Diffusion processes during creep at intermediate temperatures in a Ni-based superalloy

Accepted Manuscript Diffusion Processes During Creep at Intermediate Temperatures in a Ni-based Superalloy

T.M. Smith, Y. Rao, Y. Wang, M. Ghazisaeidi, M.J. Mills PII:

S1359-6454(17)30760-7

DOI:

10.1016/j.actamat.2017.09.027

Reference:

AM 14057

To appear in:

Acta Materialia

Received Date:

10 June 2017

Revised Date:

13 September 2017

Accepted Date:

13 September 2017

Please cite this article as: T.M. Smith, Y. Rao, Y. Wang, M. Ghazisaeidi, M.J. Mills, Diffusion Processes During Creep at Intermediate Temperatures in a Ni-based Superalloy, Acta Materialia (2017), doi: 10.1016/j.actamat.2017.09.027

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Diffusion Processes During Creep at Intermediate Temperatures in a Ni-based Superalloy T.M. Smitha, Y. Raoc, Y. Wangc, M. Ghazisaeidic, M.J. Millsb a. b. c.

NASA Glenn Research Center, 21000 Brookpark Rd. Cleveland OH 44135, USA

Center for Electron Microscopy and Analysis, The Ohio State University, Columbus OH 43212, USA

Department of Materials Science and Engineering, The Ohio State University, Columbus OH 43210, USA

Abstract: The local compositional changes associated with stacking fault and microtwin formation during creep at intermediate temperatures in a commercial Ni-base disk superalloy are explored. In order to investigate microtwin formation, an [001] single crystal of ME3 was tested in compression at 760C under a stress of 414 MPa – a stress-temperature regime found to promote microtwinning. Atomic resolution scanning transmission electron microscopy combined with state-of-the-art energy dispersive X-ray (EDX) spectroscopy analysis reveals the presence of Co and Cr rich Cottrell atmospheres around leading dislocations responsible for the creation of SISFs, SESFs, and microtwins. This analysis also highlights the role that tertiary  particles inside  precipitates have on  shearing deformation mechanisms. Through the use of CALPHAD calculations, combined with new experimental observations, new insights into the rate-controlling processes during creep deformation are discussed.

1. Introduction Ni-base superalloys are essential materials used primarily in the hot section of jet turbine engines. With the creation of each new generation of turbine engine the goal remains the same: increase the operating temperature of the engine, thereby reducing CO2 emissions and fuel costs. This increase in temperature promotes changes in deformation modes in Ni-base superalloys that are still not fully understood. Multiple studies have found that the manner in which the 

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precipitates are defeated shifts from an athermal APB shearing at lower temperatures to a diffusion-mediated reordering at stacking faults during creep at temperatures above 700C [1–5]. One of these precipitate shearing modes is microtwinning, which has been found to adversely affect creep properties in Ni-based disk superalloys [6–9]. Thus, improved understanding of the rate-limiting mechanisms responsible for the formation of microtwins is needed to further improve the high temperature properties of these superalloys. Mechanical microtwinning was first reported in Waspalloy by Guimier and Strudel [10]. Interestingly, it was found that a similar alloy tested using comparable parameters but without the presence of  precipitates did not exhibit twinning, demonstrating that  precipitates played an important role in the formation of microtwins [11]. In later work, microtwinning was determined to be orientation dependent, occurring in [110] and [111] oriented single crystals under tensile creep and [001] oriented crystals under compression creep [4,9,11–13]. Knowles and Chen [12], found that microtwinning occurred in orientations that also promoted superlattice extrinsic stacking fault (SESF) formation, implying the formation of both SESFs and microtwins were connected. This correlation was supported in future studies; however, early work incorrectly supposed that these faults were created by adjacent a/3<112> super-Shockley partials shearing the  precipitates on adjacent {111} planes [12,14]. Rather, later experimental evidence revealed that SESFs and microtwins were created by like-sign a/6<112> Shockley partials shearing adjacent {111} planes [2,13][15]. In order for this shearing process to produce a low energy SESF, a reordering process, first proposed by Kolbe, must occur to the high energy complex extrinsic stacking fault (CESF) that would otherwise be created in the wake of the shearing Shockley partials [16]. Karthikeyan, et al. [15] developed a quantitative model for microtwinning based on the hypothesis that the rate of partial shearing is controlled by the rate by which reordering can lower

