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Grain boundary mobilities during recrystallization of Al–Mn alloys as measured by in situ annealing experiments
Materials Science and Engineering A 403 (2005) 144–153
Grain boundary mobilities during recrystallization of Al–Mn alloys as measured 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 characterized by in situ SEM annealing experiments. Polycrystals of high purity, single-phase Al–Mn alloys were deformed in channel-die plane strain compression at room temperature to strains of 1.3. The specimens were in situ annealed in an SEM/EBSD in order to measure grain boundary mobilities 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 and the stored energies, were consistent with the solute drag theories of Cahn, L¨ucke and St¨uwe. The diffusion rates controlling the solute drag were of the same order for both theories and the activation energy for boundary migration was found to be intermediate between that of solute diffusion in the lattice and along the grain boundaries. © 2005 Elsevier B.V. All rights reserved. Keywords: Al–Mn alloys; In situ annealing; SEM/EBSD; Grain boundary mobility; Solute drag; Effective diffusion; Activation energy
1. Introduction Al–Mn alloys are important materials for applications in the packaging, aerospace and car industries (often used in heat exchangers). Manganese improves the resistance to corrosion, hardens the material and generally leads to good formability. It also increases the recrystallization temperature. Quantitative characterization of the evolution of the microstructure during processing and heat treatment is crucial to future developments of these alloys. One important tool in the rapid development of new products is computer simulation of the recrystallization processes and grain growth as a function of the physical parameters of the material. This needs an understanding of the mechanisms of nucleation, recrystallization and grain growth in real commercial purity alloys under typical conditions of industrial processing. In this context, one of the difficulties is to know how the solute atoms interact with the grain bound∗
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0921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2005.05.010
ary and consequently influence the mobilities of the grain boundaries. The influence of trace quantities of solute atoms (<0.1 at.%) on grain boundary migration rates in Al has been studied many years ago, for example by Dimitrov et al. [1] and Gordon and Vandermeer [2], and correlated with the solute drag theories of Cahn [3] and L¨ucke and St¨uwe [4,5]. However, little experimental work has been carried out on higher solute contents typical of most real alloy systems. For example, the standard AA 3103 Al–Mn alloy contains about 1 wt.% Mn of which about 0.3–0.5 wt.% stays in solid solution after processing by hot rolling. This amount of Mn in solution then has a major influence on subsequent recrystallization following cold rolling. The aim of this paper is first to describe an in situ SEM technique to measure 2D grain boundary mobilities in industrially relevant Al–Mn alloys and then to estimate the diffusion rates responsible for the boundary mobilities by comparison with the solute drag theories of Cahn, L¨ucke and St¨uwe (CLS). Two alloy compositions have been selected; 0.3 wt.% Mn approximately representing the solid
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solution of industrial AA 3103 and a 0.1 wt.% Mn alloy for comparison with previous work on solute drag effects.
particular form: Pi (V, C) =
2. Solute drag theory L¨ucke et al. [6] and L¨ucke and Detert [7] demonstrated that the addition of 0.01 at.% of Mn and Fe to aluminium could slow down the recrystallization kinetics by factors of 1012 and 1016 , respectively, compared with pure Al. These observations led to the development of the classical solute drag theories that quantitatively predict the influence of solute atoms on the migration rates of grain boundaries. In pure materials grain boundary migration theory predicts that the boundary velocity (V) can be expressed as the product of two terms – the “intrinsic” mobility (Mint ) of the pure grain boundary and the driving pressure (P) for the process; during recrystallization by isothermal annealing this is the reduction in free energy of the system accumulated in the deformed material essentially as dislocations. For pure metals the rate of grain boundary migration during recrystallization is written as follows: V = Mint P
(1)
The mobility follows a standard Arrhenius equation Mint = M0 exp(−Q/RT), where M0 is the pre-exponential mobility factor and Q the activation energy for boundary migration. However, for metals containing solute atoms the above linear relationship becomes somewhat more complicated. The “extrinsic” mobility differs from the “intrinsic” mobility because of the presence of a new effective driving pressure (P ) which is the difference between the current pressure (P) and the solute drag Pi (V, C) produced by the interaction of solute atoms (concentration C) with the grain boundaries moving at a velocity (V). The rate of grain boundary migration becomes: V = Mint P = Mint [P − Pi (V, C)]
(2)
Cahn [3] described the impurity drag pressure Pi (V, C) by a model with a triangular interaction energy profile for the solute atoms close to the boundary (Fig. 1a). In this model, a treatment of the diffusion of foreign atoms with respect to a moving grain boundary, gives for Pi (V, C) in Eq. (2) the
Fig. 1. Profile of the interaction energy E(x): (a) triangular profile of Cahn [3] and L¨ucke and St¨uwe [4], (b) step function profile of L¨ucke and St¨uwe [5].
145
αCV 1 + β2 V 2
(3)
where α and β are parameters depending on the form of the interaction energy E(x) and the effective diffusion (Deff ) of the solute atoms in the grain boundary: N(kT )2 E0 E0 α= sinh − δ E0 Deff kT kT β2 =
αkTδ 2NE02 Deff
where N is the number of atoms/unit volume (N ≈ 1/b3 ); C the macroscopic atomic concentration; V the grain boundary velocity; E0 the solute atom interaction energy in the centre of the boundary; δ the half thickness of the grain boundary b, the interatomic distance in the lattice and k the Boltzmann constant. Independently, L¨ucke and St¨uwe [4] developed at the same time a very similar theory called the continuum model where the interaction energy between solute atoms and grain boundary is described by a triangular shape. Later, the authors developed the model for higher solute contents [5] where the drag pressure is described by an atomistic model with an interaction energy profile as a step function (Fig. 1b). The expression for Pi (V, C) now takes the particular form [5]: Pi (V, C) =
¯ −ψ ¯ 2 ) + ϕ2 (ψ − ψ)) ¯ 1/2(ϕ(ψ2 + ψ − ψ CNE0 ¯ + ϕ) (ψ + ϕ)(1 + ϕ)(ψ (4)
¯ = exp(−η/2), where the parameters are ψ = exp(η/2), ψ ϕ ≈ bV/Deff and η = E0 /kT. In both models, the interaction between the solute atoms and the moving grain boundary can produce three different velocity regimes as a function of the solute content, the stored energy and the annealing temperature: the first regime corresponds to the migration of the pure material (without solute drag) with a unique solution “V1 ”, the second regime corresponds to the migration of the “loaded” grain boundary (with solute drag) with a unique solution “V3 ” and the third regime corresponds to an instability behaviour of the grain boundary where three velocities can exist: “V1 ”, “V2 ” (intermediate velocity) and “V3 ”. To evaluate Pi (V, C) it is thus necessary to know the effective diffusion rates (Deff ) and the soluteboundary interaction energy (E0 ). Although the latter can be estimated theoretically [7], the diffusion rates depend upon the relative contributions of boundary and lattice diffusion. These vary with annealing conditions and, in principle, are accessible from experimental data for boundary migration under different conditions. Over the years there have been several further theoretical developments in the analysis of solute drag, see for example [8–12], but the general physical principles of the Cahn, L¨ucke, St¨uwe models still hold. The present work will use the
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latter as a basis for analysing boundary migration behaviour in simple binary alloys.
