Recovery facilitated by interphase boundary motion circumvents recrystallization in superalloy single crystals

Dislocation recovery lowering the driving force for recrystallization would be able to suppress the latter in Ni-based superalloy single crystals, but was believed unlikely due to their low stacking-fault energy. Defying this traditional wisdom, here we show that efficient recovery can be realized once the γ′-precipitates start to dissolve. Our microscopy evidence tracking the distribution/configuration of dislocations reveals that the shifting γ/γ′ interphase boundaries release the dislocations trapped there, facilitating their annihilation and rearrangement into low-energy network configurations. Our finding explains the success of a recent recovery protocol that kept superalloys as single crystals after supersolvus homogenization heat treatment. GRAPHICAL ABSTRACT IMPACT STATEMENT In γ/γ′ two-phase Ni-based superalloy single crystals, dislocation recovery is achieved via an interphase-boundary motion enabled mechanism, defying the traditional wisdom of dislocation climb/cross-slip controlled by stacking-fault energy.


Introduction
Ni-based superalloys are the materials of choice to manufacture turbine components in aerospace and power generation industries [1].Their superior properties rely on the large volume fraction of strengthening γ -particles embedded in the solid-solution γ -framework [2,3].To further improve their creep resistance, superalloy single crystals with no high-angle grain boundaries have been developed [4].However, manufacturing with significant shape changes via solidification and machining inevitably involves plastic strains mediated by dislocations, and post-manufacturing heat treatment easily triggers recrystallization [5][6][7].Although annealing the single crystals at temperatures well below the γ -solvus Table 1.In those cases, recrystallization was not avoided successfully at higher plastic strains because the recovery annealing temperature was either rather low ( ∼ 0.5 homologous temperature or lower, as for single-phase alloys) or too high (solvus temperature or higher, which triggered recrystallization).The poor recovery capabilities of superalloys were ascribed to their low stackingfault energy [11,12] (SFE, about 20-30 mJ/m 2 ) [13][14][15].However, such attention to SFE, while appropriate to understand the recovery/recrystallization behaviors of single-phase materials, is nevertheless inadequate for two-phase alloys as complex as superalloys, which, unlike alloys dispersed with low volume fractions (usually no more than 5%) of precipitates, contain abundant (volume fraction up to 70%) γ -particles [16][17][18][19].Because of the influence of the high-volume fractions of the strengthening precipitates, the dislocation microstructures in the deformed superalloys become more complicated and harder to characterize.Therefore, significant discrepancies and even contradictions have been reported on the dislocation distribution and configuration in the literature.a detailed summary of which can be found in Supplementary Table 2.For room-temperature deformed superalloys, some demonstrated [20][21][22] transmission electron microscope (TEM) images of straight dislocations aligned in γ -channels, while others believed that [23,24] those parallel lines were superpartial dislocation pairs separated by planar defects, evidencing that high densities of dislocations had cut into the γ -particles.Moreover, since the previous investigations continued to follow the ideas for recovery/recrystallization of singlephase materials, they focused on SFEs rather than on dislocation-precipitate interactions.
Recrystallization renders the microstructure polycrystalline, which would forfeit the single-crystal benefits and significantly degrade the high-temperature creep performance of superalloys [4].Thus, recrystallization has been a formidable obstacle for the manufacturing and application of Ni-based superalloy single crystals.In this study, advanced TEM tomography is applied to directly track the distribution of dislocations and their configurations in the as-deformed state and then their annihilation during annealing.Based on the understanding of the interplay between the dislocations and precipitates, in particular the role played by the interface boundaries, we demonstrate when and how recrystallization can be completely pre-empted by a recovery annealing.The latter has been optimized to as short as 30 min, which is significant for the manufacturing and repair of superalloys.Our discovery reveals that the recovery mechanism in the two-phase superalloys defies the conventional knowledge for single-phase alloys.

