Splitting of γ′ Precipitates in the Context of Phase Equilibrium

Abstract

The splitting of γ′ (Ni₃Al and Ni₃Si) precipitates in five binary Ni-Al alloys and one Ni-Si alloy is reviewed in the context of phase equilibrium. Two mechanisms are considered: Purely Elastic (PE) splitting, driven solely by competition between elastic and interfacial free energies; Thermodynamically Driven (TD) splitting, involving precipitation of the Ni-Al or Ni-Si solid solution γ phases within supersaturated γ′ particles. The main assertion is that TD splitting is responsible for all the observations, with the possible exception of dendritic growth of Ni₃Si precipitates; dendritic morphologies can mimic split configurations. In three of the six investigations splitting was reported for alloy compositions lying within the single-phase γ regions of the binary Ni-Al and Ni-Si phase diagrams wherein the γ′ phases are unstable. For the three others the aging temperatures were at or barely below the solvus temperatures, suggesting that five of the alloys were compositionally heterogeneous, “solution treatment” having failed to dissolve pre-existing γ′ particles. TD splitting was thus a byproduct of slow cooling to the aging temperatures, as in the formation of hierarchical microstructures. The nature of secondary γ′ precipitation in some of the alloys indicates that their compositions exceeded the authors’ quoted values, the enrichment enabling precipitation of γ′ during solution treatment followed by TD splitting on slow cooling. PE splitting is the only possible mechanism in solution-treated specimens that are quenched and subsequently isothermally aged. Splitting under such conditions has never been reported, lending further support to the viability of the TD mechanism.

1 Introduction

The stunning reports in the early 1980s of coherent γ′ (Ni₃Al) precipitate “doublets” in an aged binary Ni-Al alloy^[1,2] stimulated a significant body of theoretical and experimental research on the roles of the sparring contributions of interfacial and elastic energies in the coarsening kinetics and shapes of γ′ precipitates. Miyazaki et al.^[1,2] suggested that doublets, or pairs of γ′ precipitates approximately equal in size, were favored by a reduction in the total energy, the increase in interfacial energy more than compensated by the reduction in elastic energy. Soon thereafter, the splitting of coherent Ni₃Si precipitates into an octet array was reported,^[3] such arrays resembling those observed decades earlier in an aged ternary Ni-Al-Cr alloy by Taylor and Floyd^[4] and an aged ternary Ni-Al-Ti alloy by Westbrook,^[5] who referred to the octets as ogdoadically diced cubes. These early observations have since been augmented by numerous others of split patterns of γ′ precipitates, not only in binary Ni-Al alloys, but also in Ni-base superalloys^[6,7,8,9] as well as in a few published micrographs of Co-base superalloys.^[10,11]

It was alleged that when the γ′ particles attained large sizes the nucleation and growth of γ precipitates within them was favored uniquely by elastic energy considerations, continued growth of the internal γ particles ultimately leading to splitting of the mother γ′ precipitates. In this paper the unique role of elastic energy is challenged by considering the observations of γ′ precipitate splitting in six investigations, five on Ni₃Al^{[2,12,13,14,15]} and one on Ni₃Si.^[3] In all these research projects the alloys were continuously cooled, most often furnace cooled, from the solution-treatment temperature to an aging temperature ostensibly near the solvus temperature for the designated alloy concentration. In none of these investigations were specimens of the alloys rapidly quenched from the solution-treatment temperature to room temperature and isothermally aged afterwards. The aging conditions were deliberately chosen to ensure that the volume fractions of γ′ precipitates were small, meaning that for a given alloy composition the aging temperatures were perilously close to the authors’ best available estimates of the solvus temperatures. Remarkably, we will see that the final aging temperatures in three of these studies^[2,3,14] were actually within the single phase γ regions of the Ni-Al and Ni-Si phase diagrams, where of course the Ni₃Al and Ni₃Si phases are unstable. In the other three investigations^[12,13,15] the alloy compositions were within a few °C of the Ni-Al solvus temperatures, but aging nevertheless produced considerably larger volume fractions of γ′ precipitates than expected. The results of all this work violated the demands of phase equilibrium in one way or the other.

The conundrum posed by these observations is addressed in this paper. Before proceeding further, it is important to recognize that there are two mechanisms of splitting. The first one is the one advocated initially by Miyazaki et al.,^[1,2] which we will refer to as Purely Elastic (PE) splitting, wherein splitting is driven solely by the competition between interfacial free energy considerations (which oppose splitting) and elastic energy considerations (which favor it). The second mechanism is driven by thermodynamics. It involves the precipitation of the γ phase within supersaturated γ′ particles, and will be referred to as Thermodynamically Driven (TD) splitting. The basis for TD splitting is firmly established. In brief, the precipitation of γ (Ni-Al) within large γ′ (Ni₃Al) precipitates was initially observed by Cornwell and Purdy,^[16] whose observations stimulated later work by Ma and Ardell to investigate the shape of the (γ + γ′)/γ′ phase boundary (the γ solvus)^[17] and subsequently to investigate the coarsening of γ precipitates within the γ′ matrix.^[18,19]

It is argued that the observations of splitting discussed in this paper are consequences of TD splitting, produced by the nucleation and growth of the γ phase within γ′ particles within the 2-phase regions of the phase diagrams, with elastic energy playing at most a secondary role. The explanation is based on thermodynamic requirements imposed by the Ni-Al and Ni-Si phase diagrams, and is reinforced by published knowledge regarding precipitation kinetics associated with inhomogeneities endemic to alloy preparation. PE splitting is considered in the context of all available experimental evidence, and ultimately found wanting as a unique splitting mechanism.

