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Microconstituent development and coarsening in certain three-phase systems
Acta mater. Vol. 44, No. 8, pp. 3321-3329, 1996 Copyright 0 1996 Acta Metallurgica Inc. Published by Elsevier Science Ltd Printed in Great Britain. All rights reserved 1359-6454/96 $15.00 + 0.00
Pergamon
MICROCONSTITUENT DEVELOPMENT IN CERTAIN THREE-PHASE G. C. MUKIRA Department
of Metallurgical
and Materials
AND COARSENING SYSTEMS
and T. H. COURTNEY
Engineering, Michigan MI 49931, U.S.A.
Technological
(Received 3 May 1995; in revised form 28 September
University,
Houghton,
1995)
Abstract-We
report on a three-phase coarsening phenomenon in which an initially random dispersion of two phases in a matrix of a third phase evolves into two “microconstituents”. The matrices of the microconstituents differ, as do the phase volume fractions within them. Once developed, the dispersed “microconstituent” coarsens, just as a dispersed phase in a two-phase system does. We describe the conditions that we believe lead to microconstituent development. We also provide an approximate description of microconstituent morphology and other microconstituent features. Experimental illustrations are given. Copyright 0 1996 Acta Metallurgica Inc.
1. INTRODUCTION Coarsening in two-phase alloys has been extensively investigated during the past 30 years [14]. The basic physics of dispersed phase coarsening are well established, although nuances associated with it (e.g. strain and particle volume fraction effects) [5-71 remain incompletely resolved. Coarsening in three-phase systems has been much less thoroughly studied. It is generally thought that a triplex structure, consisting of, say, phases 2 and 3 dispersed in a matrix of phase 1 (Fig. 1) should be relatively coarsening resistant. This is so for much the same reason that duplex two-phase structures are more coarsening resistant than are particle dispersed microstructures [8,9]. In particular, the common phase boundaries (i.e. l-l and 2-2 boundaries) found in a duplex structure place a restriction on phase growth not found in a dispersed particulate microstructure. The principle is put to good advantage in superplastic alloys where the restricted grain growth maintains the desired fine grained microstructure during superplastic forming [lo]. In this paper we describe how coarsening can be manifested in three-phase systems having certain interphase boundary energy relationships. What prompted our interest is shown in Figs 2. Figure 2(a) is a micrograph of a hot isostatically pressed Fe-Ni-W alloy. (Details of processing and material composition are provided in Section 4 and Ref. [ 111.) The hot-pressed structure contains three phases; a f.c.c. matrix (dark), an intermetallic compound
tC1oser inspection of Fig. 2(a) reveals some heterogeneity in phase distribution. This marks the onset of the type of coarsening we deal with in this paper. 3321
isomorphous to NiW (gray), and b.c.c. W (white). The phases are crystallization products that have precipitated from a noncrystalline structure [12]. The b.c.c. and intermetallic phases in the consolidated structure are more-or-less randomly distributed in the f.c.c. matrix;? the structure bears resemblance to the schematic triplex structure of Fig. 1. Figure 2(b) shows this material after having been heat-treated for 20 h at 1473 K. It is clear that phase segregation, manifested by the presence of two “microconstituents”, has taken place during heat-treatment. One constituent is rich in the intermetallic; the other has little or none of this phase in it. We note that the segregation pattern exists over large distances, of the order of tens of micrometers, and this distance can be contrasted to a microstructural scale on the order of a micrometer in the as-consolidated structure. In this paper, we argue that the structure of Fig. 2(b) apparently forms a result of surface energy effects, and that the growth of the microconstituents is driven by this same factor. In brief, microconstituent formation and growth is a threephase coarsening phenomenon. We term the process “microconstituent” coarsening. Microconstituent coarsening is discussed in several stages. First, we describe the microstructure expected to evolve in systems for which the specified surface energy relationships hold, and offer comments on the synthesis conditions that can lead to microstructures prone to microconstituent coarsening. Second, we discuss some kinetic aspects of the phenomenon. Finally, we provide further examples of microconstituent coarsening. These observations lend credence to the mechanisms suggested for its occurrence and for some of the details by which it is speculated to take place.
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Fig. I. Random distribution of phase 2 (hatched) and phase 3 (light) in a phase 1 (dark) matrix in a triplex structure.
2. QUALITATIVE
DESCRIPTION EVOLUTION
OF STRUCTURAL
Consider Fig. 3(a); a particle of phase 3, immersed in a “matrix” of phase 1, is placed on a flat surface of phase 2. Provided the inequality
DEVELOPMENT
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(a,, = interphase boundary energy between phase i and phase j) holds, phase 2 spontaneously “wets” phase 3 [Fig. 3(b)]. While Figs 3 are drawn for a flat surface of phase 2, wetting of phase 3 by phase 2 occurs regardless of the curvature of phase 2 (Fig. 4). The phase arrangement of Fig. 4(a) is of the type expected in a triplex alloy. In this instance, wetting of phase 3 by phase 2 reduces the system surface energy irrespective of the relative radii of the phases (although the fractional change in system surface energy depends on the relative sizes of the two particles), and leads to envelopment of phase 3 by phase 2. However, if takes place primarily by r2 > rj, “envelopment” “sintering” of the juncture of the original phase 2 and the final (coated) phase 3 particle (which now behaves as a “pseudo” phase 2 particle). If r? < r3, envelopment takes place by mass transfer to the larger “pseudo” phase 2 particle, and results in a “composite” or coated particle. Once envelopment has taken place, the “composite” phase 2 particle grows at the expense of other, smaller phase 2 particles, regardless of whether they are composite [as shown in Fig. 5(a)] or single phase. When a growing particle of this kind encounters a phase 3 particle, it envelops it. The microstructural features of such a coarsened “particle” will resemble those illustrated in Fig. 5(b). A “particle” of this nature can be termed a microconstituent.