Materials and methods
The AM3 superalloy single-crystalline boule (chemical composition is shown in Supplementary Table 3) growing along [001] direction was machined into cylindrical (5 mm in diameter and 10 mm in height) specimens for compression tests at room-temperature at a constant strain rate of 1.69 × 10 −4 s −1 .The plastic strain, 4.5% in this work, was measured from the height reduction of the deformed cylinders.The deformed cylinders were sliced perpendicular to the [001] direction into 1-mm-thick discs for heat treatment investigations.More information can be found in Supplementary Figure 1 and Note 1.
The as-deformed and heat-treated samples were characterized using scanning electron microscope (SEM), electron backscattered diffraction (EBSD), TEM, and synchrotron radiation micro-Laue diffraction (SR-μLaue) techniques.The deformation microstructure characterizations were carried out on samples taken from the interior of the bulk superalloys, and the absence of recrystallization was confirmed both on the surface and in the bulk.TEM thin foils were made from the strainconcentrated areas, and then ten bright-field images were collected for each deformation or annealing state to improve reproducibility, all along the [001] zone axis.Subsequently, the dislocation density was measured from each image using the line-intercept method [25] and averaged.TEM tomography was performed on a FEI TECNAI G20 TEM operated at 200 kV.To optimize the contrast of dislocations, g = [ 220] and g = [2 20] twobeam conditions were selected to acquire a series of weakbeam dark-field images from −47 o to 44 o and −55 o to 66 o for deformed and 1 min-annealed at 1100 °C specimens, respectively, with an angular step of 1 o .More details can be found in Supplementary Note 1.

Results
The residual lattice strain and misorientation distributions in the 4.5% room-temperature compressed superalloy single crystal, mapped using the SR-μLaue method, are highly non-uniform.Von Mises strains near the deformation concentrated regions (indicated by blue arrows in Figure 1a), especially at their intersections, reach up to 50 × 10 −3 , almost two orders of magnitude higher than the average, proving severe lattice distortions and hence concentrated strain energy in the narrow zones.Along the deformation concentrated zones, low-angle misorientations are also detected (Figure 1b), up to 1 o .As highlighted by the dashed orange lines in the bright-field TEM image of the deformation concentrated region in Figure 1c, the cuboidal γ -particles projected onto the (111) crystallographic plane appear as triangles and hexagons surrounded by narrow γchannels, into which most of dislocations are jammed (indicated by the blue arrows).Only a small number of dislocations are detected cutting into the γ -particles (pointed using green arrows).Along various zone axes, those dislocations in γ -channels are straight and aligned in < 110 > crystallographic directions (Supplementary Figure 2).Exploiting TEM tomography (Figure 1d, as well as in Supplementary Figure 3), the morphology and spatial distribution of the dislocations in the γchannels can be better visualized.Dislocation loops, either residing in a certain γ -channel [20,21] (those in the blue box) or surrounding a γ -particle [26] (those in the red box), are commonly observed.Some other dislocations have partially bowed out of its original γ -channel and extruded into the perpendicular ones [26,27] (yellow box).Based on the TEM observations, the dislocation configurations are schematically displayed in Figure 1e.
The dislocation density in the deformation concentrated regions is measured to be 2.3 × 10 15 m −2 .Based on detailed analysis under different two-beam conditions (Supplementary Figure 4 and Note 2), the Burgers vector of most of the dislocations are determined to be ± a 2 [101] for the locations analyzed here.
To investigate the recovery and the associated dislocation behavior, the deformed single crystal was annealed at various temperatures for nominally 1 min each (as schematically shown in Supplementary Figure 1c).As clearly seen in Figure 1f, the dislocation density drop and γ partial dissolution are strongly coupled.The dislocations are by and large recovered (by ∼ 80%) after being annealed at 1100 °C for only 1 min.More detailed analysis will be described in Figure 2. Annealing at temperatures below 900 °C is not able to induce any significant change in terms of both the γ volume fraction/morphology and the dislocation density/configuration (Figure 2a).Above 900 °C, the volume fractions of primary γ -precipitates keeps decreasing with increasing temperature.Along with this subsolvus solutionizing, the density of left-over dislocations drops monotonically with increasing temperature.After annealing at 1000 °C (Figure 1f and Figure 2b), about 30% of the dislocations are annihilated.Some left-over dislocations become curly (blue arrows), while some still keep their original straight shape (red arrows).When the temperature is elevated to 1100 °C, more than 80% dislocations are annealed out, leaving a low density of only 4.7 × 10 14 m −2 (Figure 1f).Detailed TEM tomography analysis (Figure 2c, as well as in Supplementary Figure 5) proves that almost all the remaining dislocations are still lying in γ -channels, but become well separated from one another.In the field of view, all dislocations turn highly curly (blue box), or even shrink into small loops (yellow box), with few straight ones left.Despite the significant morphology and density evolution, the Burgers vector of the left dislocations remains unchanged (Supplementary Figure 6 and Note 2).As the annealing temperature is further elevated (to 1200 °C for example), although the γ volume fraction keeps decreasing, no further significant change is observed in terms of dislocation density and configuration, compared to the 1100 °C annealed specimen (Figure 2d).
The key observation above is that the onset temperature (T onset ) of dislocation recovery above which accelerated dislocation annihilation can be realized is the same as the one that γ -particle starts to dissolve (900 °C in this case).Moreover, from the plot in Figure 2a, another characteristic temperature, the plateau temperature (T plateau ), is also figured out, at which the dislocation annihilation rate is maximum (1100 °C in this case).
In order to achieve a more complete relief of the stored elastic strain energy, we design a stepped recovery heat treatment as shown in Figure 3a.The recovery takes 30 min in total, which is less than 1/20 compared to the previously reported long term/cyclic protocol [6], and 1/4 of our own former study [22].After such short recovery, although the deformation concentrated regions are still detectable (blue arrows in Figure 3b), much lower and more homogeneous residual strains and misorientations are measured around them (Figure 3b,c), indicating effectively diminished driving force for recrystallization.After the stepped recovery, a supersolvus treatment is conducted at 1300 °C for 30 min, which is much longer than that previously found for the recrystallizing grains -if any -to nucleate and grow [28,29].Yet, EBSD scan over the entire sample surface evidences the single crystalline structure and excludes the existence of recrystallized grains (Figure 3d).In contrast, recrystallized grains readily form at 1300 °C without recovery (Figure 3e).After recovery and supersolvus treatment, dislocations can be hardly detected (Figure 3f).
The microstructure evolution during the stepped recovery treatment is studied in detail.With the temperature increasing and the holding time prolonging, γ -particles in the deformation concentrated zones gradually evolve from the cuboidal shape (Figure 3g) to the rafts (Figure 3h) and eventually to the butterfly shape (Figure 3i).Since the γ -particles dissolution rate is higher along the dislocation pipes, grooves are generated on the γ -particles [30].The coarsening directions observed in the γ -precipitates displayed in Figure 3h,i are non-uniform, because of the locally inhomogeneous stresses in these deformation concentrated zones (Supplementary Figure 7b and 7d).In the meantime, the curly dislocations (Figure 3j) begin to react with each other (Figure 3k) and finally form regular hexagonal dislocation networks at γ /γ interface (Figure 3l, as well as in Supplementary Figure 8), a low-energy dislocation configuration [31,32], which result the stored energy further decreasing.