2 Review of Relevant Results

We consider here the results of five reports and investigations of splitting of γ′ precipitates in binary Ni-Al alloys, in addition to the sole report of splitting of γ′ precipitates in a binary Ni-Si alloy. To set the stage the microstructures characteristic of splitting are described schematically. By now it is well known that coherent γ′ precipitates are spherical when small and become cuboidal in shape as their sizes increase, the cuboidal designation representing particles that are approximately cubes in shape, with rounded corners and slightly convex interfaces parallel to the {100}. At large sizes and small volume fractions, f < 0.05 or so, γ′ precipitates can become nearly perfectly cubic in shape, and at even larger sizes their interfaces can become concave; this shape is referred to herein as concave cuboidal. Examples of these shapes in isothermally aged Ni-Al alloys are seen in papers by Maheshwari and Ardell^[20,21,22] and in isothermally aged Ni-Si alloys in a paper by Meshkinpour and Ardell^[23]. In those investigations the specimens were solution-treated and quenched into a refrigerated brine solution prior to aging. As noted previously and reiterated here, the Ni₃Al and Ni₃Si microstructures that comprise the subject of this paper^{[2,3,12,13,14,15]} were generated by continuous cooling to the aging temperatures.

Figure 1 illustrates the main types of split precipitates in a 2-dimensional (2-D) representation of typical split patterns observed in thin foils in [100] orientation, taken using a superlattice reflection from the L1₂ crystal structure in the transmission electron microscope (TEM). The same features are observed in the scanning electron microscope (SEM), where the images are taken of γ′ particles intersecting the surfaces of specimens in [100] orientation. The presumption^[12,24] is that these shapes are the offspring of larger concave cuboidal shaped precipitates, but 3-D examination is always necessary to verify this assertion.

Fig. 1

Schematic representations of stable split patterns seen in TEM and SEM images of specimens in [100] orientation. All the drawings are plane cuts through the center, parallel to the (100) plane of the diagram. The shapes of the precipitates in (a) are interpreted as plates in 3-dimensions (3-D), visible as adjacent rectangles in 2-D. The precipitates in (b) and (c) are considered to be split plates, while the precipitates in (d) are considered to be part of an octet, or ogdoadically diced cube, as described by Westbrook^[5]

The drawings in Fig. 2 are meant to illustrate the evolution of the morphologies in depicted in Fig. 1. It is assumed that the initiation of splitting commences near the geometrical center of concave cuboidal Ni₃Al and Ni₃Si precipitates that formed under continuous cooling conditions. Sidestepping the issue of whether or not the concave cuboidal shape is a thermodynamically equilibrium shape, it appears that the most favorable sites for the initiation of splitting are the geometric centers of the of the γ′ particles and the centers of their faces. This is consistent with the schematic drawings in Fig. 2. While there is no doubt that the configurations shown in Fig. 1(a) and (d) are final split shapes, it is possible that the configurations shown in Fig. 1(b) and (c) are transitional.

Fig. 2

Schematic representations of the evolution of a γ′ precipitate from its initial shape to the final shapes shown in Fig. 1. All the drawings are plane cuts through the center, parallel to the (100) plane of the diagram. (a) Plan view of a concave cuboidal precipitate; (b) nucleation of a spherical γ precipitate in the geometric center; (c) elongation of the γ precipitate into a lath or plate; (d) nucleation and growth of a γ precipitate at the outer edge of a γ′ particle; (e) and (f) illustrate two possible pathways to the formation of an octet, with the γ phase encroaching from the center (e) or outer edge (f) of the plate at the left

2.1 Observations of Splitting of Ni₃Al and Ni₃Si Precipitates

2.1.1 The First Reports of Splitting by Miyazaki, Imamura, Mori and Kozakai^[1,2]

The initial reports of splitting of Ni₃Al precipitates^[1,2] were based on experiments performed on single crystals of a Ni-12 at.% Al alloy¹ grown by the Bridgman method. No details about the growth rate were provided. After preparing slices parallel to (100) the specimens were solution treated for 30 min at 1200 °C and furnace-cooled to the aging temperature of 860 °C. The aging temperature was chosen to produce a small volume fraction of γ′ precipitates, the expectation being that 860 °C was just a few degrees Celsius below the solvus temperature of the 12% Al alloy. No information was provided on the cooling rate from 1200 to 860 °C in the original papers by Miyazaki et al., but a subsequent paper by Doi et al.^[25] suggests that the furnace-cooling rate was in the range 10^–1 to 10^–2 K s^–1. The dispositions of the alloy concentration and heat-treatment temperatures are shown in the Ni-rich portion of the binary Ni-Al phase diagram in Fig. 3(a). Quite remarkably, it seems, that all the specimens were aged in the single-phase γ region of the phase diagram, nevertheless producing the γ′ doublets seen in Fig. 3(b). This most disconcerting observation is a clear violation of phase equilibrium. On checking and double-checking the publications of Miyazaki and co-workers there is no doubt that the alloy composition and heat-treatment temperatures were correctly reported by the authors. Unless the phase diagram is grievously erroneous, there is only one inescapable conclusion, namely that the Ni-12% Al alloy heat treated at 860 °C should be a single-phase γ solid solution.

Fig. 3

(a) The Ni-rich portion of the Ni-Al phase diagram, illustrating the alloy composition (X_Al = 0.12) and the two temperatures (1200 and 860 °C) used in the experiments of Miyazaki et al. ^[2]—they are indicated by asterisks in the single-phase γ region; (b) The precipitate microstructure after furnace cooling and holding for 40 h, showing many doublets; (c) A sequence from left to right illustrating the evolution of splitting into a doublet—the magnification is identical in all 3 images. The precipitate in (b) indicated by the arrow and the particles in (c) are similar to the sketches in Fig. 2. The data on the solubility limits of Al in the γ phase are from Williams,^[26] Hornbogen and Kreye,^[27] Rastogi and Ardell,^[28] Janssen,^[29] Chellman and Ardell,^[30] Verhoeven et al.,^[31] Jia (via Okamoto),^[32] Ardell ^[33] and Watanabe et al.^[34] The solid curve representing the γ′ solvus is from Ardell,^[33] which is essentially in perfect agreement with the γ′ solvus in the thermodynamic assessment of Dupin et al.^[35] The γ solvus curve is from the work of Ma and Ardell.^[17] The legend is identical in Fig. 4, 6, 8 and 10

The other inescapable explanation of splitting is that the 30 min “solution treatment” at 1200 °C not only failed to homogenize the alloy, but enabled the precipitation of large γ′ precipitates within which γ particles nucleated and coarsened on slow-cooling and aging at 860 °C. It is not a simple matter to estimate the sizes of the γ′ precipitates after the solution treatment, but the microstructural evidence strongly suggests that they were too large to dissolve on aging for 40 h at 860 °C, and that the nucleation of TD splitting was already well underway, producing the microstuctural features seen in Fig. 3(c).

