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Acta Materialia 60 (2012) 229–237

Observation of changing crystal orientations during grain coarsening

Hemant Sharma a,⇑, Richard M. Huizenga a, Aleksei Bytchkov b,1, Jilt Sietsma a,S. Erik Offerman a

a Department of Materials Science and Engineering, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlandsb European Synchrotron Radiation Facility, BP 200, 38043 Grenoble Cedex, France

Received 30 August 2011; received in revised form 28 September 2011; accepted 29 September 2011Available online 29 October 2011

Abstract

Understanding the underlying mechanisms of grain coarsening is important in controlling the properties of metals, which stronglydepend on the microstructure that forms during the production process or during use at high temperature. Grain coarsening of austeniteat 1273 K in a binary Fe–2 wt.% Mn alloy was studied using synchrotron radiation. Evolution of the volume, average crystallographicorientation and mosaicity of more than 2000 individual austenite grains was tracked during annealing. It was found that an approxi-mately linear relationship exists between grain size and mosaicity, which means that orientation gradients are present in the grains.The orientation gradients remain constant during coarsening and consequently the character of grain boundaries changes during coars-ening, affecting the coarsening rate. Furthermore, changes in the average orientation of grains during coarsening were observed. Thechanges could be understood by taking the observed orientation gradients and anisotropic movement of grain boundaries into account.Five basic modes of grain coarsening were deduced from the measurements, which include: anisotropic (I) and isotropic (II) growth (orshrinkage); movement of grain boundaries resulting in no change in volume but a change in shape (III); movement of grain boundariesresulting in no change in volume and mosaicity, but a change in crystallographic orientation (IV); no movement of grain boundaries (V).� 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Synchrotron radiation; Iron alloys; Coarsening; Annealing

1. Introduction

At high temperatures coarsening of grains occurs in orderto reduce the total energy of the system [1]. Understandinggrain coarsening in three-dimensional (3-D) structures isessential if we are to control of microstructures of metalsand ceramics, which has a direct influence on the resultingmechanical and functional properties. For example, controlof grain size at high temperatures is very important in main-taining the high strength of materials over time during theoperation of energy conversion systems.

For many decades extensive effort has been devoted tounderstanding and predicting grain coarsening at high

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

doi:10.1016/j.actamat.2011.09.057

⇑ Corresponding author. Tel.: +31 15 2784055; fax: +31 15 2786730.E-mail address: h.sharma@tudelft.nl (H. Sharma).

1 Present address: Institute Laue Langevin, BP 156, 38043 GrenobleCedex, France.

temperatures. However, even for very simple systems, ourknowledge of the process of grain coarsening is still incom-plete [2,3]. A substantial part of the work has focused onthe development of models for predicting grain coarsening[3–8]. These models assume that grains are perfect crystals,the character of which does not change during coarsening,and attribute coarsening entirely to a reduction in the totalinterface area of the system [9], but they cannot yet accu-rately reproduce real material behavior [1].

Classically, grain coarsening at high temperatures inpolycrystalline materials is attributed to a reduction inthe grain boundary area and, consequently, in the totalenergy of the system. A widely used semi-empirical graincoarsening equation to fit the experimental data for aver-age grain sizes is expressed as

Dn ¼ Dn0 þ kt ð1Þ

where D is the average grain size at time t, D0 is the averagegrain size at the start of isothermal annealing (t = 0) and k

rights reserved.

5.7

5.2

2.5

0.5

1.9

1

1.5

Note: All dimensions are in mm.

1

- x-ray beam

1.20.5

Fig. 1. Schematic geometry of the sample. The location of the X-ray beamis highlighted.

230 H. Sharma et al. / Acta Materialia 60 (2012) 229–237

and n are empirical fitting parameters [1]. In most studiesthe values of n are commonly much higher than the idealvalue of 2, which is based on proportionality of the localgrain curvature driving coarsening and the grain size [1].A higher value of n means that the rate of grain coarseningdecays faster than if n had a lower value. This effect is com-monly attributed to solute drag (i.e. a slowing down ofgrain boundaries by foreign atoms present in the matrix),to non-regular microstructures or to the presence of texture[1], but no underpinning observations for these assump-tions have been presented. More recently a model basedon stagnation of grain coarsening induced by grain bound-ary smoothing has been proposed [3]. In the present paperan additional contribution to the often observed fast decayof the rate of grain coarsening is presented.

