In situ small-angle scattering study of the precipitation kinetics in an Al–Zr–Sc alloy

Acta Materialia 55 (2007) 2775–2783 www.actamat-journals.com

In situ small-angle scattering study of the precipitation kinetics in an Al–Zr–Sc alloy A. Deschamps *, L. Lae, P. Guyot SIMAP, INPGrenoble-CNRS-UJF BP 75, 38402 St Martin d’He`res, France Received 18 July 2006; received in revised form 12 December 2006; accepted 15 December 2006 Available online 12 February 2007

Abstract A time-resolved small-angle X-ray scattering (SAXS) study was carried out to investigate the precipitation kinetics of L12 Al3(Zr, Sc) precipitates in aluminium at temperatures ranging between 400 and 475 C. It is shown that the chemical heterogeneity of the precipitates, which consist of a Sc-rich core and a Zr-rich shell, results in a characteristic SAXS signal, which can be fitted by a three-phase model to extract the chemical and morphological features of the precipitate size distribution. The experimental results show a strong effect of the heating rate on the precipitation kinetics, and a precipitate density strikingly constant with time in the investigated range. These results are discussed in view of the mechanisms proposed in the existing literature for the formation of the core–shell structure of these precipitates.  2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Small angle X-ray scattering; Aluminium alloys; Al–Zr–Sc; Precipitation; Chemical heterogeneity

1. Introduction Formation of Al3Zr precipitates (called dispersoids) in aluminium alloys has been used for a long time, especially in alloys for aerospace applications (such as AA7000 series). This is due to their ability to pin grain and subgrain boundaries, leading to the desired very low recrystallized fractions; in addition, Al3Zr dispersoids are less efficient sites for heterogeneous precipitation as compared with chromium-based dispersoids, for instance, leading to the development of less quench-sensitive alloys. The Al3Zr precipitate’s equilibrium crystal structure is DO23; however, the metastable L12 form is always found in technologically relevant situations. Since the mid-1980s, there has been a strong interest in the addition of scandium to zirconium as solutes in aluminium [1,2]. It was shown that such an addition resulted in a significant enhancement of the resistance to recrystallization, and consequently in better mechanical properties [3– *

Corresponding author. Fax: +33 4 76 82 66 44. E-mail address: [email protected] (A. Deschamps).

10]. Scandium also forms L12 Al3Sc precipitates with aluminium, which is in this case the stable phase [11–16]. When Sc and Zr are both present, Al3(Zr,Sc) precipitates are formed, Sc and Zr having a complete miscibility [2,10,17]. Several studies have shown that these spherical precipitates have a distinct chemical heterogeneity [17– 20]: the precipitate core is essentially scandium rich and the shell shows a higher zirconium concentration. This peculiar chemical structure was attributed to two complementary effects: the combination of the very different diffusion coefficients of the two species [21,22], associated with the fact that the energy for creating a vacancy in the L12 lattice is extremely high [20], which results in a conservation of the history of formation of the precipitate; and the decrease of interfacial energy by the presence at the sample surface of a high Zr concentration [4,17]. The aim of the present paper is to analyse in detail the precipitation kinetics in an Al–Zr–Sc alloy and, notably, to evaluate whether this particular chemical heterogeneity of the precipitate results in distinct kinetic features. For this purpose, small-angle X-ray scattering (SAXS), which provides a quantitative analysis of the precipitate size and

1359-6454/$30.00  2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2006.12.015

A. Deschamps et al. / Acta Materialia 55 (2007) 2775–2783

10 4

As detailed above, it is now widely recognized that the Al3(Zr,Sc) precipitates are not chemically homogeneous. The precipitates have been shown to consist of a Sc-rich core, surrounded by a shell rich in Zr, this chemical heterogeneity evolving with time. Since Zr and Sc atoms have very different atomic numbers, it can be expected that such a chemical inhomogeneity results in a specific SAXS signal, such as been observed in the Al–Ag system [26]. In a previously published paper [20], it was shown that the chemical heterogeneity results in oscillations of the SAXS signal, which can be used for quantification of the microstructural features. Moreover, the outcome of this quantification was demonstrated to be consistent with that of two other experimental techniques, namely tomographic atom probe and high angle annular dark field (HAADF) transmission electron microscopy (TEM).