2.1.2 The Observations of Splitting of Ni₃Al Reported by Kaufman et al.^[12]

Kaufman et al.^[12] investigated splitting in a much more concentrated alloy than that used in the work of Miyazaki et al.^[2] namely 17% Al. The alloy studied was a (100)-oriented single crystal grown using the Bridgman method; the solidification rate was not reported. The specimens were solution-treated at 1250 °C for an unspecified length of time, furnace cooled to 1100 °C and aged for times ranging from 15 min to 2 h. After aging, the specimens were water-quenched. These temperatures are indicated in the Ni-Al phase diagram shown in Fig. 4(a). Kaufman et al. intended the aging treatment at 1100 °C to be done at a temperature just below the solvus temperature of a 17% Al alloy. This intention was very close to being fulfilled, as seen in Fig. 4(a), where the asterisk representing this heat treatment essentially intersects the solvus curve.

Fig. 4

(a) The Ni-rich region of the Ni-Al phase diagram illustrating the alloy composition (X_Al = 0.17) and heat-treatment temperatures (1250 and 1100 °C) used in the experiments of Kaufman et al.^[12]—they are indicated by the asterisks. The micrographs (b)-(f) illustrate various different features of the γ′ precipitate microstructures observed after furnace-cooling from 1250 to 1100 °C and holding for 15 min (see text)

Representative γ′ microstructures are presented in Fig. 4(b) through (f), where nearly all the variations sketched in Fig. 1 and 2 are represented among the larger particles. A striking feature characteristic of these microstructures is the presence of copious quantities of secondary cuboidal γ′ precipitates, some of which are quite large, having edge lengths approaching 100 nm. Smaller secondary γ′ precipitates are also visible within the split larger ones in Fig. 4(c) to (f). Kaufman et al. claimed that the secondary γ′ precipitates formed during quenching, but it is highly improbable that secondary precipitates of these sizes could have nucleated, grown and coarsened during a water quench from the 1100 °C aging temperature. If their conjecture were correct, it is reasonable to conclude that the average sizes of the secondary γ′ precipitates would all have approximately the same size. This is because the supersaturation of the matrix during quenching is essentially identical and the driving force for precipitation is therefore nearly identical in all the specimens. However, on examining microstructures at two different aging times side-by-side, as in Fig. 5, it is obvious that the sizes of the secondary γ′ precipitates increase significantly with aging time at 1100 °C. The only logical conclusion is that the secondary γ′ precipitates were already present in the aged microstructure. This is also quite consistent with the idea that significant compositional inhomogeneities existed in the 17 at.% Al alloy single crystal, leading to precipitation of both the larger primary γ′ precipitates on holding at 1250 °C and the nucleation, growth and coarsening of the secondary precipitates on furnace cooling to the aging temperature of 1100 °C. TD splitting of the primary γ′ precipitates is a straightforward corollary to this scenario.

Fig. 5

Dark-field TEM photos of the γ′ precipitate microstructures in 2 specimens aged for (a) 15 min and (b) 1h at 1100 °C before quenching into water; from Kaufman et al.^[12] Both microstructures are shown at the same magnification

2.1.3 The Observations of Splitting of Ni₃Al Reported by Yeom et al.^[13]

The investigation by Yeom et al.^[13] differs from all the others in that the alloy used was polycrystalline and processed by conventional ingot metallurgy methods. The reported composition of the alloy was 15.91% Al (8 wt.%). It was prepared by induction-melting Ni, adding Al ingots to the melt and casting the alloy into a Cu mold about 28 mm in diameter. After machining the alloy cylinder to 25.4 mm, it was swaged to a rod about 7 mm in diameter, utilizing intermediate anneals at 1225 °C. No mention is made about double-checking the final composition of the alloy after preparation, but it can be safely concluded that the alloy investigated by Yeom et al. was far more homogeneous than the single-crystal specimens investigated by Miyazaki et al.^[2] and Kaufman et al.^[12] The specimens were solution-treated at 1200 °C for 2 h, furnace-cooled at an estimated rate of 30 °C min^–1 to aging temperatures between 950 and 1020 °C and water-quenched to room temperature. Polished and etched specimens were examined by SEM, care being taken to seek grains oriented as near as possible to (100). The phase diagram in Fig. 6(a) illustrates the reported alloy composition of 15.91% Al, as well as the solution treatment temperature (1200 °C) and two aging temperatures, 1020 and 990 °C.

Fig. 6

(a) The Ni-rich region of the Ni-Al phase diagram illustrating the alloy composition (X_Al = 0.1591) and three of the heat-treatment temperatures (1200, 1020 and 990 °C) used in the experiments of Yeom et al.^[13]—they are indicated by the asterisks. The two data points indicated by the black hexagons are discussed in the text. The microstructures in (b) to (d) were produced by furnace-cooling from 1200 to 1020 °C and aging for 30 min. They were all taken from the same specimen and are presented here in enhanced contrast at the same magnification. The particles encircled are represented by the sketches in Fig. 1 and 2. Secondary γ′ precipitates are seen in the background of all three microstructures

Most of the SEM micrographs reported by Yeom et al. show the γ′ microstructures after different aging times at 1020 °C. The microstructures in a specimen aged for 30 min at 1020 °C are shown in Fig. 6(b)-(d). They were chosen here because many of the splitting variants (particles encircled) are represented in Fig. 1 and 2. The contrast has been enhanced from the originals to see the precipitates more clearly and to show more definitively the presence of the secondary γ′ precipitates in the background. Yeom et al. did not discuss the secondary precipitates in the γ′ microstructures of their alloy, although they are plainly visible in Fig. 6(b) to (d).

Yeom et al. reported that the γ′ volume fractions in the alloy aged at 1020 and 990 °C were approximately 0.15 and 0.25, respectively. In an alloy containing 15.91% Al, the volume fractions of γ′ precipitates calculated using the γ′ and γ solvus curves in Fig. 6(a) would be approximately 0.0088 and 0.0660, respectively. Even allowing for small errors in the locations of the phase boundaries, the discrepancies between the expected and reported volume fractions are quite large. Alternatively, we can estimate the γ′ solvus compositions required to achieve volume fractions of 0.15 and 0.25 in a 15.91% Al alloy aged at 1020 and 990 °C. These compositions are 14.81 and 13.83% Al, respectively and are represented by the black hexagons added to the phase diagram in Fig. 6(a).

