Microstructural stability of nanostructured Cu–Nb–W alloysduring high-temperature annealing and irradiation

X. Zhang, N.Q. Vo, P. Bellon ⇑, R.S. Averback

Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, IL 61801, USA

Received 29 December 2010; received in revised form 25 April 2011; accepted 1 May 2011

Available online 27 May 2011

Abstract

The microstructural evolution of dilute Cu-based ternary Cu–Nb alloys during high-temperature annealing was investigated using acombination of transmission electron microscopy, X-ray diffraction and kinetic Monte Carlo (KMC) simulations. The experimentsshowed that, during annealing, the Cu90Nb10 binary alloy undergoes extensive coarsening at 600 �C, with precipitate sizes increasingto >40 nm. Additions of just 1.5 at.% W to this alloy, however, dramatically suppresses the growth; the average precipitate size inthe ternary alloy now increases to only �10 nm at 600 �C, and only to 18 nm at 700 �C. On annealing at still higher temperatures,the precipitate size then, surprisingly, decreases. The precipitate size distribution at the higher temperatures, moreover, is bimodal. Itis also observed that irradiation has no effect on the microstructure of the ternary alloys above 600 �C. KMC simulations indicate thatthe saturation of the average precipitate size, followed by its decrease as the annealing temperature is increased and the development of abimodal size distribution can be explained by competition between thermodynamic and kinetic effects during precipitation in this ternaryalloy.� 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Copper alloys; Precipitation; Transmission electron microscopy; Monte Carlo techniques

1. Introduction

A key to developing radiation-resistant materials foradvanced nuclear systems is providing high densities ofinternal, unbiased sinks and traps for irradiation-induceddefects. One of the difficulties with this strategy has beenmaintaining the high densities of these traps/sinks duringprolonged irradiation, particularly at very high tempera-tures, owing to such processes as radiation-induced (orenhanced) segregation, precipitation and grain growth. Inprevious work [1], it was shown that one method forachieving a stable nanostructure is simply to add highlyinsoluble alloying additions to a nanostructured matrix,particularly those that have low solute diffusivities. It wasdemonstrated, for example, that additions of a few per centMo or W to Cu can stabilize the grain size at �30–40 nm,

and precipitates sizes to <20 nm at temperatures as high as0.65Tm and 0.85Tm, respectively, Tm being the melting tem-perature of Cu.

Other considerations for developing radiation-resistantmaterials are that (i) the alloy must have good properties,such as providing a good sink structure, and (ii) it mustbe readily processed. Because of the extreme immiscibilityof Mo and W in Cu, these refractory metals are difficultto incorporate into Cu at levels of more than a few per cent,even by high-energy methods such as ball milling. The pres-ent work explores the possibility of gaining far greater flex-ibility in the production of radiation-resistant materials,using only small amounts ofMo orW to stabilize the micro-structure of Cu, and then adding a third element to addfunctionality. This first investigation using ternary alloysfor this purpose examines the stability of Cu–Nb–W alloys.Nb was selected for this study because Cu/Nb interfaceshave been shown to provide efficient sinks for point defectsin Cu as well as traps for He gas [2–4]. Previous work

1359-6454/$36.00 � 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

doi:10.1016/j.actamat.2011.05.009

⇑ Corresponding author. Tel.: +1 217 265 0284; fax: +1 217 333 2736.E-mail address: bellon@illinois.edu (P. Bellon).

www.elsevier.com/locate/actamat

Available online at www.sciencedirect.com

Acta Materialia 59 (2011) 5332–5341

showed, however, that Nb precipitates in binary Cu–Nballoys undergo extensive coarsening above �400 �C [5].The present study investigates whether this coarsening canbe suppressed by a small addition of the more refractory ele-ment W. Suppression of precipitate coarsening by additionof a second solute has indeed been observed in other alloysystems, in particular in Al–Sc–Zr [6,7]. Clouet et al. [8]showed that the slower diffusivity of Zr compared with Scin the Al matrix leads to the formation of core–shellAl3(ScxZr1�x) precipitates, which contribute to higher resis-tance to coarsening compared with that of Al3Sc precipi-tates. The present work shows that, by adding just1.5 at.% of W to a Cu90Nb10 alloy, the microstructure ofthe alloy is stabilized to temperatures exceeding 0.8Tm.Moreover, it shows the surprising result that the precipitatesize reaches a maximum during annealing at 750 �C, anddecreases at higher temperatures. Kinetic Monte Carlo(KMC) simulations are presented, which help to rationalizethis experimental observation, based on competitionbetween thermodynamic and kinetic effects.