3. Experimental procedures 3.1. Sample preparation The Al–Mn ingots were prepared from high purity Mn and a high purity aluminium, provided by the Voreppe-Research Centre of Alcan with the following major impurity contents in wt. ppm: 7 Si, 1 Fe, 4 Mn, 1 Cr, 4 Zn and 3 Ga. Controlled solidification was carried out in alumina moulds under a partial pressure of argon, to form 1 kg Al–Mn ingots of nominal composition 0.1 and 0.3 wt.% Mn. Only the centres of the ingots were used for the experiments to avoid the effects of impurity segregation. Emission spectrometry confirmed the homogeneity of the manganese in the central parts of the two alloys, i.e. 0.10 ± 0.008 and 0.30 ± 0.006 wt.% Mn corresponding respectively to 490 and 1480 at. ppm Mn The ingots were processed into specimen bars by hot forging at 550 ◦ C to 10 mm thickness; they recrystallized during cooling 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 strain compression at room temperature using a channel-die device to strains εVM = 1.3 at constant strain rates of 10−2 s−1 . To reduce friction, the samples were wrapped in Teflon films. The specimens used for the annealing experiments were taken from the central part of the samples along the deformed direction (denoted RD for the equivalent rolling direction). They were mechanically and electropolished (−30 ◦ C/12 V) with 15% HNO3 and methanol before annealing. A preliminary set of standard annealing experiments was carried out to determine recrystallization kinetics in the temperature range 200–450 ◦ C. Some thermoelectric power measurements made at the ALCAN Voreppe-Research Centre (ANATECH with an accuracy of ±0.007 wt.%) also confirmed that all the Mn stayed in solid solution after one-hour annealing at temperatures between 200 and 350 ◦ C. 3.2. The heating stage The aim of the in situ experiments is to study the grain boundary mobility of Al–0.1 and –0.3 wt.% Mn alloys in a SEM during multiple annealings at various temperatures between 200 and 450 ◦ C. A heating stage was constructed [13] based on the design and operating principle of Liao and Le Gall et al. [14,15], as developed for studying grain boundary migration in stainless steels and cold rolled nickel. Some modifications of the design were necessary to use the heating stage at a 70◦ tilted position as required for the EBSD technique (Fig. 2). The aluminium sample is welded to a tantalum strip, heated by electrical resistance. The samples were checked to ensure that the weld zone did not recrystallize. The
Fig. 2. Schematic representation of sample and in situ heating stage in the SEM.
chromel–alumel thermocouple (K), welded on the Ta-strip, controls the temperature of the Ta and thus the Al-sample through a temperature regulator and power supply. The desired temperature is computed on the regulator and the heating rate is manually controlled to reduce the time to heat the sample to the required temperature. In order to improve the heating rate to more than 5 K/s different voltages were used according to the thickness of the Al-sample. In this way the required temperature is reached in less than 40 s with good stabilisation (±2 K) and with rapid cooling rates (10–20 s) down to 150 ◦ C. The sample thickness varied from 0.4 to 0.8 mm, i.e. about 3 or 4 times the deformed grain thickness and the section examined on the ND/RD plane. 3.3. Data analyses The in situ experiments were carried out in a SEM JEOL 6400 (W filament, vacuum ∼10−4 Pa). During each in situ heating experiment, the evolution of the microstructure was followed on the 70◦ tilted sample with a backscattered electron detector. After each annealing, the heater was switched off and the EBSD orientation maps were made with Channel 5-acquisition software (HKL technology). The beam scanning was made in a raster of typically 150 m × 100 m with a step size of 0.5 m/step. The crystallographic and microstructural data, i.e. grain and subgrain reconstruction, misorientation and boundary character were analysed with an EBSD data analysing program VMAP developed by J. Humphreys (Manchester Materials Science Centre).
4. Results 4.1. Deformed specimens Fig. 3 gives the stress–strain curves for the two Al–Mn alloys. The flow stress increases rapidly with strain towards εVM ≥ 0.05, then at a lower rate to εVM ≈ 1.3 and values of about 110 MPa. The σ(ε)-curves are similar for the two
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dom” or “cube” orientations and typically were misoriented 30–45◦ to the local deformed matrix. The grain boundaries which showed impingement were excluded from the present study. During the in situ annealing experiments different grain boundary behaviours were observed. The typical behaviour of the majority of the grain boundary migration experiments is denoted “Standard Rex”. However, in both Al–Mn alloys, some experiments indicated slower or even no recrystallization at all (Slow Rex). Quite frequently some very rapid recrystallization (Rapid Rex) occurred in the Al–0.1 wt.% Mn alloy.
Fig. 3. Typical experimental stress–strain curves of plane strain compressed Al–0.1% Mn (lower plots) and Al–0.3% Mn (upper plots).
Al–Mn alloys and the manganese hardens moderately the material. The microstructure of the longitudinal sections of the plane strain deformed samples is shown in Fig. 4. Deformation heterogeneities such as shear and deformation bands are observed in many of the grains. Fig. 4 shows long banded structures along RD developed within single coarse grains cut by classical microshear bands at ∼35◦ to RD. 4.2. In situ annealing 4.2.1. Grain boundary velocities The velocity of each HAGB was determined by measuring the equivalent circle diameter of the recrystallizing grains after each in situ annealing time interval. Using the 15◦ misorientation criterion with respect to the standard texture components, most of the new grains could be classed as “ran-
4.2.2. Stored energy The local driving pressures for recrystallization P were obtained through the usual Read and Shockley equation [16]: 3γm θ θ P= 1 − ln (5) d θm θm where γ m is the energy of a HAGB taken as 0.324 J/m2 for aluminium [17] and θ m is the misorientation at which a boundary is defined as a HAGB, usually taken as 15◦ . The subgrain sizes (d) and subgrain misorientations (θ) of the as-deformed material after plane strain compression were obtained from the EBSD maps and quantified by the equivalent circle diameter (ECD); they showed typical ECDs of 1.3 m ± 0.2 with subgrain misorientations of 4.5◦ ± 0.3. Comparison with some FEGSEM measurements of subgrains (85% indexed patterns) made on the same material showed that the error in determining the subgrain sizes with the classical W-filament SEM (∼70% indexed patterns) was less than 15%. The local stored energies P after plane strain compression of the Al–Mn alloys were between 300 and 550 kJ/m3 . During annealing these values decrease by recovery (before recrystallization) as illustrated in Fig. 5. The recovery rate can be fitted with the phenomenological description of St¨uwe et al. [18]. te P = P∞ + (P0 − P∞ ) (6) t + te where P0 is the initial stored energy; P∞ the residual stored energy of the fully recovered material and te the time in which recovery would be complete if the initial slope of the stored energy–time curve could be extrapolated. Some typical values of P0 , P, P∞ and te are given in Table 1. It is seen that the current stored energies can be reduced by recovery before (and during) recrystallization by up to 20%, for Al–0.1 wt.% Mn, and ∼26% for Al–0.3 wt.% Mn. The measured values of P are comparable to those calculated and estimated from the flow stresses obtained from the σ(ε) plane strain compression curves using:
Fig. 4. Optical micrograph (ND/RD section) of a channel-die compressed Al–0.1% Mn alloy (ε = 1.3).
P≈
µb2 ρ σ2 ≈ 2e2 2 2α M µ
(7)
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Fig. 5. Stored energy variations by recovery during annealing between 200 and 450 ◦ C after ε = 1.3: (a) “Slow Rex” in Al–0.1% Mn, (b) “Standard Rex” in Al–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 initial true values at t = 0 are not known before the heating experiments.
where b is the Burgers vector (2.86 × 10−10 m); ρ the dislocation density; σ e the estimated flow stress (∼110 MPa); M the Taylor factor (for FCC metals M ∼ 3) and µ the shear modulus (26 GPa). The parameter α varies for Al between
0.20 and 0.35 [19]. In the present work on Al–Mn, a value of α ≈ 0.24 was found to give a reasonable fit for the estimated dislocation densities (∼4 × 1014 m−2 ) and the stored energies.