The copious quantities of secondary γ′ precipitates seen in Fig. 6(c) are semi-quantitatively comparable to those reported by Kaufman et al.^[12] in that their sizes increase with increasing aging time at 1020 °C, as is evident in Fig. 7; such behavior would be quite unexpected simply on water-quenching to room temperature. The most logical explanation for these results is that the true Al concentration in the alloy of Yeom et al. was greater than the reported value of 15.91% Al.

Fig. 7

SEM photos of the γ′ precipitate microstructures in three specimens aged at 1020 °C by Yeom et al.^[13] for (a) 15 min; (b) 6 h; (c) 10 h. The increase in the average size of the secondary γ′ precipitates as the aging time increases is palpable

An additional observation by Yeom et al. further supports the assertion that the concentration of their alloy exceeded the nominal composition of 15.91% Al. They reported that γ′ precipitates were observed in a specimen aged at 1045 °C but not in one aged at 1050 °C, effectively bracketing the solvus temperature. At 1050 °C the predicted equilibrium composition of the γ phase is 16.12% Al, which is lower than the compositions estimated from the discussion of the volume fractions but nevertheless larger than the stated composition of the alloy. All the signs point to the inescapable conclusion that the composition of the alloy used by Yeom et al. exceeded 15.91% Al. This is the only explanation for the apparent violation of phase equilibrium in their alloy. Once again, the logical corollary to this series of observations is that TD splitting was the operative splitting mechanism.

2.1.4 The Splitting of Ni₃Al Reported by Qiu^[14]

Qiu investigated γ′ precipitate splitting in a Ni-14% Al alloy prepared from a single crystal^[14] grown using electron-beam zone melting. In an earlier publication^[36] the composition of this same alloy was identified as 13.5% Al, and the composition was reported as having been checked using electron probe microanalysis. Some of the details of preparation and heat-treatments in the two papers differ, so the decision was taken to use the details reported in the later publication.^[14] Specimens were taken from slices parallel to (100), solution-treated at 1200 °C for 24 h, furnace cooled to either 1140 or 1000 °C at 0.3 K s^–1, and aged at these lower temperatures for times ranging from 3 to 120 min. The aging temperatures are indicated in the phase diagram in Fig. 8(a). Several split γ′ morphologies in a specimen aged for 15 min at 1000 °C are shown in Fig. 8(b) to (g). The six seen in Fig. 8(b) to (g) are represented in Fig. 1 and 2. The arrow in Fig. 8(e) points to the possible onset of splitting of the L-shaped γ′ precipitate, which suggests that this configuration might not be a final one.

Fig. 8

(a) The Ni-rich region of the Ni-Al phase diagram illustrating the alloy composition (X_Al = 0.14) and heat-treatment temperatures (1200, 1140 and 1000 °C) used in the experiments of Qiu^[14]—they are indicated by the asterisks in the single-phase γ region; (b)-(g) Dark-field TEM micrographs, all at the same magnification, illustrating various stages of the splitting of γ′ precipitates in a specimen aged for 15 min at 1000 °C after furnace-cooling from 1200 °C—the arrow in (e) points to possible incipient splitting of the L-shaped precipitate

As is evident in Fig. 8(a), all the aging temperatures are within the single-phase γ region of the Ni-Al phase diagram in obvious violation of phase equilibrium, just as in the investigation of Miyazaki et al.^[2] Perhaps even more remarkable is the presence of secondary γ′ precipitation at both aging temperatures. The secondary precipitates in Fig. 8(b) are large and readily visible whereas those present in the alloy aged at 1000 °C are much finer, and most clearly visible in Fig. 8(c) and the larger micrographs in Fig. 4 of Qiu’s paper from which Fig. 8(c) to (h) were taken. Qiu states that the specimens were quenched into ice water after aging, but no information is provided on how the specimens were protected from oxidation during the heat-treatments.

Secondary γ′ precipitates are also quite clearly visible in micrographs of the specimens aged for various times at 1140 °C. Examples are shown in Fig. 9. As is the case for the secondary γ′ precipitates in the alloys of Kaufman et al.^[12] and Yeom et al.,^[13] Qiu claimed that they were formed during quenching. The main difference between the secondary γ′ precipitates in Qiu’s specimens and those of the other two is that they are roughly the same size as a function of aging time. Qiu, in an earlier paper, indicates that the aging time chosen for the structure seen in Fig. 9(c) was 240 min, not 120 min. Whichever aging time is correct, it seems that the volume fraction of secondary γ′ increases with aging time, but the sizes are comparable. The smaller sizes of the secondary γ′ precipitates in the specimens aged at 1000 °C compared to those in the specimens aged at 1140 °C is also consistent with their having nucleated and coarsened to some extent during quenching. The arguments supporting TD splitting as the mechanism in Qiu’s specimens are identical to those in the case of Miyazaki et al.^[2]

Fig. 9

SEM microstructures observed in a 14% Al alloy aged at 1000 °C for (a) 6 min; (b) 12 min; (c) 120 min; from Qiu^[14]

2.1.5 The Observations of Splitting of Ni₃Al Reported by Calderon et al.^[15,37,38]

Calderon et al.^[15] investigated the splitting of γ′ precipitates in a monocrystalline Ni-12% Al alloy. The objective of the investigation was to use lattice imaging by high-resolution TEM (HREM) to determine whether or not split γ′ particles in any of the ensembles depicted in Fig. 1 and 2 were anti-phase related. The idea behind these experiments is based on the knowledge that adjacent γ′ precipitates have only a 25% probability that the lattices in their long-range ordered crystal structures are in perfect registry. If not, the interface between neighboring precipitates would be equivalent to an anti-phase boundary (APB). It is well known that the (100) APB energy is much larger than the γ/γ′ interfacial free energy ~180 mJ m^–2[39] cf. 20 mJ m^–2.^[40] Since both TD and PE splitting must produce in-phase pairs, quartets, and indeed any of the groups depicted in Fig. 1 and 2, the detection of out-of-phase split configurations must mean that the neighboring γ′ particles cannot be a product of either splitting mechanism. The first experiments were deemed inconclusive, so additional investigations were undertaken^[37,38] to evaluate the statistics of anti-phase lattice registry across the narrow gaps of γ separating closely spaced γ′ particles.

