4Al±4Ti±5Cr±5Mo (by

wt%) was made by spray forming. The ingots werehot isostatically pressed at 10508C for 6 h under apressure of 20 ksi and specimens of 7 mm in diam-

eter and 12 mm in length were cut out from thesame region of the ingot. The specimens were heat-treated by rapidly pushing to the center zone of a

tube furnace preheated to either 1200 or 13008C.After holding for various periods ranging from5 min to 12 h at these temperatures in a ¯owing Ar

atmosphere, the specimens were quenched in water.In order to examine the grain boundary mor-phology at the fracture surface, notched impactspecimens of 1� 1� 5:5 cm3 were made and heat-

treated under the same conditions. These were frac-tured with a Charpy impact tester after immersingin a liquid nitrogen bath. The fracture surface was

examined under a scanning electron microscope(SEM).

3. RESULTS AND DISCUSSION

Before the heat treatments (but after the hot iso-

static pressing) the grains were fairly uniform in

size ranging from about 100 to 200 mm as shown in

Fig. 1. Because the hot isostatic treatment was per-

formed at 10508C, which is below the solvus tem-

perature (11508C) of the g ' phase, the grain growth

was probably limited by the g '-precipitates. After

heat-treating for 5 min at 12008C (above the g ' sol-vus temperature) large grains appeared surrounded

by small grains which had approximately the same

size as those in the initial state. Thus a typical

AGG structure was observed as shown in Fig. 2(a).

After 10 min at the same temperature more large

grains appeared as shown in Fig. 2(b), and after 2 h

most of the small grains had disappeared and the

large grains had impinged upon each other as

shown in Fig. 2(c). The equivalent sphere diameters

of the grains were measured by an image analyzer

and their size distributions for the specimens in

Fig. 2 are shown in Fig. 3. For the specimens heat-

treated for 5 and 10 min about 150±200 grains were

measured, but for the specimens heat-treated for

Fig. 2. The optical microstructures after heat treatments at 12008C for (a) 5 min, (b) 10 min, and (c)2 h.

LEE et al.: ABNORMAL GRAIN GROWTH 3073

2 h, their grain sizes were so large that only about50 grains could be measured. After heat-treating for

5 min at 13008C, there was very little growth of thegrains as shown in Fig. 4(a), and after 10 min, thereappeared to be a slight growth as shown in

Fig. 4(b). There was a substantial growth after 2 has shown in Fig. 4(c). These micrographs and themeasured grain size distributions of Fig. 5 show

that the grain growth at 13008C was normal.Comparisons of the micrographs (Figs 2 and 4) andthe grain size distributions (Figs 3 and 5) show that

the largest grains after heat-treating at 12008C werelarger than the largest grains after heat-treating at13008C for the same periods.The specimens heat-treated at 12008C showed

some jagged grain boundaries which could be seeneven under an optical microscope as shown in

Fig. 6(a), but the specimens heat-treated at 13008Cshowed only curved grain boundaries as shown inFig. 6(b). The grain boundary morphology was

more clearly revealed at the fracture surface of thespecimens which were broken by impact as shownin Figs 7 and 8. The fracture appeared to be predo-

minantly intergranular and the specimens heat-trea-ted at 12008C showed striations with steps at mostof the grain boundaries as shown in Fig. 7(a). The

faceted morphology of the grain boundaries wasmore clearly visible at higher magni®cations asshown in Fig. 7(b). Previously, faceted grain bound-aries were also observed at the intergranular frac-

Fig. 3. The measured distributions of the equivalent sphere diameters of the grains in the specimensheat-treated at 12008C for (a) 5 min, (b) 10 min, and (c) 2 h.


ture surfaces of Ni [38] and Fe with Te [48, 49]. In

contrast, the specimens of this alloy heat-treated at

13008C showed smoothly curved grain boundaries

without any faceting as exhibited in Fig. 8. These

observations show that the defaceting transitionoccurred for most of the grain boundaries at tem-

peratures between 1200 and 13008C. Some of the

grain boundary facet planes observed after heat-

treating at 12008C are expected to be singular with

the local minimum boundary energies correspond-

ing to the cusps in the s-plot. The defaceted grain

boundaries at 13008C are expected to have an

atomically rough structure.