Even though significant advances have been made inmodeling coarsening, direct experimental observation ofthe coarsening process is lacking. Direct experimentalobservation of grain coarsening at high temperaturerequires a combination of experimental settings that, untilrecently, had not been accomplished, in situ observationsof 3-D grain volumes in the bulk of the material duringcoarsening. To date experimental studies have been limitedto ex situ observations on cross-sections of quenched mate-rials [10] or in situ observations of the surface of specimensat high temperature [11]. In the first approach the timeresolution and accuracy of the observations are limited,especially if the microstructure (e.g. austenite in steel)undergoes a phase transformation upon cooling. In the lat-ter case coarsening at the surface was studied, which canessentially differ from the bulk behavior [12]. In both casesonly a two-dimensional (2-D) analysis of the grain size dis-tribution was performed.

The recent advances made in third generation synchro-tron sources capable of generating high energy X-rays withincreased flux have made it possible to observe the bulk ofmaterials [13] and study individual grains in polycrystals[14–18]. In a promising study, Schmidt et al. [19] studiedgrain coarsening in an aluminum alloy employing a 3-DX-ray diffraction (XRD) technique [20]. However, in thecase of alloys which undergo a phase transformation uponcooling to room temperature the technique of interruptedheat treatment followed by Schmidt et al. [19] cannot beused. In the present paper the first in situ 3-D observationsof bulk grain coarsening at high temperatures in an alloythat undergoes a phase transformation upon cooling arepresented. It will be shown that experimental observationsat the level of individual grains reveal essential informationabout the behavior of grains during coarsening.

2. Experimental details

2.1. Sample

The alloy under investigation was manufactured fromelectrolytic (99.999% purity) iron and manganese to obtaina composition of 2 wt.% Mn. The concentration of other

impurities was kept very low in order to minimize anyinfluence of other solute particles on the rate of grain coars-ening. The composition was chosen in order to slow downthe rate of grain coarsening by solute drag compared withpure iron. This was warranted by the time resolution of the3-D XRD technique used. The initial material was homog-enized at 1553 K for 21 days, followed by furnace coolingto room temperature. The sample was manufactured usingelectro discharge machining (EDM) with the dimensionsshown in Fig. 1 in order to fit into the furnace describedin Sharma et al. [21]. The diameter of the sample changedfrom 1 to 1.5 mm in the middle, which was used to define areference by scanning with the X-ray beam.

2.2. 3-D XRD experiment

The experiment was carried out in beamline ID11 of theEuropean Synchrotron Radiation Facility (ESRF), Greno-ble, France. Fig. 2 shows the experimental set-up. The sam-ple was placed in a furnace developed especially for 3-DXRD measurements, described in Sharma et al. [21]. AnS-type thermocouple was spot welded to the top of thesample for accurate temperature control. The samplechamber was purged with helium and sealed at a pressureof 0.4 atm. The X-ray beam, 500 lm high and 1200 lmwide with energy equal to 88.005 keV, calibrated using aPb foil, was incident on the sample at the location depictedin Fig. 1. The sample was heated rapidly to a temperatureof 873 K over 60 s, followed by isothermal holding for900 s and heating to a temperature of 1173 K at a rate of0.033 K s�1, followed by rapid heating in 120 s over1273 K. The sample was then held isothermally at 1273 Kfor 7740 s (2.15 h). During the heat treatment the furnacewas repeatedly rotated over a total angle x equal to 24�(a so-called sweep equal to one full rotation of 24�).Diffraction patterns were recorded every 0.3� rotation withan exposure time of 0.2 s. This set-up means that a

yz

x

Sample

Beamstop

Area detector

Furnace

Incident x-ray beam ω

2θ

Fig. 2. Schematic showing the experimental set-up. The dimensions are not to scale. The angles 2h, x and g are defined.

