Effect of solute segregation on thermal creep in dilute nanocyrstalline Cu alloys

Materials Science and Engineering A 546 (2012) 307 313

Contents lists available at SciVerse ScienceDirect

Materials Science and Engineering A

jo ur n al hom epage: www.elsev ier .co

Effect o n d

Jonathan bera Technische Un almodb Racah Instituc Department o IL, US

a r t i c l

Article history:Received 20 JaReceived in reAccepted 8 MaAvailable onlin

Keywords:CreepNanocrystallinGrain boundarGrain boundarMolecular dyn

erma usinechnie dilutrain.

at a dariehemgh, 3

atomothern dis

1. Introduction

The mecand alloys aent high strhas been demechanicalpered by thavailable tothem actingmechanismremained lia nc materiathat the detiments or smaterials torent undersmetals [6,7,ics (MD) simetals and characteriz

The effeinterest, bu

CorresponE-mail add

solutes have been used to prevent grain growth in nc metals[1012], as it is known that solutes can decrease GB energies and

0921-5093/$ http://dx.doi.ohanical properties of nanocrystalline (nc) metals [1]re of great technological interest owing to their inher-ength and reasonable ductility [2]. While much workvoted to understanding the mechanism controlling the

properties of these materials, this effort has been ham-e large number of potential deformation mechanisms

these systems, and with the possibility of some of in synergistic ways [3]. Attempts to create deformation

maps have been made [4], but their transferability hasmited since grain size alone is not sufcient to describel of a given composition. It is now known, for example,ails of simply preparing these systems, either by exper-imulation [5], matter greatly in the response of these

applied stresses. Recent reviews summarize our cur-tanding of the mechanical behavior of nanocrystalline5], much of which has derived from molecular dynam-mulations. For low temperature deformation of puresimple alloys, MD has indeed been able to identify ande the active deformation mechanisms [8,7,9,6].cts of solutes on the properties of nc metals are also oft currently they are poorly understood. Experimentally,

ding author. Tel.: +49 6151 166318; fax: +49 6151 166335.ress: [email protected] (J. Schfer).

thereby reduce the driving force for grain growth. This effect hasalso been observed in MD simulations [1316]. The introductionof solutes also affects the mechanical properties of the materialas demonstrated by experiment and simulation [1719], wherestudies on segregating solutes show a signicant enhancement inthe strength of the nc material [20]. Related to grain growth andstrength is the question of diffusional creep, which has receivedmuch less attention in nc materials despite its obvious implicationsfor the use of these materials at elevated temperatures. For exam-ple, it is still uncertain whether GB diffusion processes in pure ncCu contribute to deformation at low homologous temperatures,T/Tm < 0.3 [21]. In this regard, it has been demonstrated that purenc Cu (about 28 nm grain size) can be elongated to more than5000% at room temperature without strain hardening, suggestingGB-based mechanisms are indeed operative [2,6]. Several studieshave shown further that creep rates in nc metals are proportionalto d3 [22] or d2 [23], suggesting Coble or Nabarro-Herring creepbehavior [24,25]. Other results, however, report a creep resistanceorders of magnitude higher than Coble creep [26,27]. Meyers et al.suggest that contamination of the GB with impurities suppressesgrain-boundary sliding and thus explains these differences [6]. Forexample, interstitial dopants (Boron in Nickel) have been shownto signicantly enhance the creep resistance of nc materials [28].

Only few studies on creep in nc-structures using MD simu-lation have been reported, largely due the limited time-scales

see front matter 2012 Elsevier B.V. All rights reserved.rg/10.1016/j.msea.2012.03.078f solute segregation on thermal creep i

Schfera,, Yinon Ashkenazyb,c, Karsten Albea, Roiversitt Darmstadt, Fachbereich Material- und Geowissenschaften, Fachgebiet Materi

te of Physics, Hebrew University of Jerusalem, Jerusalem, Israelf Materials Science and Engineering, University of Illinois, Urbana Champaign, Urbana,

e i n f o

nuary 2012vised form 7 March 2012rch 2012e 29 March 2012

e materialsy structurey segregationamics

a b s t r a c t

The effect of solute segregation on thwas studied at elevated temperaturesand molecular dynamics simulation ting solutes. Then the creep rates of thcomposition, load and accumulated sinitially with strain, but then saturatelocating the solute in the grain bounary volume and energy with added cenergy for creep was anomalously hidependence is found to correlate withnanocrystalline Cu alloys containing scales with their atomic volumes whem/locate /msea

ilute nanocyrstalline Cu alloys

t S Averbackc

ellierung, Petersenstr. 32, D-64287 Darmstadt, Germany

A

l creep in dilute nanocrystalline alloys (CuNb, CuFe, CuZr)g molecular dynamics simulations. A combined Monte-Carloque was rst used to equilibrate the distribution of segregat-ted Cu samples were measured as functions of temperature,

