Effects of tantalum on the temporal evolution of a model ...arc.nucapt.northwestern.edu/refbase/files/booth-morrison/2008/Boot… · volume fraction of the c0-precipitate phase, /eq,

$Page 1: Effects of tantalum on the temporal evolution of a model ...arc.nucapt.northwestern.edu/refbase/files/booth-morrison/2008/Boot… · volume fraction of the c0-precipitate phase, /eq,$
Effects of tantalum on the temporal evolution of a modelNi–Al–Cr superalloy during phase decomposition

Christopher Booth-Morrison a, Ronald D. Noebe b, David N. Seidman a,c,*

aDepartment of Materials Science and Engineering, Northwestern University, 2220 Campus Drive, Evanston, IL 60208, USAbNASA Glenn Research Center, 21000 Brookpark Rd., Cleveland, OH 44135, USA

cNorthwestern University Center for Atom-Probe Tomography (NUCAPT), 2220 Campus Drive, Evanston, IL 60208, USA

Received 1 August 2008; received in revised form 7 October 2008; accepted 17 October 2008

Abstract

The effects of a 2.0 at.% addition of Ta to a model Ni–10.0Al–8.5Cr (at.%) superalloy aged at 1073 K are assessed using scanningelectron microscopy and atom-probe tomography. The c0(L12)-precipitate morphology that develops as a result of c-(fcc)matrix phasedecomposition is found to evolve from a bimodal distribution of spheroidal precipitates, to {001}-faceted cuboids and parallelepipedsaligned along the elastically soft h001i-type directions. The phase compositions and the widths of the c0-precipitate/c-matrix heterophaseinterfaces evolve temporally as the Ni–Al–Cr–Ta alloy undergoes quasi-stationary state coarsening after 1 h of aging. Tantalum isobserved to partition preferentially to the c0-precipitate phase, and suppresses the mobility of Ni in the c-matrix sufficiently to causean accumulation of Ni on the c-matrix side of the c0/c interface. Additionally, computational modeling, employing Thermo-Calc, Dictraand PrecipiCalc, is employed to elucidate the kinetic pathways that lead to phase decomposition in this concentrated Ni–Al–Cr–Ta alloy.� 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Nickel-based superalloys; Tantalum; Atom-probe tomography; Nanostructures

1. Introduction

Tantalum is an important refractory addition to com-mercial nickel-based superalloys as both a solid-solutionstrengthener and a precipitate former. Tantalum has beenshown to increase the high-temperature strength and duc-tility, and to improve the resistance to creep, fatigue andcorrosion of these high-performance materials used inland-based and aerospace turbine engines at operating tem-peratures up to 1373 K [1–6]. The effects of Ta on themicrostructure and mechanical properties of nickel-basedsuperalloys have been investigated [5,7–11]; however, littlehas been done to characterize the morphological and com-positional changes due to the addition of Ta.

Phase decomposition in model Ni–Al–Cr alloys hasbeen investigated in detail by atom-probe tomography(APT) [12]. The research of Schmuck et al. [13,14] andPareige et al. [15,16] combined APT and lattice kineticMonte Carlo (LKMC) simulation to analyze the decompo-sition of a Ni–Al–Cr solid-solution at 873 K. A similarapproach was applied by Sudbrack et al. [17–21], Yoonet al. [22,23], Mao et al. [24] and Booth-Morrison et al.[25] for studying Ni–5.2Al–14.2Cr and Ni–7.5 Al–8.5Cr(at.%) aged at 873 K, and Ni–10Al–8.5Cr (at.%), Ni–10Al–8.5Cr–2.0W (at.%) and Ni–10Al–8.5Cr–2.0Re(at.%) aged at 1073 K, which decompose via a first-orderphase transformation to form a high number density(�1020–1025 m�3) of nanometer-sized c0-precipitates. Wereport on the temporal evolution of a model Ni–10.0Al–8.5Cr–2.0Ta (at.%) alloy aged at 1073 K that decomposesto form a microstructure consisting of c0(L12)-precipitatesin a face-centered cubic c-matrix. Chromium is added tothe binary Ni–Al system to reduce the lattice parameter

1359-6454/$34.00 � 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

doi:10.1016/j.actamat.2008.10.029

* Corresponding author. Address: Department of Materials Science andEngineering, Northwestern University, 2220 Campus Drive, Evanston, IL60208, USA. Tel.: +1 847 491 4391; fax: +1 847 467 2269.

E-mail address: [email protected] (D.N. Seidman).

www.elsevier.com/locate/actamat

Available online at www.sciencedirect.com

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Please cite this article in press as: Booth-Morrison C et al., Effects of tantalum on the temporal evolution of a model ..., Acta Mater(2008), doi:10.1016/j.actamat.2008.10.029

misfit between the c0-precipitates and the c-matrix. Theaddition of Ta increases the volume fraction of the c0-pre-cipitate phase, providing significant strengthening. Tanta-lum also decreases overall alloy diffusivity, therebyimproving phase stability and service life by retarding dif-fusion mediated processes such as c0-precipitate coarsening,creep and oxidation [2,3]. The effect of a 2.0 at.% additionof Ta to a model Ni–Al–Cr superalloy is studied usingscanning electron microscopy (SEM) and APT. The exper-imental results are complemented by computational model-ing employing the commercial software packages Thermo-Calc, Dictra and PrecipiCalc, to elucidate the thermody-namic and kinetic pathways that lead to phase decomposi-tion in a concentrated Ni–Al–Cr–Ta alloy.

2. Experimental

High-purity constituent elements were induction-meltedunder a partial pressure of Ar and chill cast in a 19 mmdiameter copper mold to form a polycrystalline masteringot. Samples from the cast ingot then underwent athree-stage heat-treatment (1) homogenization at 1573 Kin the c-phase field for 20 h; (2) a vacancy anneal in thec-phase field at 1503 K for 3 h followed by a water quench;(3) an aging anneal at 1073 K under flowing argon fortimes ranging from 0.25 to 256 h, followed by a waterquench. Microtip specimens and metallographic sampleswere prepared from each of the aged sections for studyby APT and SEM.