Fig. 2. (a) Distribution of W (light) and NiW (gt.ay) phases in Ni-rich f.c.c. matrix of an alloy of 30 at.% Ni, 26 at.% Fe, 45 at.% W alloy as-consolid ated at 1473 K at the onset of coarsening leading to (b) microconstituent developmer tt upon heat-treatment for 20 h.
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Fig. 3. (a) Phase 3 (light) initially in minimal contact with phase 2 (hatched); (b) wetting of phase 3 by phase 2 due to reduction of system’s surface energy.
The “microconstituent” of Fig. 5(b) is rich in phase 2. Thus, another microconstituent, one lean in phase 2, must be present. Taking this into account, the overall structure will resemble that shown in Fig. 5(c). (Here we assume, as we do throughout, that the phase 2 rich microconstituent constitutes the minor microconstituent by volume.) Thus, the structure consists of 2-3 microconstituent “particles” (the designation refers to the phases of the microconstituents; the order is that of the matrix-dispersed phase in it) dispersed throughout a l&(3%2) microconstituent. Here 3-2 indicates that phase 3 particles are coated with a thin layer of phase 2.t Coarsening of the microstructure proceeds by 2-3 “microconstituent” coarsening; mass transfer takes place from smaller than average size 2-3 microconstituents through the l-(3-2) microconstituent to 2-3 microconstituents having a larger than average size. In brief, the 2-3 microconstituent coarsens in much the same way as does a dispersed single phase in a two-phase system. The dispersed phase 3 particles concurrently coarsen within the 2-3 microconstituent and, of course, they also coarsen in the l&(3%2) microconstituent. Here, the phase 3 components must additionally diffuse through the phase 2 coating for such coarsening to occur. What types of structures might be susceptible to microconstituent development and coarsening? Clearly, their initial microstructures must contain a significant fraction of high energy (i.e. o13) boundaries. These can be introduced by “artificial” processing; e.g. mechanical deformation in mechanical alloying or pressure consolidation of three-phase structures. Initial structures of this nature can be formed through phase transformations, too. However, the transformation must take place with a large driving force which permits establishment of high energy interfaces in the as-transformed structure. Examples might include crystalline phases precipitating
from
noncrystalline
provide
later
formed
at large
solids
are of this kind) undercooling.
(the
or solid
examples state
In contrast,
eutectic three-phase structures, which form at low undercooling, do not exhibit high energy interphase boundaries. The basic ideas dealing with microconstituent development and coarsening are presented above. Before providing empirical examples, it is worthwhile to discuss some kinetic factors possibly affecting the morphology of these structures, and causing them to deviate from the “ideal” morphology of Fig. 5(c). 3. POTENTIAL KINETIC FACTORS AFFECTING MICROCONSTITUENT MORPHOLOGY The schematics of Fig. 5 suggest that the distribution of phase 3 within the structure remains the same throughout microconstituent development and coarsening. That is, the respective volume fractions of this phase are the same in each microconstituent and the same as that in the original microstructure. On this description, all that has happened by microconstituent development is that two kinds of matrices have supplanted a single (the original) matrix. Moreover, the mass transfer needed for microconstituent coarsening is presumed controlled by volume diffusion through the l-(3-2) microconstituent; this is analogous to volume diffusion control of coarsening in two-phase systems. However, kinetic factors, may influence the phase distribution and arrangement in microconstituents undergoing coarsening. Some of these factors and their influence on microstructural morphology are discussed here. Discussion is facilitated by a change in terminology, which has the additional benefit of relevance to examples provided later. Although three-phase systems are ternary or higher order, microconstituent coarsening can be conveniently
we
structures solidified
l_The schematic of Fig. 5(c) is not to scale. The thickness of the phase 2 coating on phase 3 particles in the l-(3-2) microconstituent is apt to be quite thin, perhaps of the . r oraer 01 nanometers.
(a)
(b)
Fig. 4. (a) Phase 2 initially in contact with phase 3; (b) phase 2 wets phase 3 regardless of the relative radii of the phases.
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(b)
Fig. 5. (a) The relative sizes of growing and shrinking phase 2 particles during coarsening; (b) development of 2-3 microconstituent where phase 3 particles are enveloped in a matrix of phase 2; (c) subsequent morphology of the structure of a system containing the two microconstituents: i.e. 2-3 and l-(3-2) microconstituents.
discussed in the context of a binary system. We take phase 1 to be (nominally) pure A, phase 3 to be likewise pure B, and phase 2 to be an intermediate compound, AB. Coarsening in two phase systems can also be controlled by interface reactions (i.e. attachment/ detachment kinetics at the interface of the growing/ shrinking particle). We suggest that something comparable can take place during microconstituent coarsening. Consider advancement of an AB rich microconstituent. As it progresses through the A-B microconstituent, it “encounters” the two phases, A and B. The AB phase can form (and the AB rich microconstituent therefore advance) through the chemical reaction A+B-+AB with the reverse reaction taking place “interface” of a shrinking microconstituent. driving force for the growth/shrinkage of the microconstituent is the same as when diffusion controls the process. However, the
(2) at
the The AB rich volume immedi-
ate source of A and B atoms differs between the two descriptions. When a chemical reaction [e.g. equation (2)] controls growth of the AB rich microconstituent, either A or B particles (as opposed to only B particles in the earlier description) may be encompassed during growth. Moreover, the volume fraction of B in the two microconstituents is now not necessarily the same. The criterion for defining whether either A or B particles reside in the AB rich microconstituent is simple. We define VA and V, as the overall respective volume fractions of A and B phases in the system. Assuming equal atomic volumes in all three phases, it is easy to show that if VA < Vs, B particles will be found in AB rich microconstituent. Conversely, if VA > VB, A particles will be contained therein. Of course the relative volume fractions of the microconstituents, and the volume fraction of the phases within them, depend on VABas well. The surface of a growing AB rich microconstituent will encounter the usual statistical fluctuations in local volume fractions of both A and B phases in the other microconstituent. As a consequence we expect
Fig. 6. Variation in appearance of the AB microconstituent with change in volume fraction of B phase: (a) VB > VA, (b) VB < VA, (c) both phases present due to local fluctuations in volume fractions of both phases, (d) ideal structure when VB = VA.