H. Sharma et al. / Acta Materialia 60 (2012) 229–237 231

diffraction pattern is recorded at the same orientation ofthe sample with respect to the incident beam every 180 s.The sample was then cooled to room temperature. Dueto the limited number of grains in the illuminated volumewhich satisfy the Bragg condition for diffraction at a cer-tain orientation of the sample, individual spots from indi-vidual grains were observed in the diffraction patterns.An example of a diffraction pattern is shown in Fig. 3.The sample to detector distance was adjusted in such away that four complete diffraction rings of the austenitephase were recorded. An austenite grain of any crystallo-graphic orientation when rotated through 24� would forthe first four families of hkl planes produce a diffractionpattern between 3 and 9 times. Thus, all the grains in theilluminated volume were studied in the present experiment.The small rotation angle of 24� means that the spatial char-acteristics of the grains cannot be determined. However,this angle was chosen in order to obtain a good time reso-lution. At the beginning and end of isothermal annealingthe vertical height of the X-ray beam was increased to600 lm in order to verify the diffraction spots originating

Fig. 3. Example of a diffraction pattern showing austenite reflections at1273 K. Dark regions show pixels with a positive intensity. The solid ringsindicate the expected location of Debye–Scherrer rings for the austenitephase at 1273 K for the following hkl planes (radially outwards): {111},{200}, {220} and {311}. The deviation of diffraction spots from the ideallocation at the diffraction rings is due to the effect of positioning of thediffracting grain inside the sample.

from the grains situated partially in the illuminatedvolume.

3. Data analysis method

3.1. Grain volume

After correction for beam current, electronic noise anddetector imperfections a minimum intensity threshold(200 counts, corresponding to a minimum detectable grainvolume of �35 lm3) was applied to characterize all theinterconnected pixels as diffraction peaks. The pixels withan intensity above the threshold and overlapping in succes-sive diffraction patterns with changing x were merged andcounted as a single diffraction peak. The diffraction peakswere assigned to families of hkl planes using the Fablepackage (http://sourceforge.net/apps/trac/fable/wiki) andthe location of the centre of mass of the peaks was calcu-lated in terms of g, 2h and x (Fig. 2). The volume of grainsgiving rise to the diffraction spots was calculated accordingto the expression

V g ¼1

2mhkl cosðhÞV gauge

Ig

kIpDh ð2Þ

where mhkl is the multiplicity of the hkl ring, h is the Braggdiffraction angle, Vgauge is the volume of the sample illumi-nated by the X-ray beam, Ig is the integral of the diffractionspot, k is the normalization factor for Ig and is equal to thenumber of diffraction patterns in which the diffraction spotis observed, Ip is the powder intensity of each diffractionpattern for the hkl ring and Dh is the rotation of the planenormal over which the diffraction spot is observed or, inother words, the change in the scattering angle due to rota-tion over Dx. Dh is given by the expression

Dh ¼ sin�1ðsinðhÞ cosðDxÞ þ cosðhÞ sin jgj sinðDxÞÞ� h ð3Þ

where Dx is the rotation angle of the sample over which thediffraction spot is observed.

Using a relatively small tolerance (±3 pixels on thedetector and ±0.3� in x), diffraction spots from the samegrain were identified in different sweeps. Furthermore, dif-fraction spots having a similar volume (within a toleranceof 5%) and similar evolution of volume during annealing

232 H. Sharma et al. / Acta Materialia 60 (2012) 229–237

were identified as belonging to the same grain. In this way97.3% of the sample volume illuminated by the X-ray beamwas characterized. The spots which showed an increase inintensity of more than 5% of the integrated intensity uponopening the X-ray beam were rejected as coming fromgrains which were partially illuminated by the X-ray beam.

The equivalent radius of the grains was calculated fromthe grain volume assuming a spherical shape of the grains.

3.2. Mosaicity and rotation of the average plane normal of

grains

Mosaicity, Dt, defined for each grain as the maximumdifference in crystallographic orientation between any tworegions in the grain [22], was calculated as the rotation ofthe diffracting plane normal required to produce a diffrac-tion spot of the observed size in x and g. The mosaicity cal-culated in either x or g is the maximum difference inorientation in a single direction of the grain.