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the energy of the CESF. Kovarik et al. expanded upon Kolbe’s theory, using density functional theory analysis, and revealed an energetically favorable diffusion process that could remove wrong nearest-neighbor violations, thereby converting the high energy CESF into a low energy SESF[17]. Later, Smith et al. first reported the presence of a Co and Cr Cottrell atmosphere around shearing Shockley partials in a  precipitate, which they hypothesize is necessary to further reduce the energy of two layer CSF and promote precipitate shearing [18]. Kovarik et al. also provided qualitative evidence for the presence of segregation along SESFs and microtwin interfaces using atomic resolution high angle annular dark field (HAADF) imaging [17]. Indeed, elemental segregation has been recently confirmed along superlattice intrinsic (SISF) and SESFs in both Co and Ni based superalloys after intermediate temperature creep [18–20]. Furthermore, Smith et al. discovered that the type of elemental segregation along SESFs controlled whether the fault would thicken into a twin or not, thereby affecting the overall creep properties of the alloy. They predicted that the formation and extension of microtwins were reliant on the segregation of Co and Cr along the twin’s interface, although no direct evidence for this was provided. Most recently, using atom probe tomography, Barba et al. [21], report evidence of Co and Cr along microtwins in a single crystal Ni-base superalloy, with higher concentrations along the twin interface. The purpose of this study is to provide new insights into the formation of microtwins and the diffusional processes that enable it. Using high resolution Super-X EDX and CALPHAD calculations, a new microtwin formation model is presented highlighting the role of elemental segregation. Other observations include the presence and effect that newly discovered tertiary  particles inside secondary  precipitates [18,22] have on creep performance. In addition, new evidence of Cottrell atmospheres around shearing Shockley partials inside  precipitates is

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provided, including for the first time around partials at a microtwin interface in association with the twin thickening process. Together, these new insights will help the creation of improved deformation models and ultimately provide insights that may enable improvement of the high temperature capabilities of disk superalloys. 2. Experimental Methods 2.1 Creep Sample and Testing A single crystal analog of the currently used commercial disk alloy ME3 was obtained from the GE research center. The composition of ME3 can be found below in Table 1 Table 1: The elemental composition of ME3 in wt%

After a heat treatment that resulted in a bimodal  precipitate distribution, an [001] oriented rectangular parallelepipeds with a 1:1:2.5 dimension ratio were extracted using electrical discharge machining (EDM). The sides of the sample were then polished to a 1200 fine grit using SiC polishing pads to remove the subsequent damage layer. A 414 MPa monotonic compression creep test was performed at 760 C on an [001] oriented sample in order to promote re-order mediated precipitate shearing modes; specifically, microtwinning and isolated faulting. The test was performed using a MTS 810 Compression creep frame with two linear variable displacement transducers (LVDTs) to record plastic strain. Both tests were ended when about 0.5% plastic strain was reached and the specimens were quickly fan-cooled to room temperature in order to capture the deformation and microstructure present at the end of the test, as well as to minimize diffusional changes during cool-down.

2.2 Microscopy and Chemical Analysis Post creep, the sample was again polished to a fine 1200 grit using SiC polishing paper and

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then followed by a .05 um colloidal silica finish. To confirm that Microtwinning had occurred during the creep test, electron channeling contrast imaging (ECCI) was conducted using a FEI Sirion scanning electron microscope (SEM) while utilizing the backscatter detector at high accelerating voltages. ECCI allows for large areas to be imaged for improved statistical deformation analysis [23,24]. To validate the ECCI results, which found microtwinning to be the prominent deformation mode, transmission electron microscopy (TEM) samples were created using a FEI Helios Nanolab Dualbeam 600 focused ion beam (FIB). The FIB foils were further cleaned to remove ion damage using a Fischione Nanomill at 900eV. First, foils were extracted orthogonal to the compression axis to confirm the orientation of the sample and for STEM analysis. These foils were analyzed using low angle annular dark field (LAADF) detectors on an FEI Tecnai F20 STEM at 200 kV and again found evidence for microtwinning. For atomic resolution HAADF imaging and high resolution EDX, [110] oriented FIB foils were extracted from the post compression creep samples to image the microtwins and superlattice stacking faults (SFFs) edge on. HAADF Imaging was conducted on a FEI probe-corrected Titan3 80–300 kV STEM. While the EDX was performed on an image-corrected Titan3 60–300 kV with Super-X detector technology utilizing the Bruker Esprit software. All quantified and summed EDX spectra were done using standard Cliff-Lorimer k factors and the Bruker Esprit 2™ software. 3. Results 3.1 Evidence of Segregation Along Microtwins To better understand if segregation occurs along microtwins, low magnification EDX maps were obtained from a  precipitate containing a microtwin that had sheared through its center. The results are shown below in Figure 1. In the HAADF image and EDS maps, the microtwin is observed along a [10-1] direction such that the coherent (111) interfaces of the microtwin are

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observed “edge-on.” In this case, the microtwin is about 15 nm in width. Figure 1: Elemental maps of microtwin shearing through a  precipitate. The presence of tertiary  is evident in the Co and Cr maps.

Several noteworthy features can be seen in Figure 1. The presence of tertiary  particles can be seen in the Co and Cr elemental maps. Instead of these particles being present throughout the bulk of the precipitate there appears to be a denuded zone along the edge of the precipitate where they dissipated during the heat treatment and creep testing. The denuded zones have also been reported by Yardley et al. [22]. The elemental maps in Figure 1 also indicate the presence of Co and Cr segregation along the microtwin; yet, the segregation does not appear to be uniform. In the region of the ʹ precipitate where the tertiary  particles are present, the twin has Co and Cr along the interface as well as inside the twin region, although the intensity of the Co and Cr signal inside the twin is not consistent. In the region of the precipitate without the tertiary  particles, chemical partitioning still occurs (although this is not obvious from Figure 1, as the Co and Cr signatures are much less pronounced approaching the main ʹ/ interface). Confirmation of this feature is provided by the higher magnification EDX scan of Figure 2 which was taken from the region indicated by the white box shown in the HAADF image in Figure 1, where the secondary precipitates are denuded of tertiary .