2. Experimental procedure

Dilute Cu alloy specimens were grown on oxidized Siwafers using a DC magnetron system with three separatesources. Typical film thicknesses were �1.2 lm. The basepressure in the growth system was �2 � 10�8 torr, andthe operating pressure during growth was �2 � 10�3 torrAr. The precise compositions and thicknesses of the alloyfilms were determined after growth using Rutherford back-scattering. All samples were annealed under a pressure of5 � 10�8 torr. A second batch of films, with thicknesses�200 nm, were grown for the irradiation studies. Thesesamples were irradiated with 1.8 MeV Kr+ ions at differenttemperatures; the pressures during irradiation were lessthan �5 � 10�8 torr. The projected range of Kr at1.8 MeV is �300 nm [9], which is more than the thicknessof the film. The deposited damage energy, moreover, isnearly uniform throughout the entire film, increasing by�30% from the front to the back of the film. The beam cur-rent was maintained at �100 nA, which limited beam heat-ing to less than �10 �C, as measured during irradiation.The samples were characterized primarily by X-ray diffrac-tion (XRD), using the Scherrer equation to determine thesizes of the precipitates and Cu grains. Selected sampleswere examined by transmission electron microscopy(TEM) using a JEOL 2010 F microscope, and some addi-tional characterization was performed using a TEM-STEMJEOL 2200 FS aberration-corrected microscope, bothmicroscopes operating at 200 keV.

3. Experimental results

The XRD data shown in Fig. 1 illustrate the strongeffect of W additions on coarsening in Cu alloys. Cu–Nb,Cu–W and Cu–Nb–W alloys were all annealed for�1 � 104 s at �600 �C. Nb in the binary Cu90Nb10 alloy

shows extensive precipitation. Notice that the latticeparameter of the Cu-rich phase attains the value expectedfor pure Cu, while the Nb peak is slightly shifted to largerdiffraction angles. W in the Cu–W alloy, however, showsonly weak precipitation, and the lattice parameter of Cuis dramatically shifted to smaller Bragg angles. The precip-itate peak in the ternary alloy indicates that the Nb precip-itates are not pure, but contain W or possibly Cu. Inaddition, the precipitate size in the ternary alloy appearsto be much smaller than that in the Cu–Nb binary alloy.

The results for precipitate coarsening and grain growthduring thermal annealing at high temperatures are shownin Fig. 2 for a series of Cu–Nb–W alloys. As shown inFig. 2a, Nb and W begin to precipitate at �300 �C, and�600 �C, respectively. Following this precipitation stage,the W precipitate size remains nearly constant, until theannealing temperature is raised an additional 300 �C(0.85Tm), while Nb precipitates grow rapidly above400 �C. If one assumes that the nucleation barrier for pre-cipitation is negligible owing to the very large solute super-saturation, the bulk diffusion coefficient required forprecipitation can be roughly estimated by calculating thetime required for the solute atoms to reach the grainboundaries (note that precipitation takes place both homo-geneously and heterogeneously; see below). Using a sinkstrength of 3p2/L2 for point defect elimination on grainboundaries, where L is the average grain diameter, thecharacteristic time for solute diffusion to grain boundariesis s ¼ L2=3p2D, so the observations of onset of precipita-tion for times of the order of s � 104 s for L � 30 nm yielda solute diffusion coefficient D � 3 � 10�17 cm2 s�1. Thediffusion coefficient of Nb in Cu reaches this value at�400 �C [10]. The diffusion coefficient of W in Cu is notavailable in the literature, but if one assumes that it is sim-ilar to those of refractory solutes such as Ir and Ru [10],one would expect W to begin precipitating at �550 �C.These estimates are thus in good agreement with the exper-imental findings.

The coarsening behaviors of Cu89Nb9.5W1.5 andCu86Nb10W4 are intermediate to Cu90Nb10 and Cu90W10.

Fig. 1. XRD spectra from Cu90Nb10, Cu90W10 and Cu89Nb9.5W1.5

annealed at �600 �C for 1 � 104 s. Dashed lines correspond to (1 1 0)

Bragg peak position for pure Nb and W, and to (1 1 1) peak for pure Cu.

X. Zhang et al. / Acta Materialia 59 (2011) 5332–5341 5333

Both alloys show precipitation by �500 �C, but the sizes ofthe precipitates are very significantly reduced comparedwith those in Cu90Nb10. The precipitates continue to growin both alloys up to �700 �C, at which point they begin toshow an apparent inverse coarsening behavior, i.e., the pre-cipitate sizes decrease with further increase in the annealingtemperature. By �850 �C, the precipitate sizes in thesealloys approach those observed in Cu90W10. It is remark-able that an addition of only �1 at.% W to a Cu–Nb alloysuppresses precipitate coarsening up to �0.82Tm. Fig. 2bshows that the grain size in the Cu matrix is extremely sta-ble for all the alloys during annealing, remaining at�30 nm. For Cu90Nb10, the precipitate size, in fact,becomes as large as, or even larger than, the grain size.