Table 1 Typical parameters and experimental values used in Eqs. (5) and (6)
Al–0.1 wt.% Mn
Standard Rex
Slow Rex
Al–0.3 wt.% Mn
Standard Rex
T (◦ C)
P¯ 0∗ (kJ/m3 )
P¯ (kJ/m3 )
P¯ ∞ (kJ/m3 )
te (min)
P¯ (%)
220 240 260 280 300 315 330 320 350 390
490 450 422 429 460 427 430 533 526 548
479 406 378 363 434 327 330 450 430 434
440 400 355 350 400 320 300 400 400 n.d.
50 50 15 4 2 30 15 7 10 n.d.
4 10 10 15 6 21 23 16 18 21
P¯ 0∗ is determined from the measured values of mean subgrain sizes and mean misorientations in the as-deformed samples.
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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 island subgrain formation by grain growth around the subgrains.
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4.2.3. Mobilities The grain boundary mobility (M) of each HAGB of the recrystallizing grains was obtained by dividing the grain boundary migration rate (V) by the current driving pressure (P) for temperatures of 200–450 ◦ C. Fig. 6 shows the typical growth (Standard Rex) of an Al–0.3 wt.% Mn grain after several anneals at 320 ◦ C. Fig. 7 gives an example of the same alloy where no recrystallization occurred at 260 ◦ C but standard behaviour was subsequently observed at 320 ◦ C. An interesting feature is the presence of “island subgrains” that are left in the recrystallizing grain. Orientation line scans indicate that the island subgrains are misoriented by 5–10◦ with respect to the growing grain. Fig. 8 shows an example of 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 exhibited boundary migration rates that were at least an order of magnitude lower than the standard rates (samples denoted “Slow Rex”).
Fig. 9. Mobility of grain boundaries in Al–Mn as a function of inverse annealing temperature (each point represents the average of 3–5 in situ measurements).
Fig. 8. EBSD maps of the “Rapid Rex” behaviour of Al–0.1% Mn during in situ annealing at 220 ◦ C for (a) 40 s, (b) 100 s.
To give some idea of the dispersion in the mobility results, one can estimate the relative proportions of Standard, Rapid and Slow Rex as 70, 15 and 15% respectively from close to 200 in situ measurements. The effect of the annealing temperature on the mobilities of HAGB for these different regimes is summarized in Fig. 9. In the same figure we have included data on high angle mobilities in pure Al together with some results on Al–17 at. ppm Cu [2] and Al–500 at. ppm Si [20]. The results on the latter alloy, taken from the work of Huang and Humphreys, concern 40◦ 1 1 1 tilt and twist grain mobilities, measured in a similar manner, during recrystallization of a cold deformed Al–Si single crystal. From Fig. 9, it is clear that the high angle boundary mobilities in Al–Mn (about 0.05 and 0.15 at.% Mn) are close to the mobilities of the 40◦ 1 1 1 twist boundaries in Al–0.05 at.% Si, i.e. those which, according to Huang and Humphreys, represent the behaviour of “random” high angle boundaries in Al–Si. The activation energies for boundary migration in Al–Mn as deduced from Fig. 9 are 140 ± 20 kJ/mol for the standard recrystallization of both alloys and 170 ± 20 kJ/mol for the Slow Rex of the 0.1 wt.% Mn alloy. Table 2 summarizes the mobilities at a fixed temperature of 280 ◦ C, from the set of results described above. They show that for a majority of grain boundaries (Standard Rex), the mobility ranges from 1.5 × 10−14 m4 /J s (0.3 wt.% Mn) to 3.8 × 10−13 m4 /J s (0.1 wt.% Mn) with M0 between 0.9 and 2.7 m4 /J s, respectively. In Al–0.1 wt.% Mn, some slower recrystallizing grains (Slow Rex) possess mobilities of the same order as the Standard Rex in Al–0.3 wt.% Mn but with higher values of
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Table 2 Estimation of the migration parameters for in situ annealing at 280 ◦ C
Al–0.1 wt.% Mn
Standard Rex Slow Rex Rapid Rex Standard Rex
Al–0.3 wt.% Mn
V (×10−9 m s−1 )
P (kJ/m3 )
M (×10−14 m4 /J s)
M0 (m4 /J s)
Q (kJ/mol)
141 3.7 1260 6.6
370 370 370 440
38 1.0 340 1.5
2.71 75.33 – 0.09
136 168 – 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 most boundary mobilities are consistent with the activation energies for solute Mn atoms moving behind the grain boundary, i.e. between Qv for bulk volume diffusion of Mn (217 kJ/mol) [21] and QGB = 0.55Qv taken for boundary diffusion. It is then interesting to estimate the relative contributions of grain boundary and lattice diffusion using the CLS solute drag theories. 4.2.4. Estimation of the diffusion rates The effective diffusion rates were estimated from the logarithmic mean values, as proposed by Liao [22] using Eq. (8) ξ1 ln DGB + ξ2 ln Dv Deff = exp (8) 2 This is an empirical relation which has the advantage of giving a weighted average of diffusion coefficients which can differ by orders of magnitude and thereby enables one to estimate their relative contributions. According to St¨uwe [23] this just means that the activation energy assumed for atoms moving behind the grain boundary is between Qv for bulk diffusion and QGB for boundary diffusion. The values of DGB and Dv are taken from the Arrhenius equation with D0 = 0.0317 m2 /s [21] and the above activation energies. The ξ 1 and ξ 2 parameters describe the relative contributions of boundary and lattice diffusion (ξ 1 + ξ 2 = 2) and are obtained by estimating Deff from Eqs. (2)–(4) of CLS theory and the experimental boundary velocity measurements. In practice, for the Cahn model this means evaluating Pi (V, C, Deff ) from Eq. (3) using the following constants: a: ˚ (lattice parameter); µ: 26 GPa (shear modulus) and 4.05 A ˚ (atomic radius of the base metal). E0 , the solute r: 1.43 A atom interaction energy in the centre of the boundary, is estimated as E0 = 0.162 eV. The experimental velocities and driving pressures are then inserted into Eq. (2), given that Mint for pure Al is taken as 1.4 × 10−3 exp(−60000/RT) m4 /J s Table 3 Estimation of the mean values of ξ 1 and ξ 2 according to Eq. (8) Standard Rex
[3] [4,5]
Slow Rex
Rapid Rex
ξ1
ξ2
ξ1
ξ2
ξ1
ξ2
1.14 1.09
0.86 0.91
0.78 0.74
1.22 1.26
1.58 1.55
0.42 0.45
Fig. 10. Experimental (dashed lines) and theoretical (continuous lines) plots of boundary velocity as a function of inverse temperature for the two Al–Mn alloys. 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 for Deff from the value of the function (aDeff /1 + bDeff ) are obtained numerically. Table 3 summarizes the mean values for the different regimes, independently of the Mn solute concentration. The values of ξ 1 typically show a spread from ∼0.7 to 1.6. Clearly, the average value of 1.09, estimated from the solute drag model of L¨ucke and St¨uwe [4,5], and of 1.14, estimated from the expression of Cahn [3], are comparable and are close to the value ξ 1 ∼ 1 used by Liao et al. [14,15]. There is a general decrease of ξ 1 with increasing the velocity regime (from Slow to Rapid Rex) and with increasing the annealing temperature, indicating a corresponding reduced contribution of grain boundary diffusion at higher temperature (and therefore the higher activation energies of lattice diffusion).