MUKIRA and COURTNEY:
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/,////////////
(4
(b)
AND COARSENING
r ,
Cc)
,
,
,
,
/
/
tCr contamination also occurs but to a much lesser extent. In distinction to the other elements, Cr remains confined to a phase that we believe to be an interstitial Cr rich compound (but may be pure Cr). These Cr rich particles are very fine and are not discernible in the photomicrographs presented here. The particles apparently do not affect the thermodynamics of coarsening, but they may influence its rate.
/
/
/
/
/
.
(4
Fig. 7. Advancement of an AB protrusion; (a) the onset of B particle consumption/envelopment, partially consumed B particle, (c) VB > VA, leads to envelopment of the B particle, (d) when the particle is entirely consumed.
the appearance of the AB rich microconstituent to vary with overall B phase volume fraction as schematically shown in Fig. 6. When the alloy is rich in phase A, it will be dispersed in the microconstituent; likewise for B. There is likely to be an intermediate range (spanning the criterion, VA = VB) of A (or B) volume fraction in which both phases are found in the AB microconstituent as shown in Fig. 6(c). We note that when VA = Ve, a pure AB microconstituent is expected [Fig. 6(d)]. However, it seems unlikely that this situation will be observed in “real” systems which always exhibit local fluctuations in the phase volume fractions. The surface topography of the AB rich microconstituent is likely to be affected when the AB phase grows by chemical reaction. Consider advancement of the AB phase by “consumption/envelopment” of a B particle for which, on previous premises, AB wets the B phase (Fig. 7; the thin “coating” of AB on the B particle is not shown). A “blunt” protrusion of AB from the major surface of the AB microconstituent is a consequence of the “envelopment/consumption.” If V, > VA, envelopment results in incorporation of the B phase within the AB microconstituent [Fig. 7(c)]. However, if Vs < VA, following B particle consumption, the protrusion is entirely AB [Fig. 7(d)]. It is expected that the protrusion will subsequently redeposit on the major microconstituent surface, with its greater curvature. The A phase, however, could be enveloped by “leapfrogging” of AB protrusions which progressively encounter B particles (this is facilitated on stoichiometric considerations, since the protrusion volume is twice that of the original B particle). This would result in “entrapped” A particles having a much less regular shape (and likely considerably greater size) than their more-or-less spherically shaped counter-part B particles. Finally, because it is pertinent to experimental illustrations of the next section, we consider the possibility of the AB phase wetting A phase grain boundaries. This would accelerate B particle con-
/
3325
(b) a VB < VA,
sumption, as indicated in Fig. 8. As the front of the AB microconstituent approaches the B particle, a cylindrical “finger” of AB forms. The process is likely abetted by more rapid surface diffusion along the A-AB interface of the finger. If the B particles are entirely consumed, a surface cusp will be formed on the AB microconstituent. We also note that grain boundary wetting of this type facilitates A phase “encapsulation”. 4. ILLUSTRATIVE EXAMPLES
We provide experimental observations of microconstituent coarsening in Ni-W-Fe heavy alloys. The materials were made by mechanically alloying Ni and W powder blends in a SPEX 8000 mill. Three binary Ni-W compositions (40, 50, 60 at.%W) were milled for varying times (up to 60 h) using a charge ratio (mass of grinding media/mass of powder) of seven. Considerable grinding media (440C martensitic steel balls were usually employed) wear takes place during milling [ 131. Thus the alloys are essentially Ni-W-Fe ternaries;? the Fe content of a specific alloy depends on milling time and on initial W content [12, 131. Milled powders are amorphous for the most part, but do contain some remnant nanocrystalline W. As-milled powders were consolidated by hot isostatic pressing at either 1273 or 1473 K. As mentioned, during consolidation the noncrystalline phase transforms into three crystalline products; a Ni rich f.c.c. phase, an intermetallic compound isomorphous to NiW, and b.c.c. W (more complete information pertaining to processing can be found in Refs [ll-131). A micrograph of a typical as-consolidated structure has been shown in Fig. 2(a). The structure has a strong resemblance to the schematic of a triplex structure of Fig. 1, but
Fig. 8. “Finger” development on the AB microconstituent. The finger extends along the APA grain boundary towards a B particle.
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i
composition
Fig. 9. Variation of volume fraction of the NiW phase with heat-treatment time at 1473 K for various alloys.
DEVELOPMENT
AND COARSENING
closer scrutiny of Fig. 2(a) indicates that microconstituent development has already initiated during consolidation. Following consolidation, selected materials were heat treated at 1473 K for varying times. The compound NiW is not stable at temperatures above 1373 K in binary Ni-W alloys [14]. However, Fe (which substitutes for Ni [ 111) stabilizes this phase so that in the materials we studied it persists for extended periods at 1473 K. The variation of the overall volume fraction of the intermetallic (determined by point counting) with time of heat-treatment is shown for some alloys in Fig. 9. For alloys with Fe/Ni atomic ratios greater than about 0.2, this
Fig. 10. Microconstituent development in the alloy containing 30, 25, 45 at.% Ni, Fe and W, respectively, heat-treated at 1473 K for; (a) 20 h showing envelopment and consumption of W particles by the NiW phase: arrows marked A indicate areas where protrusions from the surface of NiW have enhanced envelopment/consumption of the W particles; and arrows marked B indicate regions where NiW seems to leapfrog from one W particle to another; (b) 100 h; of note are the thin fingers from the surface of NiW to the W particles (arrows marked C).
MUKIRA
and COURTNEY: Table Type of microconst. A-B AB Overall
MICROCONSTITUENT 1. Volume
fraction
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of the phases in the microconstituents
Vol. % of microconst.
