The role of annealing twins during recrystallization of Cu

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Acta Materialia 55 (2007) 4233–4241

The role of annealing twins during recrystallization of Cu

D.P. Field a,*, L.T. Bradford a,1, M.M. Nowell b, T.M. Lillo c

a Washington State University, P.O. Box 642920, Pullman, WA 99164-2920, USAb EDAX/TSL, 392 E. 12300 Street, Draper, UT 84020, USA

c Idaho National Laboratory, Idaho Falls, ID, USA

Received 17 November 2006; received in revised form 15 March 2007; accepted 17 March 2007Available online 15 May 2007

Abstract

The texture and grain boundary structure of recrystallized materials are dependent upon the character of the deformed matrix and theselective nucleation and growth of crystallites from the deformation structure. Annealing twin boundary formation in materials of low tomedium stacking fault energy is not only a product of the recrystallized structure, but also plays an important role in the recrystallizationprocess itself. In situ and ex situ recrystallization experiments were performed on pure copper (99.99% pure) previously deformed by equalchannel angular extrusion. Intermittent characterization of the structure on the surface of bulk specimens was accomplished using electronbackscatter diffraction. The character of the structure where nucleation preferentially occurs is presumed to be in heavily deformed regionsas nuclei were first observed in such microstructures as viewed from the specimen surface. Grain growth is observed to be heavily depen-dent upon twinning processes at the low temperatures used for in situ experiments, with twinning occurring to aid the recrystallizationprocess. It is shown at these temperatures that the slowest growing grains obtain the highest fraction of twin boundaries as the new twinorientations presumably increase the boundary energy at positions where there is insufficient driving force to continue growth.� 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Copper; Recrystallization; EBSD; ECAE; Twin boundaries

1. Introduction

The microstructures that evolve during recrystallizationof deformed polycrystals are dependent upon the characterof the deformed matrix (including stored energy contentand local chemistry), the orientation relationship betweenthe deformed structure and the growing grains, and theannealing temperature and ambient conditions. Of primaryimportance in this process are the local and neighboringlattice orientations and the dislocation density distribution.In low stacking fault energy materials, annealing twinsdevelop that complicate the recrystallization process. Thetwinned structure generally alters the energy and mobilityof a mobile interface, thereby either enhancing or retarding

1359-6454/$30.00 � 2007 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2007.03.021

* Corresponding author. Tel.: +1 509 335 3524.E-mail address: [email protected] (D.P. Field).

1 Present address: Boeing Commercial Airplanes, Seattle, Washington98124, USA.

the growth of a given orientation [1]. Many researchershave investigated the recrystallization process and havedescribed oriented nucleation and oriented growth andtheir impact on the evolving microstructures [1–4]. Theeffects of annealing twinning on recrystallization textureand the resulting grain boundary character distributionhave also been described [5–8]. Since texture and grainboundary structure affect various properties of polycrystal-line metals, it is important to better understand thesestructures.

Many researchers have demonstrated that materialswith a high fraction of certain ‘‘special’’ types of bound-aries exhibit superior ductility, corrosion resistance, frac-ture toughness, etc. The coincident site lattice (CSL)model [9] is the most common analysis used to identifysuch boundaries. Since the suggestion of grain boundarydesign by Watanabe in 1984 [10], grain boundary engineer-ing (GBE) has been a topic of much research and debate.The promotion of twin boundaries in grain boundary

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4234 D.P. Field et al. / Acta Materialia 55 (2007) 4233–4241