In CuNb samples, the creep rates were observed to increasevalue close to that obtained for alloys prepared by randomlys. This behavior is attributed to an increase in grain bound-ical disorder. At high temperatures, the apparent activation

eV, but only 0.3 eV at lower temperatures. This temperatureic mobilities in bulk CuNb glasses. Calculations of creep in

solutes, Fe and Zr, show that the suppression of creep ratesolved in Cu.

2012 Elsevier B.V. All rights reserved.

308 J. Schfer et al. / Materials Science and Engineering A 546 (2012) 307 313

accessible by these simulations. It has been shown, nevertheless,that diffusional creep in these materials can be simulated via MDsimulations if sufciently high temperatures are employed [23].While this requirement is a severe limitation, such simulationscan still bethis work, wsolutes on talloys (Cuthis study husing a hybsolute atomwhen solutplacing it rlowered. Wof free voluand thereforeduction owhen the somatrix. Theat high straand the crebehavior is compositiohigh-tempe

The papcedure, preequilibratiowith respecial compresinterplay bebehavior, ethe last sectalline Cu alcompositio

2. Method

2.1. Alloyin

Dilute nMD/MC simations, thersame time [by a semi-was constrmixing. Forinteratomic[33], respecviously appnc structurlimited mistional Montensemble. Fof the constment distribswitching athus evolvewas implemcode.

2.2. Sample

The MDent amounnanocrystal

of pure Cu was created by the Voronoi tessellation method [36]with an average grain sizes of 8 nm. Center points of grains, andthe grain orientations were randomly selected in a cubic simula-tion box. Relaxation of the structure and alloying were performed

K ovsen al exrial erage.e a

t semase de cheverthed o

of on th

howt obsd to n Cusis oen thserve

niaxi

ples0.86u (aratio

al comf 105

low ownaint

ults

arac

r relere

omphed 40], wyed t

a de the

graihesting graintion graintch b

amo with

diluttionse numr sys

total NG useful for examining different creep mechanisms. Ine employ such an approach to examine the effect of

he macroscopic creep compliance of various dilute CuNb, CuFe, CuZr), focusing on CuNb. The samples inave an average grain size of 8 nm. Solute is introducedrid MD/Monte-Carlo (MD/MC) scheme, which locatess on energetically favorable sites [29]. We show thate is introduced in this manner, as compared to simplyandomly in GBs, the creep compliance is dramaticallye suggest that this reduction is caused by the removalme in the GB (or similarly, lowering of the GB energy)re to a lowering of the mobility of GB atoms. Thef free volume by this method is found most effectivelutes have a large size mismatch when dissolved in the

study also shows that when the nc alloy is deformedin rates, the GB structure is driven out of equilibriumep compliance increases. We show further that thissimilar to that observed in bulk metallic glass of similarns and suggest that amorphous-like GBs underly therature creep behavior.er is structured as follows: First the simulation pro-paration of the nanocrystalline samples and theirn are described. These samples are then characterizedt to solute distribution and creep response to uniax-sive loading at elevated temperatures. We discuss thetween the state of GB relaxation and the observed creepnabling identication of the controlling parameters. Intion, we relate the creep behavior of dilute nanocrys-loys with that of bulk amorphous alloys having the samen as the grain boundaries of nc samples.

ology

g

anocrystalline alloys were modeled using a hybridulation method that accounts for structural relax-

mal vibrations and the exchange of atom types at the30]. The description of the atomic interactions is givenempirical EAM-type potential for CuNb [31], whichucted in part, to reproduce the large, positive heat of

comparison, CuFr and CuZr were simulated using potentials by Mendelev et al. [32] and Ludwig et al.tively. The MD/MC simulation scheme has been pre-lied to model the equilibrium element distribution ines for miscible PdAu alloys [29] as well as alloys ofcibility [34,20]. Part of this technique is a transmuta-e-Carlo scheme that samples the semi-grandcanonicalor a xed chemical potential difference = Nb Cuituents, it nds the equilibrium concentration and ele-ution in a given structure. Structural relaxation during

tomic identities is obtained by MD steps. The system isd by cycling between MD and MC steps. The MC schemeented into the framework of the LAMMPS [35] MD

preparation

/MC scheme just described was used to locate differ-ts of solute at energetically favored positions in theline structure as follows: First, a nanocrystalline model

at 500BerendMC tri5000 ton avethe samcurrenthe phand thWe nea desirvaluesregionphase,was noresponof Nb iemphabetwethe ob