Vol. % w phase
Vol. % NiW phase
Vol. % Ni phase
60 40
61 13 42
0 65 26
39 22 32
alloy
fraction initially decreases rapidly but then much more slowly (an exception is the alloy with an Fe/Ni ratio about l/l for which the volume fraction of NiW remains essentially the same at the different heat treatment times). The examples we discuss are taken from alloys heat-treated for times for which the intermetallic volume fraction is constant or nearly so. A high magnification micrograph of the material of Fig. 2(b) is given in Fig. 10(a), which illustrates some details of the microconstituent morphology after heat treatment at 1473 K for 20 h. The alloy contains 30, 25, 45 at.% Ni, Fe, W, respectively. Table 1 summarizes the volume fractions of the microconstituents and individual phases in them for this material. Numerous W particles are in contact with the intermetallic [Fig. 10(a)]. The arrows noted as A indicate contacts of this type which are also characterized by a significant protrusion from the major “surface” of the NiW microconstituent. We also note locations (with B arrows) where “leapfrogging” (perhaps facilitated by grain-boundary wetting) is apparently leading to A phase envelopment.
Finally, the encapsulated A phase is typically larger and less regular in shape than the similarly encapsulated B phase. This feature is more apparent in the micrographs that follow. Another high magnification micrograph of the same alloy but heat-treated for 100 h at 1473 K is shown in Fig. 10(b). In it we draw attention to thin “fingers” extending from the intermetallic to W particles. This may be a result of the NiW advancing along the matrix grain boundary towards the W particles. There are also well defined cusps on the NiW microconstituent surface. These evidently correspond to points where W particles have been consumed by the advancing NiW microconstituent. Figure 11 shows micrographs of an alloy of composition 35, 11, 54 at.% Ni, Fe and W, respectively (containing higher volume fraction of W and less of the NiW phase), heat-treated for 5 h at 1473 K. In Fig. 1 l(a), the initial stages of microconstituent evolvement are illustrated. Several NiW based microconstituents have developed at this time,
Fig. 11. Early stages of development of microconstituents in alloy containing 35, 11 and 54 at.% Ni, Fe and W, respectively; (a) NiW microconstituent together with smaller NiW particles distributed in a Ni rich matrix, (b) a higher magnification showing W particles in the matrix.
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Fig. 12. Microconstituents development in an alloy containing heat-treated at 1473 K for 10 h. Here the Ni rich phase is essentially microconstituent.
but we also note randomly distributed NiW particles remain in the Ni rich matrix. A higher magnification [Fig. II(b)] micrograph shows consumption and envelopment of W particles. Finally, Fig. 12 is a micrograph showing the microconstituent appearance in an alloy of lesser W content. For the most part, and in concert with the ideas illustrated in Fig. 6, the intermetallic microconstituent is of the AB-A type; i.e. globules of f.c.c. phase are encapsulated by the intermetallic. 5. SUMMARY In this paper we have attempted to describe microstructures expected to evolve on coarsening three-phase alloys for which the energy of one interphase boundary exceeds the sum of those of the other two interphase boundaries. Such a condition catalyzes development of “microconstituent” particles, which coarsen phenomenologically in much the same manner a dispersed phase does in a two-phase alloy. Although wetting is required for microconstituent development, microconstituent growth is not necessarily dependent upon the wetting. However, we have discussed some ways by which growth is facilitated by wetting. Details of the structure developed within microconstituents are not yet fully clarified. We have attempted to note some features of microconstituent development, and have illustrated them with experimental examples. Yet this report remains preliminary. We are currently investigating some unresolved issues such as possible wetting of the f.c.c. phase grain boundaries by the intermetallic and the nature of the W-f.c.c. interface in the system. In addition, we are studying microconstituent morphology over a range of respective phase volume fractions in order to better
AND
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43 at.% Ni, 14 at.% Fe, 43 at.%W, the only dispersed phase in the NiW
categorize this morphology. Furthermore, the time dependency of microconstituent growth needs to be established. We close by remarking that this type of coarsening might be more common than intuition would suggest. In particular, any multi-phase arrangement formed by artificial means (e.g. by powder consolidation, mechanical deformation or mechanical alloying) or via naturally occurring transformations taking place with a large thermodynamic driving force can result in high-energy boundaries in the as-formed or as-transformed structure. Provided the surface energy requirement of equation (1) is satisfied, such systems are expected to exhibit microconstituent development and coarsening.
Acknowledgements-This work was supported by the Army Research Office, Dr Edward Chen, grant monitor. The insightful comments of Professor Angus Hellawell, crucial to any understanding of the phenomena discussed here are, very much appreciated. Professor Steve Hackney also contributed valuable discussion, and we appreciate his interest in this work.
REFERENCES 1. I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961). 65, 581 (1961). 2. C. Wagner, Z. Electrochem. 3. A. J. Ardell, Acta metall. 20, 61 (1972). 4. T. H. Courtney, Solid-Solid Phase ?ransformations (edited bv H. I. Aaronson. D. E. Laughlin. R. F. Sekerka -and C. M. Wayman), p. 7057. TMS, Warrendale, PA (1981). 5. J. K. Lee, Scripta metall. mater. 32, 559 (1995). Acta metall. 6. P. W. Voorhees and M. E. Glicksman, 32, 2001 (1984). 7. S. C. Hardy and P. W. Voorhees, Metall. Trans. A 19A, 2713 (1988).
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8. G. Grewal and S. Ankem, Metall. Trans. A 20A, 39 (1989). 9. S. Ankem and H. Margolin, Metall. Trans. A SA, 1320 (1977). 10. J. Pilling and W. Ridley, Superplasticity in Crystalline Solids. Institute of Metals, London (1989). 11. C. G. Mukira and T. H. Courtney, Proc. 2nd Corzf. Tungsten and Refractory Metals (edited by A. Bose
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and R. J. Dowding), p. 157. MPIF, Princeton, NJ (1995). 12. A. 0. Aning, Z. Wang and T. H. Courtney, Acta. metall. 41, 165 (1993). 13. T. H. Courtney and Z. Wang, Scripta metall. 27, 777 (1992). 14. S. V. Nagender Naidu, A. M. Sriramurthy and P. Rao, J. Alloy Phase Diag. 2, 367 (1986).