No details were provided about the growth of the crystals, solution-treatment times and cooling rates from either the solution-treatment or aging temperatures in the experiments of Calderon et al.^[15,37,38] In the initial work on the alloy containing 12% Al,^[15] specimens were first aged at 840 °C for 5 h to produce “large precipitates”, then aged again at 650 °C to produce a bimodal distribution of γ′ precipitates. Continued aging at 650 °C for times up to 2000 h produced γ′ precipitates that appear to be split. The subsequent work^[37,38] also included experiments on a Ni-14% Al alloy aged only at 957 °C for times ranging from 3 to 140 h. The alloy concentrations and temperatures used in these studies are shown in the phase diagram in Fig. 10(a). It is evident that all the aging treatments of the 14% Al alloy at 957 °C, as well as the initial aging of the 12% Al alloy at 840 °C, were done in the single phase γ field of the phase diagram. The only aging treatments conducted in the 2-phase γ + γ′ region of the phase diagram were those on the 12% alloy re-aged at 650 °C.

Fig. 10

(a) The Ni-rich region of the Ni-Al phase diagram illustrating the alloy compositions (X_Al = 0.12 and 0.14) and heat-treatment temperatures (957, 840 and 650 °C) used in the experiments of Calderon et al.^[15,37,38]—they are indicated by the asterisks. The microstructure in (b) is from a specimen containing 12 at.% Al aged for 1 h at 840 °C. Micrographs (c)-(e) illustrate various different features of the γ′ precipitate microstructures observed specimens first aged at 840 °C for 5 h followed by re-aging at 650 °C for 1700 h. The magnifications in (b) and (c) are identical, as are the magnifications in (d) and (e). The γ′ precipitate microstructures for specimens of a 14 at.% Al alloy were not shown by Calderon et al.,^[37,38] Precipitates that appear to be in the process of splitting are indicated by the arrows in (c) and (e)

The γ′ microstructure of a specimen aged for 1h at 840 °C is shown in Fig. 10(b). The γ′ quartet in this specimen is the only example represented in Fig. 1, namely 1(d). The microstructures produced by aging in the 2-phase γ + γ′ region of the phase diagram at 650 °C are shown in Fig. 10(c)-(e). These bear some resemblance to the split γ′ particles depicted in Fig. 1 and 2, especially those indicated by the arrows in Fig. 10(b) and (e). However, these microstructures, even those indicated by the arrows, can also have evolved through favorable elastic interactions due to the long aging times at 650 °C. Calderon et al.^[15,37,38] concluded that the (100) lattice planes in neighboring closely-spaced γ′ precipitate pairs^[37] and quartets^[38] were statistically out of phase roughly 72 to 75% of the time. They therefore argued that the γ′ configurations in Fig. 10 were not due to splitting, but to attractive elastic interactions, possibly aided by migration of γ′ particles in the manner described by Su and Voorhees^[41].

Calderon et al. did not publish low-magnification photographs of the γ′ microstructures in their specimens, like the dark-field TEM images of Kaufman et al.^[12] or the SEM images of Yeom et al.^[13] and Qiu^[14]. This would have provided some assurance that the doublets and quartets they examined by HRTEM were in fact split γ′ particles comparable to those examined in the earlier investigations. Calderon et al.^[15,37,38] are most likely correct, but the absence of corroborating microstructural images suggests that their split microstructures were not equivalent to those in the previous investigations.^[2,12,13,14]

2.1.6 Splitting of Ni₃Si Precipitates Reported by Doi et al.^[3]

In an investigation of possible splitting of γ′-type precipitates in alloys other than Ni-Al, Doi et al.^[3] found octets of Ni₃Si in a Ni-12% Si alloy; the alloy was a single crystal grown using the Bridgman method. Specimens cut parallel to (100) were solution treated at 1200 °C for an unspecified length of time and slowly cooled (rate unspecified, but likely identical to the cooling rates in the Ni-Al experiments) to the aging temperature of 840 °C, the expectation being that this aging temperature was a few °C below the solvus temperature. These temperatures are indicated in the Ni-rich region of the Ni-Si phase diagram seen in Fig. 11(a), where it is evident that the aging temperature is almost certainly in the single-phase γ field, indicated by the lower asterisk, and that the appearance of Ni₃Si precipitates is in violation of phase equilibrium.

Fig. 11

The Ni-rich regions of the Ni-Si (a) phase diagram illustrating the alloy composition (X_Si = 0.12) and annealing temperatures (1200 and 840 °C) reported in the original paper of Doi et al.^[3]—they are indicated by the asterisks; (b) Octets of Ni₃Si in a specimen of Ni-12 at.% Si furnace-cooled from 1200 to 840 °C and aged for 20 h; (c) Sequence (top to bottom) illustrating the splitting of a concave cuboidal Ni₃Si particle into an octet of particles—the magnification is identical in all 3 images. The phase boundaries in (a) are based primarily on the thermodynamic assessments of Miettinen^[42] and Tokunaga et al.^[43]. The data on the solubility of Si in the γ solid solution phase are those of Rastogi and Ardell^[28], Oya and Suzuki^[44], Lebaili and Hamar-Thibault^[45], Ardell^[33] and Cho and Ardell^[46]. The solid curve representing the γ′ solvus is from Ardell^[33], which is essentially in perfect agreement with the γ′ solvus in the thermodynamic assessment of Miettinen^[42]