The average mosaicity was calculated as the averagemosaicity of all the grains with a radius within 5 lm inter-vals. In the case of very large grains diffraction spots in thefirst and second diffraction rings are saturated and thuscannot be used for analysis. In such cases spots from thethird and fourth rings were used to calculate the mosaicity.However, this has the disadvantage that the mosaicity ofsuch grains is underestimated, due to problems arisingfrom the background. For this reason the average mosaic-ity was calculated only for grains with radii up to 130 lm.The mosaicity per grain was calculated by averaging themosaicity calculated from all the diffraction spots identifiedas belonging to the grain. Thus the calculated mosaicity isthe average of the maximum orientation difference in mul-tiple directions. This was done in order to compare themosaicity of grains with equivalent radii.

Fig. 4. Evolution of the austenite grain size distribu

The average normal to a diffracting plane was calculatedusing the centre of mass of the diffraction spots belongingto the grain. The rotation of the average plane normalwas then calculated by calculating the angle between theaverage plane normal of the spots for the first and succes-sive sweeps.

4. Results

Fig. 4 shows the evolution of the volume-weighted grainsize distribution (Pv) in the sample as a function of isother-mal annealing time. It can be seen that, consistent with thegeneral idea of grain coarsening, the fraction of the illumi-nated volume occupied by small grains is high at the begin-ning of isothermal annealing and gradually decreases ascoarsening progresses. This is shown in Fig. 5, where thevolume averaged grain volume (red symbols) and the num-ber of grains in the illuminated volume (black symbols) as afunction of annealing time are shown. It can be seen that ascoarsening progresses the average grain volume increasesand the number of grains in the illuminated volumedecreases.

The average volume of austenite grains (Fig. 5, red sym-bols) increased from 1.24 � 106 lm3 at t = 0 s to9.08 � 106 lm3 at t = 7740 s. The best fit (Fig. 5, bluecurve) of the average austenite grain size data to Eq. (1)gives a value of the grain coarsening exponent of n = 8.3.This value is much higher than the reference value of 2,an observation often made in the literature [1]. Duringannealing the number of grains in the illuminated volumedecreased from 2385 at t = 0 s to 1201 at t = 7740 s(Fig. 5, black symbols). Of the 2385 initial grains 104increased in volume, 283 had an eventual change in volumeof less than 5%, 814 decreased in volume by more than 5%and 1184 disappeared completely.

tion (Pv) during isothermal annealing at 1273 K.

Fig. 5. Grain characteristics during isothermal annealing at 1273 K. Evolution of the number of grains in the illuminated volume as a function ofannealing time (black circles) and evolution of the volume averaged grain volume as a function of annealing time (red squares). The blue curve shows thebest fit to Eq. (1). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

H. Sharma et al. / Acta Materialia 60 (2012) 229–237 233

To highlight the relationship between the size and mosa-icity of grains the average mosaicity of all the grains in theilluminated volume is plotted in Fig. 6 as a function of theequivalent grain radius (calculated from the grain volumeassuming a spherical grain shape). The error bars for theaverage mosaicity give the standard deviation of theobserved mosaicity among the observed grains. Fig. 6shows that an approximately linear relationship existsbetween mosaicity and grain radius. For the reasons men-tioned in Section 3.2 the mosaicity of large grains is under-estimated. This effect can also be seen in Fig. 6.

Fig. 7 shows the evolution of grain volume, mosaicityand rotation of the average plane normal for five austenitegrains of the 2385 observed. It can be seen that, in compar-ison with the average grain coarsening behavior shown in

Fig. 6. Plot of the average mosaicity of all the grains duri

Fig. 5 (red symbols), the volume evolution of individualaustenite grains varies considerably. Fig. 7a shows anexample of an austenite grain that grew continuously overtime. The evolution of the grain is similar to the averagegrain coarsening behavior shown in Fig. 5. However, thegrains shown in Fig. 7b–e exhibit patterns of evolution ofsize of the grains completely different from the evolutionof the average grain size in Fig. 5. The grain in Fig. 7bshrank continuously, the grain in Fig. 7c grew rapidlyand then stabilized in volume, the grain in Fig. 7d firstgrew, then shrank, and then disappeared, and the grainin Fig. 7e shrank, stabilized in volume and thendisappeared.