Pergamon
MICROCONSTITUENT DEVELOPMENT IN CERTAIN THREE-PHASE G. C. MUKIRA Department
of Metallurgical
and Materials
AND COARSENING SYSTEMS
and T. H. COURTNEY
Engineering, Michigan MI 49931, U.S.A.
Technological
(Received 3 May 1995; in revised form 28 September
University,
Houghton,
1995)
Abstract-We
report on a three-phase coarsening phenomenon in which an initially random dispersion of two phases in a matrix of a third phase evolves into two “microconstituents”. The matrices of the microconstituents differ, as do the phase volume fractions within them. Once developed, the dispersed “microconstituent” coarsens, just as a dispersed phase in a two-phase system does. We describe the conditions that we believe lead to microconstituent development. We also provide an approximate description of microconstituent morphology and other microconstituent features. Experimental illustrations are given. Copyright 0 1996 Acta Metallurgica Inc.
1. INTRODUCTION Coarsening in two-phase alloys has been extensively investigated during the past 30 years [14]. The basic physics of dispersed phase coarsening are well established, although nuances associated with it (e.g. strain and particle volume fraction effects) [5-71 remain incompletely resolved. Coarsening in three-phase systems has been much less thoroughly studied. It is generally thought that a triplex structure, consisting of, say, phases 2 and 3 dispersed in a matrix of phase 1 (Fig. 1) should be relatively coarsening resistant. This is so for much the same reason that duplex two-phase structures are more coarsening resistant than are particle dispersed microstructures [8,9]. In particular, the common phase boundaries (i.e. l-l and 2-2 boundaries) found in a duplex structure place a restriction on phase growth not found in a dispersed particulate microstructure. The principle is put to good advantage in superplastic alloys where the restricted grain growth maintains the desired fine grained microstructure during superplastic forming [lo]. In this paper we describe how coarsening can be manifested in three-phase systems having certain interphase boundary energy relationships. What prompted our interest is shown in Figs 2. Figure 2(a) is a micrograph of a hot isostatically pressed Fe-Ni-W alloy. (Details of processing and material composition are provided in Section 4 and Ref. [ 111.) The hot-pressed structure contains three phases; a f.c.c. matrix (dark), an intermetallic compound
tC1oser inspection of Fig. 2(a) reveals some heterogeneity in phase distribution. This marks the onset of the type of coarsening we deal with in this paper. 3321
isomorphous to NiW (gray), and b.c.c. W (white). The phases are crystallization products that have precipitated from a noncrystalline structure [12]. The b.c.c. and intermetallic phases in the consolidated structure are more-or-less randomly distributed in the f.c.c. matrix;? the structure bears resemblance to the schematic triplex structure of Fig. 1. Figure 2(b) shows this material after having been heat-treated for 20 h at 1473 K. It is clear that phase segregation, manifested by the presence of two “microconstituents”, has taken place during heat-treatment. One constituent is rich in the intermetallic; the other has little or none of this phase in it. We note that the segregation pattern exists over large distances, of the order of tens of micrometers, and this distance can be contrasted to a microstructural scale on the order of a micrometer in the as-consolidated structure. In this paper, we argue that the structure of Fig. 2(b) apparently forms a result of surface energy effects, and that the growth of the microconstituents is driven by this same factor. In brief, microconstituent formation and growth is a threephase coarsening phenomenon. We term the process “microconstituent” coarsening. Microconstituent coarsening is discussed in several stages. First, we describe the microstructure expected to evolve in systems for which the specified surface energy relationships hold, and offer comments on the synthesis conditions that can lead to microstructures prone to microconstituent coarsening. Second, we discuss some kinetic aspects of the phenomenon. Finally, we provide further examples of microconstituent coarsening. These observations lend credence to the mechanisms suggested for its occurrence and for some of the details by which it is speculated to take place.
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Fig. I. Random distribution of phase 2 (hatched) and phase 3 (light) in a phase 1 (dark) matrix in a triplex structure.
2. QUALITATIVE
DESCRIPTION EVOLUTION
OF STRUCTURAL
Consider Fig. 3(a); a particle of phase 3, immersed in a “matrix” of phase 1, is placed on a flat surface of phase 2. Provided the inequality
DEVELOPMENT
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(a,, = interphase boundary energy between phase i and phase j) holds, phase 2 spontaneously “wets” phase 3 [Fig. 3(b)]. While Figs 3 are drawn for a flat surface of phase 2, wetting of phase 3 by phase 2 occurs regardless of the curvature of phase 2 (Fig. 4). The phase arrangement of Fig. 4(a) is of the type expected in a triplex alloy. In this instance, wetting of phase 3 by phase 2 reduces the system surface energy irrespective of the relative radii of the phases (although the fractional change in system surface energy depends on the relative sizes of the two particles), and leads to envelopment of phase 3 by phase 2. However, if takes place primarily by r2 > rj, “envelopment” “sintering” of the juncture of the original phase 2 and the final (coated) phase 3 particle (which now behaves as a “pseudo” phase 2 particle). If r? < r3, envelopment takes place by mass transfer to the larger “pseudo” phase 2 particle, and results in a “composite” or coated particle. Once envelopment has taken place, the “composite” phase 2 particle grows at the expense of other, smaller phase 2 particles, regardless of whether they are composite [as shown in Fig. 5(a)] or single phase. When a growing particle of this kind encounters a phase 3 particle, it envelops it. The microstructural features of such a coarsened “particle” will resemble those illustrated in Fig. 5(b). A “particle” of this nature can be termed a microconstituent.