Discussion
First of all, SFE is known to be a key factor influencing dislocation recovery [16].Previous studies [13][14][15] show that the SFE of γ -matrix in superalloy single crystals is only 20-30 mJ/m 2 , which drives the dislocations to dissolve into immobile partials that are unwilling to cross-slip and climb to annihilate, assuming the SFE keeps almost constant as the temperature increases [15].However, in the current study, the observed rapid dislocation annihilation at 1100 °C suggests that the SFE of the γ -matrix is not low near the γ -solvus temperature.To demonstrate that this is the case, we performed molecular dynamics simulations for two different states of the γ -matrix (details in Supplementary Note 3): (1) the γ -phase is assumed to be a completely random solidsolution, (2) chemical short-range order is taken into consideration.As shown in Figure 4a, the calculated SFE at room-temperature, 25-45 mJ/m 2 , is consistent with the literature reports [13][14][15].But the SFE increases at elevated temperatures.At 1100 °C, the SFE increases to about 62 mJ/m 2 (random solution) and over 80 mJ/m 2 (due to chemical short-range order), which are much higher than those of the easy-to-recrystallize metals such as Ag ( ∼ 20 mJ/m 2 ) [33,34] and austenitic stainless steel ( ∼ 20 mJ/m 2 ) [35,36].Therefore, dislocation splitting into partials with wide separation distance, which would retard the dislocations movement and hence annihilation, is not the key factor of recovery at elevated temperatures.
More importantly, by comparing the normalized dislocation density in pre-strained superalloy AM3 (this work) with deformed commercially pure aluminum (high SFE) [37] and austenite stainless steel (low SFE) [38] in Figure 4b, we can clearly see the difference in the recovery and recrystallization behaviors.Single-phase alloys, no matter the SFE is high or low, would first exhibit recovery (RV, displayed as solid blue and green curves) and then recrystallization (RX, shown as dashed curves) as the annealing temperature increases.Although the high SFE alloys show more recovery capabilities than the low SFE alloys, the recovery induced dislocation density decrease in both cases is less than 20%, because, according to the classic recovery theory, point defects will be activated and annihilated prior to the dislocations.A precipitous decrease in dislocation density sets in only upon recrystallization (dashed curves).However, in the two-phase superalloys, a barely detectable recovery stage is followed by a drastically accelerated recovery stage, which leads to a (almost abrupt) drop in dislocation density by 80% or more and a complete prevention of recrystallization at high homologous temperatures.This leads to an unusual recovery behavior: 'solid curve all the way, eliminating the dashed curve' (see Figure 4b).
The above unusual dislocation recovery behavior of superalloy single crystals is rooted in their two-phase microstructure and deformation mechanism.Through TEM tomography, the spatial distribution, configuration, and Burgers vectors of dislocations can be unequivocal characterized.The dislocations originate and multiply in single γ -channels at the beginning of the roomtemperature plastic deformation.As strain increases, dislocations move in the γ -channels until being stopped by the γ -particles.To carry more deformation, some dislocations have to bow-out into the perpendicular γchannels, following the Orowan bypass mechanism [21], because the stress is not high enough to drive the dislocations to cut into γ -particles.As the bow-out process goes further, dislocation loops surrounding γ -particles are eventually generated.Due to the coherency strain, numerous dislocations are trapped at the γ /γ interfaces.This is why the onset of dislocation recovery is coincident with the partial dissolution of γ .Partial dissolution implies adequate atomic diffusion and entails a mobile γ /γ interface, creating opportunities for the previously stuck dislocations to move around and interact with each other in less than several minutes.Regretfully, the kinetics of dislocation motion and reaction are difficult to observe during in-situ heating experiment in TEM, because for TEM observations the specimens have to be thinned down to less than 100 nm, which is only a quarter of the size of typical γ -particles, and the dislocations would be easily annealed out from the sample surfaces, before interacting with γ /γ interfaces.
It is known that the driving force of recrystallization, P, is the product of the dislocation density, ρ, and the energy per unit length of dislocation line, E dis [39], For the 4.5% deformed AM3, with merely one-minute annealing at 1100 °C, the density of dislocations drops dramatically by a factor of 5. What is more, the remaining dislocations turn curly due to the cross-slip or climb, suggesting configurational evolution that lowers the energy per unit length.As a result, P is reduced to less than 20% of the deformed state.Less dislocations are annihilated at 1000 °C than at 1100 °C because at the lower temperature some dislocations are still not let go by the γ /γ interface.1200 °C does not annihilate more dislocations than 1100 °C, indicating that at 1100 °C, γ -particle has dissolved enough such that all dislocations trapped by the interphase boundaries have become mobile.The annihilated dislocations (accounting for 80%) must have been paired ones with opposite Burgers vector (± a 2 [101]), and the spacing between each paired dislocations is only several nanometers (shown in Figure 1d), which makes the annihilation so rapid (Figure 4c,d).The remnant 20% are unpaired such that their density keeps almost constant even at higher temperatures and longer annealing times.However, they find their own way to lowering the stored strain energy by changing configurations, including climbing or crossslip to become curly (Figure 4e), interacting with each other to form irregular dislocation networks (Figure 4f), and gradually rearranging into low-energy hexagonal dislocation networks (Figure 4g).According to the classic theory [39], the energy per unit length of dislocation is consisted of self-energy and interaction-energy.The self-energy is material and temperature dependent, while the interaction-energy depends strongly on the configuration of dislocations.Dislocation reconfiguration and rearrangements reduces the interaction-energy.As a result, the energy associated with the dislocations, and thus the driving force for recrystallization, is further reduced.
Finally, we compare our current recovery protocol with the previously reported ones.In many of the previous investigations, recovery annealing was either too low to reduce recrystallization driving force [7], or too high to trigger recrystallization directly [11].In this study, two critical temperatures, T onset and T plateau , are marked (Figure 1f).Recovery annealing is better carried out from some point between these two temperatures to be efficient and safe.Our own successful experience obeyed this rule [22], and thus recrystallization is completely pre-empted even with 5.9% room-temperature plastic strain.However, we must admit that our previous heat treatment protocol, because of the unknown recovery mechanism and kinetics, was rather conservative, but not the most efficient in time and energy.In the current study, we not only optimized the recovery annealing protocol (from previous 2 h to current 30 min) for room-temperature compressed AM3, but also revealed the dislocation evolution stages (with two critical temperatures, T onset and T plateau ) using a stateof-the-art TEM methodology to figure out why the innovated protocol can circumvent recrystallization in superalloys.