A few words on this region of the Ni-Si phase diagram are in order. It is obviously more complex than the binary Ni-Al phase diagram, with a number of invariant reactions and several solid-state phase transitions involving alloys with compositions around 25% Si. The diagram presented in Fig. 11(a) is a compromise between the thermodynamic assessments of Miettinen^[42] and Tokunaga et al.^[43]. The rendering of the γ′ solvus is the most important feature. Secondary is the fact that the Ni₃Si (γ′) phase becomes richer in Ni with increasing temperature, which in principle enables the precipitation of γ from supersaturated γ′. The solvus curve of Miettinen was chosen for two important reasons: 1. It predicts equilibrium solubilities of Si in Ni that are smaller than those of Tokunaga et al.; 2. It is in nearly perfect agreement with the solvus curve evaluated^[33] from the experiments of Rastogi and Ardell^[28] and Meshkinpour and Ardell.^[23]

The only split morphology reported by Doi et al. was the octet of γ′ particles shown in Fig. 11(b). Doi et al. examined many TEM specimens to ensure that the quartets seen in Fig. 11(b) were indeed (100) sections of an octet array. The evolution of the octet array is postulated to differ from the Ni₃Al octets in that the nucleation of splitting begins in the center of each face of the initial γ′ cube, progressing towards its center. Micrographs intended to support this contention are shown in Fig. 11(c), top to bottom. It seems quite unusual that the inception of splitting begins simultaneously on all 6 faces of the original cube. While this idea is certainly consistent with the microstructures shown, in the absence of dynamic evidence it is really not possible to know whether the protrusions seen in Fig. 11(b) were products of splitting or dendritic growth.

2.1.7 Additional Comments

The most striking observation of the work considered to this point is that the splitting of γ′ precipitates was observed in specimens aged in the single-phase fields of the Ni-Al and Ni-Si phase diagrams. This is indisputably true for Ni₃Al in the work of Miyazaki et al.^[2] and Qiu,^[14] partially the case in the work of Calderon et al. ^[15,37,38] and borderline true in the work of Kaufman et al.,^[12] Yeom et al.^[13] It is also the case for Ni₃Si in the investigation of Doi et al.^[3] In fairness to the researchers, who all deliberately chose their aging temperatures to be just below the solvus temperatures for their alloy compositions, and therefore only slightly supersaturated during aging, the most definitive location of the γ′ (Ni₃Al) solvus, namely the work of Dupin et al.^[35] was not available to them because it had not yet been published. The γ′ solvus curves for Ni₃Al and Ni₃Si were established much earlier by Rastogi and Ardell,^[28] but had to be extrapolated to higher temperatures.

Considering first the three investigations^[2,3,14] conducted entirely in the single-phase fields of the phase diagrams, as well as aging treatments done at 840 and 957 °C by Calderon et al.,^[15,37,38] it is reasonable to wonder how is it possible that precipitation could proceed and be sustained under such conditions? We know that in the relevant cases the work was done using single crystal specimens grown by the Bridgman method. The authors did not provide any information on the solidification rates. Except for Qiu^[36]2, they do not appear to have double-checked the solute concentrations of their alloys, including possible variations along the length or diameters of the single crystals. The authors do not appear to have examined the as-solidified microstructures of the crystals, or at least did not report the results.

In light of these facts it is logical to assert that all the single-crystal specimens retained some γ′ phase after solidification and solution treatment. At the very least, the γ phase compositions in these alloys must have been highly inhomogeneous, with concentrations of Al approaching the solubility limits at the solution-treatment temperatures (18.4 to 18.5% at 1200 °C and 19.2 to 19.3% at 1250 °C). The concentration gradients in the γ′ phase could not possibly have been eliminated by solution-treating for ½ h in the 12% Al alloy studied by Miyazaki et al.^[2] Significant composition gradients or pre-existing γ′ precipitates would have been difficult to eliminate even after solution-treating the 14% Al alloy for 24 h at 1200 °C.^[14] Since the solution-treatment time at 1250 °C was not reported by Kaufman et al. ^[12] we can also assume that their 17% Al alloy also contained either substantial concentration gradients and/or γ′ precipitates prior to aging at 1100 °C. It is reasonable to conclude that only Yeom et al. ^[13] investigated an alloy that was nearly compositionally homogeneous alloy owing to the processing conditions used in its preparation.

The scenario for the Ni-Si alloy studied by Doi et al. ^[3] must be somewhat different due to the quite different Ni-Si phase diagram. Reference to Fig. 11 suggests that a single-phase monocrystalline Ni 12% Si alloy would have contained some amount of the β₃ and/or β₂ phases under some crystal growth conditions. Moreover, heating the alloy to 1200 °C for the purpose of homogenizing it might have resulted in melting of the second phase, which would have solidified after a suitable holding time. Absent any information provided on the solidification rate used to prepare the single crystal and solution-treatment time at 1200 °C, it is highly unlikely that the heat-treated Ni-Si specimens were homogeneous single-phase γ alloys prior to aging them. The presumption here is that the Ni-Si specimens, like the Ni-Al specimens, were either substantially compositionally heterogeneous, contained γ′ precipitates before they were aged, or both. Since the final aging temperature of 840 °C also lies in the single-phase field of the 12% Si alloy, the formation of the octet arrays suggests an explanation more complicated than PE splitting.

3 The Case for TD Splitting

It is helpful to initiate this discussion by providing a few insights into the formation of γ-phase precipitates within large γ′ particles supersaturated in Ni. Ham et al. ^[47] published the first observations of coherent γ precipitates in the interior of large γ′ particles in an as-solidified ternary Ni-Al-Ti alloy. Later on, a similar observation was made by Cornwell and Purdy in off-stoichiometric Ni₃Al^[16] this was the first such observation in binary Ni₃Al. Cornwell and Purdy reported that the γ particles were coherent and plate-shaped, with interfaces parallel to (100). Ma and Ardell^[17] subsequently investigated the shape of the phase boundary between the γ + γ′ and γ′ regions of the phase diagram (the γ solvus) and showed it to be retrograde, allowing for hypostoichiometric compositions of 22+ at.% Al to become supersaturated in Ni at temperatures below the γ solvus. Ma and Ardell also investigated coarsening of the γ precipitates and the evolution of their shape.^[18,48] It was determined that the easy, barrierless impingement of γ precipitates led to a lath shape, which was later shown^[49] to be favored by certain combinations of the differences between the single-crystal elastic constants of the γ and γ′ phases.