Bright-field TEM images of the Cu89Nb9.5W1.5 alloysthermally annealed at 600 �C and 830 �C are shown inFig. 3. The microstructures look quite similar, as mightbe expected from Fig. 2. Good qualitative agreementbetween the particle sizes deduced from the TEM imagesand XRD is obtained. The TEM images show, however,that many small particles ranging from 1 to 5 nm in sizeare observed at all temperatures, along with larger particles�10–20 nm in size. The ternary alloy thus displays abimodal particle size distribution rather than a lognormal

distribution, which is commonly observed in binary alloysystems. In order to quantify this observation, particle sizehistograms were built from bright-field images, such asthose shown in Fig. 3a and b. Note that, since precipitatesare detected using diffraction contrast, the absolute numberof precipitates cannot be determined, but the percentile sizehistogram, which is the quantity of interest here, can beaccurately measured. Precipitate–matrix interfaces wereoutlined by hand, and ImageJ software was used to gener-ate precipitate area histograms. The minimum precipitatesize detectable with the present method is �2 nm. Thesehistograms were converted to precipitate size histograms,assuming spherical precipitates. More than 350 particleswere measured at each temperature. Fig. 3c displays theparticle-diameter vs cumulative probability, with the axesscaled such that a lognormal distribution would give rise

Fig. 2. (a) Precipitate size vs temperature after thermal annealing in Cu–

Nb, Cu–W and Cu–Nb–W alloys. (b) Grain size vs temperature after

thermal annealing at high temperature in Cu–Nb, Cu–W and Cu–Nb–W

alloys.

Fig. 3. (a) Bright-field image of Cu89Nb9.5W1.5 annealed at 600 �C. (b)

Bright-field image of Cu89Nb9.5W1.5 annealed at 830 �C. (c) Precipitate

size distribution vs cumulative probability for Cu89Nb9.5W1.5 sample

annealed at 600 �C and 830 �C. Axes are scaled so that a lognormal

distribution would produce a straight line.

5334 X. Zhang et al. / Acta Materialia 59 (2011) 5332–5341

to a straight line. Fig. 3c shows that the precipitate size dis-tributions do not fit well to a single lognormal distribution.A good fit could be obtained, however, using two lognor-mal distributions, one for small sizes and one for largesizes, with a transition at �5 nm separating these tworegimes. Similar behavior was observed in the atomisticsimulations, which will be reported in Section 5. It is note-worthy that many of the large precipitates in the samplebecome faceted after annealing at 830 �C, even though theyhave not undergone additional growth >600 �C. The pre-cipitates thus equilibrate locally with the Cu matrix, form-ing lower energy configurations, such as Nishiyama–Wasserman (N–W) or Kurdjumov–Sachs (K–S) interfaces,but without undergoing significant additional coarsening.The TEM analysis also indicated that, while some precipi-tates were located at grain boundaries, many precipitates,in particular the smaller ones, formed inside the matrixgrains.

Dependence of the composition of the precipitates ontheir size was also observed. The smaller precipitates,<5 nm in diameter, tend to be richer in W than the largerprecipitates. Fig. 4a shows a Z-contrast image of some of

the small precipitates in the sample annealed at 830 �C,taken using the aberration-corrected STEM with a probesize of �1 A. The crystallographic structure of these precip-itates can be resolved, confirming that they are body-cen-tered cubic (bcc). These smaller precipitates tend to bebrighter than the larger ones, suggesting a difference incomposition, since the intensity in Z-contrast imagingscales approximately as the square of the average atomicnumber. Energy-dispersive spectroscopy (EDS) wasemployed to investigate this point further. As illustratedin Fig. 4b, the smaller precipitates are indeed richer in W,with a relative W concentration CW/(CW + CNb) of �6–10%, whereas for the larger ones this ratio is much smallerat 1–3%. A more detailed characterization of these precip-itates will be published elsewhere.

In addition to investigation of the microstructural stabil-ity of these Cu-based ternary alloys during thermal anneal-ing, their stability under high dose irradiation was alsostudied. Previously, it had been shown that irradiation ofnanostructured Cu-based alloys has little effect on themicrostructure above �450 �C; this is due to the sharpdecrease in point-defect supersaturation in Cu above thistemperature [5]. Fig. 5 shows that this general finding is alsotrue for the ternary alloys. Here, the average precipitate andgrain sizes of a series of Cu–Nb–W alloys are compared forsamples irradiated with 1.8 MeV Kr ions at 500 �C withsamples annealed at 500 �C, but not irradiated. The irradi-ation dose was �3 � 1016 cm�2, which corresponds to adamage level of �75 displacements per atom (dpa).

4. KMC simulation model

A simple KMC model was used to investigate precipita-tion pathways in immiscible ternary alloy systems, with theaim of elucidating the conditions leading to non-monoto-nous growth of precipitates, as observed experimentallyin Fig. 2 for Cu–Nb–W ternary alloys. This model is anextension of one previously developed for binary alloys[11]. An A–B–C ternary alloy on a rigid lattice with aface-centered-cubic (fcc) structure is considered here. The

Fig. 4. (a) Z-contrast image of bcc precipitates in Cu89Nb9.5W1.5 annealed

at 830 �C; the precipitate near the center of the image is at a {1 1 1} zone

axis. (b) EDS spectra collected from precipitates of three different sizes,

after background subtraction.