Vickers microhardness was measured using a BuehlerMicrometTM instrument on samples polished to 1 lm, withan applied load of 500 g sustained for 5 s, using the averagevalue of 15 independent measurements made on severalgrains. SEM was performed on samples polished to an0.02 lm finish and etched in a 100 ml HCl/100 ml deion-ized H2O/1 g K2S2O5 mixture, employing a LEO Gemini1525TM field-emission SEM operating at 5 kV with a 20–30 lm aperture and a working distance of 6 mm. APTmicrotips were prepared using standard procedures[26,27], and analyzed with a local-electrode atom-probe(LEAP�) tomograph [28–32] at the Northwestern Univer-sity Center for Atom-Probe Tomography (NUCAPT).Pulsed-laser APT data collection was performed at a targetevaporation rate of 0.04 ions per pulse, a specimen temper-ature of 40.0 ± 0.3 K, a pulse energy of 0.6 nJ, a pulse rep-etition rate of 200 kHz, and a background gauge pressureof less than 6.7 � 10�8 Pa. Pulsed-laser atom-probe tomog-raphy was employed to improve the compositional accu-racy of the APT technique by limiting preferentialevaporation [33], and to increase the tip specimen life byreducing the DC voltage required for evaporation. APTdata were analyzed with the IVAS� 3.0 software program(Imago Scientific Instruments). The c0-precipitate/c-matrixheterophase interfaces were delineated with Al isoconcen-tration surfaces generated by efficient sampling procedures[34], and detailed compositional information was obtainedwith the proximity histogram method [35]. The equilibrium

volume fraction of the c0-precipitate phase, /eq, was esti-mated by averaging the values obtained from the lever ruleof the extrapolated equilibrium concentrations of Ni, Al,Cr and Ta.

Spatial convolution effects, such as ion trajectory over-lap and local magnification effects, have been cited as pos-sible sources of misleading results in the APT analysis ofnickel-based superalloys [12]. A comparison of the compo-sition profiles across the c/c0 interfaces measured by APTto those simulated by the lattice kinetic Monte Carlo tech-nique for a model Ni–5.2Al–14.2Cr (at.%) alloy [24],showed no evidence of artificial interfacial broadening inthe APT data due to ion trajectory overlap. Local magnifi-cation effects due to differences in the required evaporationfields of different phases are unlikely in Ni–Al–Cr superal-loys containing only the c-matrix and c-precipitate phasesbecause the evaporation fields of the phases are essentiallyidentical.

The overall composition of the master ingot was deter-mined by inductively coupled plasma (ICP) atomic-emis-sion spectroscopy to be 80.01Ni–9.75Al–8.21Cr–2.02Ta(at.%) and was indistinguishable, within experimentalerror, from the targeted composition of Ni–10.0Al–8.5Cr–2.0Ta (at.%). ICP chemical analysis was also usedto determine the compositions of the c-matrix and c0-pre-cipitate phases of a sample aged at 1073 K for 256 h afterphase extraction by anodic dissolution of the c-matrixphase with a 1:1 aqueous solution of citric acid and ammo-nium nitrate at constant current density. We note that thestandard errors for all quantities are calculated based oncounting statistics and reconstruction scaling errors usingstandard error propagation methods [36], and representtwo standard deviations from the mean.

The commercial software package Thermo-Calc [37] wasused to estimate the values of /eq and the equilibrium com-positions of the c-matrix, Cc;eq

i ð1Þ, and c0-precipitatephases, Cc0 ;eq

i ð1Þ, at a pressure of 1 atm, using a databasefor nickel-based superalloys developed by Saunders [38].The tracer diffusivities of the atomic species in the c-matrixphase were calculated employing Dictra [39] with themobility database due to Campbell [40] and employingthe Saunders thermodynamic database. Additionally, pre-cipitation modeling was performed with the commercialsoftware program PrecipiCalc [41,42], employing the Saun-ders thermodynamic database and the mobility databasedue to Campbell. PrecipiCalc applies thermodynamic andkinetic data from Thermo-Calc and Dictra to continuummodels of precipitation for multi-component, multiphasealloys to provide a unified treatment of nucleation, growthand coarsening.

3. Results

A 2.0 at.% addition of Ta to a model Ni–10.0Al–8.5Cr(at.%) alloy aged at 1073 K results in a 47 ± 5% increasein the microhardness (Fig. 1) over the full range of agingtimes, t = 0–256 h. The microhardness of Ni–Al–Cr–Ta

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varies from 3.3 to 3.6 GPa, with peak microhardness occur-ring between t = 1 and 16 h. For Ni–10.0Al–8.5Cr (at.%)aged at 1073 K, the microhardness varies over a narrowrange, 2.15–2.5 GPa, with peak microhardness occurringat 4 h [19,20]. The increase in the microhardness due tothe addition of Ta is a result of both the added solid-solu-tion strengthening provided by Ta and the dramaticincrease in the value of the c0-precipitate volume fraction,/. At 256 h, for example, the value of / from the phaseextraction results is 18.9% for Ni–Al–Cr and 36.4% forNi–Al–Cr–Ta. The values of the equilibrium volume frac-tions, /eq, estimated by APT and from Thermo-Calc forNi–Al–Cr–Ta are presented in Table 1, and compared tothe values of / at 256 h, as measured by both APT andphase extraction.

3.1. Morphological development

The microstructure of the material as-quenched from1503 K consists of a bimodal distribution of c0-precipitates,with primary c0-precipitates of radii, R(t = 0 h), on theorder of 30–40 nm, and smaller secondary c0-precipitateswith an average radius, hR(t = 0 h)i, of 6.4 ± 1.1 nm. FromAPT, the number density, Nv(t = 0 h), of the primary c0-precipitates is 3 ± 2 � 1021 m�3, occupying a volume frac-tion of 28 ± 13%. The value of Nv(t = 0 h) of the secondaryc0-precipitates is 1.3 ± 0.1 � 1023 m�3, with a volume frac-tion of 11 ± 1%. The average edge-to-edge distance, ke–e,

between secondary c0-precipitates is measured to be4.3 ± 1.3 nm, while the value of ke–e for the primary c0-pre-cipitates is 109 ± 63 nm, as measured by a method devel-oped by Karnesky et al. [43]. A solute-depleted,precipitate-free shell with a thickness of 5.7 ± 1.1 nm sur-rounds the primary c0-precipitates. The bimodal distribu-tion is only observed in the as-quenched state. Withaging, the secondary c0-precipitates are likely consumedby an Ostwald ripening process to decrease the total c/c0

interfacial free energy of the system.The morphology of the Ni–Al–Cr–Ta alloy evolves from

spheroidal-to-cuboidal c0-precipitates with significantlyrounded edges, and finally to cuboidal and parallelepipedicc0-precipitates aligned along the elastically soft h001i-typedirections (Fig. 3). For aging times beyond the as-quenchedstate, the primary c0-precipitates develop an {001}-facetedcuboidal morphology with rounded corners, as seen byboth SEM (Fig. 3b) and APT (Fig. 4) for a sample agedfor 0.25 h. We note that the c0-precipitates in Figs. 3band 4 exhibit both spheroidal and cuboidal characteristics.The value of R(t = 0.25 h) at which primary c0-precipitatesin this Ni–Al–Cr–Ta alloy undergo the transformationfrom a spheroidal-to-cuboidal morphology is estimatedfrom APT to be 61 ± 7 nm.

