grain boundary mobilities during recrystallization of al–mn alloys as measured by in situ...

Materials Science and Engineering A 403 (2005) 144–153

Grain boundary mobilities during recrystallization of Al–Mn alloys asmeasured by in situ annealing experiments

A. Lens, C. Maurice, J.H. Driver∗

MMF Department, Ecole des Mines de Saint Etienne, CNRS UMR 5146 and Federation 2145, 158 Cours Fauriel,42023 Saint Etienne Cedex 2, France

Received in revised form 21 April 2005; accepted 3 May 2005

Abstract

The influence of Mn on the mobilities of grain boundaries during recrystallization of Al–0.1 and –0.3 wt.% Mn alloys has been characterizedby in situ SEM annealing experiments. Polycrystals of high purity, single-phase Al–Mn alloys were deformed in channel-die plane straincompression at room temperature to strains of 1.3. The specimens were in situ annealed in an SEM/EBSD in order to measure grain boundarymobilities at temperatures between 200 and 450◦C. Stable “loaded” boundary migration was observed in the 0.1 and 0.3% Mn alloys. However,unstable, partially “free”, boundary migration could also be found in the 0.1% alloy. The mobilities, deduced from the migration rates andt ragw at of soluted©

K

1

thrfamctpgrnmpk

rain

mseen

te

gheram-t.%fteren

llow-

EMin

theby

ensolid

0d

he stored energies, were consistent with the solute drag theories of Cahn, Lucke and Stuwe. The diffusion rates controlling the solute dere of the same order for both theories and the activation energy for boundary migration was found to be intermediate between thiffusion in the lattice and along the grain boundaries.2005 Elsevier B.V. All rights reserved.

eywords:Al–Mn alloys; In situ annealing; SEM/EBSD; Grain boundary mobility; Solute drag; Effective diffusion; Activation energy

. Introduction

Al–Mn alloys are important materials for applications inhe packaging, aerospace and car industries (often used ineat exchangers). Manganese improves the resistance to cor-osion, hardens the material and generally leads to goodormability. It also increases the recrystallization temper-ture. Quantitative characterization of the evolution of theicrostructure during processing and heat treatment is cru-

ial to future developments of these alloys. One importantool in the rapid development of new products is com-uter simulation of the recrystallization processes and grainrowth as a function of the physical parameters of the mate-ial. This needs an understanding of the mechanisms ofucleation, recrystallization and grain growth in real com-ercial purity alloys under typical conditions of industrialrocessing. In this context, one of the difficulties is tonow how the solute atoms interact with the grain bound-

∗ Corresponding author. Tel.: +33 4 77 42 01 96; fax: +33 4 77 42 66 78.E-mail address:[email protected] (J.H. Driver).

ary and consequently influence the mobilities of the gboundaries.

The influence of trace quantities of solute ato(<0.1 at.%) on grain boundary migration rates in Al has bstudied many years ago, for example by Dimitrov et al.[1] andGordon and Vandermeer[2], and correlated with the soludrag theories of Cahn[3] and Lucke and Stuwe[4,5]. How-ever, little experimental work has been carried out on hisolute contents typical of most real alloy systems. For exple, the standard AA 3103 Al–Mn alloy contains about 1 wMn of which about 0.3–0.5 wt.% stays in solid solution aprocessing by hot rolling. This amount of Mn in solution thhas a major influence on subsequent recrystallization foing cold rolling.

The aim of this paper is first to describe an in situ Stechnique to measure 2D grain boundary mobilitiesindustrially relevant Al–Mn alloys and then to estimatediffusion rates responsible for the boundary mobilitiescomparison with the solute drag theories of Cahn, Luckeand Stuwe (CLS). Two alloy compositions have beselected; 0.3 wt.% Mn approximately representing the

921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2005.05.010

A. Lens et al. / Materials Science and Engineering A 403 (2005) 144–153 145

solution of industrial AA 3103 and a 0.1 wt.% Mn alloy forcomparison with previous work on solute drag effects.