5. Discussion The grain boundary mobility results obtained by in situ annealing experiments obviously are limited to surface (2D) measurements which can be criticized for the possible effects of boundary grooving. However, several recent studies of boundary migration in Al based bicrystals [25] and polycrystals [26] have lead to the conclusion that the grooving
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effect on boundary migration in these alloy systems, if any, can be neglected. The present study is also being extended to 3D measurements of grain growth in the same alloys in collaboration with the Riso group and the 3D XRD microscope. It is therefore expected to confirm this hypothesis in the near future. The experimental mobilities of Al–Mn polycrystals are close to those measured by Huang and Humphreys [20] in an Al–0.05 at.% Si single crystal. The alloys with 0.05 and 0.15 at.% Mn are comparable in solute concentration but the solute drag mechanism controlling grain boundary migration appears to be quite different. According to the mobility results of Huang and Humphreys [20] the migration activation energy was close to that of bulk diffusion of Si in Al, while in our experiments the grain boundary migration seems to be controlled by an effective diffusion intermediate between boundary and bulk diffusion of Mn in Al. By plotting the experimental boundary velocities as a function of the inverse annealing temperature (Fig. 9) we obtain two different curves: (i) a continuous line for the Al–0.3 wt.% Mn alloy and (ii) an S-shape curve for the Al–0.1 wt.% Mn alloy. This dependency on solute concentration and temperature is coherent with solute drag theories and can explain some of the different experimental boundary migration behaviours during annealing (Fig. 10). Using Cahn’s [3] solute drag expression with E0 , Deff and M0 , theory indicates that the Al–0.3 wt.% Mn alloy should behave as a “loaded” grain boundary for all annealing conditions with one simple solution denoted “V3 ”. This is taken to correspond to our Standard Rex regime. On the other hand, for the Al–0.1 wt.% Mn alloy at T < 400 ◦ C, three possible solutions are obtained from Eq. (2): “V1 ”, “V2 ” and “V3 ” (or more precisely two solutions for V1 and V3 with an indeterminate value for V2 ). The inflexion point near ln V = −14 m s−1 is quite well predicted by theory; the slope of the theoretical curve should change at the transition velocity VT ≈ √ ◦ 3/β = 1.75 × 10−7 m s−1 at √ 300 C and at a composition C0 ≈ C = (4λ/α)[(βP/λ 3) − 1] (with λ = 1/Mint ), i.e. close to 0.05 at.% Mn. Above 400 ◦ C for this alloy there are two solutions “V2 ” and “V1 ” indicating a partially “free” (or even “free”) grain boundary migration behaviour with less or no solute drag. Below this critical temperature, the grain boundary is “loaded” with solute atoms and has to drag the solute atoms unless it can break away. From these experimental observations and calculations, the Al–0.1 wt.% Mn alloy is clearly unstable at T < 400 ◦ C. Consequently, in Al–0.1 wt.% Mn it is possible to find both totally “loaded” (Standard Rex) and partially “free” (Rapid Rex) grain boundary migration during annealing. This seems to be evidence for the stable/unstable solute drag model in a near-industrial alloy composition. The origin of “Slow Rex” behaviour is more difficult to explain. This may be due to some localized solute concentration above the values deduced from (steady state) grain boundary migration theory. The fact that the Al–0.1% Mn alloy in the Slow Rex regime behaves like the standard
Al–0.3% Mn alloy is consistent with this interpretation. However, for the moment there is no obvious reason why there should be localized solute concentrations. An alternative explanation could be a lack of easy nucleation sites in this large grained material. Further tests are being conducted to determine the origin of this behaviour.
6. Conclusions (1) An SEM/EBSD in situ annealing technique has been used to study HAGB mobilities during the recrystallization of room temperature deformed Al–0.1 and –0.3 wt.% Mn alloys in the temperature range 200–450 ◦ C. (2) During the in situ annealing experiments different grain boundary behaviours were observed. Most of the experiments on both Al–Mn alloys showed normal recrystallization of the new grains but in some other experiments faster, slower or even no recrystallization at all took place. (3) Comparison of experimental data with solute drag theories confirmed instability for the case of the deformed Al–0.1 wt.% Mn alloy. Boundary migration during in situ annealing is characterized by “loaded” and “mixed” behaviour whereas the Al–0.3 wt.% Mn alloy exhibits only “loaded” grain boundary behaviour. (4) The activation energy for boundary migration is intermediate between that of solute (Mn) diffusion in the lattice and along the grain boundaries. (5) The diffusion rates controlling solute drag in Al–Mn were estimated via the solute drag models of Cahn [3], L¨ucke and St¨uwe [4,5]. The results were highly comparable.
Acknowledgements The authors would like to acknowledge R. Le Gall for the many useful comments about the heating stage and J. Humphreys for the VMAP software. They are also particularly grateful to R.D. Doherty and to H.P. St¨uwe for their comments and interest in the results. This work has been partially funded by a Rhˆone-Alpes Regional Avenir programme “Mobility of grain boundaries in Al alloys” in cooperation with the Centre for Fundamental Research: Metal Structures in 4 Dimensions, Riso National Laboratory.
References [1] O. Dimitrov, R. Fromageau, M.O. Dimitrov, in: F. Haessner (Ed.), Recrystallization of Metallic Materials, Reider Verlag, Berlin, 1978, p. 131. [2] P. Gordon, R.A. Vandermeer, Trans. AIME 224 (1962) 917–928. [3] J.W. Cahn, Acta Metall. 10 (1962) 789–798. [4] K. L¨ucke, H.P. St¨uwe, in: L. Himmel (Ed.), Recovery and Recrystallization of Metals, Gordon and Breach, New York, 1962, pp. 171–209.
A. Lens et al. / Materials Science and Engineering A 403 (2005) 144–153 [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
K. L¨ucke, H.P. St¨uwe, Acta Metall. 19 (1971) 1087–1099. K. L¨ucke, G. Masing, P. N¨olting, Z. Metallk. (1956) 64. K. L¨ucke, K. Detert, Acta Metall. 5 (1957) 628. J.D. Powers, A.M. Glaeser, Interf. Sci. 6 (1998) 23. Z.-K. Liu, J. Agren, M. Suehiro, Mater. Sci. Eng. 247 (1998) 222. P.-R. Cha, S.G. Kim, D.-H. Yeon, J.-K. Yoon, Acta Mater. 50 (2002) 3817–3829. N. Ma, S.A. Dregia, Y. Wang, Acta Mater. 51 (2003) 3687–3700. M. Hillert, Acta Mater. 52 (2004) 5289–5293. A. Lens, C. Maurice, J.H. Driver, Mater. Sci. Forum 467–470 (2004) 771–776. G. Liao, R. Le Gall, G. Saindrenan, Mater. Sci. Technol. 14 (1998) 411. R. Le Gall, G. Liao, G. Saindrenan, Scripta Mater. 41 (1999) 427–432. W.T. Read, W. Shockley, Phys. Rev. 78 (1950) 275.
153
[17] L.E. Murr, Interfacial Phenomena in Metals and Alloys, AddisonWesley, Reading, MA, 1975. [18] H.P. St¨uwe, A.F. Padilha, F. Siciliano Jr., Mater. Sci. Eng. A333 (2002) 361–367. [19] F.R.N. Nabarro, Z.S. Basinski, D.R. Holt, Adv. Phys. XII (1964) 193. [20] Y. Huang, F.J. Humphreys, Acta Mater. 48 (2000) 2017–2030. [21] H. Bakker, Diffusion in Solid Metals and Alloys, 26, LandoltB¨ornstein/Springer-Verlag, Berlin, 1990. [22] G. Liao, Etude exp´erimentale des cin´etiques de recristallisation et des vitesses de migration des joints de grains dans le nickel e´ croui, Ph.D. Thesis, Universit´e de Nantes, France, 1998. [23] H.P. St¨uwe, University Vienna, Private communication, 2003. [24] A.P. Sutton, R.W. Balluffi, Interfaces in Crystalline Materials, Oxford Science Publications, 1995, p. 819. [25] G. Gottstein, L.S. Shvindlerman, Scripta Metall. 27 (1992) 1521. [26] Y. Huang, F.J. Humphreys, Acta Mater. 47 (1999) 2259–2268.