Aging time (h)0 0.25 4 16 64 256

Vick

ers

Mic

roha

rdne

ss (G

Pa)

1.5

2.0

2.5

3.0

3.5

4.0Ni-10.0 Al-8.5 Cr-2.0 Ta at.%Ni-10.0 Al-8.5 Cr at.%

1

Fig. 1. Vickers microhardness measurements for Ni–10.0Al–8.5Cr–2.0Taand Ni–10.0Al–8.5Cr (at.%) aged at 1073 K. The addition of 2.0 at.% Taresults in a 47 ± 5% increase in the microhardness over the full range ofaging times, t = 0–256 h, due to increases in solid-solution strengtheningand to a dramatic increase in the value of /.

Table 1Equilibrium c0-precipitate volume fraction, /eq, determined by APT, ICPchemical analysis, and thermodynamic modeling employing Thermo-Calcfor Ni–10.0Al–8.5Cr–2.0Ta (at.%) aged at 1073 K.

Technique used to estimate /eq /eq (%)

Lever rule with APT compositions, 256 h 37.2 ± 8.9Lever rule with APT equilibrium compositions 37.0 ± 9.0ICP chemical analysis, 256 h 36.4Thermo-Calc using Saunders database [38] 38.17

Fig. 2. APT reconstructed three-dimensional (3D) image of a Ni–10.0Al–8.5Cr–2.0Ta (at.%) alloy aged at 1073 K for 0 h. The solute elements thatpartition to the c0-precipitates, Ta and Al, are shown in black, while Cr,which partitions to the c-matrix, is shown in white; Ni atoms are omittedfor clarity. The morphology of the c0-precipitate phase is spheroidal in theas-quenched state, and a bimodal particle size distribution is apparent.

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The cuboidal morphology of the primary c0-precipitatespersists with longer aging, and for aging times of 4 h andlonger, the c0-precipitates align along orthogonal h001i-type directions (Figs. 2 and 5). For aging times of 64 and256 h, the primary c0-precipitates have a non-equiaxed,rectangular parallelepipedic morphology with {001}-typefacets. We note that the direction of c0-precipitate align-ment was verified employing selected-area electron diffrac-tion patterns using conventional transmission electronmicroscopy, with an Hitachi HF-8100 at an acceleratingvoltage of 200 kV, for a sample aged for 256 h at 1073 K(Fig. 6).

3.2. Compositional evolution

The compositional information generated by APT per-mits the study of the temporal evolution of the phase com-positions, and of the concentration profiles at the c0-precipitate/c-matrix interface (Fig. 7). The c0/c interfacesare defined by employing the inflection-point approach todetermine a threshold isoconcentration surface that repre-sents the average of the far-field plateau concentrationsof the c0-precipitate and c-matrix phases [19]. The phasecompositions at and away from the interface evolve tempo-

rally, and the interfacial widths, defined as the distancebetween the plateau concentrations of the two phases,decrease with aging time (Fig. 8). Interestingly, an accumu-lation of Ni is observed �2 nm into the c-matrix. We notethat there is no evidence of non-monotonic (confined) seg-regation of Ta at the c0-precipitate/c-matrix heterophaseinterface.

3.3. Partitioning of elemental species

The partitioning behavior of the elements can be deter-mined quantitatively by calculating the partitioning ratio,Kc0=c

i , the ratio of the concentration of an element i in thec0-precipitates, to the concentration of the same element iin the c-matrix (Fig. 9). Aluminum and Ta are observedto partition to the c0-precipitates, while Cr and Ni partitionto the c-matrix. The strong partitioning of Ta to the c0-pre-cipitates increases the partitioning of Cr to the c-matrixand of Al to the c0-precipitates when compared to theresults obtained for a ternary Ni–10.0Al–8.5Cr (at.%) alloy[19,20]. For example, for a sample aged at 1073 K for256 h, the value of Kc0=c

Cr decreases from 0.63 ± 0.01 to0.26 ± 0.03 and the value of Kc0=c

Al increases from2.20 ± 0.02 to 3.17 ± 0.01, due to the formation of a signif-

Fig. 3. SEM images of a Ni–10.0Al–8.5Cr–2.0Ta (at.%) alloy aged at 1073 K for (a) 0 h, (b) 0.25 h, (c) 1 h, (d) 4 h, (e) 16 h and (f) 64 h. The primary c0-precipitate morphology evolves from spheroidal c0-precipitates to a cuboidal and parallelepipedic morphology with primary c0-precipitates aligned alongthe elastically soft h001i-type directions.


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icantly higher volume fraction of c0-precipitates. The valueof Kc0=c

Ta for the Ni–Al–Cr–Ta alloy at 256 h is 10.25 ± 0.07,and the partitioning of Ni is unaffected by the addition ofTa.

4. Discussion

4.1. Morphological development

The morphology of the c0-precipitates is observed toevolve from a bimodal distribution of spheroidal c0-precip-itates in the as-quenched state to cuboids with significantlyrounded edges, and finally to cuboids and rectangular par-allelepipeds aligned along orthogonal h001i-type direc-tions. The c0-precipitates that form the bimodaldistribution in the as-quenched state nucleate rapidly dur-ing the quench due to the small barrier height to nucleationcaused by the large supersaturations of alloying elements.