2. Solute drag theory

Lucke et al.[6] and Lucke and Detert[7] demonstratedthat the addition of 0.01 at.% of Mn and Fe to aluminiumcould slow down the recrystallization kinetics by factors of1012 and 1016, respectively, compared with pure Al. Theseobservations led to the development of the classical solutedrag theories that quantitatively predict the influence of soluteatoms on the migration rates of grain boundaries.

In pure materials grain boundary migration theory predictsthat the boundary velocity (V) can be expressed as the productof two terms – the “intrinsic” mobility (Mint) of the pure grainboundary and the driving pressure (P) for the process; duringrecrystallization by isothermal annealing this is the reductionin free energy of the system accumulated in the deformedmaterial essentially as dislocations. For pure metals the rate ofgrain boundary migration during recrystallization is writtenas follows:

V = MintP (1)

The mobility follows a standard Arrhenius equationM alm rym thea mpli-c ”m riv-i entp eib -a

V

Ca thes ,a t toa

F n[[

particular form:

Pi(V,C) = αCV

1 + β2V 2 (3)

whereα andβ are parameters depending on the form of theinteraction energyE(x) and the effective diffusion (Deff) ofthe solute atoms in the grain boundary:

α = N(kT )2

E0Deff

(sinh

E0

kT− E0

kT

)δ

β2 = αkTδ

2NE20Deff

whereN is the number of atoms/unit volume (N≈ 1/b3); Cthe macroscopic atomic concentration;V the grain boundaryvelocity;E0 the solute atom interaction energy in the centreof the boundary;δ the half thickness of the grain boundaryb, the interatomic distance in the lattice andk the Boltzmannconstant.

Independently, Lucke and Stuwe[4] developed at the sametime a very similar theory called thecontinuummodelwherethe interaction energy between solute atoms and grain bound-ary is described by a triangular shape. Later, the authorsdeveloped the model for higher solute contents[5] wherethe drag pressure is described by anatomistic modelwith anie

P

wϕ

tomsa rentv torede orre-s luted e-s iths ec darywv ryt -b ee ont ion.T area tionu

eticald xam-p hn,L the

int =M0 exp(−Q/RT), where M0 is the pre-exponentiobility factor andQ the activation energy for boundaigration. However, for metals containing solute atomsbove linear relationship becomes somewhat more coated. The “extrinsic” mobility differs from the “intrinsicobility because of the presence of a new effective d

ng pressure (P′) which is the difference between the currressure (P) and the solute dragPi(V,C) produced by th

nteraction of solute atoms (concentrationC) with the grainoundaries moving at a velocity (V). The rate of grain boundry migration becomes:

= MintP′ = Mint [P − Pi(V,C)] (2)

ahn[3] described the impurity drag pressurePi(V,C) bymodel with a triangular interaction energy profile for

olute atoms close to the boundary (Fig. 1a). In this modeltreatment of the diffusion of foreign atoms with respecmoving grain boundary, gives forPi(V,C) in Eq. (2) the

ig. 1. Profile of the interaction energyE(x): (a) triangular profile of Cah3] and Lucke and Stuwe[4], (b) step function profile of Lucke and Stuwe5].

nteraction energy profile as a step function (Fig. 1b). Thexpression forPi(V,C) now takes the particular form[5]:

i(V,C) = 1/2(ϕ(ψ2 + ψ − ψ − ψ2) + ϕ2(ψ − ψ))

(ψ + ϕ)(1 + ϕ)(ψ + ϕ)CNE0

(4)

here the parameters areψ = exp(η/2), ψ = exp(−η/2),≈bV/Deff andη=E0/kT.In both models, the interaction between the solute a

nd the moving grain boundary can produce three diffeelocity regimes as a function of the solute content, the snergy and the annealing temperature: the first regime cponds to the migration of the pure material (without sorag) with a unique solution “V1”, the second regime corrponds to the migration of the “loaded” grain boundary (wolute drag) with a unique solution “V3” and the third regimorresponds to an instability behaviour of the grain bounhere three velocities can exist: “V1”, “V 2” (intermediateelocity) and “V3”. To evaluatePi(V,C) it is thus necessao know the effective diffusion rates (Deff) and the soluteoundary interaction energy (E0). Although the latter can bstimated theoretically[7], the diffusion rates depend up

he relative contributions of boundary and lattice diffushese vary with annealing conditions and, in principle,ccessible from experimental data for boundary migrander different conditions.