Fig. 5. Particle and grain size in ternary Cu–Nb–W alloys as a function of

the relative W concentration, after annealing (solid symbols) or irradiation

(empty symbols) at �500 �C.

X. Zhang et al. / Acta Materialia 59 (2011) 5332–5341 5335

simulation box, built using the rhombohedral primitive cellof the fcc lattice, contains 64 � 64 � 64 lattice sites andemploys periodic boundary conditions. Atomic interac-tions are modeled using pairwise interaction energies eij,with i,j = A,B,C, with the interactions restricted to firstnearest neighbors. The equilibrium phase diagram is fullydetermined by specifying three ordering energies, xAB,xBC, xCA, defined as xij = 2xij � xii � xjj. In alloy systemsforming coherent precipitates with negligible lattice mis-match with the matrix, it is possible to parameterize accu-rately these pairwise interaction energies, in particularusing input data from ab initio calculations, as demon-strated by Mao et al. in the Ni–Al–Cr system [12]. In thepresent case, the goal is not to achieve an accurate param-eterization of the Cu–Nb–W system, which would in factbe quite problematic because of the coexistence of fccand bcc phases, but to capture the thermodynamic andkinetic features that play a key role in precipitation. Inorder to mimic the thermodynamic interactions of theCu–Nb system, the A–B system is given an orderingenergy, xAB ¼ 0:0553 eV , which yields a heat of mixingof 8 kJ mol�1 for the equiatomic composition, and a binarymiscibility gap with critical temperature Tc = 1573 K [13].The A–C system is made highly immiscible, withxAC ¼ 3xAB ¼ 0:1659 eV, to reflect the higher immiscibilityof W in Cu compared with Nb in Cu. The C–C interaction,moreover, has been set �10% stronger than the B–B attrac-tion to reflect the higher cohesive energy of W (�8.9 eV)than Nb (�7.57 eV). The W–Nb phase diagram, of whichonly the high temperature region is experimentally known,indicates that Nb and W form a solid solution, so it wasassumed that Nb and W form an ideal solid solution,xBC = 0. Two compositions are selected, A89B10C1 andA86B10C4, for comparison with the two ternary alloys stud-ied experimentally.

Atomic transport takes place in the model by vacancy–atom exchanges. For this purpose, a single vacancy is intro-duced into the simulation cell, thus resulting in a vacancyconcentration CKMC

V ¼ 1=643 � 3:81� 10�6 . The activa-tion energy for the vacancy to exchange with an X atomfirst nearest neighbor (with X = A, B or C) is calculatedusing a broken bond model.

EVX ¼ ESX �

X

p2nnðvÞ

X

Y¼A;B;C

nVY eVY �X

p2nnðX Þ

X

Z¼A;B;C;V

nXZeXZ ð1Þ

where the summations are performed over the p and q

atoms that are nearest neighbors of V and X, respectively,and nVY and nXY are the number of nearest neighbors oftype Y around the sites occupied by the vacancy and the

X atom, respectively. Note that effective atom–vacancyinteractions are used, so as to distinguish the vacancy for-mation energy from the cohesive energy in the pure metals;details are found in Refs. [11,14]. In Eq. (1), ES

X representsthe contribution of the jumping atom X to the overall sad-dle point energy. Different values for ES

X were used to yieldslow diffusion of the C solute, mimicking the slow diffusionof W in Cu. These saddle point energies are deduced fromthe vacancy migration energies in the A, B, C pure ele-ments. For simplicity, these energies are considered hereto be EB

V ;mig ¼ EBV ;mig ¼ 0:8 eV and EC

V ;mig ¼ 1:8 eV , thusresulting in a much slower diffusion of C atoms comparedwith A and B atoms. Values of parameters used in the sim-ulation are provided in Table 1.

The kinetic evolution of the simulation cell is generatedusing a residence time algorithm to move the vacancy fromsite to site [11,15]. The pre-exponential factor for thevacancy jump frequency is set to 1014 s�1. The KMC timetKMC is scaled to correct for the arbitrarily imposedvacancy concentration. Owing to the possible trapping ofthe vacancy on solute atoms and solute clusters, thevacancy concentration in the pure A-matrix CKMC

V ðAÞ ismonitored during the simulations, and the rescaled timeis given by [16].

t ¼ tKMC CKMCV ðAÞ

CeqV ðAÞ

¼ tKMCCKMCV ðAÞ exp

EformV ðAÞ

kTð2Þ

Precipitation kinetics is analyzed by counting clusters ofsolute atoms. A cluster is defined by a set of B and C soluteatoms connected by at least one first nearest neighborbond. Owing to the very low solubility of A in pure Band C, the possible inclusion of A atoms in these soluteclusters is ignored. The average precipitate size �n refers tothe volume-averaged size, i.e.,

�n ¼X

N tot

i¼1

ni

ntot� ni ð3Þ

where ni is the size of precipitate i, ntot is the total numberof atoms in all precipitates, i.e., N tot ¼

PN tot

i�1ni , and Ntot isthe total number of precipitates.