These grain boundary shapes were con®rmed by

observations under transmission electron mi-

croscopy (TEM). Out of the six grain boundaries in

the specimen heat-treated for 10 min at 12008C[Fig. 2(b)] examined under TEM, four grain bound-

aries clearly showed faceted grain boundaries as

exhibited in Fig. 9(a). Five grain boundaries exam-

ined in the specimen heat-treated at 13008C for

10 min, as exhibited in Fig. 9(b), did not show any

faceting but smoothly curved ®ne bumps which are

also visible at the fracture surfaces shown in

Fig. 8(b). These bumps are the g '-precipitates whichnucleated at the grain boundaries during quenching

after the heat treatment. The g '-precipitates of sizes

slightly smaller than 0.1 mm, which are visible in the

grains in both Figs 9(a) and (b), are sphericalbecause their lattice parameter is almost equal to

that of the matrix g phase [57]. These bumps were

absent at the grain boundaries heat-treated at

12008C as can be seen in Figs 9(a) and 7(b). It thus

appears that the preferential nucleation of the g '-precipitates at the grain boundaries occurred only

in the specimen heat-treated at 13008C. The rough

grain boundaries at 13008C will tend to undergofaceting transitions during rapid cooling (by

quenching) at temperatures close to 12008C (which

is higher than the g ' solvus temperature), but the

transition is apparently slow enough to retain the

rough structure until the g '-precipitates begin to

form below the g ' solvus temperature. Although it

is likely that the precipitation of a second phase atgrain boundaries will depend on the grain boundary

structure, de®nitive conclusions cannot be drawn

until further studies are made.

The observations in this alloy thus show that

Fig. 4. The optical microstructures after heat treatments at 13008C for (a) 5 min, (b) 10 min, and (c)2 h.


when the grain boundaries are faceted AGG occurs

and when defaceted normal growth occurs as

shown previously in Ni [37] and Ag [54]. Gleiter

[31] also noted that AGG occurred at temperatures

below the transition temperatures of the two grain

boundaries in Pb. A similar correlation between the

interface atomic structure and the coarsening beha-

vior exists also for the grains dispersed in liquid

matrix [25, 26]. Only when the grains are polyhedral

with ¯at singular surfaces AGG occurs [26±28, 58,

59]. When the grains are spherical with a rough sur-

face normal growth occurs and is controlled by dif-

fusion in the liquid matrix [17±19]. It is well known

that the growth behavior of crystals from melt or

solution depends on the crystal surface structure

[12, 22±24]. If it is atomically rough, the growth is

continuous with the rate linearly increasing with the

supersaturation. For a system of many spherical

grains in liquid matrix, normal di�usion controlled

growth was predicted [60, 61] and veri®ed exper-

imentally [17±19].

If the surface is atomically ¯at, the crystals which

are free of defects grow by two-dimensional nuclea-

tion as proposed by Burton et al. [12]. Then the

growth rate is predicted to be very low at low

supersaturation and increase abruptly when a

threshold supersaturation is exceeded as for the

nucleation process in three dimensions. Such crystal

growth by two-dimensional nucleation was veri®ed

experimentally, for example, for 4He [62] and Ga

Fig. 5. The measured distributions of the equivalent sphere diameters of the grains in the specimensheat-treated at 13008C for (a) 5 min, (b) 10 min, and (c) 2 h.


[63] crystals. For a system of many polyhedralgrains dispersed in a liquid matrix, the driving force

for their coarsening arising from the size di�erenceis usually assumed to be proportional to 1=r�±1=r,where r is the size of a particular grain and r� is

roughly the average size which has to be determinedby the ¯ux balance condition among all the grains.As proposed by Park et al. [26], those grains which

are slightly larger than r� will grow very slowlybecause they are under low driving forces and onlythose which are large enough to exceed the critical

driving force for rapid two-dimensional nucleationwill grow at substantial rates, thus resulting inAGG. Wynblatt [28] observed abnormal growth offaceted Pt particles deposited on alumina substrate

in oxygen atmosphere and proposed the samegrowth mechanism. Wynblatt and Gjostein [27]obtained numerical solutions for the two-dimen-

sional nucleation mechanism which exhibited AGGin agreement with the observations.If there are dislocations the steps at the surface

can grow in spiral form and the growth rate is pre-dicted to vary parabolically with the driving force