Perhaps unaware of the work of Cornwell and Purdy, Miyazaki et al. ^[1,2] concluded that the splitting of γ′ precipitates must be a consequence of the competition between elastic energy due to coherency strains and the interfacial free energy of the coherent γ/γ′ interface, as noted in the Introduction. The theory of Miyazaki et al. was the first of many theories of PE Splitting; a partial compendium is cited here.^{[24,50,51,52,53,54,55,56,57,58]} From a theoretical perspective there is little doubt that splitting by the PE mechanism is favored as its size increases, but based on the evidence in section 2 an alternative scenario is preferred that not only takes into account the apparent violation of the demands of the phase equilibrium, but can also account for the apparent splitting of large γ′ particles.

The basic postulate presented herein is that all the observations of splitting described in section 2 can be attributed TD Splitting by the precipitation of the γ phase within the γ′ precipitates that either nucleated and grew above the aging temperatures or were present in the alloy after solidification and solution treatment. Elastic energy might have played a role in the nucleation and especially propagation of the γ precipitates within the much larger γ′ particles, but is in no way entirely responsible. This postulate requires a certain amount of speculation, but we shall see that it is well supported by the results in section 2, the arguments presented in section 3 and additional ones to follow.

The concept of TD Splitting, i.e. that the precipitation of γ-phase particles can engender the splitting of large γ′ precipitates within them, is not new. Doi et al. ^[59] observed TD splitting and recognized it as a viable mechanism in a ternary Ni-8.5% Al-5.4% Ti alloy. The alloy in this case was not monocrystalline, but was processed by standard ingot metallurgy, involving hot forging of a vacuum-induction-melted ingot, slices of which were solution-treated, quenched into iced brine, isothermally aged at 940 °C for various lengths of time and finally quenched into iced brine. Representative TEM micrographs from the ternary Ni-Al-Ti alloy are shown in Fig. 12, taken from the work of Doi et al. ^[59] and Hata et al. ^[60] Doi et al. recognized that the shape of the γ solvus in the ternary alloy was retrograde, similar to the shape seen in Fig. 3, as originally suggested by Oblak et al.,^[61] and used this shape to explain their observations of γ precipitates in γ′ particles. Doi et al. thus were the first to propose TD splitting as a new mechanism. It is easy to envision that the growth of many of the features seen in Fig. 12 will lead to the types of splitting configurations depicted in Fig. 1 and 2.

Fig. 12

taken from the paper by Doi et al. ^[59] and the image in (c) was taken from the paper by Hata et al.^[60] The particles indicated by “P” show plates of γ parallel to the plane of the figures. The particle labelled “B” illustrates the intersection of 2 γ particles in the shape of a boomerang. The particle labelled “S” shows a γ precipitate in the process of splitting a γ′ particle. The reasons for the labels P and B are discussed later in the text

Dark-field TEM images of γ′ particles containing γ at various stages of aging a Ni-8.5% Al-5.4% Ti alloy initially at 940 °C for 45 min, and then reaging at 750 °C for (a) 12 h; (b) 48 h; (c) 192 h. The images in (a) and (b) were

The genesis of γ precipitation within large pre-existing γ′ particles has been investigated by Vogel et al.,^[62,63,64] not necessarily to add to the literature on splitting, but to explore the properties and evolution of what they call “hierarchical” microstructures. During the course of their work on the same 8.55 Al-5.4% Ti alloy investigated by Doi et al.,^[59] Vogel et al. ^[63] confirmed that the growth of γ particles could indeed lead to the TD splitting of γ′ precipitates. The suggestion that hierarchical microstructures could lead to improvement in mechanical properties has stimulated additional investigations of precipitation of γ within γ′ particles.^[65,66,67]

Hierarchical microstructures in diverse multicomponent γ/γ′ alloys invariably begin with the nucleation of γ precipitates inside pre-existing γ′ particles produced by aging at relatively high temperatures. The γ particles inevitably nucleate either during isothermal aging at lower temperatures or by furnace cooling from an initial aging temperature to a lower one.^[61] The connection to the hypothesis in this paper, i.e. that splitting is a consequence of γ precipitation within pre-existing γ′ particles, is illustrated in Fig. 13, which is presented here to emphasize that hierarchical microstructures are not limited to multi-component Ni-base alloys, but are also potentially viable in binary alloys. Additionally, Fig. 13 clearly shows that the origin of TD splitting of Ni₃Al^[16] and Ni₃Ge^[68] precipitates need not be the nucleation of a single γ particle in its center, as implied in Fig. 2(b) and (c) and seen in Fig. 3(b) and (c). There have not been any investigations of the splitting of Ni₃Ge precipitates, though the microstructures in Fig. 13(b) suggest that such a study would successfully produce them.

Fig. 13

Dark-field TEM images of incipient hierarchical microstructures in (a) a binary Ni-17% Al alloy ^[16] and (b) a binary Ni-14% Ge alloy.^[68] In (a) the specimen was cooled during 3 h from 1200 to 700 °C and aged at the lower temperature for 4 weeks. In (b) the specimen was aged for ½ h at 1150 °C, quenched to room temperature and re-aged for 2h at 714 °C

The precipitation of Ni-Ge precipitates within supersaturated Ni₃Ge is connected to the current investigation in another way. Ardell and Ma^[69] have shown that in so-called “inverse” Ni-Ge alloys, the morphologies of γ precipitates are quite similar to those seen in Fig. 12, particularly the plate-shaped γ particles indicated by “P”, and the boomerang shaped γ particle indicated by “B”. There are two implications. The first is that boomerang-shaped γ precipitates can grow and produce split γ′ particles like those in Fig. 1(b), 4(f), 5(b) and (f), though it is far more likely for this to occur when the γ particles are plate shaped rather than lath shaped. The second is associated with the auxetic Poisson’s ratios ν[001] and ν $[1\overline{1}0]$ of Ni₃Ge.^[70] Of four binary Ni₃X phases for which the single-crystal elastic constants are reasonably well-known (Ni₃Al, Ni₃Ga, Ni₃Ge and Ni₃Si), Ni₃Ge is the only one for which ν $[1\overline{1}0]$ is positive. The similarities between the microstructures of the Ni₃(Al,Ti) and Ni₃Ge phases might portend similar elastic properties of these phases.