Over the years there have been several further theorevelopments in the analysis of solute drag, see for ele [8–12], but the general physical principles of the Caucke, Stuwe models still hold. The present work will use

146 A. Lens et al. / Materials Science and Engineering A 403 (2005) 144–153

latter as a basis for analysing boundary migration behaviourin simple binary alloys.

3. Experimental procedures

3.1. Sample preparation

The Al–Mn ingots were prepared from high purity Mn anda high purity aluminium, provided by the Voreppe-ResearchCentre of Alcan with the following major impurity contentsin wt. ppm: 7 Si, 1 Fe, 4 Mn, 1 Cr, 4 Zn and 3 Ga. Controlledsolidification was carried out in alumina moulds under a par-tial pressure of argon, to form 1 kg Al–Mn ingots of nominalcomposition 0.1 and 0.3 wt.% Mn. Only the centres of theingots were used for the experiments to avoid the effects ofimpurity segregation. Emission spectrometry confirmed thehomogeneity of the manganese in the central parts of thetwo alloys, i.e. 0.10± 0.008 and 0.30± 0.006 wt.% Mn cor-responding respectively to 490 and 1480 at. ppm Mn

The ingots were processed into specimen bars by hot forg-ing at 550◦C to 10 mm thickness; they recrystallized duringcooling to a grain size of 500–800�m.

Samples of dimension (8 mm× 7 mm× 10 mm),machined from these bars, were deformed in plane straincompression at room temperature using achannel-diedevicetr lms.T weret rmedd n).Tw i-n out tod ange2 entsm CHw allt g att

3

rainb ina uresb ted[ andL nd-a omem heat-i Dt

trip,h eckedt The

Fig. 2. Schematic representation of sample and in situ heating stage in theSEM.

chromel–alumel thermocouple (K), welded on the Ta-strip,controls the temperature of the Ta and thus the Al-samplethrough a temperature regulator and power supply. Thedesired temperature is computed on the regulator and theheating rate is manually controlled to reduce the time to heatthe sample to the required temperature. In order to improvethe heating rate to more than 5 K/s different voltages wereused according to the thickness of the Al-sample. In this waythe required temperature is reached in less than 40 s with goodstabilisation (±2 K) and with rapid cooling rates (10–20 s)down to 150◦C. The sample thickness varied from 0.4 to0.8 mm, i.e. about 3 or 4 times the deformed grain thicknessand the section examined on the ND/RD plane.

3.3. Data analyses

The in situ experiments were carried out in a SEM JEOL6400 (W filament, vacuum∼10−4 Pa). During each in situheating experiment, the evolution of the microstructure wasfollowed on the 70◦ tilted sample with a backscattered elec-tron detector. After each annealing, the heater was switchedoff and the EBSD orientation maps were made withChannel5-acquisition software (HKL technology).

The beam scanning was made in a raster of typically150�m× 100�m with a step size of 0.5�m/step. The crys-t rainr wereao n-t

4

4

Mna ardsε so o

o strainsεVM = 1.3 at constant strain rates of 10−2 s−1. Toeduce friction, the samples were wrapped in Teflon fihe specimens used for the annealing experiments

aken from the central part of the samples along the defoirection (denoted RD for the equivalent rolling directiohey were mechanically and electropolished (−30◦C/12 V)ith 15% HNO3 and methanol before annealing. A prelimary set of standard annealing experiments was carriedetermine recrystallization kinetics in the temperature r00–450◦C. Some thermoelectric power measuremade at the ALCAN Voreppe-Research Centre (ANATEith an accuracy of±0.007 wt.%) also confirmed that

he Mn stayed in solid solution after one-hour annealinemperatures between 200 and 350◦C.