10 2

10 1

10 0

10 -1 0

0.1

0.1

0.2

0.2

0.2

0.2

-1

q (Å )

7 10 6 10 5 10 4 10

-4

-4

Experimental Calculated (core + shell) Calculated (homogeneous)

-4

-4

4

3. Evidence of the core–shell structure of the precipitates

Experimental Calculated (core+shell) Calculated (homogeneous)

10 3

-7

The alloy studied was provided by Alcan – Centre de Recherches de Voreppe. The composition is Al–0.16 wt.% Sc, 0.1 wt.% Zr (or 0.09 at.% Sc and 0.03 at.% Zr). Fe and Si contents are approximately 30 and 100 ppm, respectively. Ingots were cast at 695 C, air cooled and subsequently homogenized at 630 C for 360 h (to remove the micro-segregation of zirconium), followed by a 800 C min1 quench to room temperature. Subsequent heat treatments were carried out between 400 and 475 C, with heating rates ranging between 5 and 430 C min1. All SAXS experiments have been carried out on the D2AM beamline (BM02-CRG) of the European Synchrotron Radiation Facility (ESRF). X-rays are generated by a bending magnet, are focused and monochromated to better ˚ . Acquisithan dk/k = 2 · 104 at a wavelength of 1.61 A tion is carried out with a 2D-CCD camera. A sample-todetector distance of 0.8 m was used, giving access to a ˚ 1. CCD images range of scattering vectors [0.01, 0.2] A are corrected for electronic noise, spatial distortion, pixel efficiency and background noise. A circular average is then performed for the calculation of the intensity scattered at a given angle. Intensity is converted in absolute units by measuring the sample transmission and by measuring reference samples, leading to an overall precision better than ±10%. For in situ experiments, the 70-lm-thick samples are placed in a resistance furnace in vacuum which enables a maximum heating rate of 10 K s1.

-3

2. Experimental method

Fig. 1 shows an example of an experimental scattering curve, represented both in a log(I) vs q plot, and in an Iq4 vs q plot. The latter plot converges in a classical twophase system with sharp interfaces to a horizontal curve reflecting the asymptotic 1/q4 behaviour (called Porod approximation). In the present case, both curves show strong oscillations, which are highly unusual in metallic systems. It is possible to predict the scattering curve of a size distribution of spheres, and compare it with the experimental spectrum. It was shown in former studies of binary systems such as the Fe–Cu system, to enable a very good descrip-

Scattered intensity (Å )

volume fraction [23–25], will be used. It was shown recently in a former paper that SAXS is a quantitative tool which can provide measurements of several microstructural features in chemically heterogeneous precipitates. It will be shown how in situ measurements carried out with a synchrotron source can highlight the complex microstructural evolution in this system.

I.q (Å )

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3 10 2 10 1 10

-4 -4

-4

0 10

0

0

0.1

0.1 -1

q (Å ) Fig. 1. Experimental and simulated scattering curves for an AlZrSc sample heat treated for 256 h at 450 C. Symbols: experimental signal. The dotted line is the scattered intensity modelled with a log-normal distribution of spheres of homogeneous composition, and the solid line is the intensity modelled with a log normal distribution of spheres with a core–shell chemical structure; parameters of the simulation: log normal distribution (s = 0.08, R = 13 nm), shell 13% of the precipitate size, composition in solute atoms of the shell 55% Zr. (a) ln(I) vs q plot; (b) Iq4 vs q plot.