Conclusion
In sum, through TEM tomography, we confirm that with about 4.5% plastic strain in superalloy single crystals, dislocations are generated and multiplicated in the γ -channels, but almost impossible to cut into the γ particles, leading to numerous dislocations pinned at the γ /γ interfaces.Due to such microstructural features, annihilation of dislocations cannot be achieved unless the annealing temperature is above T onset , to dissolve the γ -particles partially such that the γ /γ interfaces are set in motion to liberate the stuck dislocations.Systematic investigation suggests 1100 °C (T plateau ) as an optimized temperature to have dislocations annihilated thoroughly with little risk of recrystallization.Short annealing reduces the driving force for recrystallization by more than 80%.What is more, with prolonged annealing time above T plateau , dislocations keep evolving into lower-energy networks, further diminishing the driving force for recrystallization.Based on these findings, an efficient and inexpensive (only half an hour) heat treatment protocol has been established for superalloy single crystals to completely avoid recrystallization during supersolvus homogenization heat treatment.Therefore, our study offers an efficient way to lower the rejection rate and thus the overall cost of superalloy single crystal blades.In terms of advances in materials science, we have discovered a new recovery-controlling mechanism for high-volume fraction multiphase alloys, for which the interphase-boundary-detrapping becomes the rate-limiting step, in lieu of the traditional dislocation climb/cross-slip processes.This leads to unusual consequences as depicted in Figure 4b, where the normal recovery of dislocations with increasing temperature, well known to be gradual until recrystallization, is replaced by a wide 'hold before burst' regime up to a threshold temperature at which a precipitous drop kicks in (red curve), to the level that the recrystallization can be pre-empted altogether.