Figure 2: High resolution elemental maps of twin shearing a  precipitate through the denuded zone area highlighted in Figure 1. Figure 3: (a) Combined Cr, Co, Ni, and Al elemental map of microtwin near the / interface. The red box represents where the integrated line scan was performed. (b) The results of the integrated line scan. The interface of the twin can easily be discerned by the segregation of Co, Cr, and Mo and depletion of Ni and Al from the interface.

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The combined elemental map in Figure 3(a), from the same dataset as shown in Figure 2, better illustrates the chemical partitioning present along the twin interfaces. The red box represents the area used for the integrated line scan, the results of which are shown in Figure 3(b). The integrated line scan shows significant chemical segregation along both microtwin interfaces with little to no segregation inside the twin. In other words, the composition within the twin and in the adjacent ʹ precipitate are very similar, and the chemical fluctuations are concentrated at the microtwin interfaces. This is similar to the microtwin segregation observed using atomprobe tomography and modeled by Barba et al. with the notable exception they reported higher concentrations of Co and Cr inside the microtwin as compared to the surrounding precipitate. [21]

3.2 Evidence of Co- and Cr-Rich Cottrell Atmospheres Along Thickening Twin Boundaries Below in Figure 4, is an example of a twin being thickened by two atomic planes through the shear of adjacent 1/6<112> Shockley partials.

Figure 4: An atomic resolution MAADF image of a twin boundary extending by the shear of adjacent Shockley Partials.

As has been reported in earlier literature [2,15,17], in Figure 4 the twin is being thickened by the cooperative shear of 1/6<112> Shockley partial pairs on adjacent {111} planes. The red oval represents the region containing the Shockley partial pairs, and the step in the twin interface is indicated by the red lines. High resolution EDX mapping was also conducted on this area and the results are shown below in Figure 5. The red ovals in Figure 4 and Figure 5 represent the same area, which is where the twin thickening Shockley partials are located at the microtwin/ interface.

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Figure 5: Elemental maps of a twin extending by two atomic planes.

Figure 5 reveals for the first time a prominent Co and Cr Cottrell atmosphere around the twin thickening Shockley partials along a twin interface. Subtle segregation along the twin interface can also be seen with what appears to be an increase of Co and Cr in conjunction with a depletion of Ni and Al. In contrast, there does not appear to be a uniform increase of Co and Cr segregation within the twin region. The rest of the elemental maps are not shown due to high noise levels and/or no evidence of segregation. The composition around the partials, again highlighted by the red oval in Figure 5, were quantified and compared to the composition of the  as shown below in Table 2.

Table 2: The quantified EDX compositions of the Cottrell atmosphere around the twin thickening Shockley partials compared to the composition of the  precipitate.

Again, significant Co, Cr and Mo segregation around the microtwin thickening Shockley partials is evident. 3.3 Evidence of Co and Cr Rich Cottrell Atmospheres Ahead of Stacking Faults in ME3 To further explore and confirm the existence of Cottrell atmospheres around shearing Shockley partials, both SISFs and SESFs terminating inside a  precipitate were sought out. Figure 6 shows an example of both a SESF and SISF terminating inside a  precipitate in ME3.

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Figure 6: Atomic resolution HAADF image of a SESF (upper fault) and SISF (lower fault) terminating inside a  precipitate. The red ovals represent where each fault has ended and the hole was purposely burnt into the sample to help with EDS scan correction.

In Figure 6, the red rectangles represent the location of each fault, with the upper fault being a SESF and the lower one a SISF. The red ovals highlight the areas that the faults have terminated by Shockley partial arrangements [17,18]. This area is more easily recognized when imaged in a medium angle annular dark field (MAADF) condition that highlights diffraction contrast and strain instead of Z-contrast. A hole approximately 2nm in diameter was purposely burnt into the sample by dwelling a high current (> .6nA) converged electron beam over one spot of the sample for a period close to 60 seconds. The nano-hole acts as an effective fiducial marker for the drift correction software used during acquisition of the EDS scans, which were typically acquired over a 60 minute time period. The strong moiré contrast is believed to be a result of a thin layer of redeposition from the nanomilling prep and is not believed to have any effect on the EDS results. High resolution EDX mapping was conducted in the area shown in Figure 6 and the results are revealed below in Figure 7.