A. Deschamps et al. / Acta Materialia 55 (2007) 2775–2783

tion of the experimental data when compared with precipitate size distributions measured by TEM [27]. The scattered intensity of a distribution f(R) of dilute spheres of homogeneous composition in a homogeneous matrix can be exactly calculated by the following equation: Z 1 IðqÞ ¼ Iðq; RÞf ðRÞ dR ð1Þ 0

where I(q, R) is the intensity scattered by a single sphere of radius R: " # 2 sinðqRÞ  qR cosðqRÞ Iðq; RÞ ¼ KV ð2Þ 3 ðqRÞ V is the volume of the sphere, and K is a constant. The result of such a calculation is shown in Fig. 1 along with the experimental data. It is apparent that the first peak of the (Iq4 vs q) plot is well predicted by the simulation; in fact, this peak (at smallest scattering angles) is characteristic of the largest correlation distance of the solute atoms, i.e., to the precipitate size. However, the other strong oscillations cannot be properly described by a two-phase model of precipitates in a matrix. In light of the known heterogeneous nature of the chemical composition inside the Al3(Zr,Sc) precipitates, the experimental data will be interpreted using a three-phase model, which will now be presented in detail. The precipitates are considered as a core of radius R1 and composition Al3ZrX1 Sc1X1, and a shell of radius R2 and composition Al3 ZrX2 Sc1X2 (Fig. 2). This model is itself an approximation of the real structure of the precipitates, as in reality the interface between the Sc-rich and the Zr-rich regions of the

ρ1

R2

ρ2

R1

Electronic density

Precipitate

Matrix

r2 r1

rM

R1 R2

Radius

Fig. 2. Scheme of the core–shell structure of the precipitates used for the scattering model, and related parameters: inner radius R1, outer radius R2, core electronic density q1, outer electronic density q2, matrix electronic density qm.

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particles is diffuse and not perfectly sharp. Electronic densities q1 and q2 correspond to these compositions, defined from the scattering lengths f1 and f2 of the different elements at the wavelength used: 1 ð3f Al þ X i fZr þ ð1  X i ÞfSc Þ; i ¼ 1; 2 ð3Þ 4X where X is the atomic volume, assumed constant for the matrix and precipitate. If the relative thickness of the shell is defined by:

qi ¼

t¼

R2  R1 R2

ð4Þ

The average electronic density writes: 3

qp ðq1  q2 Þð1  tÞ þ q2

ð5Þ

The amplitude scattered by this sphere of heterogeneous chemical composition can then be written as the sum of the amplitudes of two spheres of respective radii and electronic density (R1, q1  q2) and (R2, q2), leading to the following equation for the intensity scattered at vector q: Iðq; R1 ; R2 ; q1 ; q2 Þ ¼ F ðq; R1 ; R2 ; q1 ; q2 Þ

2 2

¼ ½F ðq; R1 ; q1  q2 Þ þ F ðq; R2 ; q2 Þ

ð6Þ

In order to evaluate the intensity scattered by a collection of particles, some hypotheses have to be made. It will be assumed that the relative thickness (t/R2) of the shell is constant for all particles in a given metallurgical state, as well as the inner and outer precipitate compositions. Another important assumption, based on the existing experimental evidence, is that the precipitate core consists of pure Al3Sc (X1 = 0). Moreover, a log-normal distribution of the particle size will be assumed, described by an average radius Rm and a standard deviation r. The scattered intensity is now defined by: Z 1 IðqÞ ¼ Iðq; Rð1  tÞ; R; qðX 1 ¼ 0Þ; qðX 2 ÞÞf ðRÞ dR ð7Þ 0 !  2 1 1 log R  log Rm and f ðRÞ ¼ pffiffiffiffiffiffi exp  ð8Þ 2 r Rr 2p This intensity can be fitted to the experimental data. The fitting parameters are the average outer radius Rm, the standard deviation r, the relative thickness t and the shell composition X2. The two first parameters are adjusted to provide a good description of the scattered intensity at small angles, whereas the two last parameters are adjusted so as to describe the large-angle oscillations, and especially the positive slope of the Iq4 vs q plot. Fig. 1 shows that a very good description of the experimental data is obtained using parameters which are consistent with the existing experimental evidence on similar systems. Once these parameters are known for a given metallurgical state, the average precipitate composition is known and the precipitate volume fraction fv can be calculated from the integrated intensity Qo:

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fv ffi

A. Deschamps et al. / Acta Materialia 55 (2007) 2775–2783

Qo 2p2 ðqp

 qm Þ

ð9Þ

2

qp and qm are the Relectronic densities of the precipitate and 1 matrix, and Qo ¼ 0 IðqÞq2 dq is calculated from the experimental data. It is particularly important to evaluate the uncertainty on the main results of the fitting procedure. The discussion in the following sections will notably focus on the evolution of size, volume fraction and number density of precipitates, and thus an evaluation of the relative errors on these values will now be given. First, the uncertainty on the precipitate size can be evaluated. Its measurement is determined mainly on the first peak of the Iq2 vs q plot, and is little influenced by any parameter of the core–shell model. Consequently it can be measured with high relative precision. A conservative estimate gives an error of 5% on this parameter.