engineered materials of medium to low stacking faultenergy is typically important as it tends to lower the overallenergy of the interface network, albeit indirectly [10–16].One thermomechanical process that leads to high fractionsof twin boundaries in the microstructures of annealedmaterials with moderate to low stacking fault energies con-sists of small plastic deformations followed by annealingtreatments, a process known as strain annealing or strainrecrystallization. The relatively low energy in the system(from the low plastic strain level) motivates annealing twinsto form preferentially, thereby improving certain materialproperties [15,16]. The core idea behind GBE is to increasethe mechanical, chemical and/or electrical performance ofa material by increasing the fraction of special boundariespresent in the microstructure. Special boundaries aredefined simply as those with superior properties for a givenapplication and will vary from one material to the next andfrom one application to another. Grain boundary engi-neered fcc metals with low to moderate stacking fault ener-gies tend to have a preponderance of annealing twinboundaries up to a limiting value dictated by the twin-lim-ited microstructure described by Palumbo et al. [11]. Asindicated in reviews by Aust [12] and later by Randle[13], the role of twin boundaries in GBE is likely indirect,but the twins are often necessary in ultimately obtainingthe desired properties. Fullman and Fisher [14] speculatedover 50 years ago that one driving force for annealing twinboundary development was to reduce the overall boundaryenergy of the system. For these reasons, there has been con-siderable effort to design processes that promote twinboundaries, with strain annealing (or strain recrystalliza-tion) proving to be an effective GBE tool [15,16]. Triplejunctions and the grain boundary network play a majorrole in the determination of grain boundary statistics [17].It is actually this overall boundary network and the spatialarrangement of grain boundaries (including percolation ofspecial boundaries) that control boundary specific materialbehavior.

With GBE having a potentially large impact on materialproperties, research into the mechanisms of twin boundaryformation continues to be important. The objective of thepresent work was to observe in situ the recrystallizationof heavily deformed pure copper and to identify mecha-nisms of both nucleation and growth processes to theextent possible. This has led to a better understanding ofannealing twin boundary formation and twin-dominatedstructure evolution during recrystallization of these heavilydeformed microstructures.

2. Experimental procedures

Oxygen free, high-conductivity (OFHC) copper billets(99.99% pure) were deformed by a four-pass equal channelangular extrusion (ECAE, also referred to as ECAP) pro-cess using the B processing route (90� rotation betweendeformation passes) [18,19]. The cross-sectional area ofthe billets was 25 · 25 mm2 and specimens were machined

from only the center part of the billets. Samples �2 mmin thickness with areal dimensions of 10 · 5 mm2 or10 · 10 mm2 were cut using a slow-speed diamond sawwith liberal application of lubricant for cooling. Each spec-imen was cold-mounted into a quick drying acrylic epoxyto prevent any structural changes in the sample while cur-ing. The copper samples were ground and mechanicallypolished up to 0.02 lm colloidal silica on a vibratory pol-isher and then removed from their mounts.

Electron backscatter diffraction (EBSD) patterns andautomated scans were obtained in a Schottkey field emis-sion source scanning electron microscope (SEM) usingstandard procedures. Several in situ recrystallization exper-iments were performed using a heating stage designed spe-cifically for in situ EBSD analysis. Some of the highertemperature recrystallization experiments were performedby ex situ EBSD subsequent to salt bath annealing fol-lowed by water quenching. Thermocouples were positionedagainst the sample surfaces in the heating stage for thein situ experiments to monitor heat treating temperatures.Since the sample thickness was small and conductivity ofthe specimens high, only a negligible temperature gradientwas assumed to exist in the specimens during heating. Tem-peratures of 155, 160, 165, 170 and 175 �C were used forin situ analysis and 200 and 400 �C for ex situ experiments.For the in situ experiments the time to reach the specifiedtemperature was �3–5 min, while the salt bath anneals pre-sumably brought the specimens to the desired temperatureswithin a second or so. Temperature of the salt bath solu-tions was controlled to within ±1 �C, while the in situexperiments were performed at constant temperature towithin ±3 �C after the initial heating period. The EBSDanalyses for the ex situ specimens were performed on thesurface of the specimens so as to obtain a reasonable com-parison with those samples annealed in the SEM chamber.Specimens were later sectioned and polished to comparethe bulk structure with that of the surface regions. Theaverage grain diameter of internal sections was smallerthan that observed on the surface, but the twin boundarycontent was similar to that observed on the surface.

Orientation imaging scans were collected from an anal-ysis area of �18 · 18 lm2 for the in situ analysis and�80 · 80 lm2 for specimens analyzed at room temperature.The scans were made over a regular hexagonal grid using astep size of 0.2 lm. EBSD patterns were collected over eachanalysis area at rates of �70 patterns per second for thein situ experiments yielding scan times of 2–3 min per scan.Therefore, EBSD images were essentially collected every3 min during annealing to monitor the recrystallizationprocess. This rapid scan rate was necessary for the recrys-tallization process to be accurately observed. At tempera-tures above �170 �C, the recrystallization rate was toofast for in situ observation by EBSD, so the salt bathanneals were employed. Fiducial marks were made on thespecimen surface of each sample to ensure that the EBSDscans were made on the same region of the specimen sur-face for the initial scan and all subsequent scans. Due to

D.P. Field et al. / Acta Materialia 55 (2007) 4233–4241 4235

drift while the SEM stage temperature achieved equilib-rium, the samples were repositioned to the correct analysisposition before each scan. This re-positioning requiredimage correction of as much as 1 lm for the first scans athigh temperature, but rapidly equilibrated to where virtu-ally no re-positioning was required between subsequentscans. This process of repeated imaging was continueduntil recrystallization neared completion for all samples.