for a single screw dislocation emerging vertically atthe surface [12]. At low driving forces the growth

rate will be much higher than that expected by two-dimensional nucleation but still substantially lowerthan that for a rough surface. At high driving

forces the two-dimensional nucleation can be thedominant mechanism for growth and the growthrate can approach that for a thermodynamically

rough surface by kinetic roughening [64, 65].Because the growth rate will be still nonlinearagainst the driving force, AGG can probably occur

even with dislocations which must be present in thegrains under most of the experimental conditions.Gleiter [55, 56] proposed that even in single

phase polycrystalline solids the grain growth

occurred by the same step growth mechanism basedon his observations of apparently spiral growth ofgrain boundary steps in an Al alloy [55]. Such a

mechanism is likely to operate with singular grainboundaries which are implicit in his model. Thus ifthe faceted grain boundaries move by the step

mechanism either at dislocations or by two-dimen-sional nucleation, AGG can occur. If the grainboundaries are rough, their migration rate will be

determined by the atom jump rate across the grainboundary, which will increase linearly with the driv-ing force. Then normal growth is expected as indeed

Fig. 7. The intergranular fracture surface of the specimenheat-treated at 12008C for 2 h at (a) a low and (b) a high

magni®cation.

Fig. 6. The typical optical micrographs of grain bound-aries in the specimens heat-treated for 10 min at (a)12008C and (b) 13008C. The arrow in (a) indicates a

faceted grain boundary.


observed in Ni [37], Ag [54], and the Ni-based

superalloy in this work. The analysis of Thompson

et al. [66] and the simulation of Srolovitz et al. [67]

also predicted normal growth of grains with isotro-

pic grain boundary energy. On the other hand, the

simulation results of Park [68] showed AGG with

faceted grain boundaries.

Recently, strong evidence for the step growth offaceted grain boundaries was observed by Lee et al.

[69] in BaTiO3 with excess TiO2. They found thatwhen heat-treated in air, the grain boundaries werefaceted and only those grains with double twins

grew to large sizes elongated in the direction of thetwins. They attributed this behavior to the re-entrant edges produced at the junctions of the

double twins with the faceted grain boundaries.When heat-treated in H2 the grain boundariesbecame defaceted (and therefore rough), and nor-

mal growth occurred in all directions without anypreference to the directions of the double twins.These observations are only consistent with the con-clusion that the double twins in¯uence the step

growth at the faceted grain boundaries and becomeine�ective at the rough grain boundaries.

4. CONCLUSIONS

It now appears to be quite certain that grainboundaries can become rough at high temperatures.The singular grain boundaries with the normal

directions corresponding to the cusps in the s-plotscan undergo the roughening transition and thefaceted grain boundaries can also become rough by

the defaceting transition. The correlation betweenthe faceted grain boundaries and AGG, andbetween the rough grain boundaries and normalgrowth appears to be general in pure metals and

single phase alloys. But the step growth mechanismproposed for AGG with faceted grain boundariesobviously needs to be clari®ed possibly by more in

situ observations of the growth behavior underTEM and quantitative determination of the depen-dence of the migration rate on the driving force. In

particular, if the faceted grain boundaries consist ofboth singular and rough segments, their migrationbehavior is yet to be understood, although it is

Fig. 8. The intergranular fracture surface of the specimenheat-treated at 13008C for 2 h at (a) a low and (b) a high

magni®cation.

Fig. 9. The TEM micrographs of the grain boundaries in the specimens heat-treated for 10 min at (a)12008C and (b) 13008C.


possible that the migration rate is controlled by thesingular segments. If the step growth hypothesis is

valid, the AGG behavior is expected to depend cri-tically on the heat treatment temperature because ofthe variation of the step free energy. Also dislo-

cations at grain boundaries produced by small de-formations are expected to in¯uence the growthbehavior. Our observations appear to be qualitat-

ively consistent with these expectations.

AcknowledgementsÐThis work was supported by theKorea Science and Engineering Foundation through theCenter for Interface Science and Engineering of Materials,by the General Electric Corporate Research andDevelopment Center, USA, and by the Creative ResearchInitiative Center for Microstructure Science of Materials.The authors are grateful to an anonymous reviewer fordrawing their attention to the publications of Wynblattand Gjotsten [27, 28].

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