The situation is more delicate for the measurement of volume fraction. The systematic uncertainty on the measurement of the integrated intensity Qo can be estimated to 10%. However, it has no influence on the interpretation of differences between samples of the same measurement campaign. However, large relative errors can arise in the conversion from the integrated intensity to volume fraction through Eq. (9) due to uncertainties in the precipitate composition. The stoichiometry 3:1 of the precipitate in Al:(Zr,Sc) is well established, and therefore the source of uncertainty is the relative concentrations of Zr and Sc. As shown in the introduction, the core of the precipitates consists mainly of pure Sc. Thus, the two parameters’ source of error are the concentration in Zr of the shell and the relative thickness of the shell, both of which are found as a result of the fitting procedure of the model to the experimental results.

80 400 °C 450 °C

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3 10

Precipitate radius (Å)

Precipitate volume fraction

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Time (h) 100

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Relative thickness of the shell (%)

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Zr shell

450 °C

concentration

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Time (h)

Fig. 3. Evolution of the microstructural parameters ((a) volume fraction; (b) radius; (c) Zr concentration in the shell; and (d) shell thickness) during heat treatments at 400, 450 and 475 C. In all three cases, the heat treatment temperature was reached with a 10 C min1 heating rate. Error bars correspond to 30% and 5% uncertainty on volume fraction and size, respectively.

A. Deschamps et al. / Acta Materialia 55 (2007) 2775–2783

The average composition of the precipitate in zirconium can be calculated as follows from these two parameters: 3

%Zr ¼ X 2 ð1  ð1  tÞ Þ

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4. Influence of temperature on precipitation kinetics The precipitation kinetics was measured for three different temperatures: 400, 450 and 475 C, this temperature being reached with a constant heating rate of 10 K min1. Fig. 3 represents the evolution of the different parameters of the microstructure with ageing time: volume fraction, average size, shell composition and relative shell thickness. Let us concentrate first on precipitate size and volume fraction. The size at short ageing times is roughly indepen˚ ). The time dent of the ageing temperature (about 50 A range for which the precipitate size is identical in the three cases is actually about the time of the heating ramp to the ageing temperature, where all three materials experience the same heat treatment. When the isothermal ageing stage is reached, the precipitate growth is observed unsurprisingly to be faster, the higher the temperature. However,

ð10Þ

For a typical example of X2 = 0.8 ± 0.1 and t = 0.15 ± 0.05, it is found that the relative error on the volume fraction calculation for a given value of the integrated intensity is about 30%. It must be pointed out that this evaluation is probably pessimistic, as the characteristic noise in the measurements is much lower than that. When calculating the precipitate density of a given microstructure from the values of precipitate size and volume fraction, the relative error on the volume fraction adds to that on the cube of the precipitate size. Given the 5% error estimated above for the precipitate size, a global error of 45% on the precipitate density can be expected.

200 -3

5 °C/min 10 °C/min 430 °C/min

150

1 10

Precipitate radius (Å)

Precipitate volume fraction

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Volume fraction 0 0

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5 °C/min Relative thickness of the shell (%)

Zr/(Zr+Sc) in the shell (%)

80

5 °C/min

60 430 °C/min 40

20 Zr shell concentration 1

5

60

10 °C/min

0

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Time (h)

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10 °C/min 430 °C/min 40

20

Shell thickness 0

2

3

4 Time (h)

5

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2

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4 5 Time (h)

6

7

8

Fig. 4. Evolution of the microstructural parameters ((a) volume fraction; (b) radius; (c) Zr concentration in the shell; and (d) shell thickness) during heat treatments at 450 C, reached with heating rates of 5 C min1, 10 C min1 and 430 C min1. Error bars correspond to 30% and 5% uncertainty on volume fraction and size, respectively.