Grain boundary mobilities during recrystallization of Al–Mn alloys as measured 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 characterized by in situ SEM annealing experiments. Polycrystals of high purity, single-phase Al–Mn alloys were deformed in channel-die plane strain compression at room temperature to strains of 1.3. The specimens were in situ annealed in an SEM/EBSD in order to measure grain boundary mobilities 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 and the stored energies, were consistent with the solute drag theories of Cahn, L¨ucke and St¨uwe. The diffusion rates controlling the solute drag were of the same order for both theories and the activation energy for boundary migration was found to be intermediate between that of solute diffusion in the lattice and along the grain boundaries. © 2005 Elsevier B.V. All rights reserved. Keywords: Al–Mn alloys; In situ annealing; SEM/EBSD; Grain boundary mobility; Solute drag; Effective diffusion; Activation energy
1. Introduction Al–Mn alloys are important materials for applications in the packaging, aerospace and car industries (often used in heat exchangers). Manganese improves the resistance to corrosion, hardens the material and generally leads to good formability. It also increases the recrystallization temperature. Quantitative characterization of the evolution of the microstructure during processing and heat treatment is crucial to future developments of these alloys. One important tool in the rapid development of new products is computer simulation of the recrystallization processes and grain growth as a function of the physical parameters of the material. This needs an understanding of the mechanisms of nucleation, recrystallization and grain growth in real commercial purity alloys under typical conditions of industrial processing. In this context, one of the difficulties is to know 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).
0921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2005.05.010
ary and consequently influence the mobilities of the grain boundaries. The influence of trace quantities of solute atoms (<0.1 at.%) on grain boundary migration rates in Al has been studied many years ago, for example by Dimitrov et al. [1] and Gordon and Vandermeer [2], and correlated with the solute drag theories of Cahn [3] and L¨ucke and St¨uwe [4,5]. However, little experimental work has been carried out on higher solute contents typical of most real alloy systems. For example, the standard AA 3103 Al–Mn alloy contains about 1 wt.% Mn of which about 0.3–0.5 wt.% stays in solid solution after processing by hot rolling. This amount of Mn in solution then has a major influence on subsequent recrystallization following cold rolling. The aim of this paper is first to describe an in situ SEM technique to measure 2D grain boundary mobilities in industrially relevant Al–Mn alloys and then to estimate the diffusion rates responsible for the boundary mobilities by comparison with the solute drag theories of Cahn, L¨ucke and St¨uwe (CLS). Two alloy compositions have been selected; 0.3 wt.% Mn approximately representing the solid
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solution of industrial AA 3103 and a 0.1 wt.% Mn alloy for comparison with previous work on solute drag effects.
particular form: Pi (V, C) =
2. Solute drag theory L¨ucke et al. [6] and L¨ucke and Detert [7] demonstrated that the addition of 0.01 at.% of Mn and Fe to aluminium could slow down the recrystallization kinetics by factors of 1012 and 1016 , respectively, compared with pure Al. These observations led to the development of the classical solute drag theories that quantitatively predict the influence of solute atoms on the migration rates of grain boundaries. In pure materials grain boundary migration theory predicts that the boundary velocity (V) can be expressed as the product of two terms – the “intrinsic” mobility (Mint ) of the pure grain boundary and the driving pressure (P) for the process; during recrystallization by isothermal annealing this is the reduction in free energy of the system accumulated in the deformed material essentially as dislocations. For pure metals the rate of grain boundary migration during recrystallization is written as follows: V = Mint P
(1)
The mobility follows a standard Arrhenius equation Mint = M0 exp(−Q/RT), where M0 is the pre-exponential mobility factor and Q the activation energy for boundary migration. However, for metals containing solute atoms the above linear relationship becomes somewhat more complicated. The “extrinsic” mobility differs from the “intrinsic” mobility because of the presence of a new effective driving pressure (P ) which is the difference between the current pressure (P) and the solute drag Pi (V, C) produced by the interaction of solute atoms (concentration C) with the grain boundaries moving at a velocity (V). The rate of grain boundary migration becomes: V = Mint P = Mint [P − Pi (V, C)]
(2)
Cahn [3] described the impurity drag pressure Pi (V, C) by a model with a triangular interaction energy profile for the solute atoms close to the boundary (Fig. 1a). In this model, a treatment of the diffusion of foreign atoms with respect to a moving grain boundary, gives for Pi (V, C) in Eq. (2) the
Fig. 1. Profile of the interaction energy E(x): (a) triangular profile of Cahn [3] and L¨ucke and St¨uwe [4], (b) step function profile of L¨ucke and St¨uwe [5].
145
αCV 1 + β2 V 2
(3)
where α and β are parameters depending on the form of the interaction energy E(x) and the effective diffusion (Deff ) of the solute atoms in the grain boundary: N(kT )2 E0 E0 α= sinh − δ E0 Deff kT kT β2 =
αkTδ 2NE02 Deff
where N is the number of atoms/unit volume (N ≈ 1/b3 ); C the macroscopic atomic concentration; V the grain boundary velocity; E0 the solute atom interaction energy in the centre of the boundary; δ the half thickness of the grain boundary b, the interatomic distance in the lattice and k the Boltzmann constant. Independently, L¨ucke and St¨uwe [4] developed at the same time a very similar theory called the continuum model where the interaction energy between solute atoms and grain boundary is described by a triangular shape. Later, the authors developed the model for higher solute contents [5] where the drag pressure is described by an atomistic model with an interaction energy profile as a step function (Fig. 1b). The expression for Pi (V, C) now takes the particular form [5]: Pi (V, C) =
¯ −ψ ¯ 2 ) + ϕ2 (ψ − ψ)) ¯ 1/2(ϕ(ψ2 + ψ − ψ CNE0 ¯ + ϕ) (ψ + ϕ)(1 + ϕ)(ψ (4)
¯ = exp(−η/2), where the parameters are ψ = exp(η/2), ψ ϕ ≈ bV/Deff and η = E0 /kT. In both models, the interaction between the solute atoms and the moving grain boundary can produce three different velocity regimes as a function of the solute content, the stored energy and the annealing temperature: the first regime corresponds to the migration of the pure material (without solute drag) with a unique solution “V1 ”, the second regime corresponds to the migration of the “loaded” grain boundary (with solute drag) with a unique solution “V3 ” and the third regime corresponds to an instability behaviour of the grain boundary where three velocities can exist: “V1 ”, “V2 ” (intermediate velocity) and “V3 ”. To evaluate Pi (V, C) it is thus necessary to know the effective diffusion rates (Deff ) and the soluteboundary interaction energy (E0 ). Although the latter can be estimated theoretically [7], the diffusion rates depend upon the relative contributions of boundary and lattice diffusion. These vary with annealing conditions and, in principle, are accessible from experimental data for boundary migration under different conditions. Over the years there have been several further theoretical developments in the analysis of solute drag, see for example [8–12], but the general physical principles of the Cahn, L¨ucke, St¨uwe models still hold. The present work will use the
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latter as a basis for analysing boundary migration behaviour in simple binary alloys.