The larger c0-precipitates nucleate first, and subsequentlyundergo high-temperature growth. As the alloy cools, how-ever, the diffusion fields associated with the primary c0-pre-cipitates shrink and growth slows [44]. With additionalcooling, a significant solute supersaturation develops inthe interprecipitate spaces, resulting in a secondary burstof precipitation (Fig. 2). In a recent study of multimodalprecipitation in the commercial nickel-based superalloyUdimet 720 Li, Radis et al. [44] found that multimodal pre-cipitation is highly dependent on alloy cooling rate, andnoted that this phenomenon has been observed to occurin other nickel-based alloys during continuous cooling.

The nucleation of c0-precipitates during the quench from1503 K was modeled with PrecipiCalc, which incorporatesthe results of the classical models of nucleation, growth andcoarsening. These calculations were performed assuming acontinuous quench rate of 20 K s�1 and a c0-precipitate/c-matrix interfacial free energy of 25 mJ m�2, based onresults from concentrated Ni–Al–Cr alloys [18,25] aged at873 K. The c/c0 solvus point was determined experimen-

Fig. 5. An APT reconstructed 3D image of cuboidal and parallelepipedic primary c0-precipitates aligned along h001i-type directions from a Ni–10.0Al–8.5Cr–2.0Ta (at.%) alloy aged at 1073 K for 64 h. Tantalum and Al are shown in black, Cr is shown in white, and Ni atoms are omitted for clarity.

Fig. 4. APT reconstructed 3D image of a Ni–10.0Al–8.5Cr–2.0Ta (at.%)alloy aged at 1073 K for 0.25 h. The primary c0-precipitates in the APTreconstruction have both spheroidal and cuboidal characteristics. Theradius at which the c0-precipitates undergo the spheroidal-to-cuboidalmorphological transformation is measured to be 61 ± 7 nm. Tantalumand Al are shown in black, Cr is shown in white, and Ni atoms are omittedfor clarity.

Fig. 6. After aging for 256 h, the primary c0-precipitates have cuboidaland parallelepipedic morphologies with {001}-type facets, and are alignedalong the h001i-type crystallographic directions, as confirmed by aselected-area electron diffraction pattern taken along the ½110� zone axis.


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tally by differential thermal analysis to be 1393 K, whichagrees well with the value of 1412 K predicted byThermo-Calc and employed in the PrecipiCalc modeling.The results of the PrecipiCalc modeling are shown inFig. 10, and predict a bimodal distribution of c0-precipi-tates. Primary c0-precipitate nucleation is predicted tobegin at a temperature of 1380 K due to a bulk free energydriving force for nucleation, DFnuc, of �123 J mol�1, andcontinues to a temperature of 1357 K. Primary c0-precipi-tate growth follows nucleation, and values of hR(t)i of28.2 nm, Nv(t) of 2.7 � 1021 m�3 and / of 25.7% are pre-dicted for a temperature of 1194 K. According to the sim-ulation results, significant secondary c0-precipitatenucleation begins at a temperature of 1190 K due to a valueof DFnuc of �132 J mol�1 and continues throughout theremainder of the quench. The final as-quenched micro-structure is predicted to be a bimodal distribution of c0-pre-cipitates, with primary c0-precipitates with hR(t)i and /values of 30.2 nm and 31.5%, respectively, and secondaryc0-precipitates with hR(t)i and / values of 0.8 nm and

14.2%, respectively. The predicted values of Nv(t) for theprimary and secondary c0-precipitates are 2.7 � 1021 and3.4 � 1025 m�3, respectively.

The PrecipiCalc predictions of the values hR(t)i, / andNv(t) for the primary c0-precipitates of 30.2 nm, 31.5%and 2.7 � 1021 m�3 are in good agreement with the mea-sured values of 30–40 nm, 28 ± 13%, and3 ± 2 � 1021 m�3. The PrecipiCalc predictions for the sec-

76

78

80

82

468

1012141618

Con

cent

ratio

n (a

t.%)

468

101214

Distance from γ/γ ' Interface (nm)-6 -4 -2 0 2 4 6

0

1

2

3

4

'-precipitate-matrix

Ni

Al

Cr

Ta

4 h256 h

0.25 h

γ γ

Fig. 7. The elemental concentration profiles across the primary c0-precipitate/c-matrix heterophase interface for a Ni–10.0Al–8.5Cr–2.0Ta(at.%) alloy aged at 1073 K. The phase compositions evolve temporally,and the widths of the concentration profiles decrease with increasing agingtime. An accumulation of Ni is observed to develop on the c-matrix side ofthe interface, evidence of a kinetic effect associated with the addition ofTa. The concentration profiles shown here represent the average of all ofthe interfaces in the analyzed volume.

Aging time (h)0 0.25 1 4 16 64 256

Wid

th o

f γ/γ

' in

terfa

ces

(nm

)

3.0

3.5

4.0

4.5

5.0

NiAlCrTa

Fig. 8. The temporal evolution of the widths of the concentration profilesacross the primary c0-precipitate/c-matrix interface for a Ni–10.0Al–8.5Cr–2.0Ta (at.%) alloy aged at 1073 K. The interfacial widths areobserved to decrease with increasing aging time. The species with thelargest diffusivity in the c-matrix, Al and Ta, have the smallest interfacialwidths, while the opposite is true for Ni and Cr, the slower diffusingspecies.

Aging time (h)0 0.25 1 4 16 64 256

Parti

tioni

ng R

atio

, Kiγ

'/γ

0.2

0.5

2

5

1

10

-matrix preference (Ni,Cr)

'-precipitate preference (Al,Ta)

Ni-(a)Al-(a)Cr-(a)Ta-(a)

Ni-(b)Al-(b )Cr-(b)

γ

γ

Fig. 9. The temporal evolution of the partitioning ratios, Kc0=ci , of the

constituent elements i of (a) Ni–10.0Al–8.5Cr–2.0Ta and (b) Ni–10.0Al–8.5Cr (at.%) aged at 1073 K. In both alloys, Al and Ta are observed topartition to the c0-precipitates, while Cr and Ni partition to the c-matrix.