.2. The heating stage

The aim of the in situ experiments is to study the goundary mobility of Al–0.1 and –0.3 wt.% Mn alloysSEM during multiple annealings at various temperat

etween 200 and 450◦C. A heating stage was construc13] based on the design and operating principle of Liaoe Gall et al.[14,15], as developed for studying grain boury migration in stainless steels and cold rolled nickel. Sodifications of the design were necessary to use the

ng stage at a 70◦ tilted position as required for the EBSechnique (Fig. 2).

The aluminium sample is welded to a tantalum seated by electrical resistance. The samples were ch

o ensure that the weld zone did not recrystallize.

allographic and microstructural data, i.e. grain and subgeconstruction, misorientation and boundary characternalysed with an EBSD data analysing programVMAPdevel-ped by J. Humphreys (Manchester Materials Science Cere).

. Results

.1. Deformed specimens

Fig. 3 gives the stress–strain curves for the two Al–lloys. The flow stress increases rapidly with strain towVM ≥ 0.05, then at a lower rate toεVM ≈ 1.3 and valuef about 110 MPa. Theσ(ε)-curves are similar for the tw


Fig. 3. Typical experimental stress–strain curves of plane strain compressedAl–0.1% Mn (lower plots) and Al–0.3% Mn (upper plots).

Al–Mn alloys and the manganese hardens moderately thematerial.

The microstructure of the longitudinal sections of theplane strain deformed samples is shown inFig. 4. Defor-mation heterogeneities such as shear and deformation bandsare observed in many of the grains.Fig. 4shows long bandedstructures along RD developed within single coarse grainscut by classical microshear bands at∼35◦ to RD.

4.2. In situ annealing

4.2.1. Grain boundary velocitiesThe velocity of each HAGB was determined by mea-

suring the equivalent circle diameter of the recrystallizinggrains after each in situ annealing time interval. Using the 15◦misorientation criterion with respect to the standard texturecomponents, most of the new grains could be classed as “ran-

F ssedA

dom” or “cube” orientations and typically were misoriented30–45◦ to the local deformed matrix. The grain boundarieswhich showed impingement were excluded from the presentstudy. During the in situ annealing experiments different grainboundary behaviours were observed. The typical behaviourof the majority of the grain boundary migration experimentsis denoted “Standard Rex”. However, in both Al–Mn alloys,some experiments indicated slower or even no recrystalliza-tion at all (Slow Rex). Quite frequently some very rapidrecrystallization (Rapid Rex) occurred in the Al–0.1 wt.%Mn alloy.

4.2.2. Stored energyThe local driving pressures for recrystallizationP were

obtained through the usual Read and Shockley equation[16]:

P = 3γm

d

θ

θm

[1 − ln

(θ

θm

)](5)

where γm is the energy of a HAGB taken as 0.324 J/m2

for aluminium [17] and θm is the misorientation at whicha boundary is defined as a HAGB, usually taken as 15◦. Thesubgrain sizes (d) and subgrain misorientations (θ) of theas-deformed material after plane strain compression wereobtained from the EBSD maps and quantified by the equiv-a s of1C rains( owedt clas-s an1

onoa ecrys-t befi .[

P

w der rede l val-u tt efore( .%M

u-l theσ

P
ig. 4. Optical micrograph (ND/RD section) of a channel-die comprel–0.1% Mn alloy (ε= 1.3).
lent circle diameter (ECD); they showed typical ECD.3�m± 0.2 with subgrain misorientations of 4.5◦ ± 0.3.omparison with some FEGSEM measurements of subg

85% indexed patterns) made on the same material shhat the error in determining the subgrain sizes with theical W-filament SEM (∼70% indexed patterns) was less th5%.