3. Experimental procedures 3.1. Sample preparation The Al–Mn ingots were prepared from high purity Mn and a high purity aluminium, provided by the Voreppe-Research Centre of Alcan with the following major impurity contents in wt. ppm: 7 Si, 1 Fe, 4 Mn, 1 Cr, 4 Zn and 3 Ga. Controlled solidification was carried out in alumina moulds under a partial pressure of argon, to form 1 kg Al–Mn ingots of nominal composition 0.1 and 0.3 wt.% Mn. Only the centres of the ingots were used for the experiments to avoid the effects of impurity segregation. Emission spectrometry confirmed the homogeneity of the manganese in the central parts of the two alloys, i.e. 0.10 ± 0.008 and 0.30 ± 0.006 wt.% Mn corresponding respectively to 490 and 1480 at. ppm Mn The ingots were processed into specimen bars by hot forging at 550 ◦ C to 10 mm thickness; they recrystallized during cooling 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 strain compression at room temperature using a channel-die device to strains εVM = 1.3 at constant strain rates of 10−2 s−1 . To reduce friction, the samples were wrapped in Teflon films. The specimens used for the annealing experiments were taken from the central part of the samples along the deformed direction (denoted RD for the equivalent rolling direction). They were mechanically and electropolished (−30 ◦ C/12 V) with 15% HNO3 and methanol before annealing. A preliminary set of standard annealing experiments was carried out to determine recrystallization kinetics in the temperature range 200–450 ◦ C. Some thermoelectric power measurements made at the ALCAN Voreppe-Research Centre (ANATECH with an accuracy of ±0.007 wt.%) also confirmed that all the Mn stayed in solid solution after one-hour annealing at temperatures between 200 and 350 ◦ C. 3.2. The heating stage The aim of the in situ experiments is to study the grain boundary mobility of Al–0.1 and –0.3 wt.% Mn alloys in a SEM during multiple annealings at various temperatures between 200 and 450 ◦ C. A heating stage was constructed [13] based on the design and operating principle of Liao and Le Gall et al. [14,15], as developed for studying grain boundary migration in stainless steels and cold rolled nickel. Some modifications of the design were necessary to use the heating stage at a 70◦ tilted position as required for the EBSD technique (Fig. 2). The aluminium sample is welded to a tantalum strip, heated by electrical resistance. The samples were checked to ensure that the weld zone did not recrystallize. The
Fig. 2. Schematic representation of sample and in situ heating stage in the SEM.
chromel–alumel thermocouple (K), welded on the Ta-strip, controls the temperature of the Ta and thus the Al-sample through a temperature regulator and power supply. The desired temperature is computed on the regulator and the heating rate is manually controlled to reduce the time to heat the sample to the required temperature. In order to improve the heating rate to more than 5 K/s different voltages were used according to the thickness of the Al-sample. In this way the required temperature is reached in less than 40 s with good stabilisation (±2 K) and with rapid cooling rates (10–20 s) down to 150 ◦ C. The sample thickness varied from 0.4 to 0.8 mm, i.e. about 3 or 4 times the deformed grain thickness and the section examined on the ND/RD plane. 3.3. Data analyses The in situ experiments were carried out in a SEM JEOL 6400 (W filament, vacuum ∼10−4 Pa). During each in situ heating experiment, the evolution of the microstructure was followed on the 70◦ tilted sample with a backscattered electron detector. After each annealing, the heater was switched off and the EBSD orientation maps were made with Channel 5-acquisition software (HKL technology). The beam scanning was made in a raster of typically 150 m × 100 m with a step size of 0.5 m/step. The crystallographic and microstructural data, i.e. grain and subgrain reconstruction, misorientation and boundary character were analysed with an EBSD data analysing program VMAP developed by J. Humphreys (Manchester Materials Science Centre).
4. Results 4.1. Deformed specimens Fig. 3 gives the stress–strain curves for the two Al–Mn alloys. The flow stress increases rapidly with strain towards εVM ≥ 0.05, then at a lower rate to εVM ≈ 1.3 and values of about 110 MPa. The σ(ε)-curves are similar for the two
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dom” or “cube” orientations and typically were misoriented 30–45◦ to the local deformed matrix. The grain boundaries which showed impingement were excluded from the present study. During the in situ annealing experiments different grain boundary behaviours were observed. The typical behaviour of the majority of the grain boundary migration experiments is denoted “Standard Rex”. However, in both Al–Mn alloys, some experiments indicated slower or even no recrystallization at all (Slow Rex). Quite frequently some very rapid recrystallization (Rapid Rex) occurred in the Al–0.1 wt.% Mn alloy.
Fig. 3. Typical experimental stress–strain curves of plane strain compressed Al–0.1% Mn (lower plots) and Al–0.3% Mn (upper plots).
Al–Mn alloys and the manganese hardens moderately the material. The microstructure of the longitudinal sections of the plane strain deformed samples is shown in Fig. 4. Deformation heterogeneities such as shear and deformation bands are observed in many of the grains. Fig. 4 shows long banded structures along RD developed within single coarse grains cut by classical microshear bands at ∼35◦ to RD. 4.2. In situ annealing 4.2.1. Grain boundary velocities The velocity of each HAGB was determined by measuring the equivalent circle diameter of the recrystallizing grains after each in situ annealing time interval. Using the 15◦ misorientation criterion with respect to the standard texture components, most of the new grains could be classed as “ran-
4.2.2. Stored energy The local driving pressures for recrystallization P were obtained through the usual Read and Shockley equation [16]: 3γm θ θ P= 1 − ln (5) d θm θm where γ m is the energy of a HAGB taken as 0.324 J/m2 for aluminium [17] and θ m is the misorientation at which a boundary is defined as a HAGB, usually taken as 15◦ . The subgrain sizes (d) and subgrain misorientations (θ) of the as-deformed material after plane strain compression were obtained from the EBSD maps and quantified by the equivalent circle diameter (ECD); they showed typical ECDs of 1.3 m ± 0.2 with subgrain misorientations of 4.5◦ ± 0.3. Comparison with some FEGSEM measurements of subgrains (85% indexed patterns) made on the same material showed that the error in determining the subgrain sizes with the classical W-filament SEM (∼70% indexed patterns) was less than 15%. The local stored energies P after plane strain compression of the Al–Mn alloys were between 300 and 550 kJ/m3 . During annealing these values decrease by recovery (before recrystallization) as illustrated in Fig. 5. The recovery rate can be fitted with the phenomenological description of St¨uwe et al. [18]. te P = P∞ + (P0 − P∞ ) (6) t + te where P0 is the initial stored energy; P∞ the residual stored energy of the fully recovered material and te the time in which recovery would be complete if the initial slope of the stored energy–time curve could be extrapolated. Some typical values of P0 , P, P∞ and te are given in Table 1. It is seen that the current stored energies can be reduced by recovery before (and during) recrystallization by up to 20%, for Al–0.1 wt.% Mn, and ∼26% for Al–0.3 wt.% Mn. The measured values of P are comparable to those calculated and estimated from the flow stresses obtained from the σ(ε) plane strain compression curves using:
Fig. 4. Optical micrograph (ND/RD section) of a channel-die compressed Al–0.1% Mn alloy (ε = 1.3).
P≈
µb2 ρ σ2 ≈ 2e2 2 2α M µ
(7)
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Fig. 5. Stored energy variations by recovery during annealing between 200 and 450 ◦ C after ε = 1.3: (a) “Slow Rex” in Al–0.1% Mn, (b) “Standard Rex” in Al–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 initial true values at t = 0 are not known before the heating experiments.
where b is the Burgers vector (2.86 × 10−10 m); ρ the dislocation density; σ e the estimated flow stress (∼110 MPa); M the Taylor factor (for FCC metals M ∼ 3) and µ the shear modulus (26 GPa). The parameter α varies for Al between
0.20 and 0.35 [19]. In the present work on Al–Mn, a value of α ≈ 0.24 was found to give a reasonable fit for the estimated dislocation densities (∼4 × 1014 m−2 ) and the stored energies.