2.3. U

Sam0.4 to pure CDeformuniaxiorder owell be(not shwere m

3. Res

3.1. Ch

Aftetures wlocal ctinguis(CSP) [emplonext topart ofand itsthe hig(accordto the inspecin the mismalargestoccurs

Forsimulaand th in ou

= (Eer a period of 1 ns at zero hydrostatic pressure using a[37] thermostat and barostat. During this MD run, anchange was carried out on each atom every 200 fs, i.e.,xchanges were performed on each atom in the system

The temperature for the Metropolis MC algorithm wass for the MD part. Without additional constraints, thei-grandcanonical MC cannot treat two-phase regions iniagram, where the relation between the concentrationmical potential difference has an innite slope [38].eless started from pure Cu and adjusted such thatverall composition was obtained during alloying. The were not necessarily restricted to the single phasee equilibrium phase diagram. Precipitation of a secondever, which requires to overcome a nucleation barrier,erved. The reported concentrations, therefore, may cor-oversaturated solid solutions, exceeding the solubility. This metastability, however, does not affect the mainf the presented work, which is to establish a connectione relaxation and/or segregation state of the GBs withd macroscopic creep behavior.

al testing

were deformed at various temperatures (ranging from Tm), where Tm denotes the melting temperature ofound 1290 K for the interatomic potential used here).n was carried out in most simulations using a constantpressive stress, 500 MPa. This led to strain rates on theto 108 s1. The applied stress, although high, remained

the yield stresses of the nc Cu alloys, which exceed 1 GPa). The stresses perpendicular to the compression axisained near zero.

terization of the nc structures

axation and the introduction of solutes, the model struc- analyzed with respect to the solute distribution andositions. Atoms located in grain boundaries were dis-from bulk atoms using the centrosymmetry-parameterhich is a measure of the local lattice disorder and can be

o detect, whether an atom is part of the perfect lattice orfect or surface. The inset of Fig. 1 shows a slice throughcomputational cell, highlighting a representative grainn boundaries following equilibration of the system with

concentration of solute. Gray markers show GB atomsto CSP), white markers correspond to atoms belonging

interior, and red markers represent Nb atoms. Visualclearly illustrates that virtually all solutes are located

boundaries, which is expected due to the large sizeetween Cu and Nb. Fig. 1 also shows that even for theunt of introduced Nb, no signicant clustering of Nbin the grain boundaries.e solid solutions, Millett et al. [14] reported, using MD, a linear relation between the grain boundary energyber of segregated solutes. We quantify the GB energy

tems at 0 K according to,

ESC)

B(1)

J. Schfer et al. / Materials Science and Engineering A 546 (2012) 307 313 309

Fig. 1. Atomicposition. Insetafter equilibraresponding to the centrosymgray corresponNb atoms are interpretationto the web ver

where Etotacell with thtalline specof atoms instructure wlibrated andGB widths, area. Fig. 1 swith solutelett et al. [140 for the hithe GB enerof the refereis dramaticshows a simvolume V

Vat = (Vto

where Vtotalis the volumcrystal of idthe numberwith increaenergy and a further inand the GB

3.2. Creep b

Studyingat high temIn previousby the micpresent woboundarieswith three-grains of va

hermPa foa for tpectivical ptationeb ver

allotion wrese

in Fne wd th

itial s ini

rateso othith h

precatesuous

wit excess volume (green) and GB energy (red) at 0 K as a function of com-: cross-section of a grain and its surrounding GBs and triple junctionstion and the introduction of solutes for 8.3 at.% of Nb in the GBs (cor-1.9 at.% global concentration). The gradient gray scale corresponds tometry-parameter (a measure of the local lattice disorder) where lightds to 0 (grain interior) and dark gray to 5 (highly distorted regions).

highlighted in red. Snapshots were generated using OVITO [39]. (For of the references to color in this gure legend, the reader is referredsion of the article.)