5. KMC results and analysis

All simulation runs were initiated using a homogeneousA–B–C solid solution. These solutions were then annealedat temperatures ranging from 300 �C to 800 �C until signif-icant precipitation had taken place, as illustrated in Fig 6.The average precipitate size �n as a function of the rescaled

Table 1

Thermokinetic parameters used in the KMC simulations; see text for definition.

eAA (meV) eAV (meV) eBB (meV) eBV (meV) eCC (meV) eCV (meV) eAB (meV) eAC (meV) eBC (meV)

�723 �255 �723 �255 �783 �285 �696 �670 �753

ESA (eV) ES

B (eV) ESC (eV)

�10.217 �10.217 �9.2

5336 X. Zhang et al. / Acta Materialia 59 (2011) 5332–5341

time is plotted in Fig. 7a for four different alloys, A90B10,A90C10, A89B10C1 and A86B10C4, annealed at 500 �C. Ini-tially, they all display exponential growth �n � ta, with theexponent a varying from 0.59 for A90B10 to 0.12 forA90C10; for the ternary systems, a falls in between. Theexponent for the A90B10 alloy is �0.5, which is expectedin the coarsening regime when it is first controlled by coag-ulation, as should be the case for the parameters chosen inthis study [17]. The kinetics for the A90C10 alloy is so slowthat the coarsening regime has not been reached. Precipi-tate growth in the two ternary alloys proceeds initially ata rate similar to that in the A90B10 alloy, but then, quiteremarkably, the average precipitate size reaches a maxi-mum value and then decreases thereafter. The larger theconcentration of C atoms, moreover, the earlier is the onsetof this apparent inverse coarsening. Fig. 7b displays theaverage precipitate size �n as a function of the rescaled timefor A89B10C1 annealed at various temperatures. The expo-nents a at early times are �0.5 for all temperatures. Note,however, that for all temperatures except 300 �C, the aver-age precipitate size reaches a maximum and then decreases(simulations at 300 �C are presumably too short to capturethis effect). Furthermore, the higher the annealing temper-ature, the smaller the precipitate size at the maximum.Fig. 7c displays the linear precipitate size as a function oftemperature for the two binary alloys and the ternary alloy,A89B10C1. The annealing time was t = 5000 s in each case.The precipitate size for the ternary alloy is seen to gothrough a maximum before decreasing at higher tempera-tures. Figs. 6 and 7 present results from one typicalKMC run for each set of simulation parameters; using

averages over several runs smears the maximum, as thetime for precipitate size saturation varies from run torun. The characteristic behaviors observed in Figs. 6 and7, however, are observed in other runs performed at thesame temperatures. KMC simulations, with suitable ther-modynamic and kinetic parameters, thus reproduce theremarkable behavior observed experimentally in Cu–Nb–W alloys reported in Fig. 2a.

Fig. 6. Typical microstructures at the end of the simulations for A89B10C1

alloy annealed at (a) 500 �C, (b) 800 �C. B and C atoms are displayed as

dark gray (blue online) and light gray (yellow online) spheres, respectively,

and A atoms are omitted. (For interpretation of the references to colour in

this figure legend, the reader is referred to the web version of this article.)

Fig. 7. Average precipitate volume (a) as a function of rescaled time for

four different alloys, A90B10, A90C10, A89B10C1, A86B10C4 annealed at

T = 500 �C; (b) as a function of rescaled time for A89B10C1 annealed at

five different temperatures, 300 �C, 400 �C, 500 �C, 600 �C, 800 �C; (c)

linear precipitate size as a function of annealing temperature for A90B10,

A90C10 and A89B10C1 annealed for t = 5000 s.

X. Zhang et al. / Acta Materialia 59 (2011) 5332–5341 5337

Additional simulations were performed with the sameparameters, except that either the A–C immiscibility waschosen to be the same as that for A–B, i.e.xAC ¼ xAB, orthe solute C was made more mobile by assigning identicalatom saddle point energies to B and C solute atoms,ESC ¼ ES

B. In these cases, the simulations did not yieldapparent inverse coarsening, but rather a monotonousgrowth and coarsening of precipitates. It is thus concludedthat, for apparent inverse coarsening to take place, the Csolute atoms must be (i) more immiscible with A atomsthan the B solute atoms, and (ii) significantly less mobilethan B atoms in the A matrix.

