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Quantitative analysis of δ′ precipitation kinetics in Al–Li alloys
Acta mater. 48 (2000) 1283±1296 www.elsevier.com/locate/actamat
QUANTITATIVE ANALYSIS OF d' PRECIPITATION KINETICS IN Al±Li ALLOYS J. I. PEÂREZ-LANDAZAÂBAL{ 1, M. L. NOÂ 2, G. MADARIAGA 1, V. RECARTE 1 and J. SAN JUAN 1{ 1 Departamento FõÂ sica Materia Condensada, Facultad de Ciencias, Universidad del PaõÂ s Vasco, Apdo. 644, 48080, Bilbao, Spain and 2Departamento FõÂ sica Aplicada II, Facultad de Ciencias, Universidad del PaõÂ s Vasco, Apdo. 644, 48080, Bilbao, Spain
(Received 30 April 1999; received in revised form 7 November 1999; accepted 7 November 1999) AbstractÐThe Rietveld method has been applied to X-ray spectra in order to study the precipitated mass fraction of d' and d in Al±Li alloys. The method allows us to obtain quantitatively the d' and d precipitate mass fractions, and their evolution with aging time. Furthermore, this method also gives directly the cell parameter evolution of the matrix phase and indirectly the mean half radius of d ' precipitates through an appropriate calibration curve. Experimentally, this calibration has been approached by previously studying the evolution of the mean half radius of d ' by transmission electron microscopy (TEM). Thermoelectric power has also been shown to be a powerful technique to study the microstructural evolution of Al±Li alloys, being sensitive to the dierent stages of precipitation associated to the d' and d phases. The comparison of the dierent experimental results allow us to stablish a clear dierence between the precipitation kinetics and the hardening kinetics. 7 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Transmision electron microscopy (TEM); X-ray diraction (XRD); Aluminum±lithium; Phase transformations; Kinetics
1. INTRODUCTION
Aluminium±lithium alloys show special characteristics and performances compared with classical aluminium alloys due to the presence of lithium. Lithium is one of the eight elements with a solubility above 1 at.% in the aluminium matrix, and among them lithium produces the highest modulus and strength increases, and the strongest density decreases [1]. Although binary Al±Li alloys show poor mechanical properties, these other advantages promoted the development of several ternary Al± Li±Cu (2090), quaternary Al±Li±Cu±Mg (2090, 8090, 8091) and more complex Al±Li alloys such as the Al±Li±Cu±Mg±Ag (W-049). See Refs [2]±[6] as overviews of technological developments. Due to their high strength and modulus and low density, Al±Li alloys have become very attractive for the aerospace industries and more and more applications are being developed using them (e.g. the
{ Present address: Departamento FõÁ sica, UPNA, 31006 Pamplona, Spain. { To whom all correspondence should be addressed. Fax: +34-94-464-8500. E-mail address: [email protected] (J. San Juan).