The local stored energiesPafter plane strain compressif the Al–Mn alloys were between 300 and 550 kJ/m3. Duringnnealing these values decrease by recovery (before r

allization) as illustrated inFig. 5. The recovery rate cantted with the phenomenological description of Stuwe et al18].

= P∞ + (P0 − P∞)

(te

t + te

)(6)

hereP0 is the initial stored energy;P∞ the residual storenergy of the fully recovered material andte the time in whichecovery would be complete if the initial slope of the stonergy–time curve could be extrapolated. Some typicaes ofP0, P, P∞ andte are given inTable 1. It is seen tha

he current stored energies can be reduced by recovery band during) recrystallization by up to 20%, for Al–0.1 wtn, and∼26% for Al–0.3 wt.% Mn.The measured values ofP are comparable to those calc

ated and estimated from the flow stresses obtained from(ε) plane strain compression curves using:

≈ µb2ρ

2≈ σ2

e

2α2M2µ(7)


Fig. 5. Stored energy variations by recovery during annealing between 200 and 450◦C afterε= 1.3: (a) “Slow Rex” in Al–0.1% Mn, (b) “Standard Rex” inAl–0.1% Mn, (c) “Rapid Rex” in Al–0.1% Mn, (d) “Standard Rex” in Al–0.3% Mn. The lines represent schematic trends for local areas given that the initialtrue values att= 0 are not known before the heating experiments.

whereb is the Burgers vector (2.86× 10−10 m); ρ the dis-location density;σe the estimated flow stress (∼110 MPa);M the Taylor factor (for FCC metalsM∼ 3) andµ the shearmodulus (26 GPa). The parameterα varies for Al between

0.20 and 0.35[19]. In the present work on Al–Mn, a valueof α≈ 0.24 was found to give a reasonable fit for the esti-mated dislocation densities (∼4× 1014 m−2) and the storedenergies.

Table 1Typical parameters and experimental values used in Eqs.(5) and(6)

T (◦C) P∗0 (kJ/m3) P (kJ/m3) P∞ (kJ/m3) te (min) �P (%)

Al–0.1 wt.% Mn Standard Rex 220 490 479 440 50 4240 450 406 400 50 10260 422 378 355 15 10280 429 363 350 4 15

Slow Rex 300 460 434 400 2 6315 427 327 320 30 21330 430 330 300 15 23

Al–0.3 wt.% Mn Standard Rex 320 533 450 400 7 16350 526 430 400 10 18390 548 434 n.d. n.d. 21

P∗0 is determined from the measured values of mean subgrain sizes and mean misorientations in the as-deformed samples.


Fig. 6. EBSD maps of an example of “Standard Rex” behaviour in Al–0.3 wt.% Mn after in situ anneals at 350◦C for (a) 14 min, (b) 16 min, (c) 18 min, (d)20 min, and (e) 22 min.

Fig. 7. EBSD maps of in situ annealed Al–0.3 wt.% Mn after 1 h at 260◦C then (a) 3 min; (b) 6 min 30 s; (c) 10 min and (d) 17 min at 320◦C, showing islandsubgrain formation by grain growth around the subgrains.


4.2.3. MobilitiesThe grain boundary mobility (M) of each HAGB of the

recrystallizing grains was obtained by dividing the grainboundary migration rate (V) by the current driving pressure(P) for temperatures of 200–450◦C. Fig. 6 shows the typi-cal growth (Standard Rex) of an Al–0.3 wt.% Mn grain afterseveral anneals at 320◦C. Fig. 7 gives an example of thesame alloy where no recrystallization occurred at 260◦C butstandard behaviour was subsequently observed at 320◦C. Aninteresting feature is the presence of “island subgrains” thatare left in the recrystallizing grain. Orientation line scansindicate that the island subgrains are misoriented by 5–10◦with respect to the growing grain.Fig. 8 shows an exampleof a grain undergoing very rapid recrystallization in the 0.1%Mn alloy at 220◦C (Rapid Rex).