l is the total potential energy, ESC is the energy of ae same number of atoms contained in a single crys-imen of identical composition, and NGB is the number

the GB according to CSP. (The single crystal referenceas prepared as a random solid solution, thermally equi-

quenched to 0 K.) Under the assumption of constant is proportional to the GB energy, as dened per unithows that the grain boundary energy decreases linearly

concentration, in agreement with the ndings of Mil-]. Noteworthy is that the GB energy falls slightly below

ghest amount of introduced Nb. The absolute value ofgy, however, depends on its denition and the choicence system. It shows, nevertheless, that the GB energy

Fig. 2. Tof 500 M(The datpink, resin spherinterpreto the w

tests tocentra

Repshowntions, oGBs, anThe insamplestrain the twalloy wtion ofcreep rcontinsampleally reduced by the segregation of Nb to GBs. Fig. 1 alsoilar dependence on composition for the atomic excess

at,

tal VSC)N

, (2)

is the total volume of the system at its current state, VSCe of the same number of atoms contained in a single

entical composition at the same temperature, and N is of atoms. The free volume in the GBs thus decreasessing content of Nb in the GBs. The observation that bothvolume decrease linearly with concentration in Fig. 1 isdication that no signicant precipitation is taking placeremains homogeneous.

ehavior inuence of solutes

diffusional creep in nc materials by MD simulationsperatures requires suppression of grain growth [23].

studies on pure metals, grain growth was suppressedrostructural design of the structure [41,42,23]. In therk, we rely solely on the solute introduced into the grain

for this purpose [13], and thus we could study systemsdimensional microstructures with randomly orientedrying size. Our procedure, however, limited the creep

follows. At tion is unliNabarro-Hesize and (ii)

Fig. 3(a)Cu6.4 at.%observed toeral behavicommon tocase of pureto the elimtion of mobirreversiblein Fig. 3(a),method, aftThe observeorder and ththan alterination of crerate after reof creep rat

Fig. 3(b)position atstrongly redtion to largal creep: Strain as a function of time at 0.8 Tm and a uniaxial loadr different compositions. The initial elastic response is not shown.he samples with 5.0 and 8.3% of Nb in the GB are shown in blue andely.) Pure Cu (red) and a structure, where the solutes were positionedrecipitates in the quadruple nodes (green) serve as references. (For

of the references to color in this gure legend, the reader is referredsion of the article.)

ys with Nb concentrations greater than 3 at.% local con-ithin the grain boundary.

ntative strain versus time curves at constant load areig. 2 for four different samples: two with solute addi-ith Nb precipitates added to the quadruple nodes of thee last, for pure Cu. The load in each case was 500 MPa.elastic response is not shown. The strain for all of thetially increases approximately linearly with time. The

in the two alloy samples are noticeably smaller than iner samples, and the reduction is seen to be larger for theigher concentration. It is noteworthy that the introduc-ipitates into the GBs appears to have little effect on the, but this was not studied in detail. For larger strains a

transition to higher creep rates is most evident for theh 5.3% Nb. This will be discussed in more detail in whatthis point, however, we can already state this transi-kely associated with grain growth, since (i) Coble andrring creep rates both decrease with increasing grain no grain growth was observed. shows the creep rate as a function of strain for the

Nb alloy at different temperatures. The creep rates are increase signicantly with temperature, but the gen-or of an increasing creep rate with increased strain is

all samples. A similar behavior was observed for the nc Pd [42], but in this case the transition was attributedination of triple junctions and the associated forma-ile dislocations. In the present study the possibility of

structural changes can be ruled out since, as shown re-equilibration of the local chemistry by the MD/MCer deformation, returns the creep rate to its initial value.d transition is thus caused by by creating chemical dis-us by driving the system from local equilibrium, ratherg microstructural features. It is noteworthy, that relax-eped samples by MD alone has little effect on the creep-loading, which provides additional that the variationes is related to chemical disordering.

shows the dependence of creep rate on the alloy com- 0.84 Tm. Increasing the Nb concentration in the GBsuces the initial creep rate. Similar to Fig. 3(a), a transi-er creep rates with increased strain can be observed.