recently built fuel tanks for the space shuttle [5, 6]). Nevertheless, in order to ful®ll the requirements of such high responsibility applications, the microstructure of the Al±Li alloys must be carefully controlled. From a microstructural point of view, Al±Li alloys are treatable and show a complex microstructure under dierent thermo-mechanical treatments with the presence of a broad family of precipitates (d', d, b', T1, S', T2, . . .). See Refs [7] and [8] for overviews of the microstructure. However, comparing with traditional aluminium alloys, the Al±Li alloys show precipitation of the metastable d' phase as a major strengthening precipitate. d ' phase precipitates homogeneously in all this family of alloys, and remains coherent even after extensive aging [9]. Due to their strong in¯uence on the mechanical properties [10], the knowledge of the d ' phase evolution during thermomechanical treatments is a critical point to control the progress of the microstructure and to establish a theoretical relation between microstructure and mechanical properties. In particular, the evolution of the d ' precipitated mass fraction ( fm) and the mean size of the precipitates (r ) should be precisely evaluated in order to determine the micro-
1359-6454/00/$20.00 7 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 5 4 ( 9 9 ) 0 0 4 2 1 - 8
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mechanisms responsible for the hardening associated to the d ' precipitates, since these parameters determine the characteristics of the d '±dislocation interaction. Nevertheless, the evaluation of the d ' mass fraction in a microstructural state can not be well determined by TEM [11] which is, on the other hand, the technique most widely used for this kind of microstructural characterization in such alloys. Although the measurement of the mean size of the precipitates, can be carried out by TEM, it represents a hard task that takes too much time to be used as a systematic method of microstructural control. As an alternative technique, we have considered the use of X-ray powder diraction together with spectra re®nement by the Rietveld method [12±15] to determine quantitatively the mass fraction and the mean size evolution of the precipitates. The Rietveld method is being applied increasingly for structure re®nement of crystal structures. However, it has been scarcely used in other scienti®c areas such as physical metallurgy, although X-ray powder diraction techniques are frequently utilized. To exploit the capabilities of the X-ray powder diraction coupled with the Rietveld method, we have applied this methodology to a pseudobinary Al±Li alloy (with Zr as grain re®ner). In Al±Li binary alloys three phases are consecutively formed during thermal treatments [16]. The a phase, which appears after quenching from high temperature solid solution treatment, is a disordered substitutional solid solution of lithium in aluminium (space group Fm3 m). The cell parameter of aluminium (aa=4.0496 AÊ) is only slightly dependent on lithium concentration [17]. Subsequently, during aging treatment, the metastable d ' (Al3Li) phase develops inside the a phase in the form of perfectly coherent spherical precipitates. The d ' phase has a Cu3Au type structure (space group Pm3 m) with practically the same cell parameter as the a phase (ad '=4.03 AÊ) [18]. The b' (Al3Zr) phase has the same structure as that of d ' phase and is obtained by the addition of Zr as grain re®ner, but in such small quantities that it can be neglected [19]. Finally for long aging times, the stable d phase forms at the grain boundaries by dissolution of d ' precipitates. The d phase is a NaTl type structure (space group Fd3 m) with a cell parameter ad=6.3685 AÊ [20]. The appearance of the d phase at the grain boundaries produces d ' precipitate-free zones that promote intergranular failures [21]. Therefore, the detection of the d phase is an important point in order to control the mechanical behaviour of this alloy. The aim of this work is to determine quantitatively the d ' mass fraction in a binary mixture of d ' (minor) and a phases for short aging times, and also the d mass fraction for longer aging times using X-ray powder diraction and the Rietveld method. In addition, we will also test the ability of this methodology to obtain the mean size of the d '
precipitates. Nevertheless, the evaluation of the d ' mean radius requires a calibration of the full width at half maximum (Hk ) of the X-ray peaks which, in our case, has been accomplished by TEM. Our purpose is to know the d ' mass fraction along the thermal treatments in a sample cut directly from a plate obtained by extrusion, which is one of the most usual treatments for industrially-produced alloys. Nevertheless, the precipitation hardening is strongly dependent on the microscopic precipitate± dislocation interaction, and becomes very complex when both precipitated fraction and precipitate size evolve simultaneously (see e.g. Refs [22] and [23] as overviews). Consequently, in this work we have also studied the microstructural evolution of Al±Li alloys at 160, 180 and 2008C through thermoelectric power (TEP) and Vickers hardness (VH) measurements. Both techniques are sensitive to microstructural changes in metallic alloys. In particular, TEP measurements have proved to be a very good tool to follow the microstructural evolution of metallic materials [24±26]. The comparison of the microstructural evolution of the precipitates (by XRD) and the precipitation kinetics (by TEP) with the hardening kinetics (by VH), during the dierent stages of the precipitation process, should give an important and useful knowledge to optimize the mechanical properties through the microstructural control. 2. EXPERIMENTAL PROCEDURES