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ondary c0-precipitate properties of 0.8 nm, 14.2% and3.4 � 1025 m�3 differ, however, from the experimental val-ues of hRi, / and Nv(t) of 6.4 ± 1.1 nm, 11 ± 1% and1.3 ± 0.1 � 1023 m�3, respectively. The accuracy of the pre-dictions for the primary c0-precipitates indicates that thethermodynamics and kinetics of the c/c0 phase transforma-tion are modeled correctly. Inaccuracies in the predictionsof the properties of the secondary c0-precipitates may bedue to the limitations in of the extant models of nucleationand growth upon which PrecipiCalc is based. These modelsare best suited for dilute, misfit-free, binary alloys withnear-zero volume fractions of the secondary phase, andhence very small elemental supersaturations. These condi-tions are not satisfied for a concentrated quaternary Ni–Al–Cr–Ta alloy with an equilibrium precipitated volumefraction of 37.0 ± 9.0%, and a complex bimodal micro-structure in the as-quenched state. We note that efforts toimprove the predictive power of this modeling techniqueand to incorporate the effects of variables such as latticemisfit are ongoing [42]. The PrecipiCalc predictions arehighly dependent on the choice of the alloy cooling rate,the shape of the cooling curve, the c/c0-interfacial energy,and the kinetics and thermodynamics of the alloy duringthe quench. Thus, the modeling predictions can be modi-fied by adjusting any of these parameters.

Fig. 11 shows the PrecipiCalc predictions of the valuesof DFnuc, the effective nucleation rate, Jeff, and the critical

radius for nucleation, R*, during the quench. Decreasesin the magnitude of DFnuc are predicted at 1380 and1190 K due to the nucleation of primary and secondaryc0-precipitates, respectively. For the remainder of thequench, the driving force for phase separation increasesrapidly. This is due to the increasing c-matrix supersatura-tion values that are not sufficiently consumed by primaryc0-precipitation growth, due, in turn, to the exponentiallydecreasing diffusivities with decreasing temperature. Asexpected, the predicted values of R* decrease rapidly asthe magnitude of DFnuc increases.

The composition of the primary c0-precipitates in theas-quenched state is measured to be 76.04 ± 0.04Ni–17.02 ± 0.02Al–3.37 ± 0.02Cr–3.57 ± 0.03Ta (at.%),while the secondary c0-precipitates have a compositionof 76.05 ± 0.05Ni–16.82 ± 0.03Al–4.60 ± 0.03Cr–2.53 ±0.03Ta (at.%). We note that the composition of thelarger c0-precipitates is closer to the equilibrium com-position of 75.24 ± 0.04Ni–16.48 ± 0.07Al–3.20 ± 0.06Cr–5.03 ± 0.07Ta (at.%) estimated from APT data. The primaryc0-precipitates reject Cr to the c-matrix and preferentiallyconsume the supersaturation of Ta, which partitionsstrongly to the c0-phase. As such, the secondary c0-precipi-tates nucleate from a Cr-enriched and Ta-depleted c-matrix,resulting in Cr and Ta concentrations that are 36% largerand 29% smaller, respectively, than those measured for theprimary c0-precipitates.

The morphological development of nickel-based super-alloys has been shown to proceed from spheroidal-to-

T (K)600800100012001400

Nv (t)

(m-3

)

105

1010

1015

1020

1025

<R(t)

> (n

m)

0.1110100

t (s)0 10 20 30 40

(%)

0

10

20

30

40

primary '-prec ipitatessecondary '-precipitates

γγ

φ

Fig. 10. The values of the c0-precipitate number density, Nv(t), radius,hR(t)i, and volume fraction, /, during the water quench from 1503 K forNi–10.0Al–8.5Cr–2.0Ta (at.%), as modeled by PrecipiCalc. A bimodaldistribution of c0-precipitates is predicted for the as-quenched state withprimary c0-precipitates with hR(t)i and / values of 30.2 nm and 31.5%,and secondary c0-precipitates with hR(t)i and / values of 0.8 nm and14.2%. The predicted values of Nv(t) for the primary and secondaryc0-precipitates are 2.7 � 1021 and 3.4 � 1025 m�3, respectively.

T (K)600800100012001400

Fnuc

(kJ

mol

-1)

-2.0

-1.5

-1.0

-0.5

0.0

Jeff (m

-3 s

-1)

1010

1015

1020

1025

F nuc

J eff

t (s)10 20 30 40

R* (

nm)

0.1

1.0

10.0

Δ

Δ

Fig. 11. The evolution of the bulk driving force for nucleation, DFnuc, theeffective nucleation rate, Jeff, and the critical radius for nucleation, R*,during the quench. Decreases in the magnitude of DFnuc are predicted at1380 and 1190 K due to the nucleation of primary and secondary c0-precipitates, respectively. The magnitude of DFnuc increases and the valuesof R* decrease during the quench. This figure was calculated usingPrecipiCalc.


ARTICLE IN PRESS


cuboidal-to-cuboidal arrays and finally to solid-state den-drites [45]. The c0-precipitates of the Ni–Al–Cr–Ta alloystudied herein undergo the first two transitions, transform-ing from spheroids-to-cuboids at an aging time of 0.25 h,and forming cuboidal arrays by an aging time of 4 h. Thesizes at which these transitions occur are a function ofthe magnitude of the lattice parameter misfit, and are par-tially diffusion controlled [45]. The elastic self-energy of aprecipitate increases as R3, while the heterophase interfa-cial free energy increases as R2. Thus, as growth and coars-ening proceed, and the average c0-precipitate radiusincreases, the elastic energy ultimately determines the pre-cipitate morphology and is decreased by the formation ofcuboidal c0-precipitates. The evolution of the spheroidalc0-precipitates into cuboids in the Ni–Al–Cr–Ta alloy com-mences at an aging time of 0.25 h, when the c0-precipitateshave an average radius of 61 ± 7 nm. In contrast, theradius at which the microstructure becomes cuboidal forthe base Ni–Al–Cr alloy was estimated to be �88 nm atan aging time of 64 h at 1073 K [20]. The lattice parametersof the c-matrix and the c0-precipitates of the Ni–Al–Cr–Taalloy are estimated from PrecipiCalc to be 0.3589 and0.3603 nm, respectively, resulting in a lattice parametermisfit, d, of 0.0039. The value of d of the Ni–Al–Cr alloywas previously estimated to be 0.0022 ± 0.0007 [20]. Theaddition of 2.0 at.% Ta increases the lattice parameter mis-fit by 78%, resulting in a spheroid-to-cuboid transition thatoccurs at a smaller c0-precipitate size, and at an earlieraging time. For aging times of 64 and 256 h (Figs. 3f, 5and 6), the c0-precipitates have a non-equiaxed, rectangularparallelepiped morphology with {001}-type facets. Theparallelepipedic morphology of the c0-precipitates furtherminimizes the elastic energy [46,47].