Figure 7: Elemental maps of the terminated SESF and SISF inside a  precipitate

Several observations can be made from the elemental maps in Figure 7. Importantly, the segregation along both the SISF and SESF appear to be similar, with Co and Cr segregating to the fault replacing Al and Ni (see Table 3 for quantified segregation values). In addition, a Co- and Cr-rich Cottrell atmosphere exists around the shearing Shockley partial configurations for both faults. The observed Cottrell atmosphere ahead of the SISF is particularly significant as it is the first time a Cottrell atmosphere has been observed without the clear influence of a tertiary  particle

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nearby, which can be seen most prominently in the Cr map near the SESF. Due to its shape, it is unclear if the SESF Cottrell atmosphere is terminated in a tertiary  particle or not. To further examine the extent of segregation in the Cottrell atmospheres and SISF, the quantified elemental concentrations of the four areas highlighted in Figure 8 are given in Table 3 below (the SESF quantification was excluded because it shears through the tertiary  particle). Figure 8: Four regions highlighted to compare concentration values. 1 = region of  precipitate, 2 = SISF, 3 = SISF Cottrell atmosphere, and 4 = SESF Cottrell atmosphere. Table 3: The quantified concentrations of the four regions highlighted in Figure 8.

The following important trends are observed in Table 3: (a) all segregation appears to show an increase in  formers (Co, Cr and Mo) and a decrease of the  formers (Ni, Al, and Ti with respect to the Cottrell atmospheres); (b) no change in composition is observed for Nb, Ta, and W; (c) the greatest amount of segregation occurs around the Cottrell atmospheres of both the SISF and SESF. In fact, the weight percentage of Cr in the leading SISF Cottrell atmosphere is over double that found along the SISF itself (2.53 wt% compared to 5.13 wt%). 3.4 Eliminating Tertiary  Particles in ME3 While it has now been clearly established that tertiary  particles are a common feature in both single crystal and polycrystal disk superalloys [18,20] after conventional solutionizing and aging treatments, it is not presently clear whether their presence has a significant affect on subsequent creep response. Furthermore, several of the Cottrell atmospheres presented above at the termination of stacking faults might also be attributed to interactions with pre-existing tertiary  particles rather than being a natural consequence of the shearing processes. Therefore, heat treatments were explored with the goal of eliminating the tertiary  particle population in order to

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evaluate both creep response and segregation phenomena in their absence.

As was observed in Figure 1, the presence of the denuded tertiary  particles near the / interface inside the precipitate implies that the  forming elements within the small  particles are able to diffuse to the larger (and flatter) γ/ interfaces of the  channels when given enough time at high enough temperatures. In order to further explore this process, a sample of alloy ME3 was heat treated at 815C for 100 and 200 hours, after which EDX maps were performed to observe the changes in the tertiary  particle sizes and morphologies. Figure 9 shows the elemental Cr maps for both alloys after each heat treatment. Figure 9: The result of the heat treatment study on tertiary  particles in ME3. The particles were found to mostly dissipate in ME3 after 100 hours and completely disappeared after 200 hours.

After 100hrs, there was a clear decrease in the number density of tertiary  precipitates, while after 200 hours there was no evidence of tertiary  particles. The tertiary  volume fractions after each heat treatment were also examined in the same samples. Interestingly, the tertiary  precipitates were more stable in ME3 compared to the tertiary  particles. Table 4 below shows the measured tertiary  volume fractions in ME3 after each heat treatment.

Table 4: The tertiary  volume fractions after heat treated at 815C for 100 and 200 hours in ME3

3.5 Effect of Tertiary Gamma Particles To completely remove the confounding effects that the tertiary  have on segregation events inside  precipitates, ME3 samples were aged for 300 hours at 815C. This ageing step removed all the

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tertiary  and  particles, as is shown in Figure 9. [001] and [110] oriented samples were then crept under 414 MPa of stress at 760C to compare the creep properties of the new overaged samples to the original tests. The results are shown below in Figure 10.

Figure 10: Compression creep curves of overaged ME3 vs original ME3. Tested under 414MPa of stress at 760C.

As shown in Figure 10, the overaged ME3 samples, without the tertiary  and  particles, performed poorly compared to the original ME3 microstructures. Interestingly, both orientations still retained the overall creep curve shape exhibited by the original tests. From the compression creep test results, it appears that the tertiary γ particles may play a positive role towards creep strength in Ni-base superalloys. For example, the slower creep rates may be a result of these tertiary γ particles acting as additional interfaces that shearing dislocations must overcome. Indeed, qualitatively, the majority of Cottrell atmospheres observed in the study and others [18] are found within the vicinity or possibly locked within tertiary γ particles, suggesting that they act as attractive sites during the shearing processes. Nevertheless, further work must be performed to unambiguously establish that the differences in creep properties observed in Figure 10 is from the loss of the tertiary γ particles and not due to the absence of tertiary γʹ precipitates. Extraction of TEM foils was then performed for the [001] overaged sample by the same methods as those used for the original samples. As shown in Figure 11(a), the deformation observed in the overaged sample exhibited many of the same mechanisms as observed for the original [001] oriented sample crept at 760C. For example, numerous stacking faults and twins were observed throughout the TEM foil. One notable difference was an increased frequency of

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SISFs in the overaged samples. One of these SISFs can be seen in Figure 11(a), where it has terminated inside of a  precipitate.

Figure 11: (a) An HAADF image of deformation observed in the [001] overaged ME3 post creep. (b) The elemental Cr map clearly illustrating the complete dissolution of tertiary  particles.