Fig. 3. Tempefor an uniaxia6.4% Nb in the MD/MC schemtion is plottedand a uniaxialstates (equilibrate as a funccolor in this g

For referentures wherGBs and noples underwincluding induction of short-rangeing that thethe solute ia strain of method to trature and equilibration effects: (a) Creep rate as a function of strainl load of 500 MPa and different temperatures for the structure withGB. For one case (0.82 Tm), the structure was re-equilibrated using thee after a strain of 6%. The subsequent creep rate following equilibra-

as a blue dashed line. (b) Creep rate as a function of strain at 0.84 Tm load of 500 MPa for different compositions and different relaxationrated by MD/MC or not equilibrated (n.e.)). (c) Observed initial creeption of testing temperature. (For interpretation of the references toure legend, the reader is referred to the web version of the article.)

ce, Fig. 3(b) additionally shows creep data for struc-e solutes were introduced at random positions in thet equilibrated using the MD/MC algorithm. (These sam-ent otherwise identical treatments as the MD/MC ones,itial equilibration by MD for 1 ns at 500 K.) The intro-Nb at random positions does not provide chemical

order, and thus leads to larger creep rates. It is interest- creep rate (i) is insensitive to solute concentration whens not located in equilibrium sites and (ii) requires only4% to convert the samples prepared with the MC/MDhe non-equilibrated state. As we will show later, most

Fig. 4. GB moity of the Nb temperatures of the fractionto neighboringdata for differ

of the soluta strain of 4

Fig. 3(c)temperaturdependencthree alloysperature dethe apparen

3.3. Atomic

In previtemperaturcreep [42]. CuNb alloduring straerence framstudy sinceof the sampplacement

Ri = [xi(t +where x is center of mtively. No aundergo relobserved tolocation moSince virtuthese atomcient. Thermquenching puting Ri. Inthan half oplacementsthe NN disthe barrier tent with th(not shownwhere a strundergoing(200 ps) anvarious conferent stagebility controlling deformation: Creep rate as a function of the mobil-atoms in the grain boundary, for different compositions, differentand different relaxation states. The mobility is measured in terms

of Nb atoms which underwent a relative displacement with respect Nb atoms, which exceeded half of the NN distance. (For clarity, the

ent compositions is not shown independently.)

e atoms have moved at least one atomic distance after%.

shows the dependence of the initial creep rate one for three of the MD/MC alloys. The same generale of initial creep rate on temperature is observed for the. Clearly seen, however, is a strong change in the tem-pendence in going from low to high temperatures, witht activation energy increasing from 0.3 eV to 3 eV.

mobility in the GBs and GB excess volume

ous work on pure nc Pd, it was shown that high-e deformation takes place by GB diffusional (Coble)We examined the deformation mode in the present ncys by monitoring the relative displacements of atomsining. Relative atomic motion, i.e., the Lagrangian ref-e, is convenient for measuring diffusion in the present

it avoids complications arising from the change in shapele. Similar to Ref. [43], we thus dene the relative dis-vector Ri by

t) xi(t)] [xCOM(t + t) xCOM(t)], (3)the position vector and i and COM label atom i and theass of the neighbors of atom i at the time t, respec-toms located in the grain interiors were observed toative motion with neighbors; only atoms in the GBs are move. This excludes Nabarro-Herring creep and dis-tion as potential contributors to plastic deformation.

ally all Nb atoms are located in the GBs we use onlys, for convenience, to obtain the GB diffusion coef-al noise in the displacement vectors was suppressed by

the structures to 0 K after each time interval before com- addition, we excluded relative displacements smaller

f the rst nearest-neighbor (NN) distance to avoid dis- arising from local relaxations. The threshold of halftance was chosen for this purpose because it reectsfor diffusional atomic displacements, and it is consis-e observed minima in the histogram of displacements). The results of these calculation are presented in Fig. 4,ong correlation is found between the fraction of atoms

relative displacements during a xed time step td the measured creep rates. Remarkably, the data forcentrations, different temperatures, and even for dif-s of excitation follow on the same trend. The data thus


Fig. 5. Correladisplacement atomic excess is dened as thof identical costructure equilibrated (blue,between the frexcess volumethis gure lege

clearly illuswithin the thus focus oin GBs.