In the interpretation of the data, we assumed that theimages provide a snapshot in time of the true structure,so analysis of a single image yields the fraction recrystal-lized at that given time. In reality, there is approximatelya 2 min time difference between the top of the EBSD imageand the bottom of the image for the specimens annealedin situ. For the low annealing temperatures used, this rela-tively small amount of time is presumed to be insignificant.

3. Results and analysis

3.1. The deformed microstructure

Two representative EBSD orientation maps of thedeformed, polycrystalline copper specimen are shown inFig. 1. These images were taken from a cross-sectionthrough the ECAE billet where the output extrusion direc-tion was aligned normal to the specimen surface. Care wastaken to analyze only the center portion of the billets, thusavoiding end effects and irregularities near the surfaces.The shading indicates the pole orientation with respect tothe sample surface normal direction. Dark regions indicatea {100} pole aligned normal to the specimen surface withprogressively lighter shading to 45� away from {100}. Thedeformed microstructures contained a high component ofgeometrically necessary dislocations (GNDs, or excess dis-location content), as determined by EBSD data [20–22].These are the dislocations that exist in the microstructureto account for the curvature of the crystallite lattice. Thegradient in shading seen in the images of Fig. 1 is an indi-

Fig. 1. EBSD orientation maps of the deformed microstructures, such that darincreasingly lighter shading to 45� away from {100}. Boundaries are indicate

cation of this dislocation content. Of course, the informa-tion obtained from a single plane EBSD scan necessarilyretrieves only the components of the curvature tensor relat-ing to the directions of the specimen lying in the sectionplane analyzed. The curvature changes in the normal direc-tion are neglected only because there is no informationobtained in that direction. The relationship between thedislocation density tensor, a, and the lattice curvature, j,was given by Nye [23] as

aij ¼ jij � dijjjj ð1ÞThe lattice curvature is defined simply as the gradient in therotation of the lattice, or

jij ¼d/i

dxjð2Þ

with /i indicating the angular rotation about an axis ofdirection i. In more direct terms, the dislocation densitytensor is given in terms of individual orientation measure-ments by

aij ¼ eiklgjl;k ð3Þ

where g is the direction cosine matrix that rotates the refer-ence, or specimen, coordinate frame into that defined bythe crystallite lattice. The dislocation density tensor is alsodefined directly by

a ¼XK

k¼1

qk bk � zk� �

ð4Þ

where qk is the dislocation density for dislocations of type k

for all K possible dislocation types. The Burgers vector isgiven by band the dislocation line direction by z. Disloca-tion densities are then obtained by equating the right-handside of Eq. (3) with the right-hand side of Eq. (4) using theminimum possible combination of dislocation densities. Amore complete discussion of this method is found in thework of Sun et al. [20].

k regions have the {100} pole aligned normal to the specimen surface withd for misorientations >10�.


A proper analysis of excess dislocation content wouldrequire three-dimensional information not available fromsingle plane sections such as those observed in the presentstudy. In addition, it is presumed that a grain boundaryexists at locations for which misorientation angles greaterthan 15� between neighboring measurements are observed.The GND density is determined with the assumption of nocurvature across the boundary for these positions. Theoverall average GND density of the heavily deformedmicrostructures determined by this technique was justunder 1015/m2. Fig. 2 contains a map of the excess disloca-tion content for the sample shown in Fig. 1a. This particu-lar sample was later annealed at �155 �C. The numbers inFig. 2, labeled in bold on the image, indicate the regionswhere recrystallization nuclei were first observed. It isassumed that nucleation typically took place below theobservation surface and that the structure surroundingthe nuclei as it appears on the surface is only an estimateof that where nucleation took place. In some instances anew grain would first appear as two or more islands thatlater coalesced into a crystallite of a single orientation mak-ing it apparent that the grain was growing up to the surfacefrom a single nucleus that originated below the plane ofobservation. For our purposes the microstructure justbelow the surface is assumed to be similar to that observedon the surface in terms of excess dislocation density. There-fore, it could be presumed that nucleation occurred inregions of relatively high GND density as determined fromthe EBSD data. It should be noted that using the excessdislocation content to describe the dislocation density givesno information on the statistically stored component of thedislocation structure. It is assumed in this study that theGND component scales somewhat to the statisticallystored component of the dislocation structure for thesespecimens. Some evidence in support of this assumptionhas been observed in lightly deformed aluminum alloys[24].