Fig. 2. (a) Distribution of W (light) and NiW (gt.ay) phases in Ni-rich f.c.c. matrix of an alloy of 30 at.% Ni, 26 at.% Fe, 45 at.% W alloy as-consolid ated at 1473 K at the onset of coarsening leading to (b) microconstituent developmer tt upon heat-treatment for 20 h.
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Fig. 3. (a) Phase 3 (light) initially in minimal contact with phase 2 (hatched); (b) wetting of phase 3 by phase 2 due to reduction of system’s surface energy.
The “microconstituent” of Fig. 5(b) is rich in phase 2. Thus, another microconstituent, one lean in phase 2, must be present. Taking this into account, the overall structure will resemble that shown in Fig. 5(c). (Here we assume, as we do throughout, that the phase 2 rich microconstituent constitutes the minor microconstituent by volume.) Thus, the structure consists of 2-3 microconstituent “particles” (the designation refers to the phases of the microconstituents; the order is that of the matrix-dispersed phase in it) dispersed throughout a l&(3%2) microconstituent. Here 3-2 indicates that phase 3 particles are coated with a thin layer of phase 2.t Coarsening of the microstructure proceeds by 2-3 “microconstituent” coarsening; mass transfer takes place from smaller than average size 2-3 microconstituents through the l-(3-2) microconstituent to 2-3 microconstituents having a larger than average size. In brief, the 2-3 microconstituent coarsens in much the same way as does a dispersed single phase in a two-phase system. The dispersed phase 3 particles concurrently coarsen within the 2-3 microconstituent and, of course, they also coarsen in the l&(3%2) microconstituent. Here, the phase 3 components must additionally diffuse through the phase 2 coating for such coarsening to occur. What types of structures might be susceptible to microconstituent development and coarsening? Clearly, their initial microstructures must contain a significant fraction of high energy (i.e. o13) boundaries. These can be introduced by “artificial” processing; e.g. mechanical deformation in mechanical alloying or pressure consolidation of three-phase structures. Initial structures of this nature can be formed through phase transformations, too. However, the transformation must take place with a large driving force which permits establishment of high energy interfaces in the as-transformed structure. Examples might include crystalline phases precipitating
from
noncrystalline
provide
later
formed
at large
solids
are of this kind) undercooling.
(the
or solid
examples state
In contrast,
eutectic three-phase structures, which form at low undercooling, do not exhibit high energy interphase boundaries. The basic ideas dealing with microconstituent development and coarsening are presented above. Before providing empirical examples, it is worthwhile to discuss some kinetic factors possibly affecting the morphology of these structures, and causing them to deviate from the “ideal” morphology of Fig. 5(c). 3. POTENTIAL KINETIC FACTORS AFFECTING MICROCONSTITUENT MORPHOLOGY The schematics of Fig. 5 suggest that the distribution of phase 3 within the structure remains the same throughout microconstituent development and coarsening. That is, the respective volume fractions of this phase are the same in each microconstituent and the same as that in the original microstructure. On this description, all that has happened by microconstituent development is that two kinds of matrices have supplanted a single (the original) matrix. Moreover, the mass transfer needed for microconstituent coarsening is presumed controlled by volume diffusion through the l-(3-2) microconstituent; this is analogous to volume diffusion control of coarsening in two-phase systems. However, kinetic factors, may influence the phase distribution and arrangement in microconstituents undergoing coarsening. Some of these factors and their influence on microstructural morphology are discussed here. Discussion is facilitated by a change in terminology, which has the additional benefit of relevance to examples provided later. Although three-phase systems are ternary or higher order, microconstituent coarsening can be conveniently
we
structures solidified
l_The schematic of Fig. 5(c) is not to scale. The thickness of the phase 2 coating on phase 3 particles in the l-(3-2) microconstituent is apt to be quite thin, perhaps of the . r oraer 01 nanometers.
(a)
(b)
Fig. 4. (a) Phase 2 initially in contact with phase 3; (b) phase 2 wets phase 3 regardless of the relative radii of the phases.
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(b)
Fig. 5. (a) The relative sizes of growing and shrinking phase 2 particles during coarsening; (b) development of 2-3 microconstituent where phase 3 particles are enveloped in a matrix of phase 2; (c) subsequent morphology of the structure of a system containing the two microconstituents: i.e. 2-3 and l-(3-2) microconstituents.
discussed in the context of a binary system. We take phase 1 to be (nominally) pure A, phase 3 to be likewise pure B, and phase 2 to be an intermediate compound, AB. Coarsening in two phase systems can also be controlled by interface reactions (i.e. attachment/ detachment kinetics at the interface of the growing/ shrinking particle). We suggest that something comparable can take place during microconstituent coarsening. Consider advancement of an AB rich microconstituent. As it progresses through the A-B microconstituent, it “encounters” the two phases, A and B. The AB phase can form (and the AB rich microconstituent therefore advance) through the chemical reaction A+B-+AB with the reverse reaction taking place “interface” of a shrinking microconstituent. driving force for the growth/shrinkage of the microconstituent is the same as when diffusion controls the process. However, the
(2) at
the The AB rich volume immedi-
ate source of A and B atoms differs between the two descriptions. When a chemical reaction [e.g. equation (2)] controls growth of the AB rich microconstituent, either A or B particles (as opposed to only B particles in the earlier description) may be encompassed during growth. Moreover, the volume fraction of B in the two microconstituents is now not necessarily the same. The criterion for defining whether either A or B particles reside in the AB rich microconstituent is simple. We define VA and V, as the overall respective volume fractions of A and B phases in the system. Assuming equal atomic volumes in all three phases, it is easy to show that if VA < Vs, B particles will be found in AB rich microconstituent. Conversely, if VA > VB, A particles will be contained therein. Of course the relative volume fractions of the microconstituents, and the volume fraction of the phases within them, depend on VABas well. The surface of a growing AB rich microconstituent will encounter the usual statistical fluctuations in local volume fractions of both A and B phases in the other microconstituent. As a consequence we expect
Fig. 6. Variation in appearance of the AB microconstituent with change in volume fraction of B phase: (a) VB > VA, (b) VB < VA, (c) both phases present due to local fluctuations in volume fractions of both phases, (d) ideal structure when VB = VA.