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the evolution of volume fraction is not so classical: although it seems that at all temperatures a relatively constant value of volume fraction is reached, this value is obviously not the equilibrium volume fraction, as it increases with increasing temperature. This confirms that a specific kinetics path is experienced in this ternary system, and will be discussed in detail below. The concentration of the Zr-rich shell is plotted as a function of ageing time in Fig. 3c. In fact, the precision of the measurement of this parameter is quite low, especially in the first stages of precipitation where the volume fraction is low (and thus the signal is very noisy). Thus, the prominent feature is that the concentration in zirconium (relative to the Zr and Sc atoms, i.e., not counting the Al atoms of the L12 structure) is approximately independent of the heat treatment temperature and of time, and is close to 80%. The thickness of the Zr-rich shell is also observed to be constant in relative value (Fig. 3d). 5. Influence of heating rate on precipitation kinetics At the temperature of 450 C, the precipitation kinetics was measured for three different heating rates: 5, 10 and 430 C min1. Fig. 4 shows the evolution of the precipitate parameters obtained from small-angle scattering data, as a function of ageing time. The situation is strikingly different from that of the influence of ageing temperature. If one first concentrates on the evolution of precipitate volume fraction, it is now relatively independent of the heating rate, except for the short ageing times, when the samples are being heated. However, the situation is very different for the precipitate size. Large differences in size are found for the different heating rates: the lower the heating rate, the smaller the precipitate size. Actually, the differences in precipitate size which result from the nucleation process during the heating ramp stay remarkably constant during the 8 h of heat treat-

35 5 ºC/min 30

10 ºC/min 430 ºC/min

Shell thickness (Å)

25 20 15 10 5 0

0

1

2

3

4 5 Time (h)

6

7

8

Fig. 5. Shell thickness, measured for the same experiments as in Fig. 4.

ment at 450 C. No growth or coarsening is found in the material containing the smallest precipitates. Moreover, significant differences exist in the shell composition and shell thickness. The shell thickness is larger in relative value when the heating rate is smaller. However, since large differences exist in precipitate size, it is worth characterizing the shell not only in terms of relative thickness, but also in absolute value. This is plotted in Fig. 5; it becomes apparent that the shell thickness is approximately independent on the heating ramp, and stabilizes at a value ˚ . Finally, the Zr concentration of of approximately 10 A the shell is observed also to depend on the heating rate. Although the data are somewhat scattered, the highest heating rate clearly shows a lower zirconium shell concentration. 6. Discussion In order to understand the complex microstructural evolution resulting from the above presented data better, it is useful to calculate the precipitate number density from the volume fraction and the precipitate average radius. Given the relatively narrow precipitate size distribution, the approximate particle density is calculated as: 3f v Np ffi ð11Þ 4pR3m where fv is the precipitate volume fraction, and Rm the average precipitate size. The evolution of precipitate number density as a function of ageing time is shown in Fig. 6a for the influence of temperature at constant heating rate and in Fig. 6b for the influence of heating rate at constant temperature. The first prominent feature is that the precipitate number density is absolutely constant (within experimental precision) in the time range explored. This means first that the experimental set-up is not precise enough to give access to the nucleation stage, but also that the material is remarkably insensitive to coarsening. In fact, in most systems where a continuous measurement of precipitate number density is available, one observes very rapidly a decrease in the precipitate number density due to coarsening, and the pure growth stage (i.e., at constant number density) is not observed or for very short durations. Recent examples include the Fe–Cu of the Fe–NbC system [28,29]. This can be simply understood, as the fact that when nucleation is over, the supersaturation has fallen to a very low level, for which some precipitates become unstable because of the Gibbs–Thomson effect, resulting in the onset of coarsening. Thus, the present case is obviously a strong exception in this respect. The second prominent feature is that the precipitate number density is independent of temperature (within experimental precision) for the common heating rate of 10 C min1. Again the classical situation is that higher temperatures result in lower precipitate number density [28], owing to both more difficult nucleation (due to a lower chemical driving force) and more rapid coarsening (due to a larger diffusion coefficient).