Fig. 2. Excess dislocation density map from the region shown in theorientation image of Fig. 1a.

3.2. Annealing microstructure and recrystallization kinetics

Fig. 3 contains several EBSD orientation maps of themicrostructure of the sample annealed at 155 �C obtainedin situ during the heating stage recrystallization experi-ments. These images were created from the EBSD datausing thin lines to characterize low angle grain boundaries(1–10� misorientations) and thicker lines to characterizehigh angle grain boundaries (>10�). The development andmigration of the high angle grain boundaries is evident inthe maps as the growing grains sweep into regions of highdislocation density while new grains and annealing twinsform. The area fraction of recrystallized grains in each ofthe samples was determined from the measure of grain ori-entation spread (GOS). The GOS can only be used todetermine the fraction of recrystallized structure if thegrain definition parameters are selected properly. In thiscase, a grain was defined by a minimum misorientationangle of 5� and the minimum grain size was set to 10 con-tiguous measurement points. GOS is given by the followingequation:

GOS ¼ 1

N

�XN

A¼1

min cos�1trace gave higAð Þ�1

h i� 1

2

0@

1A

24

35

8<:

9=;ð5Þ

where A indicates the Ath measurement point in a grainconsisting of N measurements, gave is the average orienta-tion of the grain, gA is the orientation measured at theAth position within the grain and hi is the appropriate sym-metry element yielding the minimum misorientation anglebetween the average orientation and the Ath measurement.In essence, the GOS is the average difference in orientationbetween the average grain orientation and all measure-ments within a single grain. This value usually increasesfor increasingly deformed microstructures, but is smallfor recrystallized grains since it is simply the noise or uncer-tainty in the EBSD orientation determination (�0.5�).There is essentially no step size dependence for the GOSparameter as long as there are several measurements withinthe grain, making it a nice measure to use in determiningthe fraction of recrystallized structure. Analysis of the par-tially recrystallized structures indicated two well-separatedpeaks for the GOS value of grains that were recrystallizedand free from dislocation structure as compared with thosefrom deformed grains. A criterion of 2� or less was used forthe GOS tolerance to indicate a recrystallized grain, butanything from �1� to 3� gives similar results for thesestructures.

Using the definition that recrystallized grains have aGOS value <2�, the kinetics of the recrystallization processwere determined and are shown in the standard fractionrecrystallized vs. log time plot shown in Fig. 4 for all tem-peratures except 400 �C, where there were not enough data

Fig. 3. Orientation images of the sample during several stages of recrystallization while at a temperature of 155 �C. Low angle grain boundaries (1–10�)are shown as thin lines, with high angle boundaries shown as thick lines.

Fig. 4. Recrystallization kinetics for various temperatures as measuredusing the GOS parameter.


points to reliably retrieve the recrystallization kinetics. Attemperatures of 170 and 175 �C, recrystallization had sig-nificantly progressed before the first elevated temperatureEBSD map could be obtained for the in situ experiments.The data in the regions where the recrystallization fractionsapproach unity can be reasonably ignored because theGOS parameter will always slightly underestimate therecrystallization fraction due to the quality of the data.For example, positions of low confidence EBSD data, suchas those around the fiducial marks on the specimen sur-faces, are ignored in the GOS calculation, but are includedin the overall area determination. Thus, complete recrystal-lization will not be observed using this measure. The dataobtained are reasonably regular, however, and typical sig-moidal recrystallization curves are retrieved. There are no

error bars shown on the data since each point indicatedwas obtained from a single set of EBSD data. For all ofthe in situ measurements, the observation area is reason-ably small, and is not necessarily representative of therecrystallization kinetics in heavily deformed pure copper.Compared with experimental results from the literature,however, it appears that the kinetic data shown here arereasonable for recrystallization of pure copper [1,25–27].