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(4
(b)
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r ,
Cc)
,
,
,
,
/
/
tCr contamination also occurs but to a much lesser extent. In distinction to the other elements, Cr remains confined to a phase that we believe to be an interstitial Cr rich compound (but may be pure Cr). These Cr rich particles are very fine and are not discernible in the photomicrographs presented here. The particles apparently do not affect the thermodynamics of coarsening, but they may influence its rate.
/
/
/
/
/
.
(4
Fig. 7. Advancement of an AB protrusion; (a) the onset of B particle consumption/envelopment, partially consumed B particle, (c) VB > VA, leads to envelopment of the B particle, (d) when the particle is entirely consumed.
the appearance of the AB rich microconstituent to vary with overall B phase volume fraction as schematically shown in Fig. 6. When the alloy is rich in phase A, it will be dispersed in the microconstituent; likewise for B. There is likely to be an intermediate range (spanning the criterion, VA = VB) of A (or B) volume fraction in which both phases are found in the AB microconstituent as shown in Fig. 6(c). We note that when VA = Ve, a pure AB microconstituent is expected [Fig. 6(d)]. However, it seems unlikely that this situation will be observed in “real” systems which always exhibit local fluctuations in the phase volume fractions. The surface topography of the AB rich microconstituent is likely to be affected when the AB phase grows by chemical reaction. Consider advancement of the AB phase by “consumption/envelopment” of a B particle for which, on previous premises, AB wets the B phase (Fig. 7; the thin “coating” of AB on the B particle is not shown). A “blunt” protrusion of AB from the major surface of the AB microconstituent is a consequence of the “envelopment/consumption.” If V, > VA, envelopment results in incorporation of the B phase within the AB microconstituent [Fig. 7(c)]. However, if Vs < VA, following B particle consumption, the protrusion is entirely AB [Fig. 7(d)]. It is expected that the protrusion will subsequently redeposit on the major microconstituent surface, with its greater curvature. The A phase, however, could be enveloped by “leapfrogging” of AB protrusions which progressively encounter B particles (this is facilitated on stoichiometric considerations, since the protrusion volume is twice that of the original B particle). This would result in “entrapped” A particles having a much less regular shape (and likely considerably greater size) than their more-or-less spherically shaped counter-part B particles. Finally, because it is pertinent to experimental illustrations of the next section, we consider the possibility of the AB phase wetting A phase grain boundaries. This would accelerate B particle con-
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(b) a VB < VA,
sumption, as indicated in Fig. 8. As the front of the AB microconstituent approaches the B particle, a cylindrical “finger” of AB forms. The process is likely abetted by more rapid surface diffusion along the A-AB interface of the finger. If the B particles are entirely consumed, a surface cusp will be formed on the AB microconstituent. We also note that grain boundary wetting of this type facilitates A phase “encapsulation”. 4. ILLUSTRATIVE EXAMPLES
We provide experimental observations of microconstituent coarsening in Ni-W-Fe heavy alloys. The materials were made by mechanically alloying Ni and W powder blends in a SPEX 8000 mill. Three binary Ni-W compositions (40, 50, 60 at.%W) were milled for varying times (up to 60 h) using a charge ratio (mass of grinding media/mass of powder) of seven. Considerable grinding media (440C martensitic steel balls were usually employed) wear takes place during milling [ 131. Thus the alloys are essentially Ni-W-Fe ternaries;? the Fe content of a specific alloy depends on milling time and on initial W content [12, 131. Milled powders are amorphous for the most part, but do contain some remnant nanocrystalline W. As-milled powders were consolidated by hot isostatic pressing at either 1273 or 1473 K. As mentioned, during consolidation the noncrystalline phase transforms into three crystalline products; a Ni rich f.c.c. phase, an intermetallic compound isomorphous to NiW, and b.c.c. W (more complete information pertaining to processing can be found in Refs [ll-131). A micrograph of a typical as-consolidated structure has been shown in Fig. 2(a). The structure has a strong resemblance to the schematic of a triplex structure of Fig. 1, but
Fig. 8. “Finger” development on the AB microconstituent. The finger extends along the APA grain boundary towards a B particle.
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composition
Fig. 9. Variation of volume fraction of the NiW phase with heat-treatment time at 1473 K for various alloys.
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closer scrutiny of Fig. 2(a) indicates that microconstituent development has already initiated during consolidation. Following consolidation, selected materials were heat treated at 1473 K for varying times. The compound NiW is not stable at temperatures above 1373 K in binary Ni-W alloys [14]. However, Fe (which substitutes for Ni [ 111) stabilizes this phase so that in the materials we studied it persists for extended periods at 1473 K. The variation of the overall volume fraction of the intermetallic (determined by point counting) with time of heat-treatment is shown for some alloys in Fig. 9. For alloys with Fe/Ni atomic ratios greater than about 0.2, this
Fig. 10. Microconstituent development in the alloy containing 30, 25, 45 at.% Ni, Fe and W, respectively, heat-treated at 1473 K for; (a) 20 h showing envelopment and consumption of W particles by the NiW phase: arrows marked A indicate areas where protrusions from the surface of NiW have enhanced envelopment/consumption of the W particles; and arrows marked B indicate regions where NiW seems to leapfrog from one W particle to another; (b) 100 h; of note are the thin fingers from the surface of NiW to the W particles (arrows marked C).
MUKIRA
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MICROCONSTITUENT 1. Volume
fraction
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of the phases in the microconstituents
Vol. % of microconst.