In order to better understand the origin of the saturationand decrease in precipitate size in the KMC simulations,the chemical compositions of the solute clusters were ana-lyzed as a function of the size of the clusters at varioustimes during the precipitation sequence. It was found thatthe first clusters that form are almost pure B clusters. Theseclusters grow in size until a second population of clustersstarts to form, with their compositions enriched in C sol-ute. At the time that the average precipitate size hasreached its maximum value during annealing of theA89B10C1 alloy at 500 �C, the large precipitates contain �3 at.% C atoms, while the small clusters contain �18 at.%C atoms, as shown in Fig. 8. Moreover, the formation ofthese C-rich clusters is accompanied by a decrease in theB solubility below the equilibrium B solubility limit ofthe A–B alloy system, as shown in Fig. 9. The B-atom sol-ubility in the ternary alloys is estimated from the totalnumber of B atoms found in clusters containing fewer thanfive B atoms (similar solubility values are obtained with athreshold size of 10). For comparison, the equilibrium sol-ubility of the A–B alloy system has been calculated sepa-rately using semi-grand canonical simulations.

Based on these simulation results, the following explana-tion is proposed for the saturation and decrease in averageprecipitate size in the ternary alloy systems investigatedhere. The first stage of precipitation in these dilute ternaryalloys is essentially identical to the precipitation kinetics

in the corresponding A–B binary alloys. The C atoms areboth too few and too sluggish to influence the precipitationkinetics (for instance, at 500 �C, the diffusivity of C solute inA calculated using the five-frequency model [18], is threeorders of magnitude slower than that of the B solute). Thesefirst precipitates, however, have a composition far from thatexpected at equilibrium, as they are highly depleted in Catoms. Once the diffusion length of C atoms becomes suffi-cient for these atoms to meet and react with each other, newC-rich clusters form in the matrix. These new clusters alsocontain a significant number of B atoms, owing to the com-plete mutual solubility of the B and C atoms. The B atomsintegrated into these new clusters are drawn from the B insolution in the matrix, leading to a local depletion of Bbelow its solubility limit. The depletion thus leads to aneffective flux of B atoms from large B-rich precipitates tothe newly forming C-rich precipitates. Shrinkage of largeB-rich precipitates leads to an overall decrease in the aver-age precipitate size. It is anticipated that the first-formedprecipitates will eventually dissolve completely, and the C-rich clusters will evolve into larger precipitates, with compo-sition approaching that dictated by equilibrium.

In addition to the decrease in the average precipitatesize, a key feature of the novel precipitation behavior inthese dilute ternary alloys is that the precipitate size distri-bution deviates significantly from that observed in binaryalloys. In the latter case, this size distribution is welldescribed by a lognormal distribution, as illustrated inFig. 10a. In the case of the ternary alloys that display atransient maximum and shrinkage of the average precipi-tate size, the precipitate distribution deviates significantlyfrom lognormal, with an excess of large precipitates (seeFig. 10b). Note that the initial plateau in Fig. 10b is dueto the use of a threshold size, here 10 atoms, in identifyingprecipitates. The bimodality observed in the ternary alloyin the simulation is similar to that observed in the experi-ments in Cu–W–Nb alloys (see Fig. 3c).

6. Discussion and conclusions

Thiswork showed that the addition of small amounts ofWto Cu90Nb10 alloys has dramatic effects on the precipitation

Fig. 8. Number of C atoms contained in a precipitate as a function of

precipitate size, for alloy A89B10C1 annealed at 500 �C for �1600 s. Note

the difference in composition (given by slope) between small and large

precipitates.

Fig. 9. Relationship between the solubility of B atoms and the number of

B atoms in the biggest precipitate during annealing of A89B10C1 at 500 �C.

The dashed line is the equilibrium B solubility limit in the A–B system.

5338 X. Zhang et al. / Acta Materialia 59 (2011) 5332–5341

kinetics and grain size stability during thermal annealing andduring ion irradiation at elevated temperature. In particular,the precipitate sizes attained during annealing ofCu89Nb9.5W1.5 and Cu86Nb10W4 >500 �C remain below�20 nm, in contrast to the rapid precipitate growth observedin Cu90Nb10 at these temperatures (see Fig. 2a). This firsteffect of addingWtoCu90Nb10 is, perhaps, not too surprising,since the precipitation kinetics for these ternary alloys areintermediate between those of Cu90Nb10 and Cu90W10. Moreremarkable in these ternaries is that the average precipitatesize reaches a maximum with annealing temperature at�500 �C, then decreases as the temperature is increased to830 �C. Furthermore, in that second regime, two size popula-tions of precipitates are observed by TEM, as illustrated inFig. 3a and b, leading to precipitate size distributions thatdeviate from a lognormal distribution (see Fig. 3c). Thisbimodal distribution suggests that a different mechanismfor precipitate growth and coarsening is taking place in theternary alloys.

Precipitation kinetics in a ternary alloy such as Cu–Nb–W can in fact be complex, since the driving force for precip-itation is larger for W than for Nb, owing to the higherimmiscibility of W with Cu, but the kinetics is faster forNb than for W, owing to its faster diffusion in Cu. Thiscompetition between driving force and kinetics wasexplored by KMC simulations, and it was observed that,for a range of thermokinetic parameters reproducing these

competing effects, the average precipitate size reached for afixed time saturates and then decreases as the annealingtemperature is increased, as exemplified in Fig. 7. In thatregime, the precipitate size distribution deviates from a log-normal distribution, with an excess of large precipitates(see Fig. 10), as observed in the experiments (see Fig. 3c).