Table 1 Typical parameters and experimental values used in Eqs. (5) and (6)
Al–0.1 wt.% Mn
Standard Rex
Slow Rex
Al–0.3 wt.% Mn
Standard Rex
T (◦ C)
P¯ 0∗ (kJ/m3 )
P¯ (kJ/m3 )
P¯ ∞ (kJ/m3 )
te (min)
P¯ (%)
220 240 260 280 300 315 330 320 350 390
490 450 422 429 460 427 430 533 526 548
479 406 378 363 434 327 330 450 430 434
440 400 355 350 400 320 300 400 400 n.d.
50 50 15 4 2 30 15 7 10 n.d.
4 10 10 15 6 21 23 16 18 21
P¯ 0∗ is determined from the measured values of mean subgrain sizes and mean misorientations in the as-deformed samples.
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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 island subgrain formation by grain growth around the subgrains.
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4.2.3. Mobilities The grain boundary mobility (M) of each HAGB of the recrystallizing grains was obtained by dividing the grain boundary migration rate (V) by the current driving pressure (P) for temperatures of 200–450 ◦ C. Fig. 6 shows the typical growth (Standard Rex) of an Al–0.3 wt.% Mn grain after several anneals at 320 ◦ C. Fig. 7 gives an example of the same alloy where no recrystallization occurred at 260 ◦ C but standard behaviour was subsequently observed at 320 ◦ C. An interesting feature is the presence of “island subgrains” that are left in the recrystallizing grain. Orientation line scans indicate that the island subgrains are misoriented by 5–10◦ with respect to the growing grain. Fig. 8 shows an example of 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 exhibited boundary migration rates that were at least an order of magnitude lower than the standard rates (samples denoted “Slow Rex”).
Fig. 9. Mobility of grain boundaries in Al–Mn as a function of inverse annealing temperature (each point represents the average of 3–5 in situ measurements).
Fig. 8. EBSD maps of the “Rapid Rex” behaviour of Al–0.1% Mn during in situ annealing at 220 ◦ C for (a) 40 s, (b) 100 s.
To give some idea of the dispersion in the mobility results, one can estimate the relative proportions of Standard, Rapid and Slow Rex as 70, 15 and 15% respectively from close to 200 in situ measurements. The effect of the annealing temperature on the mobilities of HAGB for these different regimes is summarized in Fig. 9. In the same figure we have included data on high angle mobilities in pure Al together with some results on Al–17 at. ppm Cu [2] and Al–500 at. ppm Si [20]. The results on the latter alloy, taken from the work of Huang and Humphreys, concern 40◦ 1 1 1 tilt and twist grain mobilities, measured in a similar manner, during recrystallization of a cold deformed Al–Si single crystal. From Fig. 9, it is clear that the high angle boundary mobilities in Al–Mn (about 0.05 and 0.15 at.% Mn) are close to the mobilities of the 40◦ 1 1 1 twist boundaries in Al–0.05 at.% Si, i.e. those which, according to Huang and Humphreys, represent the behaviour of “random” high angle boundaries in Al–Si. The activation energies for boundary migration in Al–Mn as deduced from Fig. 9 are 140 ± 20 kJ/mol for the standard recrystallization of both alloys and 170 ± 20 kJ/mol for the Slow Rex of the 0.1 wt.% Mn alloy. Table 2 summarizes the mobilities at a fixed temperature of 280 ◦ C, from the set of results described above. They show that for a majority of grain boundaries (Standard Rex), the mobility ranges from 1.5 × 10−14 m4 /J s (0.3 wt.% Mn) to 3.8 × 10−13 m4 /J s (0.1 wt.% Mn) with M0 between 0.9 and 2.7 m4 /J s, respectively. In Al–0.1 wt.% Mn, some slower recrystallizing grains (Slow Rex) possess mobilities of the same order as the Standard Rex in Al–0.3 wt.% Mn but with higher values of
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Table 2 Estimation of the migration parameters for in situ annealing at 280 ◦ C
Al–0.1 wt.% Mn
Standard Rex Slow Rex Rapid Rex Standard Rex
Al–0.3 wt.% Mn
V (×10−9 m s−1 )
P (kJ/m3 )
M (×10−14 m4 /J s)
M0 (m4 /J s)
Q (kJ/mol)
141 3.7 1260 6.6
370 370 370 440
38 1.0 340 1.5
2.71 75.33 – 0.09
136 168 – 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 most boundary mobilities are consistent with the activation energies for solute Mn atoms moving behind the grain boundary, i.e. between Qv for bulk volume diffusion of Mn (217 kJ/mol) [21] and QGB = 0.55Qv taken for boundary diffusion. It is then interesting to estimate the relative contributions of grain boundary and lattice diffusion using the CLS solute drag theories. 4.2.4. Estimation of the diffusion rates The effective diffusion rates were estimated from the logarithmic mean values, as proposed by Liao [22] using Eq. (8) ξ1 ln DGB + ξ2 ln Dv Deff = exp (8) 2 This is an empirical relation which has the advantage of giving a weighted average of diffusion coefficients which can differ by orders of magnitude and thereby enables one to estimate their relative contributions. According to St¨uwe [23] this just means that the activation energy assumed for atoms moving behind the grain boundary is between Qv for bulk diffusion and QGB for boundary diffusion. The values of DGB and Dv are taken from the Arrhenius equation with D0 = 0.0317 m2 /s [21] and the above activation energies. The ξ 1 and ξ 2 parameters describe the relative contributions of boundary and lattice diffusion (ξ 1 + ξ 2 = 2) and are obtained by estimating Deff from Eqs. (2)–(4) of CLS theory and the experimental boundary velocity measurements. In practice, for the Cahn model this means evaluating Pi (V, C, Deff ) from Eq. (3) using the following constants: a: ˚ (lattice parameter); µ: 26 GPa (shear modulus) and 4.05 A ˚ (atomic radius of the base metal). E0 , the solute r: 1.43 A atom interaction energy in the centre of the boundary, is estimated as E0 = 0.162 eV. The experimental velocities and driving pressures are then inserted into Eq. (2), given that Mint for pure Al is taken as 1.4 × 10−3 exp(−60000/RT) m4 /J s Table 3 Estimation of the mean values of ξ 1 and ξ 2 according to Eq. (8) Standard Rex
[3] [4,5]
Slow Rex
Rapid Rex
ξ1
ξ2
ξ1
ξ2
ξ1
ξ2
1.14 1.09
0.86 0.91
0.78 0.74
1.22 1.26
1.58 1.55
0.42 0.45
Fig. 10. Experimental (dashed lines) and theoretical (continuous lines) plots of boundary velocity as a function of inverse temperature for the two Al–Mn alloys. 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 for Deff from the value of the function (aDeff /1 + bDeff ) are obtained numerically. Table 3 summarizes the mean values for the different regimes, independently of the Mn solute concentration. The values of ξ 1 typically show a spread from ∼0.7 to 1.6. Clearly, the average value of 1.09, estimated from the solute drag model of L¨ucke and St¨uwe [4,5], and of 1.14, estimated from the expression of Cahn [3], are comparable and are close to the value ξ 1 ∼ 1 used by Liao et al. [14,15]. There is a general decrease of ξ 1 with increasing the velocity regime (from Slow to Rapid Rex) and with increasing the annealing temperature, indicating a corresponding reduced contribution of grain boundary diffusion at higher temperature (and therefore the higher activation energies of lattice diffusion).