The alignment of the c0-precipitates results from theminimization of the elastic interactions between the c0-pre-cipitates, where the elastic interaction energy depends onthe elastic anisotropy, the difference in the elastic constantsof the two phases, and the sign and magnitude of the misfitstrain [48–50]. The alignment of c0-precipitates into cuboi-dal and parallelepipedic arrays was found to occur after64 h of aging at 1073 K for the base Ni–Al–Cr alloy [20],while the formation of arrays begins at 4 h for the Ni–Al–Cr–Ta alloy. The increased lattice parameter misfitdue to the addition of Ta leads to c0-precipitate alignmentat smaller precipitate radii and earlier aging times in theNi–Al–Cr–Ta alloy. The cuboidal c0-precipitates in bothalloys have a coherent cube-on-cube relationship with thec-matrix, with clearly defined {001}-type facets, and arealigned along the elastically soft h001i-type directions(Fig. 6).

4.2. Compositional evolution

From the APT results, Al and Ta partition strongly tothe c0-precipitate phase, while Ni and Cr partition to thec-matrix phase, in agreement with past experimental results[5,10,11,51–54]. The equilibrium composition of the c0-pre-

cipitates suggests that Al, Ta and Cr occupy the Al sublat-tice sites of the L12-ordered c0-phase of the Ni–Al–Cr–Taalloy at 1073 K. A recent first-principles study of this alloyconfirms that Ta and Cr substitute preferentially at the Alsublattice sites of the Ni3Al-L12 structure [55], in agree-ment with previous work on this subject [12,53,56–71].

The measured c0-precipitate volume fractions (Table 1)are close to their equilibrium values, suggesting that theNi–Al–Cr–Ta alloy may be undergoing quasi-stationarystate coarsening. The first comprehensive mean-field treat-ment of precipitate coarsening, due to Lifshitz and Slyozov[72] and Wagner [73], is limited to very dilute binary alloyswith spatially fixed spherical precipitates whose initial com-positions are equal to their equilibrium values. Umantsevand Olson (UO) demonstrated that the exponents of thetemporal power-laws predicted for binary alloys by LSW-type models are identical for concentrated multi-compo-nent alloys, but that the explicit expressions for the rateconstants depend on the number of components [74]. Inthe UO model, the asymptotic solution for the supersatura-tion of solute element i, DCi(t), the difference between theconcentration in the far-field c-matrix, < Cc;ff

i ðtÞ >, andthe equilibrium c-matrix solute-solubility, Cc;eq

i ð1Þ, is:DCc

i ðtÞ ¼< Cc;ffi ðtÞ > �Cc;eq

i ð1Þ ¼ ji;UOt�1=3; ð1Þwhere ji;UO is the coarsening rate constant for DCc

i ðtÞ and isrelated to the partial derivatives of the chemical potentials,the c0-precipitate/c-matrix interfacial free energy, the parti-tioning ratios of the alloying elements and the diffusivitiesof the elements [74]. The temporal evolution of the super-saturations of the alloying elements in the c-matrix andc0-precipitate are observed to follow approximately thet�1=3 prediction of the UO model (Fig. 12). The supersatu-rations of Ni, Al, Cr and Ta in the c-matrix evolve ast�0.33±0.04, t�0.35±0.05, t�0.31±0.04 and t�0.30±0.04, respec-tively, while the supersaturations of the same elements inthe c0-precipitates evolve as t�0.33±0.03, t�0.36±0.05,t�0.28±0.04 and t�0.36±0.03, respectively. Quasi-stationarystate coarsening has begun by an aging time of 1 h, andcontinues throughout the aging times studied here.

The values of Cc;eqi ð1Þ and Cc0 ;eq

i ð1Þ estimated fromAPT data employing Eq. (1) are listed in Table 2, and com-pared to the equilibrium values predicted by Thermo-Calcand the concentrations measured by APT and ICP analysisat 256 h. The phase compositions after 256 h of aging arenear their equilibrium values, suggesting that the magni-tudes of the c-matrix supersaturations are small and thatthe c0-precipitate growth and coarsening regime is nearlycomplete.

The most striking feature of the concentration profilesacross the c0-precipitate/c-matrix heterophase interface(Fig. 7) is the accumulation of Ni in the c-matrix roughly2 nm from the interface. This effect was observed at all c/c0 interfaces, regardless of direction, and is likely kineticin origin, resulting from a decrease in the diffusivity of Niin the c-matrix. Estimates of the tracer diffusivities fromDictra predict a threefold decrease in the calculated c-


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matrix tracer diffusivity of Ni, DcNi, from 6.06 to

2.02 � 10�18 m2 s�1 due to a 2.0 at.% addition of Ta (Table3). This decrease in Ni diffusivity is significant because Nibecomes the least mobile species in the c-matrix phase.Hence, as phase decomposition proceeds, Ni partitions tothe c-matrix and accumulates on the c-matrix side of the

c0/c interface. The diffusivities of all of the atomic speciesdecrease due to the addition of Ta, thus the c0-precipitatecoarsening kinetics are expected to decrease. We note thatthe calculations of the c-matrix diffusivities used herein aredependent on the thermodynamic predictions from theSaunders database. Since the Saunders database predicts

C(t)

' Al (a

t.%)

0.05

0.5

0.1

1

Cγ'(t) ~ tm

C(t)

γN

i(a

t.%)

0.05

0.5

0.1

Aging time (h) Aging time (h)

Aging time (h)Aging time (h)

0.25 1 4 16 64 256

m= -0 .33 ± 0.04C

(t)γ C

r (a

t.%)

0.05

0.5

0.1

103 104 105 106

C(t)

γ Ta (a

t.%)

0.05

0.2

0.1

C(t)

γ Al (a

t.%)

0.05

0.5

0.1

m= -0 .35 ± 0.05

m= -0 .31 ± 0.04

m= -0 .30 ± 0.04

Cγ(t) ~ tm

C(t)

' Ni

(at.%

)

0.05

0.5

0.1

0.25 1 4 16 64 256

m= -0 .33 ± 0.03

C(t)

' Cr

(at.%

)0.05

0.5

0.1

103 104 105 106

C(t)

' Ta(a

t.%)

0.2

0.5

2

0.1

1

m= -0 .36 ± 0.05

m= -0 .28 ± 0.04

m= -0 .36 ± 0.03

Δ

γΔ

γΔ

γΔ

γΔ

ΔΔ Δ Δ

Δ⏐

⏐⏐

⏐ ⏐⏐

⏐⏐

Fig. 12. The magnitude of the values of the supersaturations, DCiðtÞ, of Ni, Al, Cr and Ta in the c-matrix and c0-precipitates for Ni–10.0Al–8.5Cr–2.0Ta(at.%) alloy aged at 1073 K. The magnitudes of the DCiðtÞ values decrease as approximately t�1=3 in the coarsening regimes for both phases, as predicted bythe Umantsev and Olson (UO) models for quasi-stationary state coarsening.