A crucial feature of Fig. 7a is the development of mosa-icity of the grain, which follows the evolution of volume of

ng isothermal annealing as a function of grain radius.

Fig. 7. Evolution of the grain volume (black squares), cumulative rotation of the average plane normal with respect to the original orientation (reddiamonds) and change in mosaicity (green circles) of individual austenite grains during isothermal annealing at 1273 K. Different shading colors representregions of different mode shown in Fig. 8. (a) Example of an austenite grain which increased in size. (b) An austenite grain which shrank continuously overtime. (c) Example of an austenite grain which first grew and then maintained a constant volume. (d) Example of a grain which initially grew and thenshranks to nothing. (e) Example of a grain which decreased in volume, became stable and then shrank to nothing. The error bars are calculated based onthe error in measurement. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

234 H. Sharma et al. / Acta Materialia 60 (2012) 229–237

the growing grain. This is consistent with the results foraverage mosaicity of all the grains shown in Fig. 6. Thegrains shown in Fig. 7b–e exhibit the same behavior, i.e.the mosaicity of a grain follows the evolution of its volume.This shows that the direct relationship between mosaicityand size of the grains is also maintained during coarsening.Furthermore, Fig. 7a–e shows that the average orientationof the diffracting plane normal for the grains changes dur-ing coarsening. The information in Figs. 6 and 7 is uniquein terms of the extended insight that can be obtained intothe behavior of individual grains during coarsening.

5. Discussion

Figs. 6 and 7 show that the mosaicity of a grain isdirectly proportional to its radius and that this relationshipholds true during coarsening. The direct relationshipbetween grain mosaicity and radius implies that crystallo-graphic orientation gradients exist in the grains, which per-sist during coarsening such that during growth of a grainthe variations in its orientation increase. The presence of

orientation spreads in well-annealed grains has beenobserved before in the literature [23], but the present mea-surements of constant orientation gradients in grains dur-ing coarsening are the first of their kind. This is veryinteresting, since even though, from a theoretical view-point, the presence of variations in the orientations of crys-tals is thermodynamically unfavorable [1], the presentobservations show that not only are crystallographic orien-tation gradients present in the grains but also that theirmagnitude does not reduce during coarsening, but remainsconstant.

Based on the observation of the maintenance of con-stant orientation gradients, a total of five different modesof grain evolution (shown in Fig. 8 and Table 1) can occur.

1. Mode I. Anisotropic growth, I(a), or shrinkage, I(b),leads to an increase in the total mosaicity of thegrain and a change in the average orientation.

2. Mode II. Isotropic growth, II(a), or shrinkage, II(b),leads to an increase in total mosaicity but the aver-age orientation remains constant.

Table 1Features of the different modes of evolution of grains shown in Fig. 9.

Mode no. Volume Mosaicity Rotation of average plane normal

I(a) + + 4I(b) � � 4II(a) + + =II(b) � � =III(a) = ± 4III(b) = ± =IV = = 4V = = =

The corresponding change in grain volume, rotation of the average planenormal and mosaicity is listed. For rotation of the plane normal there is nodistinction between + or � and change is indicated by 4. For mosaic-ity ± indicates an increase in one direction and decrease in anotherdirection.

H. Sharma et al. / Acta Materialia 60 (2012) 229–237 235

3. Mode III. A combination of anisotropic growth andshrinkage result in the same volume, however, themosaicity increases in one direction while itdecreases in another direction. The average orienta-tion changes after annealing in mode III(a). Anothervariant, mode III(b), of this mode is when the aver-age orientation of the grain remains constant whilethe mosaicity in different directions changes.

4. Mode IV. A combination of anisotropic growth andshrinkage results in the same volume and mosaicityof the grain, whereas the average orientationchanges after annealing.