3.3. Observation of annealing twin boundary development

A preponderance of boundaries with twin type misorien-tation relationships, R3n, was observed in all recrystallizedstructures regardless of annealing temperature. The aver-age number of twin grains within a parent grain was calcu-lated by determining the number of grains in the regionboth including and excluding twin boundaries as definingindividual grains. The quotient of these values gives theaverage number of twin grains for each parent grain. Thegrain definitions for this calculation defined a grain usinga 5� minimum misorientation angle and a minimum grainsize of 10 measurement points. The twin boundaries thatwere excluded in the calculation of the numerator wereboth R3 and R9 boundary types to within a tolerance of3�. Table 1 shows the relationship between the averagenumber of twins per grain vs. annealing temperature oncerecrystallization was near completion. In this analysis,grains were defined using a misorientation angle of 5�and twins were not included as separate grains. It is evidentfrom these data that the number of twins that developedper grain generally increased as the annealing temperaturedecreased. These numbers were obtained from EBSD data

Table 1The average number of twins per grain for each temperature when thespecimens were at near-complete recrystallization

Temperature(�C)

Twins pergrain

Average grainsize(twins aregrains) (lm)

Twin length per unitarea (lm�1)

155 6.4 2.4 1.62160 4.9 2.6 1.76165 5.0 2.3 1.47170 3.6 2.2 1.03175 4.8 1.8 1.08200 4.3 1.9 1.11400 3.2 2.2 0.86


obtained over larger regions than those observed in situ,with �80 · 80 lm2 images obtained. The 400 �C scans cov-ered �200 · 200 lm2 in an attempt to include roughly thesame number of grains for each annealing temperature.The data show a reasonably consistent trend, with theexception of the specimen annealed in situ at 170 �C. Eventhe specimens annealed in the salt baths appear to follow

Fig. 5. Boundary image sequence showing the development of a ‘‘new’’ graistagnated. The large arrow indicates the first apparent position of the twin nucposition of a twin boundary with the same crystallite lattice orientation as the

the same trend, even though the recovery before recrystal-lization must have been much more prevalent in the sam-ples annealed in situ. Also shown in Table 1 is the totaltwin boundary length per unit area observed on the planesections. A similar trend is observed where more twinboundary length per unit area is seen at the lower anneal-ing temperatures. Another interesting observation is thatgrain size generally decreases with increasing annealingtemperature for twin grains being defined as individualgrains. This may occur because the higher temperatureanneals were performed by rapidly heating the specimen,thereby restricting the amount of recovery that wouldoccur. The higher temperatures would also provide ahigher driving force for nucleation so the growing grainswould impinge upon one another at a smaller grain size.At lower temperatures, fewer nuclei would form becausethe structure was allowed to recover at lower temperaturesbefore reaching the final recrystallization temperature. Itshould be pointed out that the grain sizes shown in Table1 are not the equilibrium grain sizes for the temperaturesgiven, only the grain sizes at the completion, or near com-pletion, of recrystallization. Grain sizes of similar copper

n nucleated from a twin that emanated from a grain whose growth hadleus that grows into a new grain. The A with the small arrow indicates the

new grain indicated.


specimens after annealing at various temperatures arereported elsewhere [28,29].

During recrystallization it was often observed that whenthe growth of grains became stagnant, annealing twinswould form so that growth could resume. When growthstagnation occurred, the boundary between the recrystalliz-ing grain and the deformed matrix was often in a region oflow dislocation density and/or low misorientation angle.Twinning would alter the misorientation and apparentlyoffer the additional boundary energy required to continuegrowth. An example of this is shown in Fig. 5 that containsa story board presentation of consecutive EBSD imagessimilar to that shown in Fig. 3. The arrow shows the posi-tion where the nucleus of a new twin grain was firstobserved. This nucleus has the same orientation as the twingrain labeled A on the image. As recrystallization occurs,the twin continues to grow – and appears to be completelyindependent of the parent grain whose growth had previ-ously stagnated. This type of behavior was observeddirectly for several boundaries during in situ annealing atvarious temperatures. Such analysis would be impossibleusing optical metallography techniques or even ex situ ori-entation mapping techniques. This observation emanatessolely from in situ analysis of the evolving structure.