The detailed analysis of the precipitate composition as afunction of size and of the amount of solute atoms left insolution clearly illustrates the origin of this complex precip-itation kinetics. In the early annealing stages, only B sol-utes have sufficient mobility to participate in theprecipitation reaction, leading to the formation of almostpure B precipitates. This first population of precipitatesgrows and coarsens as if precipitation was proceeding inan A90B10 binary alloy, leading to the decrease in the Batoms left in solution. In a true binary alloy, this B solubil-ity would level off once it reached the curvature-dependentconcentration dictated by local equilibrium with precipi-tates (Gibbs–Thomson effect). In a second stage, the mobil-ity of C solute atoms has become sufficient for these atomsto form new precipitates in the matrix, which then competewith the first-formed and almost pure B precipitates. Thecharacteristic time for the start of this second stage canbe estimated by setting the C diffusion length equal to theaverage separation distance between C atoms. Indeed, oncenearest-neighbor pairs of C atoms have formed, B atomsbind very effectively to them, as this binding energy,220 meV for the present simulation parameters, is well inexcess of kT. For a C concentration of 1 at.%, the initialaverage separation distance between C atoms is

�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

3� 100=ð16pÞ3p

a � 3:6a , where a is the fcc lattice

parameter. The C solute diffusion in a pure A matrix DAC

is estimated using the five-frequency model, yielding valuesof 1.1 � 10�2 a2 s�1 at 500 �C, and 2.9 � 102 a2 s�1 800 �C.Equating the average separation distance to the diffusion

length, 3:6a ¼ffiffiffiffiffiffiffiffiffiffi

6DACt

q

, predicts times of the onset of pre-

cipitation size saturation of 2 � 102 s at 500 �C and7.6 � 10�3 s at 800 �C. These values agree well with theKMC simulations (see Fig. 7b). Note, however, that withthis simple analysis, increasing the C concentration from1 at.% to 4 at.% should only reduce the saturation onsettime by �42/3�2.5, whereas a larger reduction is measuredin the simulations (Fig. 7a). This larger effect suggests that,for high solute concentration, the nucleation of C-rich pre-cipitates may involve C clusters already present in a ran-dom configuration, possibly assisted by B atoms. Lastly,it is not surprising that this second population of precipi-tates is enriched in C atoms compared with the nominalC/(B + C) relative composition, as shown in Fig. 8, sincethese precipitates form in a matrix that is significantlydepleted in B atoms. Overall, this two-stage precipitationnaturally results in a bimodal distribution for the precipi-tate size.

The consequence of this two-stage precipitation is that itleads to the saturation and then the decrease in the average

Fig. 10. Cumulative precipitate size distribution during annealing at

500 �C for (a) a binary A90B10 alloy (annealing time 4 s), and (b) a ternary

A89B10C1 (annealing time 1450 s). Axes are scaled so that a lognormal

distribution yields a straight line (solid lines are fit to data).

X. Zhang et al. / Acta Materialia 59 (2011) 5332–5341 5339

precipitate size. The average precipitate size decreasespartly because new small precipitates are forming, but thiscontribution is negligible when using the volume-averageprecipitate size defined by Eq. (3), and as employed inFig. 7. The more important contribution comes from anactual shrinkage of the large B-rich precipitates. Thisshrinkage results from the depletion of the matrix in B sol-utes, below its local solubility limit. The large B-rich pre-cipitates are then thermodynamically constrained to emitB atoms to replenish the matrix, but these B atoms areincorporated into the smaller C-rich precipitates, whichhave a larger driving force for precipitation owing to theirlarger C concentration. As a result, for an appropriatebalance between these competing precipitation rates, thevolume-averaged precipitate size can shrink, either asannealing time increases at a fixed temperature, or as tem-perature is increased for a constant annealing time.

The formation of metastable phases during the earlystages of precipitation from supersaturated solid solutionsis observed in many alloy systems [19]: for instance Gui-nier–Preston zones in Al alloys. The transient existence ofthese metastable phases can be seen as examples of Ost-wald’s ‘rule of stages’ [20–22]. High nucleation barriersoften hinder the formation of the equilibrium phase. In thiscase, the formation of equilibrium precipitates, accompa-nied by the progressive dissolution of metastable ones,requires very long isothermal annealing. An example of thissituation is the formation of the equilibrium d phase in Al–Li, after the homogeneous precipitation of the metastablecoherent d0 phase [23]. The dissolution of the metastablephase can also take place during up-quench, that is, agingat a temperature exceeding the stability limit of this phase.In this case, precipitates re-dissolve, a process also referredto as reversion or retrogression [19]. This process can beemployed to optimize microstructures and mechanicalproperties; see, for instance. Refs. [24,25]. In contrast tothese previous works, the effects reported here do not resultfrom a higher nucleation barrier for the precipitation of theequilibrium phase over the metastable phase, nor do theyresult from an up-quench heat treatment. In the simula-tions, the slower diffusivity of the C solute atoms, combinedwith their larger driving force for precipitation, leads to thegrowth, saturation and dissolution of metastable precipi-tates. This result is similar to those reported by Gendtet al. [26], using KMC simulations to model homogeneousprecipitation kinetics in Fe–Nb–C. In these studies, the fastinterstitial diffusion of carbon atoms leads to the transientformation of a metastable Fe carbide, FeC, in these simula-tions, owing to the simplicity of the model, before precipita-tion of the more stable NbC phase. The transient formationof cementite has in fact been reported recently by Mulhol-land and Seidman, who studied the competition betweenformation of Fe carbide andM2C (M = Cr,Mo, Fe, Ti) sec-ondary carbides during annealing of the BA 160 high-strength low-carbon steel [27].