A. Deschamps et al. / Acta Materialia 55 (2007) 2775–2783

therefore precipitates may be chemically heterogeneous, depending on the sequence of events leading to their formation.

10000

Precipitate number density (µm-3 )

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Thus, the sequence of precipitation can be decomposed in several stages of distinct kinetic signature:

1000

In order to understand better the sequence of events leading to these very unusual characteristics of the precipitation kinetics, it is useful to recall the specific features of this system:

 A stage of rapid nucleation: the nucleation of Al3Sc precipitates is catalysed by relatively immobile Zr atoms, which serve to reduce the entropy of the nuclei.  A stage of rapid growth: the newly formed precipitates can absorb very fast the Sc in solid solution, since the diffusion coefficient of this element is high;  The formation of a Zr-rich shell around these precipitates containing mainly Sc atoms, enabled by a sufficiently high temperature (towards the end of the heating stage), and by the fact that the growth rate due to the absorption of scandium becomes very low when all the scandium was removed from the solid solution.  Once the composition of the outer shell of the precipitates becomes rich in zirconium, the evolution of the precipitates becomes quite complex. The growth rate of a single precipitate is governed by the difference between the average solute concentration in each element and their interfacial values at the precipitate interface. Thus, any precipitate can grow indifferently by the absorption of Zr or Sc, depending on the relative solute concentrations in both elements and their diffusivities. Since in the first stages mostly Sc was incorporated to the precipitates, a large amount of Zr is still present in solid solution, and a slow growth stage should happen. Given the diffusion rate of Zr at the investigated temperatures, this growth stage can be sufficiently slow so that no significant evolution is observed during the 8 h of the heat treatment.  Finally, if a precipitate has become unstable with respect to the solid solution (which occurs for a growing proportion of the precipitates at the onset of coarsening), its dissolution needs first to involve the atoms of the outer shell, which include in a large amount the slow Zr atoms. Therefore any precipitate dissolution would occur at the slowest diffusion rate and may be not observed in the range of temperature and times investigated here.

 Zr and Sc are chemically almost identical. They can occupy in any proportion the sites of the L12 Al3ZrxSc1x structure.  Owing to a different interaction with vacancies, Zr atoms diffuse much more slowly than Sc atoms (by more than two orders of magnitude at the investigated temperatures).  The energetic cost of a vacancy inside a L12 precipitate is very high; thus interdiffusion between Sc and Zr atoms inside the precipitates is impossible in practice, and

The expected sequence of events thus involves a fast nucleation stage (stopped by the lack of Sc atoms), a two steps growth stage (one fast controlled by Sc and one slow controlled by Zr), and a slow coarsening stage (controlled by Zr). Now we can interpret the present experimental data in light of these mechanisms. First concentrate on the influence of temperature at constant heating rate. The fact that the number density of precipitates is exactly the same at the three investigated temperatures indicates:

100 400 ºC 450 ºC 475 ºC 10 0

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2

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Precipitate number density (µm )

10000

1000

100 5 ºC/min 10 ºC/min 430 ºC/min 10 0

1

2

3

4

5

6

7

8

Time (h) Fig. 6. Precipitate density, as calculated using the volume fraction and size shown in Figs. 3 and 4: (a) for the three different temperatures, using a heating rate of 10 C min1; (b) for the three heating rates for a heat treatment temperature of 450 C min1. Error bars correspond to 45% relative uncertainty.