Table 2Equilibrium compositions (at.%) of the c0-precipitate, Cc0 ;eq

i ð1Þ, and c-matrix, Cc;eqi ð1Þ, determined by APT, ICP chemical analysis, and thermodynamic

modeling employing Thermo-Calc for Ni–10.0Al–8.5Cr–2.0Ta (at.%) aged at 1073 K.

Technique Cc0 ;eqNi ð1Þ Cc0 ;eq

Al ð1Þ Cc0 ;eqCr ð1Þ Cc0 ;eq

Ta ð1ÞAPT, 256 h 75.37 ± 0.05 16.56 ± 0.08 3.25 ± 0.09 4.82 ± 0.09APT, extrapolated 75.24 ± 0.08 16.48 ± 0.07 3.20 ± 0.06 5.03 ± 0.07ICP, 256 h 75.56 16.57 3.28 4.58Thermo-Calc 76.47 17.00 2.66 3.88

Technique Cc;eqNi ð1Þ Cc;eq

Al ð1Þ Cc;eqCr ð1Þ Cc;eq

Ta ð1ÞAPT, 256 h 81.65 ± 0.01 5.23 ± 0.03 12.66 ± 0.03 0.47 ± 0.03APT, extrapolated 81.68 ± 0.04 5.18 ± 0.08 12.70 ± 0.02 0.44 ± 0.06ICP, 256 h 83.17 5.49 10.74 0.60Thermo-Calc 81.37 5.68 12.11 0.84


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an equilibrium partitioning ratio for Ta of 4.61, while avalue of 11.4 is measured herein, the predictions of thedatabase are not absolutely accurate. As such, the predic-tions of the c-matrix kinetics likely suffer from some inac-curacy, as previously observed in comparisons ofmicroanalysis results of diffusion couples to Dictra predic-tions [42].

The widths of the concentration profiles across the c0-precipitate/c-matrix interface are observed to decrease withincreasing aging time (Fig. 8), which is a kinetic effect. Asaging progresses, the two species with the largest predicteddiffusivities in the c-matrix, Al and Ta (Table 3), have thesmallest interfacial widths, while the opposite is true for Niand Cr, the slower species. This is expected, though the dif-fusivities of the atomic species in the c0-precipitate, forwhich there are no extant kinetic databases that includeTa, also play an important role in determining the interfa-cial widths. The interfacial widths of model nickel-basedsuperalloys have been measured to range from a singleatomic layer to up to 5 nm, depending on the alloy systemand temperature studied [24,75,76].

4.3. Comparison with other Ni–Al–Cr–X alloys

This work is part of a systematic investigation of theeffects of dilute refractory additions on the c/c0 phasedecomposition of a model Ni–10.0Al–8.5Cr (at.%) alloyaged at 1073 K. A 2.0 at.% addition of W [19,20] was pre-viously found to increase the microhardness and decreasethe coarsening kinetics of the c0-phase. Tungsten was foundto partition preferentially to the c0-precipitates, with no evi-dence of non-monotonic (confined) segregation of W at theheterophase interface. The addition of W led to strongerpartitioning of Al to the c0-precipitates, and of Cr to thec-matrix, than was measured for the base Ni–Al–Cr alloy.The Ni–Al–Cr–W alloy, like Ni–Al–Cr–Ta and the baseNi–Al–Cr alloys, undergoes a c0-precipitate morphologicalevolution from spheroids-to-cuboids, as well as alignmentof the cuboids along the elastically soft h001i-typedirections.

A 2.0 at.% addition of Re [22,23] was found to result inthe strong partitioning of Re to the c-matrix, and increasedthe partitioning of Al to the c0-precipitates and of Cr to thec-matrix. Rhenium was found to decrease the coarseningkinetics, and to stabilize the spheroidal morphology ofthe c0-precipitates, allowing the c0-phase to remain spheroi-dal after aging to 256 h. A high degree of c0-precipitatecoagulation and coalescence was detected, in contrast withthe Ni–Al–Cr–Ta and Ni–Al–Cr–W alloys. Additionally,

no evidence of confined (non-monotonic) interfacial Resegregation was detected for Ni–Al–Cr–Re, unlike com-mercial nickel-based superalloys, such as Rene N6, whichexhibits significant confined (non-monotonic) interfacialsegregation of Re of 2.41 atoms nm�2 [77,78]. The effectsof Re and Ta in modern nickel-based superalloys are dra-matically different, though both decrease the kinetics ofc-phase decomposition, leading to phase stability at hightemperature.

The accumulation of Ni on the c-matrix side of the c0/cheterophase interface is unique to the addition of Ta, dueto a decrease in the value of Dc

Ni from 6.06 to2.02 � 10�18 m2 s�1 for a 2.0 at.% addition of Ta. Thevalue of Dc

Ni was calculated to decrease to4.92 � 10�18 m2 s�1 [20] and 4.05 � 10�18 m2 s�1 [23] dueto the additions of W and Re, respectively, leading to adeceleration of the coarsening kinetics. The values of Dc

Ni

are, however, apparently still sufficient to transport Niatoms away from the c0/c interface during phase decompo-sition of the Ni–Al–Cr–W and Ni–Al–Cr–Re alloys,avoiding Ni accumulation. The bimodal distribution ofc0-precipitates in the as-quenched state is also unique toNi–Al–Cr–Ta among the Ni–based alloys we have studiedto date. The bimodal distribution is due to the initially highvalue of the Ta supersaturation in the c-matrix, and to therelatively large diffusivity of Ta in the c-matrix. The valueof Dc

Ta of 5.14 � 10�18 m2 s�1 is significantly greater thanthe values of Dc

W and DcRe of 4.93 and 1.07 � 10�19 m2 s�1,

respectively, in the model Ni–Al–Cr alloys.