When the grain boundary growth rate was high, fewertwins developed, but when the growth rate was low, moretwins were generally found. Fig. 6 shows a plot of bound-ary velocity vs. twin density for the specimen annealed at165 �C. The boundary velocity was calculated from theincrease in average grain radius as a function of time.The number of twins per grain was obtained by first deter-mining the number of grains by considering twin bound-aries as regular grain boundaries and again by ignoringtwin variants as boundaries. The ratio of these values givesthe number of twins per grain plotted on the horizontalaxis. These data are in direct contradiction to data pre-sented by various authors that show a general increase intwin density as the growth rate increases [25–27]. Thegrowth accident model is generally used to explain thathigher boundary velocities result in a higher probability

Fig. 6. The comparison of twin density (average number of twins pergrain) with the average grain boundary velocity for the sample annealed at165 �C. The average boundary velocity was measured as the change ingrain radius over the annealing time.

of growth accidents and thus an increase in twin density.In the present experiments, the driving force for recrystal-lization was necessarily very small to ensure that therewas sufficient time to obtain several orientation maps dur-ing the recrystallization process. With this constraint, eventhe more rapidly moving boundaries in this study migratedat a relatively low rate. The range of boundary velocitieswas perhaps slow enough that a difference in the rate ofgrowth accidents as a function of boundary velocity wasinsignificant.

The mechanism for more twin grains appearing atslower growth rates appears to be that of the twin misori-entation with the deformed matrix offering an advantage togrowth over that of the parent grain. Since the drivingforce for growth is directly affected by temperature, twin-ning may have been necessary for the growth of grains tocontinue to complete recrystallization at the lower temper-atures. At higher temperatures, the growth of grains mayhave had less of a dependence on twinning, since adequatedriving force was supplied by thermal energy. This is anal-ogous to the lower driving force applied during strainannealing that is used to create special boundaries in grainboundary engineered structures; namely, that of small plas-tic deformations. If larger deformations are imposed, thedriving force for recrystallization overwhelms any bound-ary effects that might contribute to the process and specialboundaries fail to be created to the same extent [16].

In the each of the recrystallized structures, many neigh-boring grains that appeared completely unrelated by mor-phology were twin related, or higher order twin related(R3n). Fig. 7 contains a representative image of a structureannealed at 200 �C that shades grains only according to thegrain definition. Fig. 7a defines grains simply as a set ofcontiguous points whose misorientation with neighboringmeasurements is <5�. Fig. 7b shows the same image butthose boundaries having a twin related misorientation towithin 5� are not considered to separate different grains.This same effect is apparent in all recrystallized structures,but is more pronounced when the fraction of twin bound-aries is highest. This observation tends to support the con-cept first proposed by Haasen [1], that twinning is animportant mechanism in determining the recrystallizationstructure for such materials and that twin boundariesdevelop to further the recrystallization process. It was fur-ther observed in various locations that the first nuclei toappear had either an orientation that was similar to thatof the deformed matrix or that was twin related withrespect to the deformed matrix. It is proposed that thosenuclei that had a twin relation to the deformed matrix firstnucleated with the orientation of the matrix. Because of thelow angle relationship the nuclei necessarily had with thematrix, stacking faults developed forming twins to the ori-ginal nuclei that provided new grains with high angle rela-tionships to the deformed matrix. These grains grewrapidly and were the first apparent nuclei to be observedat the specimen surface, even though the original nucle-ation events were perhaps not observed.

Fig. 7. Unique grain shading maps for the copper sample fully recrystallized at 200 �C for (a) individual grains defined as having a minimum grain size of10 with a tolerance of 5� and (b) the same grains but shaded as groups of grains that are twin related (first and second order twin boundaries excluded witha 5� tolerance).