Previousfusion and between GBthis latter reatoms withdistance anan initially relationshipdisplacemerelationshiptures and thrandom poVat or GBnd the simfusion to GB

DGB = DL ex

ransfe for d

andtively

voluion e].Fig. 6. T500 MPa

DGBrespecarea toactivat[46,47tion to excess volume: (a) Fraction of atoms undergoing a relativeexceeding rst nearest neighbor distances (lines with symbols) andvolume (lines) as a function of time, where the atomic excess volumee difference in average atomic volume as compared to a single crystalmposition at the same temperature (see text). Shown is the data for alibrated by MD/MC (green, red) and a structure which was not equi-

pink) with 6.4 and 5.2% of Nb in the GB, respectively. (b) Correlationaction of atoms undergoing a diffusive displacement and the atomic

for the two data sets. (For interpretation of the references to color innd, the reader is referred to the web version of the article.)

trate that creep indeed derives from atomic motionGBs. To better understand the creep mechanism, weur attention on the effect of solutes on atomic mobility

studies have revealed a relationship between GB dif-GB energy [44]. A similar connection can also be found

diffusion and excess volume (Eq. 2), and we examinelationship here. In Fig. 5, we plot both the fraction of Nb

relative displacements larger than the next-neighbord the excess atomic volume as functions of time forrandom and an equilibrated solute distribution. A clear

between Vat and the number of atoms undergoingnts (t = 200 ps) is observed as shown in Fig. 5(b). This

holds, moreover, for both the fully equilibrated struc-e structures where the solute atoms were inserted at

sitions. While a correlation between GB diffusion and energy is found during creep deformation, we do notple relationship reported by Gupta [44] linking GB dif-

energy, namely the so called Borisov model [45], where

p(

RT

). (4)

3.4. Transfe

We calcuof ncCu towere produabove, start

Fig. 6 shofor 3 differedissolved incorrespondreproducedvolume as ohand, has afcc Cu matrreduce the rable to thaestablishingparameter CuFe, but creep rateson solute sitent with thby atomic m

3.5. Atomis

A detailduring creerelaxation, ments or byfollows. Firthan half thdow were iof those atoet al. [48], lective if thanother moindependen(top) or collthe simulatrability: Strain as a function of time at 0.82 Tm and an uniaxial load ofifferent material systems. (Pure Cu is shown as a reference.)

DL refer to the GB and lattice diffusion coefcients,, is the GB energy, and is a constant relating the GBme. Notice also that at high temperatures, the apparentnergy is larger than lattice diffusion in Cu (2.032.09 eV)

rability to other Cu alloys

lated the effect of other solutes on the creep properties further test the role of excess volume. These samplesced following the same simulation scheme as describeding from identical initial ncCu congurations.ws the compressive strain as function of time at 0.82Tmnt ncCu alloys and pure ncCu as a reference. Zr, when

fcc Cu has an atomic volume of 1.8 Cu, where Cus to the atomic volume of Cu in a fcc single crystal as

by the potential [32]. This is a similarly large atomicbserved for Nb in fcc Cu (2.1 Cu) [31]. Fe, on the other

comparable atomic volume as Cu, when dissolved in aix (1.2 Cu) [33]. The Zr solutes are observed to greatlycreep rate in ncCu, a factor of 5, which is compa-t of the Nb solutes. Fe has a much reduced effect, thus

atomic volume when dissolved in the matrix as a keyin suppressing GB diffusion. In the cases of pure Cu andnot CuZr and CuNb, we observe in addition to high, severe grain growth. This dependence of grain growthze agrees with previous MD studies [14] and it is consis-e idea that grain growth and creep are both controlledobility in GBs.tic mechanisms

ed examination of the atomic motion within the GBsp deformation reveals that depending on the state of GBatomic motion occurred either as independent displace-

collective motion. We distinguish these two modes asst, all atoms (independent of their type) moving moree nearest neighbor distance within a 200 ps time win-dentied as a function of time. The nature of movementms was then analyzed, following an approach by Donatiwhere atomic motion is considered stringlike or col-e former position of a moving particle is occupied bybile particle. Otherwise the motion was consideredt. Fig. 7 identies those atoms undergoing independentective (bottom) motion in a representative slice throughion cell at different stages of deformation. The sample


Fig. 7. Atomis ation at T = 0.84 Tm. The upper line shows the atoms, which underwent anindependent d ctive displacement where the number of involved atoms was larger thantwo. (The disp

in this gurtially equiliof deformatin the GBs o2 ns, howevis observedatoms havethe system tribution bycontributio

These npublished ptions that sdynamics oThese authwas very siming these obgrain boundlimit, a regalso employin bulk metcooperativehighly excitthe atomic These ndinin nanocrysnounced insystem is dvolume in t

We furthin GBs in thparing the cprepared bytion and ththe same Mresponse ofthen obtainpressive loa

nc aius p

nc a low

just empe

nclu

he prolutC algd poof ttic mechanisms: Cross-sections through the structures at different stages of deformisplacement. The lower line shows the atoms which underwent a string-like collelacements occurred during a xed time interval of 200 ps.)