The presence of a terminated fault inside a tertiary  free precipitate allows for the observation of segregation and Cottrell atmospheres without the convolution of the surrounding  particles. A higher resolution EDX map of the terminated SISF seen in Figure 11(a) is shown in Figure 12.

Figure 12: The HAADF, Al, Cr, and Co maps of a terminated SISF observed in the overaged ME3 sample post-test.

These additional EDX maps shown in Figure 12 prove that the observed Cottrell atmospheres in the original EDX maps are in fact a fundamental aspect of the shearing process, and not solely a consequence of interaction with pre-existing tertiary  particles. Indeed, the Cottrell atmosphere exhibits a very noticeable “comma” shape that has not been observed in the other EDX maps. The segregation along the fault also reveals that the tertiary  particles are not major contributors of the segregated  forming elements (Co and Cr) noticed along the faults in ME3, since this feature is still clearly present. It is also unlikely that these Cottrell atmospheres form during the cool down after a creep test has ended. Upon termination of the creep test, the samples are rapidly cooled under load by opening the clam-shell furnace and blowing forced air on the sample, producing an approximate cooling rate of 4°C/s. At this cooling rate, samples reach a temperature of 450°C, where these long range diffusion processes are unlikely to occur, in little over a minute. In fact, using the

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measured concentrations of the Cottrell atmosphere and γ/γʹ phases, and utilizing the diffusion data that will be presented in more detail in section 4.2, we can create an estimate of the spatial extent of a Cr-rich Cottrell atmosphere within a γʹ region during cool down. The Zener approximation equation (equation 1) is used under the simple assumption that there would have to be conservation of Cr in creating the Cottrell atmosphere during cool-down [25]. 𝑥 = 𝜆1𝐷 𝐷𝐶𝑟𝑡

(1)

In equation 1, x is the distance the Cottrell atmosphere can diffuse into the γʹ precipitate after time (t). λ1D is the growth constant which takes into account the concentrations per unit volume of the Cottrell atmosphere, γ, and γʹ phases. Utilizing a highly conservative, isothermal estimate that the sample was held at the 760°C for 60 seconds in order to mimic the actual cooling down process, the Cottrell atmosphere would only be able to extend into the precipitate 1.5nm–far smaller than the observed extent of the atmospheres. Pipe diffusion could also potentially enhance the speed by which an atmosphere is created [26], by diffusion of Co, Cr, and Mo from the γ phase. In this scenario, the Cottrell atmosphere would only able to extend 15nm into the precipitate. Given that the TEM foils are usually less than 30nm in thickness and an average γʹ precipitate diameter is around 300nm, even if these Cottrell atmospheres could extend 15 nm into the precipitate along the dislocation cores, they would not be noticed with this STEM-EDS analysis. Therefore, it can be concluded that even under these highly conservative scenarios, there is not enough time for the Cottrell atmospheres to develop during cool down, demonstrating that they are in fact a consequence of the creep deformation process. Finally, this result indicates that there are three primary mechanisms that must be considered as possible rate-limiting processes for fault and twin formation: Cottrell atmospheres, reordering, and segregation/phase transformation along faults.

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4. Discussion 4.1 Microtwin Formation Based on the present EDX mapping results, a new model for microtwin formation in Ni-base superalloys can be created, inspired by previous models proposed by Smith et al. [4] and Barba et al. [21]. Below in Figure 13 is a diagram detailing the new model, and the potential rate limiting processes. Figure 13: The Twin formation model recently described by Smith et al. [4], where two unlike ½<110> dislocations interact at the interface and dissociate (b) so like-signed Shockley partials can shear into the  precipitate forming a SESF. (c) The same process occurs again alongside the SESF to form a 3 layer twin inside the  precipitate. (d) This model has now been updated to include the diffusion processes observed in the results section and by Barba et al. (e) where  formers Co, Cr and possibly Mo segregate along the formed SESF. (f) Then when the process occurs again Some of the  formers segregate to the new twin interface from the  channel while the other source of the  formers come from what segregated along the SESF, leaving a pristine  state inside the twin boundaries.

The new microtwin formation model presented in Figure 13 includes the diffusion processes now known to occur during twin formation and extension. The proposed mechanics for the twin formation (i.e. the type of dislocations and interactions) remains similar to past studies [2,17]. It is still assumed that the formation of a SESF created by the interaction of two unlike 1/2 <110> dislocations interacting at the / interface is the precursor to microtwin formation as shown in Figure 13(a) and Figure 13(b). This same process then can occur adjacent to the planes of the SESF in order to form a three-layer twin, as shown in Figure 13(c). It has been recently revealed that the segregation of  formers Co, Cr, and Mo along the SESF promotes further shearing along the fault through the minimization of possible nearest neighbor violations and consequently microtwin formation [27]. This type of segregation has been confirmed for alloy ME3 in Figure 7, and is now represented in the model as shown in Figure 13(d) and Figure 13(e). Our findings also prove the existence of Co and Cr-rich Cottrell atmospheres around the leading