5. Mode V. No movement of grain boundaries occurs.Volume, mosaicity and average orientation of thegrain remain constant.

The case of shrinkage is analogous to growth and addi-tional features of each mode are explained in Table 1. Dif-ferent shading colours in Fig. 7 are used to highlight themode of evolution of the grains at different times duringannealing. An interesting case is the grain shown inFig. 9, the volume of which remains constant duringannealing while the grain exhibits a combination of modeIII (which indicates changes in shape), mode IV (whichindicates no change in shape but a change in the centreof mass position) and mode V (which indicates no apparent

Fig. 8. Schematic illustration of the possible effects of grain evolution onmosaicity and average orientation of the austenite grains for the simplifiedcase of grains having a constant orientation gradient in the radialdirection. Colors represent orientation. The cases of shrinkage areanalogous to growth. (For interpretation of the references to colour inthis figure legend, the reader is referred to the web version of this article.)

grain boundary movement). In order to highlight shapeeffects the mosaicity of the grain in Fig. 9 is calculatedusing a single diffraction spot such that mosaicity in onlyone direction is measured. Even though the total volumeof the grain remains constant, local grain boundary motioncombined with constant orientation gradients can lead tochanges in mosaicity and average orientation, as seen inFig. 9.

It has been proposed in the literature, by the use of sim-ulations, that grains in the nano-crystalline size range canrotate during coarsening [24,25], similarly to the observedchange in orientation of the average diffracting plane nor-mal for the grains in Fig. 7. However, the grains shown inFig. 6 are of a much bigger size (of the order of tens to hun-dreds of microns in radius) and rotation of the whole vol-ume of these large grains during coarsening in the absenceof external stresses is not expected. The constant orienta-tion gradients in grains can be considered to explain theobserved changes in the average diffracting plane normal.The average orientation of a grain, if the observed constantgradients in orientation are present, is essentially the orien-tation of the centre of mass of the grain. Thus, in the caseof anisotropic growth (or shrinkage) of grains, when thecentre of mass of the grains shifts, the average orientationof the grains changes as well. An extreme case is the grainin Fig. 6e shown in Fig. 10, where the error bars for rota-tion of the average diffracting plane normal are equal to themosaicity of the grain and thus the limits of the error barsrepresent the extremes of orientation in the grain. Theobserved change in average orientation and the reductionin mosaicity mean that no part of the grain remaining at4000 s has the same orientation as any part of the grainwhich was present at the start of isothermal annealing. Thisis particularly interesting, since in an ex situ study if thesame grain was observed at the beginning of annealingand at 4000 s into annealing the different orientationswould suggest that a new grain had nucleated.

Having established that grains at high temperatureshave orientation gradients which remain constant duringcoarsening, the possible implications of the results on theprocess of grain coarsening are now examined. Even

Fig. 9. An example of evolution of the grain volume (black squares), cumulative rotation of the average plane normal with respect to the originalorientation (red diamonds) and change in total mosaicity (green circles) of an austenite grain with constant volume. The axis on the left is for volume of thegrain and the axis on the right is for rotation of the diffracting plane normal and the mosaicity of the grain. Different shading colors (see legend to Fig. 7)represent regions of different mode shown in Fig. 8. (For interpretation of the references to colour in this figure legend, the reader is referred to the webversion of this article.)

236 H. Sharma et al. / Acta Materialia 60 (2012) 229–237

though the presence of orientation spreads in grains is wellknown [1,2,23], their influence on the process of coarseninghas not been explored before.

Grain coarsening at high temperatures in polycrystallinematerials occurs in order to reduce the total interfaceenergy of the system (

RcdA, where c is the specific interfa-

cial energy and the integration runs over the grain bound-ary area in the microstructure). For each grain boundaryits contribution to the total interface energy of the systemcan be reduced either by reducing the contributing inter-face area A or the specific interface energy c. A reductionin A takes place on increasing the radius of curvature of

Fig. 10. Example of an austenite grain, the same one as in Fig. 7e, forwhich the orientation at the beginning of isothermal annealing wascompletely different from the orientation just before disappearing.Evolution of the grain volume is shown by black squares and cumulativerotation of the average diffracting plane normal with respect to theoriginal orientation is shown by red diamonds. The error bars of rotationof the average diffracting plane normal are equal to the mosaicity of thegrain. (For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this article.)

the grain boundaries, so-called capillarity-driven graincoarsening [1]. It has previously been proposed by meansof simulations that c can be reduced by changes in the incli-nation of the grain boundaries [26]. The average interfaceenergy can also be reduced by direct elimination of highenergy grain boundaries during grain coarsening [9].