Figure 1 .
Figure 1.The microstructures in the superalloy single crystal compressed in the [001] direction.(a) Von Mises strain map, showing the elastic strain associated with the accumulated dislocations.(b) Kernel average misorientation map.(c) Bright-field TEM image of the deformed sample observed in [111] crystallographic direction.(d) Snapshot from the dark-field tomography video of the deformed sample.(e) The schematic of dislocations in the deformed sample.(f) The γ volume fraction and dislocation density after annealing at elevated temperatures (the width of the bands corresponds to the measurement error, and the vertical dash lines indicate the onset and plateauing temperatures of the dislocation density drop), showing a strong coupling between the γ dissolution and accelerated dislocation density decrease.

Figure 3 .
Figure 3. Thorough recovery of the 4.5% plastically deformed superalloy single crystal.(a) The schematic of stepped recovery strategy and solutionizing heat treatment (details in Supplementary Note 1).The von Mises strain map (b) and the KAM map (c) of the fully recovered single crystal.The IPF-Z figure of the supersolvus solutionizing heat-treated superalloys (d) with and (e) without recovery annealing.(f) Bright-field TEM image of stepped recovered and solutionized sample.The evolution of γ -particles and dislocation interrupted the rapid stepwise recovery heat treatment at (g, j) 1100 °C, (h, k) 1200 °C, and (i, l) 1250 °C, respectively.

Figure 4 .
Figure 4. (a) Temperature-dependent SFE of the γ -phase under the random solid-solution and chemical short-range order conditions, from molecular dynamics simulations.(b) Schematic showing dislocation density as a function of annealing temperature in recovery/recrystallization (RV/RX), comparing our pre-strained two-phase superalloy with single-phase alloys with either high (commercially pure aluminum [37]) or low (austenite stainless steel [38]) stacking-fault energies.(c-g) Schematics showing the (c) trapping, (d) detrapping, (e) annihilation and climbing/cross-slip, (f) irregular network, and (g) hexagonal network formation of the dislocations in the vicinity of the γ /γ interface.