Vol. % w phase
Vol. % NiW phase
Vol. % Ni phase
60 40
61 13 42
0 65 26
39 22 32
alloy
fraction initially decreases rapidly but then much more slowly (an exception is the alloy with an Fe/Ni ratio about l/l for which the volume fraction of NiW remains essentially the same at the different heat treatment times). The examples we discuss are taken from alloys heat-treated for times for which the intermetallic volume fraction is constant or nearly so. A high magnification micrograph of the material of Fig. 2(b) is given in Fig. 10(a), which illustrates some details of the microconstituent morphology after heat treatment at 1473 K for 20 h. The alloy contains 30, 25, 45 at.% Ni, Fe, W, respectively. Table 1 summarizes the volume fractions of the microconstituents and individual phases in them for this material. Numerous W particles are in contact with the intermetallic [Fig. 10(a)]. The arrows noted as A indicate contacts of this type which are also characterized by a significant protrusion from the major “surface” of the NiW microconstituent. We also note locations (with B arrows) where “leapfrogging” (perhaps facilitated by grain-boundary wetting) is apparently leading to A phase envelopment.
Finally, the encapsulated A phase is typically larger and less regular in shape than the similarly encapsulated B phase. This feature is more apparent in the micrographs that follow. Another high magnification micrograph of the same alloy but heat-treated for 100 h at 1473 K is shown in Fig. 10(b). In it we draw attention to thin “fingers” extending from the intermetallic to W particles. This may be a result of the NiW advancing along the matrix grain boundary towards the W particles. There are also well defined cusps on the NiW microconstituent surface. These evidently correspond to points where W particles have been consumed by the advancing NiW microconstituent. Figure 11 shows micrographs of an alloy of composition 35, 11, 54 at.% Ni, Fe and W, respectively (containing higher volume fraction of W and less of the NiW phase), heat-treated for 5 h at 1473 K. In Fig. 1 l(a), the initial stages of microconstituent evolvement are illustrated. Several NiW based microconstituents have developed at this time,
Fig. 11. Early stages of development of microconstituents in alloy containing 35, 11 and 54 at.% Ni, Fe and W, respectively; (a) NiW microconstituent together with smaller NiW particles distributed in a Ni rich matrix, (b) a higher magnification showing W particles in the matrix.
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Fig. 12. Microconstituents development in an alloy containing heat-treated at 1473 K for 10 h. Here the Ni rich phase is essentially microconstituent.
but we also note randomly distributed NiW particles remain in the Ni rich matrix. A higher magnification [Fig. II(b)] micrograph shows consumption and envelopment of W particles. Finally, Fig. 12 is a micrograph showing the microconstituent appearance in an alloy of lesser W content. For the most part, and in concert with the ideas illustrated in Fig. 6, the intermetallic microconstituent is of the AB-A type; i.e. globules of f.c.c. phase are encapsulated by the intermetallic. 5. SUMMARY In this paper we have attempted to describe microstructures expected to evolve on coarsening three-phase alloys for which the energy of one interphase boundary exceeds the sum of those of the other two interphase boundaries. Such a condition catalyzes development of “microconstituent” particles, which coarsen phenomenologically in much the same manner a dispersed phase does in a two-phase alloy. Although wetting is required for microconstituent development, microconstituent growth is not necessarily dependent upon the wetting. However, we have discussed some ways by which growth is facilitated by wetting. Details of the structure developed within microconstituents are not yet fully clarified. We have attempted to note some features of microconstituent development, and have illustrated them with experimental examples. Yet this report remains preliminary. We are currently investigating some unresolved issues such as possible wetting of the f.c.c. phase grain boundaries by the intermetallic and the nature of the W-f.c.c. interface in the system. In addition, we are studying microconstituent morphology over a range of respective phase volume fractions in order to better
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43 at.% Ni, 14 at.% Fe, 43 at.%W, the only dispersed phase in the NiW
categorize this morphology. Furthermore, the time dependency of microconstituent growth needs to be established. We close by remarking that this type of coarsening might be more common than intuition would suggest. In particular, any multi-phase arrangement formed by artificial means (e.g. by powder consolidation, mechanical deformation or mechanical alloying) or via naturally occurring transformations taking place with a large thermodynamic driving force can result in high-energy boundaries in the as-formed or as-transformed structure. Provided the surface energy requirement of equation (1) is satisfied, such systems are expected to exhibit microconstituent development and coarsening.
Acknowledgements-This work was supported by the Army Research Office, Dr Edward Chen, grant monitor. The insightful comments of Professor Angus Hellawell, crucial to any understanding of the phenomena discussed here are, very much appreciated. Professor Steve Hackney also contributed valuable discussion, and we appreciate his interest in this work.
REFERENCES 1. I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961). 65, 581 (1961). 2. C. Wagner, Z. Electrochem. 3. A. J. Ardell, Acta metall. 20, 61 (1972). 4. T. H. Courtney, Solid-Solid Phase ?ransformations (edited bv H. I. Aaronson. D. E. Laughlin. R. F. Sekerka -and C. M. Wayman), p. 7057. TMS, Warrendale, PA (1981). 5. J. K. Lee, Scripta metall. mater. 32, 559 (1995). Acta metall. 6. P. W. Voorhees and M. E. Glicksman, 32, 2001 (1984). 7. S. C. Hardy and P. W. Voorhees, Metall. Trans. A 19A, 2713 (1988).
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8. G. Grewal and S. Ankem, Metall. Trans. A 20A, 39 (1989). 9. S. Ankem and H. Margolin, Metall. Trans. A SA, 1320 (1977). 10. J. Pilling and W. Ridley, Superplasticity in Crystalline Solids. Institute of Metals, London (1989). 11. C. G. Mukira and T. H. Courtney, Proc. 2nd Corzf. Tungsten and Refractory Metals (edited by A. Bose
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and R. J. Dowding), p. 157. MPIF, Princeton, NJ (1995). 12. A. 0. Aning, Z. Wang and T. H. Courtney, Acta. metall. 41, 165 (1993). 13. T. H. Courtney and Z. Wang, Scripta metall. 27, 777 (1992). 14. S. V. Nagender Naidu, A. M. Sriramurthy and P. Rao, J. Alloy Phase Diag. 2, 367 (1986).