The present observations show that orientation gradi-ents are present in grains and that these gradients remainconstant during coarsening. This means that in the caseof neighboring grains both of which have an orientationgradient the movement of a grain boundary combined withthe observed constant orientation gradient in all regions ofthe grains would change the local misorientation (a differ-ence in orientation at opposite sides of the grain boundary)across the grain boundary. This can be expected to affectthe specific grain boundary energy (c), since it is knownthat c depends on the misorientation angle (h) betweenthe grains constituting the grain boundary [2]. In simpleterms, the relation between a change in interface energy(Dc) and the change in misorientation (Dh) can be writtenas:

Dc ¼ @c@h

� �Dh ð4Þ

Depending on the sign and magnitude of (c/h), Eq. (4) canresult in three cases: Dc = 0, Dc < 0 and Dc > 0. If Dc = 0there would be no effect on the driving force for grain coars-ening G, and grain coarsening would be driven only by cur-vature. When Dc is negative, for example in the case of lowangle grain boundaries with decreasing Dh, this would resultin a decrease in G, since G is directly proportional to c. Thisresults, in turn, in additional decay of the rate of grain coars-ening during the process. The motion of the grain boundarywould in this fashion continue at an ever decreasing rateuntil the grain boundary reaches a minimum in c. Where

H. Sharma et al. / Acta Materialia 60 (2012) 229–237 237

Dc is positive the motion of the grain boundary would lead toan increase in c. Even though c increases, the total interfaceenergy contribution of the grain boundary,

RcdA, could still

continue to decrease as long as the decrease in the interfacearea A can compensate for the increase in c. A meta-stablecondition would be reached when the motion of the grainboundary in any direction leads to an increase in

RcdA, by

increasing either A or c. Thus, for materials with a distribu-tion of grain boundaries of multiple characters the combinedeffect of the latter two cases would be a reduction in the over-all rate of grain coarsening and increase in the grain coarsen-ing exponent n. It should be noted here that in situexperimental measurement of c during coarsening is impos-sible with the techniques presently available.

The next step is to examine the probability of occurrenceof the two cases which affect n. The change in misorientationdue to the movement of grain boundaries and the addedimposition of maintenance of the orientation gradient willbe of the order of a degree. This means that the grain bound-aries, the energy of which is strongly dependent on the mis-orientation, for example low angle tilt boundaries or specialP

boundaries, are strongly affected by a relatively smallchange in misorientation. It is already known that the frac-tion of these special low energy grain boundaries in materialsis high and increases during annealing [9,27,28]. Thus, alarge fraction of grain boundaries in materials will alwaysbe affected by the change in misorientation resulting frommaintenance of a constant orientation gradient.

6. Conclusions

Grain coarsening of austenite in a binary Fe–2 wt.% Mnalloy was studied by measuring the evolution of the volume,average crystallographic orientation and mosaicity of morethan 2000 individual austenite grains during annealing at1273 K. The following conclusions can be drawn from themeasurements.

1. It was observed that the average mosaicity of all of>2000 austenite grains is approximately directly pro-portional to the average size of the grains.

2. For individual grains it was shown that mosaicity isdirectly proportional to the grain volume at all timesduring coarsening at 1273 K. This means that con-stant orientation gradients exist in the grains, whichpersist during coarsening.

3. The persistence of orientation gradients coupledwith the movement of grain boundaries results inchanges in the grain boundary character, affectingthe coarsening rate.

4. Changes in the average orientation of large(10–200 lm radius) austenite grains were observedduring coarsening.

5. Five modes of grain growth are proposed: aniso-tropic (I) and isotropic (II) growth (or shrinkage);movement of grain boundaries resulting in nochange in volume but a change in shape (III) and

movement of grain boundaries resulting in nochange in volume and mosaicity but a change inthe average crystallographic orientation (IV); nomovement of grain boundaries (V).

Acknowledgements

The authors thank E.G. Dere for assistance during thesynchrotron measurements, F. Gersprach for discussionson the generation of defects by moving grain boundariesand C. Kwakernaak for EPMA analysis. This research isfinancially supported by the Foundation for Technical Sci-ences of the Netherlands Organization for Scientific Re-search. The authors thank the European SynchrotronRadiation Facility for provision of the beam time.

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