However, some samples of both alloys, but mostly 0.1%Mn, annealed in the temperature range 280–390◦C exhibitedboundary migration rates that were at least an order of mag-nitude lower than the standard rates (samples denoted “SlowRex”).

Fi

Fig. 9. Mobility of grain boundaries in Al–Mn as a function of inverseannealing temperature (each point represents the average of 3–5 in situ mea-surements).

To give some idea of the dispersion in the mobility results,one can estimate the relative proportions of Standard, Rapidand Slow Rex as 70, 15 and 15% respectively from close to200 in situ measurements.

The effect of the annealing temperature on the mobilitiesof HAGB for these different regimes is summarized inFig. 9.In the same figure we have included data on high angle mobil-ities in pure Al together with some results on Al–17 at. ppmCu [2] and Al–500 at. ppm Si[20]. The results on the latteralloy, taken from the work of Huang and Humphreys, con-cern 40◦ 〈1 1 1〉 tilt and twist grain mobilities, measured in asimilar manner, during recrystallization of a cold deformedAl–Si single crystal. FromFig. 9, it is clear that the high angleboundary mobilities in Al–Mn (about 0.05 and 0.15 at.% Mn)are close to the mobilities of the 40◦ 〈1 1 1〉 twist boundariesin Al–0.05 at.% Si, i.e. those which, according to Huang andHumphreys, represent the behaviour of “random” high angleboundaries in Al–Si.

The activation energies for boundary migration in Al–Mnas deduced fromFig. 9are 140± 20 kJ/mol for the standard

ig. 8. EBSD maps of the “Rapid Rex” behaviour of Al–0.1% Mn duringn situ annealing at 220◦C for (a) 40 s, (b) 100 s.

recrystallization of both alloys and 170± 20 kJ/mol for theSlow Rex of the 0.1 wt.% Mn alloy.Table 2 summarizesthe mobilities at a fixed temperature of 280◦C, from theset of results described above. They show that for a major-ity of grain boundaries (Standard Rex), the mobility rangesfrom 1.5× 10−14 m4/J s (0.3 wt.% Mn) to 3.8× 10−13 m4/J s( -t ins( theS of

0.1 wt.% Mn) withM0 between 0.9 and 2.7 m4/J s, respecively. In Al–0.1 wt.% Mn, some slower recrystallizing graSlow Rex) possess mobilities of the same order astandard Rex in Al–0.3 wt.% Mn but with higher values


Table 2Estimation of the migration parameters for in situ annealing at 280◦C

V (×10−9 m s−1) P (kJ/m3) M (×10−14 m4/J s) M0 (m4/J s) Q (kJ/mol)

Al–0.1 wt.% Mn Standard Rex 141 370 38 2.71 136Slow Rex 3.7 370 1.0 75.33 168Rapid Rex 1260 370 340 – –

Al–0.3 wt.% Mn Standard Rex 6.6 440 1.5 0.09 135

M0 ≈ 75 m4/J s. Also, in the same alloy and as noted before,there were a few rapidly recrystallizing grains (Rapid Rex)with mobilities of one to over two orders of magnitude higher.

The apparent activation energies measured for mostboundary mobilities are consistent with the activation ener-gies for solute Mn atoms moving behind the grain boundary,i.e. betweenQv for bulk volume diffusion of Mn (217 kJ/mol)[21] andQGB = 0.55Qv taken for boundary diffusion. It isthen interesting to estimate the relative contributions of grainboundary and lattice diffusion using the CLS solute drag the-ories.

4.2.4. Estimation of the diffusion ratesThe effective diffusion rates were estimated from the log-

arithmic mean values, as proposed by Liao[22] using Eq.(8)

Deff = exp

(ξ1 lnDGB + ξ2 lnDv

2

)(8)

This is an empirical relation which has the advantage of giv-ing a weighted average of diffusion coefficients which candiffer by orders of magnitude and thereby enables one toestimate their relative contributions. According to Stuwe[23]this just means that the activation energy assumed for atomsmoving behind the grain boundary is betweenQv for bulkd

se a-t ivecaC ure-m atingP4 ndra y, ise nddf

TE

[[

Fig. 10. Experimental (dashed lines) and theoretical (continuous lines) plotsof boundary velocity as a function of inverse temperature for the two Al–Mnalloys. According to Cahn’s theory[3] the point of inflexion should occur at∼300◦C for an alloy with∼0.05 at.% Mn.