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Shockley Partials, both for the SESF and the twinning partial pairs. These are represented in the model as light blue ovals. A recent model by Barba, et al. [21] postulated the presence of solute atmospheres at twin interfaces, but also proposed that some residual segregation exists within the bulk of the twin (and hence the twin is more akin to a phase transformation). However, our new EDX evidence does not show Co and Cr segregation through the bulk of the twin, but instead only along the twin interfaces. As represented in Figure 13(e), the bulk of the twin seems to return to a -like composition. Therefore, the  forming elements diffuse to the area of the new twin boundary where the reordering process is still active to help lower the fault energy and allow the Shockley partials to continue shearing through the precipitate. This leaves a twin with only segregation along its boundaries. This finding is also corroborated with the findings by Freund et al. [28] who also observed Co and Cr segregation along microtwin interfaces in a Co-based superalloy. However, they proposed that microtwins could extend through the shear of single a/6<112> Shockley partials inside γʹ precipitates. This is in disagreement with experimental and modeling work of twin formation in Ni-based superalloys, including this study, where it is found that passage of pairs of 1/6<112> Shockley partials on adjacent planes are operative along a twin interfaces inside γʹ precipitates [2,16,17,27]. These observed differences may be caused by a lower complex stacking fault (CSF) energy in Co-based superalloys [29] and appears to be a fascinating difference between these two classes of superalloys. It is possible that Barba et al. [21] detected segregation through the thickness of the microtwin via APT analysis due to the other source of  formers shown to segregate to the twin boundaries, namely the tertiary  particles inside the secondary  precipitates. It can be noticed in Figure 1 and Figure 14(b) that Co and Cr content is indeed enhanced locally within the twin, specifically in regions of the secondary precipitate where tertiary  particles are present. The

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presence of excess  formers within the twin, originating from the tertiary  particles, may be sufficient to lower the twin energy in the wake of the shearing twining partial pairs, such that translation of Co and Cr with the interface may not be necessary. The result is a twin that appears to have  formers distributed non-uniformly through the thickness of the twin except for the part of the twin present in the tertiary  denuded zone, where only the twin interfaces have segregation. This is represented in detail below in Figure 14(a) and Figure 14(b).

Figure 14: (a) A MAADF image of a Twin shearing both a  precipitate and  channel near the / interface. (b) A Cr map showing the two sources of  former segregation along the twin and twin interfaces. Inside the tertiary  denuded zone the source of the segregates is the  channel, however, in the area of the precipitate where there exist tertiary  particles the primary source of  former segregation along the twin is from those particles.

It is also evident that the tertiary  precipitate size distribution is altered (“smeared”) in the regions that have been sheared by the twin, further demonstrating enhanced diffusional processes associated with the twinning process. The abundance and distance of both  former sources leads to variation of segregation along the microtwin. The area of the microtwin that is sheared through the tertiary  denuded zone of the  precipitate primarily gets its source of  formers from either the  channels or the segregation that had previously occurred along the fault (SESF or earlier twin structure – see figure 13f). In the region of the  precipitate where the tertiary  particles are present, the microtwin has a diffuse segregation of Co and Cr along the inside of the twin as well, although the amount is not constant and varies depending on the distribution of tertiary  particles with which the twin interacts. The fact that segregation nonetheless occurs at the twin interfaces, even in the absence of tertiary  precipitates, indicates that this segregation is indeed fundamental to the twinning process.

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4.2 Rate Limiting mechanisms: Preliminary Discussion So far, three primary mechanisms (reordering,  phase transformation, and Cr and Co-rich Cottrell atmospheres) were shown to be active during creep deformation. For future modeling efforts and alloy design it is important to consider which of these processes may be rate-limiting during creep. Estimates for the rates of these three processes are now presented, where each process is considered the rate limiting mechanism for the translation of an SESF, which acts as the precursor to microtwins and microtwin extension. 1) The first scenario is the creation of a two layer SESF from a two layer complex stacking fault (CSF) through the reordering of Ni and Al atoms (under the simplifying assumption of Ni3Al as the  precipitate). This reordering process is controlled by short-range diffusion, i.e., atomic hops of elements across different sublattices (interdiffusion) within a unit cell of the crystal lattice. The overall driving force for the reordering process is the stacking fault energy of a SESF minus the stacking fault energy of two CSFs (SESF – 2CSF). However, in order to have SESF/b rather than 2CSF/b as the critically resolved shearing stress (CRSS) for creep deformation, reordering of Ni and Al needs to occur within the core of the partial dislocations simultaneously while dislocations cut into the  precipitate. Therefore, the speed with which this process can occur is a function of the driving force and the interdiffusivity between Ni and Al in . 2) In the second scenario, instead of reordering, the fault may directly transform into a wetting layer of the disordered phase, . In this case, the CRSS required for the shearing process becomes 2-/b and the driving force for this “wetting” transition is 2- - 2CSF. Therefore, this process is