5. Summary and conclusions

The effects of a 2.0 at.% addition of tantalum to a modelNi–10.0Al–8.5Cr (at.%) superalloy aged at 1073 K for 0–256 h were assessed using mainly SEM and APT, leadingto the following conclusions:

� The addition of Ta results in a 47 ± 5% increase inmicrohardness due to increases in solid-solutionstrengthening and to a dramatic increase in the volumefraction of the c0-phase. After 256 h of aging, the valueof / from phase extraction results is 18.9% for Ni–Al–Cr and 36.4% for the Ni–Al–Cr–Ta alloy. The equilib-rium volume fraction of the c0-phase for the Ni–Al–Cr–Ta alloy is estimated by APT to be 37.0 ± 9.0%.

� The morphology of the c0-precipitates evolves from abimodal distribution of spheroidal precipitates in theas-quenched state to primary c0-precipitate cuboids withsignificantly rounded edges, and finally to cuboidal and

Table 3Tracer diffusivity of element i in the c-matrix, Dc

i , of Ni–10.0Al–8.5Cr and Ni–10.0Al–8.5Cr–2.0Ta (at.%) calculated with Dictra, and Campbell [40] andSaunders [38] databases at 1073 K.

Alloy (at.%) DcNi (10

�18 m2s�1) DcAl (10

�18 m2s�1) DcCr (10

�18 m2s�1) DcTa (10�18 m2s�1)

Ni–10.0Al–8.5Cr 6.06 13.9 5.13 –Ni–10.0Al–8.5Cr–2.0Ta 2.02 12.6 4.80 5.14


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parallelepipedic c0-precipitates with clearly defined{001} facets, aligned along the elastically soft h001idirections.

� The morphology of the c0-precipitate phase is spheroidalin the as-quenched state and a bimodal particle size distri-bution is apparent. The smaller secondary c0-precipitatesare observed to have an average radius of 6.4 ± 1.1 nmand the larger primary c0-precipitates have radii on theorder of 30–40 nm. A solute-depleted, precipitate-freeshell with a thickness of 5.7 ± 1.1 nm surrounds the pri-mary c0-precipitates. Precipitation modeling employingthe commercial software program PrecipiCalc predictsthat primary and secondary c0-precipitate nucleationbegin at 1380 and 1190 K, respectively. The smaller sec-ondary c0-precipitates are only observed in the as-quenched state and disappear between 0 and 0.25 h ofaging at 1073 K due to coarsening of the primary c0-precipitates.

� The transition from a spheroidal-to-cuboidal morphol-ogy commences at an aging time of 0.25 h, when the pri-mary c0-precipitates have an average radius of61 ± 7 nm. In contrast, the radius at which the micro-structure becomes cuboidal for the base Ni–Al–Cr alloyis estimated to be �88 nm at an aging time of 64 h at1073 K [20]. The addition of 2.0 at.% Ta increases the lat-tice parameter misfit, d, by 78%, from 0.0022 ± 0.0007[20] to 0.0039. This increase in d results in a spheroid-to-cuboid transition that occurs at a smaller c0-precipitateradius and at an earlier aging time than for the base ter-nary Ni–Al–Cr alloys, to minimize the free energy associ-ated with elastic misfit.

� Alignment of primary c0-precipitates into cuboidal andparallelepipedic arrays occurs after 4 h of aging at1073 K for the model Ni–Al–Cr–Ta alloy, while the for-mation of arrays was observed to begin after 64 h forthe base Ni–Al–Cr alloy. The increased lattice parametermisfit due to the addition of Ta leads to alignment at smal-ler primary c0-precipitate radii and earlier aging times inthe Ni–Al–Cr–Ta alloy.

� Aluminum and Ta partition to the c0-precipitates, whileCr and Ni partition to the c-matrix. The strong partition-ing of Ta to the c0-precipitates increases the partitioningof Cr to the c-matrix and ofAl to the c0-precipitates, whencompared to the results of the base Ni–Al–Cr alloy.

� The concentration profiles of the constituent elements ofthe Ni–Al–Cr–Ta alloy across all c0-precipitate/c-matrixinterfaces exhibit an accumulation of Ni on the c-matrixside of the interface. This effect is likely due to the dim-inution of the mobility of Ni in the c-matrix caused bythe addition of Ta, and was not previously observed inalloys with 2.0 at.% additions of W or Re.

� The widths of the concentration profiles across the c0-precipitate/c-matrix interface are observed to decreasewith increasing aging time. Upon aging, the atomic spe-cies with the largest diffusivities in the c-matrix, Al andTa, have the smallest interfacial widths, while the oppo-site is true for Ni and Cr, the slower species.

� For aging times of 1 h and longer, the temporal evolu-tions of the supersaturations of the alloying elementsin the c-matrix and c0-precipitates are observed to followapproximately the t�1=3 prediction of the Umantsev–Olson quasi-stationary state coarsening model.

Acknowledgements

This research was sponsored by the National ScienceFoundation (NSF) under grant DMR-080461. The SEMand TEM studies were performed in the EPIC facility ofthe NUANCE Center at Northwestern University. TheNUANCE Center is supported by NSF-NSEC, NSF-MRSEC, the Keck Foundation, the State of Illinois andNorthwestern University. Atom-probe tomographic mea-surements were performed at the Northwestern UniversityCenter forAtom-ProbeTomography (NUCAPT).ResearchAssistant Professor D. Isheim is kindly thanked for manag-ing NUCAPT. The LEAP� tomograph was purchased andupgraded with funding from the NSF-MRI (DMR0420532) and ONR-DURIP (N00014-0400798 andN00014-0610539).We extend our gratitude toDr. C. Camp-bell of the National Institute of Standards and Technology,Metallurgy Division (Gaithersburg, MD), for diffusivitycalculations, to Dr. C.K. Sudbrack, Dr. K.E. Yoon andDr. M. Nathal for discussions, and to Mr. Y. Zhou,Mr. M. Anderson and Dr. Y. Amouyal for their assistancewith the APT, SEM and TEMwork, respectively. We thankProf. G.B. Olson and Dr. H.-J. Jou of QuesTek LLC(Evanston, IL) for use of PrecipiCalc.

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