In the Cu–Nb–W alloys studied in the present work,grain boundaries are likely to play an important role,

enhancing diffusion and providing nucleation sites for pre-cipitation. These effects are not included in the present gen-eric KMC simulations, which employ a single crystallinerigid lattice. The same competition between thermody-namic driving force and kinetics observed in the simula-tions can, however, take place in the presence of grainboundaries. This competition has been studied by Hinet al. [28,29] for the Fe–Nb–C system. These authorsextended the KMC simulations of Gendt et al. [26] byintroducing in the simulation cell extended sinks andsources for defects such as grain boundaries and disloca-tions. At low supersaturation, heterogeneous precipitationdominated, and metastable Fe carbide precipitates did notform. At high supersaturation, however, both heteroge-neous and homogeneous precipitation took place, and thetransient formation of a metastable Fe carbide wasobserved. These results suggest that the main results ofthe simulations should be applicable to highly supersatu-rated Cu–Nb–W alloys, where both heterogeneous andhomogeneous precipitation were observed. In addition,note that a competition between heterogeneous and homo-geneous precipitation can lead to bimodal precipitate sizedistributions, but this competition alone would notaccount for a variation in precipitate composition withsize, as reported above for Cu–Nb–W. The difference insolute mobility is a required condition for reproducing suchcomposition dependence, and this is fully consistent withthe KMC results of Hin et al. [29].

In addition to its effect on precipitate size, W alloyinghas a strong effect on grain size. Fig. 2b shows that grainsizes �30 nm are retained after annealing at temperaturesup to 830 �C, which corresponds to 82% of the meltingpoint of Cu. Moreover, for all Cu–Nb–W compositionsinvestigated here, this strong suppression of grain growthpersists under ion irradiation at 500 �C up to large irradia-tion doses �75 dpa, as illustrated in Fig. 5. The presentfindings thus offer a very effective way to stabilize grain sizeat the nanoscale at very high temperatures and under irra-diation. This small grain size is especially beneficial for irra-diation at large doses, as grain boundaries and precipitate/matrix boundaries may provide effective sinks for pointdefects and traps for He atoms [30], thus suppressing detri-mental effects promoted by long-range transport of pointdefects and atoms, such as swelling and irradiation-inducedsegregation and precipitation.

In conclusion, it was observed that small additions of Wcan dramatically suppress precipitation and grain growthin Cu–Nb alloys. Precipitate sizes remain <20 nm and grainsize <30 nm in Cu89Nb9.5W1.5 during annealing up to830 �C. Moreover, during isochronal annealing, the aver-age precipitate size first increases with temperature, butthen saturates and decreases as the annealing temperatureis further increased. KMC simulations of precipitation inmodel A–B–C ternary alloys reproduce these experimentalfindings when the C alloying element (W in the experi-ments) is more immiscible, but also a less mobile speciesthan the B alloying element (Nb in the experiments). The

5340 X. Zhang et al. / Acta Materialia 59 (2011) 5332–5341

resulting kinetic competition between B and C precipita-tion leads first to the formation of metastable B-rich pre-cipitates, until the mobility of C atoms becomes sufficientfor a second population of precipitates to form, leadingto an apparent inverse coarsening of the B-rich precipi-tates. It is also shown that Cu–Nb–W alloys can retaintheir small grain size during ion irradiation at large doses(75 dpa) at elevated temperatures, here 500 �C. The presentfindings can thus assist in the development of nanograinedmaterials which could operate at elevated temperatures andin harsh irradiation environments [30].

Acknowledgements

This research was supported by the US DOE-BES underGrant DEFG02-05ER46217 (supporting NQV) and by theNSF under Grant DMR 08-04615 (supporting XZ). Thework was carried out in part in the Frederick Seitz Materi-als Research Laboratory Central Facilities, University ofIllinois, which are partially supported by the USDepartment of Energy under grants DE-FG02-07ER46453 and DE-FG02-07ER46471. The authors thankDr J.G. Wen for his assistance with aberration-correctedTEM characterization.

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