4. Discussion

Since the formation and growth of twins is an increas-ingly important topic in the arena of GBE, the mechanismsfor twin formation should be better understood. A modelproposed by Gleiter in 1969 [25] considers twins to be aresult of growth accidents leading to stacking faults. Thesegrowth accidents are presumed to increase in frequency asboundary velocity during recrystallization increases. Arecent study [27] follows up with these ideas and suggeststhe utility of the model in certain circumstances and usingproperly defined constants. This model lacks a mechanisticdescription of twin formation. Two independent investiga-tions observed that annealing twins may form at irregular-ities on grain boundaries where a packet of stacking faultsis formed, resulting in a twin boundary [30,31]. Again,mechanistic details are lacking in this description. A moremechanistic model was proposed and later developed byMahajan and co-workers [26,32–34]. This model envelopesthe idea of growth accidents as suggested by Gleiter anddescribes the mechanism by which various twin geometriesare likely to occur. The model is capable of describing twinboundary formation either parallel or normal to thegrowth front, as is observed experimentally. The largeamount of deformation initially present in the copper sam-ples from this study will increase the probability of stackingfaults and therefore contribute to the development oftwins, according to this model. Another consideration froma recent paper suggests the possibility that large sheardeformation present in the specimens also increases the

likelihood of stacking faults on certain planes and leadsto an increase in twin boundary density [35]. The ECAEprocess, by which the specimens from the present studywere deformed, certainly provides a strong shearing com-ponent and may contribute to the twin densities observed.

The average grain diameters of the specimens from thisstudy generally decreased with increasing temperature, asshown in Table 1. Although the data vary from tempera-ture to temperature, the grain size appears to be relatedto the twin density, supporting the proposal made byMahajan et al. [32]. This mechanistic growth accidentsmodel is satisfactory in explaining twin density (twins pergrain) with relation to grain size. When exploring this rela-tionship, Mahajan made the conclusion that twinning isonly influenced by temperature through its effects on grainsize. In this model, twinning is controlled by the existenceof stacking faults and the behavior of the migrating grainboundaries. Although temperature is thought to have aweak influence on twinning, lower twin densities weresometimes found to develop at higher temperatures (obser-vation noted in Ref. [30]). This was again observed recentlyby a group analyzing recrystallization of cold-rolled Cu[36]. This corresponds to the same results found in the pres-ent study. Table 1 presented the trend that suggests highertwin densities developed at lower annealing temperatures.The main contribution of the present work is to describethe effects of twin boundary formation for very low drivingforces such as with the low temperature anneals of theheavily deformed copper of the present study or the smalldeformations employed in strain annealing. A mechanistic


description for this phenomenon was proposed by Kumaret al. [37] as an explanation for structure evolution duringthe strain annealing process. A unified model for annealingtwin formation should be developed to include bothgrowth accidents and the observed phenomena prevalentwith low driving forces. This is beyond the scope of thepresent work.

5. Summary

Analysis of recrystallization in most polycrystallinematerials is convenient and seemingly accurate usingin situ EBSD analysis. In the case of analyzing heavilydeformed copper at temperatures between 170 and400 �C, 3 min scans were inadequate to capture all of therecrystallization kinetics, so more rapid scanning tech-niques must be employed. Recent speed enhancements inEBSD detectors have increased the possible scanning ratesby a factor of three over that used in the present study, butthis is still too slow to capture recrystallization kineticsunder most circumstances. Nucleation was observed totypically occur below the specimen surface, which disabledthe measurement of exact nuclei/matrix orientation rela-tionships. It was apparent in some cases that the nucleuswas near the same orientation as the deformed matrixand also often occurred in a twin relationship with the sur-rounding structure.

Annealing twins played an important role during therecrystallization process. When a grain appeared to stag-nate in growth, it would often twin and rapid growthwould resume. In the final structure, there are many neigh-boring grains that appear to be independent from oneanother by morphology, but are twin related accordingto the misorientation relationship. This supports the notionthat growth is dependent upon twinning in these structures– a theory first advanced by Haasen [1] nearly two decadesago. It must be emphasized that this mechanism likelyoccurs only under conditions of low driving force forrecrystallization. The growth accidents mechanism for twinformation is probably prevalent at higher temperatures.

Acknowledgements

The authors acknowledge the experimental and analyti-cal support provided by P. Trivedi of WSU and S.I. Wrightof TSL/EDAX. This work was partially performed usingan instrument purchased under the NSF IMR program(Award No. DMR-0414294). A portion of this work wasalso supported by the US Department of Energy, Office

of Energy Efficiency and Renewable Energy, Freedom-CAR and Vehicle Technologies Program Office, underDOE Idaho Operations Office Contract DE-AC07-05ID14517.

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The role of annealing twins during recrystallization of Cu