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rate-limited by the “precipitation” of the wetting layer of the  phase, which is a long-range diffusion process. 3) The last scenario is the most complicated, but might be the closest one to what actually occurs, since it could have the lowest CRSS. The partials develop an equilibrium Cottrell atmosphere (CA) around them as they are stacked at the / interface. This CA has a certain size (depending on the solute-dislocation interactions and temperature) and it will “contaminate” the  phase adjacent to it with Co, Cr, and Mo. This contaminated  phase is expected to have a have lower fault energies and hence make the CRSS lower than any of the other scenarios (1 or 2 above). In this case, the CRSS will be the “contaminated” fault energy divided by the Burgers vector. When the dislocations travel at a steady speed, they will carry the steady state CA with it and continue to contaminate the  phase in front of it, altering the fault energy. The driving force for the formation of the CA is the interaction between solutes and the dislocations and the rate limiting process will be long-range diffusion. As discussed in Hirth & Lothe [30], diffusion within the dislocation cores is orders of magnitude higher than that in the lattice, so the rate-liming process is bulk diffusion of the segregating elements in the  phase. As illustrated in Figure 13, the initial formation of the CA around the Shockley partial pair that creates the SESF should be limited by pipe diffusion from the  channel–a relatively rapid process. However, further progress of the lead partials and CA will require long range diffusion through the  precipitate. Thus, while accelerated pipe diffusion is expected to be important initially, the propagation of the fault through the precipitate should be limited by long-range diffusion. Below, we estimate the relative rate for each of these processes once the chemical features have been established in the γʹ precipitate and draw a preliminary conclusion as to which one is the creep-rate limiting process. As all of the possible rate limiting processes are diffusion-

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mediated, we begin by obtaining estimates for the diffusivity of the relevant elemental species in the  phase. Ni-self diffusion values in Ni3Al single crystals were experimentally measured using secondary ion mass spectrometry by Frank et al. for temperatures between 731°C and 986°C [31]. Currently very little work has been done exploring the diffusivity of other elements inside a  precipitate; therefore, the CALPHAD method [32] was employed to estimate the diffusivities of seven different elements using the composition of  in ME3 at 760C, which are compared in the table below. For the reordering calculation, the Ni-Al interdiffusion coefficient in  at 760°C measured by Watanabe et al. [33] was used. Their value of DNiAl=1.44 x 10-18 m2/s was in close agreement with the simulated value of DNiAl=1.817 x 10-18 m2/s calculated using CALPHAD. Table 5: The calculated self-diffusivities of Cr, Co, Mo, Ta, and Al inside a  precipitate at 760C

Using the above measured and calculated diffusivities in Table 5, kinetics can be estimated for reordering (interdiffusivity of Ni and Al in ), -like phase transformations along stacking faults (which is dependent on the self-diffusivities of Al, Ni, Co, and Cr) and Cr-rich Cottrell atmospheres (long range diffusion of Cr solute). In order to estimate the rate by which reordering can occur along a fault, the following short-range diffusion-controlled growth relationship was used [34].

𝑣𝑟 =

𝐷𝑁𝑖𝐴𝑙 𝑘𝑇

×

∆𝑔 𝜆

(2)

Here DNiAl is the measured interdiffusion of Ni and Al in  at 760°C, k is the Boltzman constant, T is 1033K, Δg is the driving force for atomic reordering (1x10-19 J) [17], and λ is the jump distance (3.59x10-10 m). The  to  phase transformation velocity was estimated using the long-range

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diffusion controlled growth relationship, x=(Dt)1/2, where x is the linear dimension of the  phase layer in the growth direction (m), t is time (s) and D is the interdiffusion coefficient of Cr and Al (3.7 x 10-19 m2/s) that was calculated using the diffusion co-efficients from thermocalc in Table 5. This value was selected because it was the lowest calculated interdiffusivity relevant for this  to  phase transformation along the fault. This result is supported by prior experimental work by Campbell et al. [35] In comparison, the calculated interdiffusivity for Ni and Co was 1.3 x 10-18 m2/s. For the predicted Cottrell atmosphere velocity an equation was presented by Titus et al. [25] recently following Cottrell [34] that estimated the velocity of a Cottrell atmosphere surrounding dislocations and is shown below.

𝑣𝑐 =

(𝜏𝑏)𝐷𝑘𝑇 2.1𝐶0𝛽2

(3)

Here  is the relative shear stress on the atmosphere (195.3 MPa), D is the diffusivity of Cr (Cr was used since it was the element that segregated to the Cottrell atmosphere by the highest percentage) presented in Table 5, k is the Boltzman constant, T is 1033K, C0 represents 5at% Cr segregation (4𝑥1027 𝑚 ‒ 3), and  is the interaction energy between the solute and the Shockley partial dislocations (1.6𝑥10 ‒ 29 𝑁𝑚2) and comes from the value used by Titus et al., [25]. Considering a 5% Cr enriched Cottrell atmosphere and using the equations above, all three mechanism speeds (reordering, Cottrell atmospheres, and fault phase transformations) can be estimated.