e contained 6.4% Nb, was simulated at 0.84 Tm and ini-brated by the MC/MD method. During the initial stagesion, while the sample is still well equilibrated, transportccurs predominantly by collective motion of atoms. Byer, a clear shift to an independent displacement mode. From Fig. 5, it is seen that after 2 ns 50% of the Nb

moved. Thus, during straining at elevated temperature,is driven out of the well equilibrated state and the con-

independent displacements greatly increases, with then from collective motion becoming insignicant.dings can be understood in terms of several recentlyapers. Zhang et al. [49,50] showed by MD simula-

tring-like cooperative motion is a regular feature of thef structurally relaxed GBs (in nc Ni at 0.480.86 T ).

of the Arrhenent forhigh toThis isglass t

3.6. Co

In tof Nb sMD/Mfavoregrains m

ors noted, moreover, that the dynamics of GB motionilar to that found in supercooled liquids. Complement-

servations, Nagamanasa et al. report glassy dynamics ataries in colloidal crystals also for the zero-driving forceime inaccessible by MD [51]. In another study, whiched MD simulations [52], Ritter and Albe showed thatallic glasses (BMGs) below Tg, diffusion occurred by a

motion of atoms, if the glasses were well relaxed. Ined regions, on the other hand, e.g., within shear bands,motion occurred rather by individual displacements.gs are thus consistent with the present results for GBstals, where string-like cooperative motion is most pro-

the initial, well equilibrated state. During straining, theriven from this low-energy state, increasing the freehe GBs and thus allowing for individual displacements.er explored this similarity between the atomic motione nc CuNb alloys and CuNb metallic glasses by com-reep behavior in these materials. The metallic glass was

rst quenching pure liquid Cu to 50 K where equilibra-e introduction of solutes was carried out for 1 ns usingD/MC scheme as employed for the nc material. The creep

the resulting structure, which contained 7 at.% Nb, wased as a function of temperature using a uniaxial com-d of 100 MPa. The results comparing the creep behavior

driving forccases corre

Fig. 8. Compaalloys: Initial and a nanocryperatures. (Foreader is refernd amorphous CuNb alloys are shown in Fig. 8 in anlot. While the apparent activation energies are differ-nd amorphous alloys, they both show a transition from

values as the temperature is reduced below 0.50.7 Tm.the temperature regime that we nd using MD for therature, Tg, of this alloy.

sions and summary

esent work, we used MD simulations to study the effecte on thermal creep in nc Cu structures. Using a hybridorithm, the solutes were introduced at energeticallysitions. No Nb was therefore introduced within thehe nc structure, consistent with the thermodynamic

e for segregation. The amount of solutes may in somespond to an oversaturated solid solution where the

rison of initial creep rates in amorphous and nanocrystalline CuNbcreep rates of an amorphous CuNb alloy (bulk metallic glass, blue)stalline CuNb alloy (green) of similar composition for various tem-r interpretation of the references to color in this gure legend, thered to the web version of the article.)


precipitation of a second phase was suppressed by the barrier offorming a nucleus of critical size. One outcome of adding Nb soluteis that it stabilizes the structures against grain growth, allowingfor the treatment of a system consisting of grains of varying sizeand shape. The GB energy of the CuNb samples was shown todecrease linearly with Nb concentration, in agreement with earlierstudies. Thea vanishingat various observed. Tfurthermorin creep ratof grain groobserve forapplied uniwhich is higcreep tests that the apstudied ma

Monitortion of soluresults in ation to highstructures wpositions wto the introdDeformatioguration oa random d

Apparenexternal loalibrated staredistributifavored conbetween thcreep rate cthe overall nism to lowvolume. Intreduce the ing in a highdeformatio

Comparirial systemson the sizesolutes of dof nc metal

Regardinin the GBs oilarities betof similar cowell equilibmotion of sis found if tThis is similrial, where as the systeanism of aton the localis consistenmobility in rials [50]. Aof the obserlining the s

Acknowledgements

Financial support for this project was provided by DeutscheForschungsgemeinschaft through FOR714. One of us (JS) has beensupported by DAAD for his visiting stay at UIUC. Grants of computertime were received from Forschungszentrum Jlich. Research at

as ses un

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leiteru, M.Leissmamak04) 43. Moha. Mey