[24]. Solutions forDeff from the value of the function(aDeff/1 +bDeff) are obtained numerically.

Table 3 summarizes the mean values for the differentregimes, independently of the Mn solute concentration. Thevalues ofξ1 typically show a spread from∼0.7 to 1.6. Clearly,the average value of 1.09, estimated from the solute dragmodel of Lucke and Stuwe[4,5], and of 1.14, estimated fromthe expression of Cahn[3], are comparable and are close tothe valueξ1 ∼ 1 used by Liao et al.[14,15]. There is a gen-eral decrease ofξ1 with increasing the velocity regime (fromSlow to Rapid Rex) and with increasing the annealing tem-perature, indicating a corresponding reduced contribution ofgrain boundary diffusion at higher temperature (and thereforethe higher activation energies of lattice diffusion).

5. Discussion

The grain boundary mobility results obtained by in situannealing experiments obviously are limited to surface (2D)measurements which can be criticized for the possible effectsof boundary grooving. However, several recent studies ofboundary migration in Al based bicrystals[25] and poly-crystals[26] have lead to the conclusion that the grooving

iffusion andQGB for boundary diffusion.The values ofDGB andDv are taken from the Arrheniu

quation withD0 = 0.0317 m2/s [21] and the above activion energies. Theξ1 andξ2 parameters describe the relatontributions of boundary and lattice diffusion (ξ1 + ξ2 = 2)nd are obtained by estimatingDeff from Eqs.(2)–(4) ofLS theory and the experimental boundary velocity measents. In practice, for the Cahn model this means evalui(V,C,Deff) from Eq.(3) using the following constants:a:.05A (lattice parameter);µ: 26 GPa (shear modulus) a: 1.43A (atomic radius of the base metal).E0, the solutetom interaction energy in the centre of the boundarstimated asE0 = 0.162 eV. The experimental velocities ariving pressures are then inserted into Eq.(2), given thatMint

or pure Al is taken as 1.4× 10−3 exp(−60000/RT) m4/J s

able 3stimation of the mean values ofξ1 andξ2 according to Eq.(8)

Standard Rex Slow Rex Rapid Rex

ξ1 ξ2 ξ1 ξ2 ξ1 ξ2

3] 1.14 0.86 0.78 1.22 1.58 0.424,5] 1.09 0.91 0.74 1.26 1.55 0.45


effect on boundary migration in these alloy systems, if any,can be neglected. The present study is also being extended to3D measurements of grain growth in the same alloys in col-laboration with the Riso group and the 3D XRD microscope.It is therefore expected to confirm this hypothesis in the nearfuture.

The experimental mobilities of Al–Mn polycrystals areclose to those measured by Huang and Humphreys[20] inan Al–0.05 at.% Si single crystal. The alloys with 0.05 and0.15 at.% Mn are comparable in solute concentration but thesolute drag mechanism controlling grain boundary migra-tion appears to be quite different. According to the mobilityresults of Huang and Humphreys[20] the migration activationenergy was close to that of bulk diffusion of Si in Al, whilein our experiments the grain boundary migration seems tobe controlled by an effective diffusion intermediate betweenboundary and bulk diffusion of Mn in Al.

By plotting the experimental boundary velocities as afunction of the inverse annealing temperature (Fig. 9) weobtain two different curves: (i) a continuous line for theAl–0.3 wt.% Mn alloy and (ii) an S-shape curve for theAl–0.1 wt.% Mn alloy. This dependency on solute concen-tration and temperature is coherent with solute drag theoriesand can explain some of the different experimental boundarymigration behaviours during annealing (Fig. 10).