5. Discussion The grain boundary mobility results obtained by in situ annealing experiments obviously are limited to surface (2D) measurements which can be criticized for the possible effects of boundary grooving. However, several recent studies of boundary migration in Al based bicrystals [25] and polycrystals [26] have lead to the conclusion that the grooving
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effect on boundary migration in these alloy systems, if any, can be neglected. The present study is also being extended to 3D measurements of grain growth in the same alloys in collaboration with the Riso group and the 3D XRD microscope. It is therefore expected to confirm this hypothesis in the near future. The experimental mobilities of Al–Mn polycrystals are close to those measured by Huang and Humphreys [20] in an Al–0.05 at.% Si single crystal. The alloys with 0.05 and 0.15 at.% Mn are comparable in solute concentration but the solute drag mechanism controlling grain boundary migration appears to be quite different. According to the mobility results of Huang and Humphreys [20] the migration activation energy was close to that of bulk diffusion of Si in Al, while in our experiments the grain boundary migration seems to be controlled by an effective diffusion intermediate between boundary and bulk diffusion of Mn in Al. By plotting the experimental boundary velocities as a function of the inverse annealing temperature (Fig. 9) we obtain two different curves: (i) a continuous line for the Al–0.3 wt.% Mn alloy and (ii) an S-shape curve for the Al–0.1 wt.% Mn alloy. This dependency on solute concentration and temperature is coherent with solute drag theories and can explain some of the different experimental boundary migration behaviours during annealing (Fig. 10). Using Cahn’s [3] solute drag expression with E0 , Deff and M0 , theory indicates that the Al–0.3 wt.% Mn alloy should behave as a “loaded” grain boundary for all annealing conditions with one simple solution denoted “V3 ”. This is taken to correspond to our Standard Rex regime. On the other hand, for the Al–0.1 wt.% Mn alloy at T < 400 ◦ C, three possible solutions are obtained from Eq. (2): “V1 ”, “V2 ” and “V3 ” (or more precisely two solutions for V1 and V3 with an indeterminate value for V2 ). The inflexion point near ln V = −14 m s−1 is quite well predicted by theory; the slope of the theoretical curve should change at the transition velocity VT ≈ √ ◦ 3/β = 1.75 × 10−7 m s−1 at √ 300 C and at a composition C0 ≈ C = (4λ/α)[(βP/λ 3) − 1] (with λ = 1/Mint ), i.e. close to 0.05 at.% Mn. Above 400 ◦ C for this alloy there are two solutions “V2 ” and “V1 ” indicating a partially “free” (or even “free”) grain boundary migration behaviour with less or no solute drag. Below this critical temperature, the grain boundary is “loaded” with solute atoms and has to drag the solute atoms unless it can break away. From these experimental observations and calculations, the Al–0.1 wt.% Mn alloy is clearly unstable at T < 400 ◦ C. Consequently, in Al–0.1 wt.% Mn it is possible to find both totally “loaded” (Standard Rex) and partially “free” (Rapid Rex) grain boundary migration during annealing. This seems to be evidence for the stable/unstable solute drag model in a near-industrial alloy composition. The origin of “Slow Rex” behaviour is more difficult to explain. This may be due to some localized solute concentration above the values deduced from (steady state) grain boundary migration theory. The fact that the Al–0.1% Mn alloy in the Slow Rex regime behaves like the standard
Al–0.3% Mn alloy is consistent with this interpretation. However, for the moment there is no obvious reason why there should be localized solute concentrations. An alternative explanation could be a lack of easy nucleation sites in this large grained material. Further tests are being conducted to determine the origin of this behaviour.
6. Conclusions (1) An SEM/EBSD in situ annealing technique has been used to study HAGB mobilities during the recrystallization of room temperature deformed Al–0.1 and –0.3 wt.% Mn alloys in the temperature range 200–450 ◦ C. (2) During the in situ annealing experiments different grain boundary behaviours were observed. Most of the experiments on both Al–Mn alloys showed normal recrystallization of the new grains but in some other experiments faster, slower or even no recrystallization at all took place. (3) Comparison of experimental data with solute drag theories confirmed instability for the case of the deformed Al–0.1 wt.% Mn alloy. Boundary migration during in situ annealing is characterized by “loaded” and “mixed” behaviour whereas the Al–0.3 wt.% Mn alloy exhibits only “loaded” grain boundary behaviour. (4) The activation energy for boundary migration is intermediate between that of solute (Mn) diffusion in the lattice and along the grain boundaries. (5) The diffusion rates controlling solute drag in Al–Mn were estimated via the solute drag models of Cahn [3], L¨ucke and St¨uwe [4,5]. The results were highly comparable.
Acknowledgements The authors would like to acknowledge R. Le Gall for the many useful comments about the heating stage and J. Humphreys for the VMAP software. They are also particularly grateful to R.D. Doherty and to H.P. St¨uwe for their comments and interest in the results. This work has been partially funded by a Rhˆone-Alpes Regional Avenir programme “Mobility of grain boundaries in Al alloys” in cooperation with the Centre for Fundamental Research: Metal Structures in 4 Dimensions, Riso National Laboratory.
References [1] O. Dimitrov, R. Fromageau, M.O. Dimitrov, in: F. Haessner (Ed.), Recrystallization of Metallic Materials, Reider Verlag, Berlin, 1978, p. 131. [2] P. Gordon, R.A. Vandermeer, Trans. AIME 224 (1962) 917–928. [3] J.W. Cahn, Acta Metall. 10 (1962) 789–798. [4] K. L¨ucke, H.P. St¨uwe, in: L. Himmel (Ed.), Recovery and Recrystallization of Metals, Gordon and Breach, New York, 1962, pp. 171–209.
A. Lens et al. / Materials Science and Engineering A 403 (2005) 144–153 [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
K. L¨ucke, H.P. St¨uwe, Acta Metall. 19 (1971) 1087–1099. K. L¨ucke, G. Masing, P. N¨olting, Z. Metallk. (1956) 64. K. L¨ucke, K. Detert, Acta Metall. 5 (1957) 628. J.D. Powers, A.M. Glaeser, Interf. Sci. 6 (1998) 23. Z.-K. Liu, J. Agren, M. Suehiro, Mater. Sci. Eng. 247 (1998) 222. P.-R. Cha, S.G. Kim, D.-H. Yeon, J.-K. Yoon, Acta Mater. 50 (2002) 3817–3829. N. Ma, S.A. Dregia, Y. Wang, Acta Mater. 51 (2003) 3687–3700. M. Hillert, Acta Mater. 52 (2004) 5289–5293. A. Lens, C. Maurice, J.H. Driver, Mater. Sci. Forum 467–470 (2004) 771–776. G. Liao, R. Le Gall, G. Saindrenan, Mater. Sci. Technol. 14 (1998) 411. R. Le Gall, G. Liao, G. Saindrenan, Scripta Mater. 41 (1999) 427–432. W.T. Read, W. Shockley, Phys. Rev. 78 (1950) 275.
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[17] L.E. Murr, Interfacial Phenomena in Metals and Alloys, AddisonWesley, Reading, MA, 1975. [18] H.P. St¨uwe, A.F. Padilha, F. Siciliano Jr., Mater. Sci. Eng. A333 (2002) 361–367. [19] F.R.N. Nabarro, Z.S. Basinski, D.R. Holt, Adv. Phys. XII (1964) 193. [20] Y. Huang, F.J. Humphreys, Acta Mater. 48 (2000) 2017–2030. [21] H. Bakker, Diffusion in Solid Metals and Alloys, 26, LandoltB¨ornstein/Springer-Verlag, Berlin, 1990. [22] G. Liao, Etude exp´erimentale des cin´etiques de recristallisation et des vitesses de migration des joints de grains dans le nickel e´ croui, Ph.D. Thesis, Universit´e de Nantes, France, 1998. [23] H.P. St¨uwe, University Vienna, Private communication, 2003. [24] A.P. Sutton, R.W. Balluffi, Interfaces in Crystalline Materials, Oxford Science Publications, 1995, p. 819. [25] G. Gottstein, L.S. Shvindlerman, Scripta Metall. 27 (1992) 1521. [26] Y. Huang, F.J. Humphreys, Acta Mater. 47 (1999) 2259–2268.