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(1) that all nucleation has taken place during the heating stage at 10 C min1 (2) that towards the end of this heating ramp, diffusivity of Zr is sufficient to allow the formation of the Zr shell around the Al3Sc nuclei. At the end of this nucleation stage, the precipitate shell includes a large amount of Zr, and the amount of Sc in solid solution is very small. Growth becomes therefore very slow. Growth is more rapid at higher temperature, which is directly related to the increase in diffusion rate, leading to a higher volume fraction and a larger radius. The fact that lower volume fractions are experienced at lower temperatures simply results from a larger deviation from the equilibrium, due to the high residual concentration of Zr atoms in solid solution. At the highest temperature, where the volume fraction is close to equilibrium, no decrease in number density with time is observed, contrarily to what is observed in binary systems [28]. The Zr shells protect the smaller, unstable, precipitates from rapid dissolution. The influence of the heating rate can be readily understood as well. In this case, changing the heating rate drastically changes the nucleation rate (since it has been determined that nucleation occurred mainly during the heating stage), and therefore changes the precipitate number density at the end of the nucleation stage. This precipitate density in turn controls the size of precipitates, if it is assumed that most of the Sc is incorporated into the nucleated particles. When the Zr-rich shell thickness reaches 1 nm (i.e., about 2 unit cells of the L12 structure), the slow pure growth stage, controlled by Zr, is observed. The precipitate number density is kept constant to the value reached at the end of the nucleation stage, since neither nucleation (because of the low residual supersaturation) nor coarsening (because of the stabilizing effect of the Zr shell) can occur. Of course, some other scenario could be expected for experimental conditions which have not been investigated here. For instance, if the heat treatment was left at a temperature low enough so that no significant diffusion of Zr can take place, coarsening of Al3Sc could occur before the protective effect of the Zr shell could be effective, thus losing the ability to stabilize the microstructure issued from nucleation. Also, if the heat treatments at the temperatures investigated in the present study were continued, coarsening would eventually happen [4], governed by the diffusion rate of Zr. This coarsening would free the Sc atoms present at the core of the precipitates, which would join the surviving precipitates. Thus the outer concentration, which has been shown to be very rich in Zr, would progressively decrease to a value closer to the average ratio of the alloy (but still retaining the Zr rich region closer to the precipitate cores). Such assumptions need additional experimental work to be confirmed.

7. Conclusions Using an original interpretation of SAXS data, a detailed characterization of the precipitation kinetics in the Al–Zr–Sc system was achieved, not only in terms of size and volume fraction, but also in terms of the characteristics of their chemical heterogeneity (so-called core/shell structure). Owing to a combination of physical properties (the most important one being the contrast in diffusion coefficients between Zr and Sc), the precipitation kinetics in this system show very strong specific features:  Nucleation is controlled mainly by the rapid scandium diffusion; thus it occurs mainly during the heating stage to the heat treatment temperature, and is very heatingrate sensitive.  Growth occurs in two well-defined stages; the first one corresponds to the absorption of the remaining Sc atoms until their exhaustion, and the second one, much slower, to the absorption of Zr atoms.  Coarsening is strongly impeded by the presence of a 1nm-thick Zr-rich shell at the particle/matrix interface; this shell imposes coarsening to be controlled by the diffusion rate of zirconium, and this stage was thus not observed in the investigated range of temperatures and times. These features of fast nucleation and slow growth and coarsening enable one to obtain a remarkably stable microstructure of fine Al3(Zr,Sc) dispersoids, which have proved very effective in controlling the grain size of many aluminium alloys. Acknowledgements This work was part of a French scientific programme (CPR Pre´cipitation), in collaboration with Arcelor, Alcan, CNRS, CEA, INPG, INSA Lyon, Universite´ de Rouen, Universite´ Aix-Marseille III and LEM-ONERA. Alcan is acknowledged for providing the material, and Dr C. Sigli is thanked for stimulating discussions. References [1] Yelagin VI, Zakharov VV, Pavlenko SG, Rostova TD. Influence of zirconium doping on aging of Al–Sc alloys. Fizika Metallov I Metallovedenie 1985;60:97. [2] Toropova LS, Kamardinkin AN, Kandzhibalo VV, Tyvanchuk AT. Alloys of the aluminum–scandium–zirconium system in the aluminum-rich region. Fizika Metallov i Metallovedenie 1990:108. [3] Sugamata M, Fujii H, Kaneko J, Kubota M. Effect of Sc + Zr addition on structures and mechanical properties of rapidly solidified 7090 based alloys. Mater. Forum 2004;28:514A. [4] Fuller CB, Seidman DN. Temporal evolution of the nanostructure of Al(Sc,Zr) alloys: Part II-coarsening of Al3(Sc1-xZrx) precipitates. Acta Mater 2005;53:5415. [5] Rostova TD, Davydov VG, Yelagin VI, Zakharov VV. Effect of scandium on recrystallization of aluminum and its alloys. Mater Sci Forum 2000;331–337:793.

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