Using Cahn’s[3] solute drag expression withE ,D andM uldb ndi-tc hand,f esm -ni eo-r√

i-tc et( ithl , theg s tod thesee t.%M nA d”( nd-a encef striala

toe cen-t grainb Mna ard

Al–0.3% Mn alloy is consistent with this interpretation. How-ever, for the moment there is no obvious reason why thereshould be localized solute concentrations. An alternativeexplanation could be a lack of easy nucleation sites in thislarge grained material. Further tests are being conducted todetermine the origin of this behaviour.

6. Conclusions

(1) An SEM/EBSD in situ annealing technique has been usedto study HAGB mobilities during the recrystallization ofroom temperature deformed Al–0.1 and –0.3 wt.% Mnalloys in the temperature range 200–450◦C.

(2) During the in situ annealing experiments different grainboundary behaviours were observed. Most of the exper-iments on both Al–Mn alloys showed normal recrystal-lization of the new grains but in some other experimentsfaster, slower or even no recrystallization at all took place.

(3) Comparison of experimental data with solute drag theo-ries confirmed instability for the case of the deformedAl–0.1 wt.% Mn alloy. Boundary migration during insitu annealing is characterized by “loaded” and “mixed”behaviour whereas the Al–0.3 wt.% Mn alloy exhibitsonly “loaded” grain boundary behaviour.

( me-tice

( n

a-

A

fort nd J.H rtic-uc n par-t e“ nw turesi

R

d.),78,

8.

ys-pp.

0 eff

0, theory indicates that the Al–0.3 wt.% Mn alloy shoehave as a “loaded” grain boundary for all annealing co

ions with one simple solution denoted “V3”. This is taken toorrespond to our Standard Rex regime. On the otheror the Al–0.1 wt.% Mn alloy atT< 400◦C, three possiblolutions are obtained from Eq.(2): “V 1”, “V 2” and “V3” (orore precisely two solutions for V1 and V3 with an indetermiate value for V2). The inflexion point near lnV=−14 m s−1

s quite well predicted by theory; the slope of the thetical curve should change at the transition velocityVT ≈3/β = 1.75× 10−7 m s−1 at 300◦C and at a compos

ionC0 ≈ C = (4λ/α)[(βP/λ√

3) − 1] (with λ= 1/Mint), i.e.lose to 0.05 at.% Mn. Above 400◦C for this alloy there arwo solutions “V2” and “V1” indicating a partially “free”or even “free”) grain boundary migration behaviour wess or no solute drag. Below this critical temperaturerain boundary is “loaded” with solute atoms and harag the solute atoms unless it can break away. Fromxperimental observations and calculations, the Al–0.1 wn alloy is clearly unstable atT< 400◦C. Consequently, il–0.1 wt.% Mn it is possible to find both totally “loade

Standard Rex) and partially “free” (Rapid Rex) grain boury migration during annealing. This seems to be evid

or the stable/unstable solute drag model in a near-indulloy composition.

The origin of “Slow Rex” behaviour is more difficultxplain. This may be due to some localized solute conration above the values deduced from (steady state)oundary migration theory. The fact that the Al–0.1%lloy in the Slow Rex regime behaves like the stand

4) The activation energy for boundary migration is interdiate between that of solute (Mn) diffusion in the latand along the grain boundaries.

5) The diffusion rates controlling solute drag in Al–Mwere estimated via the solute drag models of Cahn[3],Lucke and Stuwe[4,5]. The results were highly comprable.

cknowledgements

The authors would like to acknowledge R. Le Gallhe many useful comments about the heating stage aumphreys for the VMAP software. They are also palarly grateful to R.D. Doherty and to H.P. Stuwe for theiromments and interest in the results. This work has beeially funded by a Rhone-Alpes Regional Avenir programmMobility of grain boundaries in Al alloys” in cooperatioith the Centre for Fundamental Research: Metal Struc

n 4 Dimensions, Riso National Laboratory.

eferences

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grain boundary mobilities during recrystallization of al–mn alloys as measured by in situ...

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