Table 6: Comparison of rate limiting mechanisms

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Comparing the calculated velocities revealed in Table 6, notable differences can be found between the three processes in ME3. The mechanism that occurs the fastest is reordering due to the short range diffusion of Al and Ni inside the  precipitate. Second, the diffusion of Co, and Cr, the main elements responsible for the  phase precipitation along the faults, are two orders of magnitude slower than the reordering process. Therefore, it appears that the reordering process should occur first, immediately after the faults are formed, followed by the segregation/phase transformation mechanism. Lastly, the Co and Cr rich Cottrell atmosphere is apparently the slowest and the principle rate-limiting mechanism associated with fault formation at intermediate temperatures. This initial conclusion is consistent with the increased complexity of the process (i.e. dislocation shearing along with long-range diffusion processes) as well as a larger amount of elemental segregation needed. The solute concentration inside the Cottrell atmospheres was consistently double that found along faults and twin interfaces (refer to Table 3). At this moment, further work is underway to better understand the formation of this critical deformation process.

5. Conclusions This study investigated the diffusive and rate controlling processes during creep in a Nibase superalloy at intermediate temperatures using high resolution EDX mapping and thermodynamic modeling. By investigating the local compositional changes occurring during fault and microtwin formation, new insights were obtained and the following conclusions could be drawn.

(i) A prominent solute atmosphere of Co and Cr replacing Ni and Al exists around  shearing Shockley partials for both SISF, SESF and Twin formation and need to be incorporated in new

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deformation models

(ii) A new microtwin formation model has been proposed incorporating the diffusive and segregating processes that are now understood to exist and promote microtwinning.

(iii) Tertiary  particles inside the  precipitates have been shown to play a significant role in providing  formers necessary to promote twin formation and thickening.

(iv) Over-aged microstructures without the presence of tertiary  and  particles consistently performed poorly compared to the original samples.

(v) The Co and Cr rich Cottrell atmospheres were determined to be the rate limiting process during fault formation in ME3.

In combination, these new conclusions suggest that diffusion processes during intermediate temperature creep play a pivotal role in stacking fault / twin formation and, therefore; the alloys overall creep properties.

Acknowledgements: TMS acknowledges the support of GE Aviation for their support of this work through the GE University Strategic Alliance (USA) programme, and MJM. the support of the National Science Foundation and the DMREF program under grant #1534826. TMS also acknowledges J. A. Nesbitt (NASA-GRC) for his help investigating diffusion co-efficients through Thermo-calc [32].

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Tables

Table 1: The elemental composition of ME3 in wt%

Alloy ME3

Ni

Co

Cr

Mo

W

Nb

Ta

Al

Ti

Hf

C

B

Zr

Bal.

20.6

13.0

3.8

2.1

0.9

2.4

3.5

3.4

0

0.05

0.03

0.03

Table 2: The quantified EDX compositions of the Cottrell atmosphere around the twin thickening Shockley partials compared to the composition of the  precipitate.

Element

 precipitate

Al Ni Co Cr Ti Nb Mo W

4.24  0.2 70.79  2.2 11.75  0.4 1.92  0.1 6.48  0.2 0.77  0.1 0.58  0.1 1.28  0.3

Twin Cottrell Atmosphere 3.13  0.1 62.35  1.9 17.21  0.6 6.91  0.2 5.32  0.2 0.77  0.1 1.19  0.2 1.24  0.3

Segregation Factor (% change) -26.2 -11.9 +46.5 +259.9 -17.9 ±0 +105.2 -3.1

Table 3: The quantified concentrations of the four regions highlighted in Figure 8.

Element

Area 1:  precipitate

Area 2: SISF

Area 4: SESF Cottrell Atmosphere

3.90  0.2

Area 3: SISF Cottrell Atmosphere 3.79  0.2

Al

4.24  0.2

Ni

70.79  2.2

69.93  2.2

65.20  2.1

63.69  2.0

Co

11.75  0.4

12.95  0.4

15.52  0.6

16.07  0.6

Cr

1.92  0.1

2.53  0.1

5.13  0.2

6.08  0.3

Ti

6.48  0.2

6.53  0.2

5.75  0.3

5.44  0.2

Nb

0.77  0.1

0.47  0.1

0.43  0.1

0.95  0.2

Mo

0.58  0.1

0.68  0.1

1.14  0.2

1.29  0.2

W

1.28  0.3

1.05  0.2

1.18  0.3

1.25  0.3

Ta

2.18  0.5

1.96  0.4

1.86  0.4

1.73  0.4

3.50  0.2

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Table 4: The tertiary  volume fractions after heat treated at 815C for 100 and 200 hours in ME3

Alloy

0 hours at 815ºC

100 hours at 815ºC

200 hours at 815ºC

ME3

3-4%

1.24%

0%

Table 5: The calculated self-diffusivities of Cr, Co, Mo, Ta, and Al inside a  precipitate at 760C

Element

Diffusion Coefficient m2/s

Al

3.9x10-18

Co

2.1x10-19

Cr

6.9x10-19

Mo

4.1x10-20

Nb

1.6x10-19

Ni

3.0x10-19 [31]

Ta

3.8x10-20

Ti

3.6x10-19

W

5.9x10-21

Table 6: Comparison of rate limiting mechanisms

Process

Rate (nm/s)

Cottrell atmosphere (5at% Cr)

0.2

 phase transformation (Cr and Co diffusion)

0.6

Re-ordering (Ni/Al interdiffusivity)

28.1