. KumchiotzWolf, 05) 1Gunth838eissm

Detor. Mille. Mille. Mille

Detorang, Yter. 56. Rajga001 (. Rajgao, J. S11) 66onradai, Q.Pamak. Waneng, 352. Sandct. Ma. Nie. Yin

chaferadigh10).. Dem. MenLudwi998) aro, D-634 limpt. VoroC. Berm. Phrhart,tukow. Kelcheblins

Haslater. 52. Chanupta,orisouper412aier,onati

t. 80 (hang,hang,09) 77. Nag.A. 108itter, highest concentration of Nb solutes corresponded to GB energy. During testing under uniaxial compressionelevated temperatures, no severe grain growth washis is consistent with a fairly reduced GB energy. It ise consistent with the observed trend for the transitione, where we nd an increasing creep rate. For the casewth, we would expect a decreasing trend, which we do

pure nc Cu, where grain growth occurs. For all tests, theaxial stress was in the range between 100 and 500 MPah as compared to the stresses applied in experimentalat elevated temperatures. We could, however, excludeplied stresses exceed the yield or ow stress of theterial at the given temperatures.ing the resulting creep rates revealed that the introduc-tes at favored positions and the successive relaxation

drastically reduced creep rate followed by a transi-er creep rates as deformation proceeds. Comparison toere the segregating solutes were introduced at random

ithin the GB proofed, that the lowered creep rate is dueuction of the solutes at energetically favored positions.

n of the samples therefore destroys the low energy con-f the GB and a transition towards the creep behavior ofistribution is observed as deformation proceeds.tly, straining at elevated temperature under a highd drives the GB conguration away from the well equi-te where the MD timescale is not sufcient to allow aon of solutes and relaxation to obtain the energeticallyguration by diffusional processes. A strong correlatione mobility of the atoms within the GB and the observedould proof that the introduction of solutes can lowermobility of the atoms located in the GB. The mecha-er the mobility in the GB is the reduction of the freeroducing solutes at energetically favored positions canfree volume and increase the density of the GB, result-er creep resistance and resistance to low temperature

n as demonstrated elsewhere [20].son of the observed creep behavior for different mate-

could show, that the magnitude of the effect depends of the solutes in the matrix. Therefore, segregatingiffering size can drastically inuence the creep behaviors by reducing the free volume in the GB.g the atomistic processes, allowing for mass transportf this nc material, we found that there are strong sim-ween the nc structures and bulk amorphous materialmposition. We demonstrated that the displacement inrated grain boundaries occurs as string-like collectiveeveral atoms while a transition to single displacementshe system is driven out of the well-equilibrated state.ar to the observations made for bulk amorphous mate-string-like collective motion also occurs, but vanishesm is disturbed (e.g., in a shear band) [52]. The mech-omic transport therefore depends in a similar manner

relaxation for both, GBs in nc material and BMGs. Thist with observations regarding the similarity betweenglass-forming liquids and GBs in single phase nc mate-dditionally, we nd a similar temperature dependenceved creep rates for nc and amorphous material, under-imilarities.

UIUC wScienc

Refere

[1] H. G[2] L. L[3] J. W[4] V. Y

(20[5] F.A[6] M.A[7] K.S[8] J. S[9] D.

(20[10] B.

833[11] J. W[12] A.J.[13] P.C[14] P.C[15] P.C[16] A.J.[17] S. J

Ma[18] R.K

055[19] R.K[20] N. V

(20[21] H. C[22] B. C[23] V. Y[24] D.L[25] J. D

349[26] P.G

tru[27] G.W[28] W.M[29] J. S[30] B. S

(20[31] M.J[32] M.I[33] M.

6 (1[34] A. C

633[35] S. P[36] G.Z[37] H.J.

Che[38] P. E[39] A. S[40] C.L[41] P. K[42] A.J.

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(20[51] K.H

U.S[52] Y. Rupported by the US Department of Energy, Basic Energyder grant DEFG02-05ER46217.

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Effect of solute segregation on thermal creep in dilute nanocyrstalline Cu alloys1 Introduction2 Methodology2.1 Alloying2.2 Sample preparation2.3 Uniaxial testing

3 Results3.1 Characterization of the nc structures3.2 Creep behavior influence of solutes3.3 Atomic mobility in the GBs and GB excess volume3.4 Transferability to other Cu alloys3.5 Atomistic mechanisms3.6 Conclusions and summary

AcknowledgementsReferences

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Effect of solute segregation on thermal creep in dilute nanocyrstalline Cu alloys