4 Final Comments, Discussion and Conclusions

It should be noted that convincing evidence of PE splitting has never been reported in alloys that are solution treated, quenched and isothermally aged. Yeom et al.^[13] themselves explicitly stated that the γ′ precipitates in quenched and isothermally aged specimens never split, but simply coarsened to thick plates after 2 h at 1020 °C. One can always argue that the specimens in many of the binary alloys were not aged for sufficiently long times, but at least in the case of Ni₃Si particles, a comparison of relative sizes provides realistic evidence that PE splitting is simply not favored. This is suggested by the micrographs in Fig. 14(a) and (b), taken from the paper by Meshkinpour and Ardell^[23]. In this figure we see concave cuboidal Ni₃Si precipitates at the same magnification as the split particles in Fig. 11(b). The particles in Fig. 14(a) were aged for 120.2 h at 650 °C, just below the γ′ solvus temperature, after having been previously aged for 48 h at 600 °C, the idea being to stimulate coarsening at a very small undercooling to see if splitting could be induced. Instead, the γ′ particles are concave cuboidal and clearly of comparable size to the split particles of Doi et al.^[3], shown again in Fig. 14(c).

Fig. 14

Ni₃Si precipitate morphologies at comparable sizes: (a) Concave cuboidal precipitates in a Ni-10.88% Si alloy aged initially at 600°C for 48 h, then at 650 °C for 120.2 h; ^[23] (b) A dendritic Ni₃Si precipitate in the 10.88% Si alloy aged for 164 h at 650 °C; (c) The same Ni₃Si precipitates seen previously in Fig. 11(c).^[3] The magnification is the same throughout

The precipitate in Fig. 14(b) was originally thought to be an ogdoadically diced cube produced by PE splitting and viewed most likely parallel to (011).^[23] It now seems far more likely that it is a product of either TD splitting or dendritic growth. However, there is one difficulty with attributing the splitting of Ni₃Si to the TD mechanism. It is the requirement that the γ solvus in the Ni-Si phase diagram, Fig. 11(a), become increasingly supersaturated in Ni with increasing temperature. Though this is the way the γ solvus is drawn, there is no evidence for the precipitation of the γ Ni-Si solid solution in supersaturated Ni₃Si. In this light it is quite reasonable to attribute the ogdoadically diced Ni₃Si cubes as having resulted from dendritic growth, especially considering the very small undercooling from the Ni-Si solvus and the inhomogeneous Ni₃Si microstructures observed by Meshkinpour and Ardell^[23] under comparable aging conditions.

Interestingly, Yeom et al.^[13] reported dendritic Ni₃Al precipitates (Fig. 15), in their alloy aged for only 10 min at 1000 °C; this is a slightly undercooled aging condition, as is evident in Fig. 6(a). The dendritic character of the γ′ precipitates (seen within the squares) is obvious, as is the fact that quite a few configurations indicate quartet shapes (encircled). Important takeaways from the microstructure in Fig. 15 is that on a true (100) plane of polish some of the configurations that are clearly dendritic would appear simply as quartets. Additionally, in a TEM thin foil 100 to 200 nm in thickness it is highly likely that dendritic precipitates would also project as quartets. Based on this reasoning it is conceivable that the Ni₃Si quartets originally reported by Doi et al.^[3] are essentially plane sections through dendritic Ni₃Si precipitates.

Fig. 15

Dendritic Ni₃Al precipitates observed by Yeom et al.^[13] in a Ni-15.91% Al alloy cooled from 1200 to 1000 °C at 25 °C h^–1. The plane of the figure is close to (100). The dendritic γ′ precipitates (enclosed in squares) have protrusions along 〈111〉. The γ′ precipitates that could easily pass for quartets are enclosed in circles

The principal assertion in this paper is that TD splitting is most likely responsible for all the observations of this phenomenon in Ni-Al and Ni-Si alloys. The major exception is the splitting investigated by Calderon et al.,^[15,37,38] who observed the statistically expected 75% of out-of-phase lattice relationships among neighboring Ni₃Al precipitates in doublets and quartets. The belief here is that the groupings examined by Calderon et al. were created by normal elastic interactions among γ′ precipitates, primarily because there was scant to no evidence presented that the groupings evolved from conventional split configurations (e.g. those depicted in Fig. 1 and 2) in the first place. It is reiterated here that both PE and TD splitting necessarily produce in-phase neighboring γ′ particles. The same is true for pseudo-split arrays produced by the dendritic growth of γ′ precipitates, which is suggested as a viable mechanism of splitting of Ni₃Si precipitates.

The strangest observations stemming from this review of the literature on splitting are the persistent findings of split precipitate configurations in the microstructures of alloys aged in the single-phase regions of the binary Ni-Al and Ni-Si phase diagrams. If nothing else, these are clear violations of phase equilibrium. For the few cases where specimens were aged in the 2-phase γ + γ′ regions of the phase diagrams, the temperatures were barely below the best estimates of the solvus temperatures. It is argued that even in these cases the most probable scenario for splitting was precipitation in highly compositionally heterogeneous specimens, including both γ′ and subsequent precipitation of γ within pre-existing γ′ particles. This is the essence of TD splitting, which is supported by the well-established production of hierarchical microstructures. Compositional heterogeneity also explains the behavior of secondary γ′ precipitates in the aged microstructures.

In all cases splitting was found only in specimens slowly cooled from an initial solution-treatment temperature to a final aging temperature. It is asserted that only TD splitting can account for these microstructures, and it is important to emphasize that this assertion is fully consistent with the requirements of phase equilibrium. This assertion is also strongly supported by a persistent negative finding, specifically the absence of splitting in alloys that have been quenched from the solution treatment temperature and isothermally aged. Splitting under these conditions can only occur by the PE mechanism, since the γ′ particles that nucleate, grow and coarsen under isothermal aging conditions always have compositions near their thermodynamic equilibrium values, can never become supersaturated in Ni and therefore cannot become hierarchical.

It is well-recognized that the explanations offered herein are conjectures, some of which are quite speculative. It is suggested that the only possible resolution of these conjectures is by sophisticated thermodynamic and kinetic modeling, beginning with solidification and through the nucleation, growth and coarsening regimes during slow continuous cooling to the final aging temperatures.