2.1. Experimental techniques The material employed in this work is an Al±2.25 wt% Li±0.1 wt% Zr (Al±8.1 at.% Li±0.03 at.% Zr) alloy supplied by Pechiney as an extruded plate. The samples were treated at 5308C for 30 min in a salt bath and quenched into iced water to obtain the a solid solution. In order to produce the evolution of the d ' and d phases mass fractions present in the alloy, the samples were further aged in salt baths at 160, 180 and 2008C along dierent times. For X-ray measurements, plane samples (10 mm 10 mm 1 mm) were cut with their normal parallel to the extrusion direction. They were electropolished to reduce the thickness below 0.3 mm in a solution of 10 vol.% perchloric acid in ethanol using a platinum electrode. It is important to point out that the powder diraction patterns were obtained with only one sample for every temperature. It means that after quenching, the dierent aging treatments were performed on the same sample, adding the aging time for each dierent heat treatments. This procedure avoids problems related with possible dierences in grain structure (texture), deformations, and in reproducibility of thermal treatments in dierent samples. Measurements were carried out on a STOE powder diractometer with Ge monochromated Cu Ka1
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radiation (l=1.54056 AÊ). Transmission X-ray powder diraction data were collected from 108 to 908 in 2y. Samples are spinning around the normal of the sample plane. In order to support the X-ray analysis, TEM at room temperature was employed to know the microstructure of the binary Al±Li alloys at dierent aging stages. After quenching from the high solid solution temperature, samples for TEM were prepared following a three step process. First, speci®c thermal treatments were performed on samples with thickness between 0.8 and 1 mm. Then, they were electropolished using a mixture of 20% perchloric acid in ethanol to reduce their thickness down to 0.2±0.3 mm. Finally, these samples were prepared for TEM observations by a Tenupol-3 (Struers) equipment (I = 0.2 A, V = 15 V at ÿ308C) using as electrolyte a mixture of 25% nitric acid in methanol. Measurements were carried out on a JEOL 1200±EX at 120 kV, working in selected area diraction pattern (SADP) and image modes. Although X-ray diraction and TEM allow analysis of the microstructural evolution of the sample, it is necessary to devote long periods of preparation and measurement. Then, in order to have a quick method of analysis, TEP measurements were also performed. The TEP samples were strips of 60 mm length and a maximum section of 2 mm2 in order to avoid temperature gradients. The TEP unit is equipped with pure aluminium blocks. The TEP values measured refer to the absolute value of the aluminium reference (ÿ1.4 mV/K). The low temperature block was set at T = 15 2 0.18C and the dierence between the low and high temperature blocks at DT = 10 20.18C. The resolution of the equipment is 20.002 mV/K. To measure the TEP along the aging time, the sample after heat treatment was quenched in water at room temperature and measured in the TEP unit. Then, the sample was introduced again into the salt bath to follow the aging treatment. Finally, to compare the hardening and precipitation kinetics, Vickers' Hardness measurements were performed using Zeiss MHP equipment. The values considered are the average of 20 dierent measurements performed in dierent points of the sample with an error of 23 Vickers' units.
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provides accurate phase analysis without the need of standards or laborious experimental calibration procedures. Quantitative phase analysis has been carried out with the program DBWS [27]. A Rietveld re®nement involves the ®tting of the full experimental diraction pattern with calculated pro®les and background. The model utilized to describe completely the intensity corresponding to the ith step (Yi ) can be written as: Yi
X X cf Lfk j F j2fk f
ÿ2Mf
e
k
1
Pfk Ak O 2yi ÿ 2yfk bi
where f and k are the phase and re¯ection labels, respectively, cf is the scale factor, Lfk contains the Lorentz, polarization and multiplicity factors, Ffk are the structure factors, Mf B sin 2 yf =l2 is the global temperature factor being B the Debye± Waller factor, Pfk is the preferred orientation function, Ak represents the absorption correction function and O is the re¯ection pro®le function which approximates the eects of both the instrumental and specimen features. Finally, bi represents the background intensity at the ith step. All these parameters are changed in a recurrent process in order to minimize the weighted squared dierence between the experimental data (Yi ) and the theoretically predicted value (Yicalc) at each angular position: X wi Yi ÿ Yicalc 2
2
i
where i varies from 1 to the number of observation, and wi=1/Yi is the reciprocal of the variance associated to the i observation. The weight of a phase in a mixture is proportional to the product of the scale factor, as derived in the multicomponent Rietveld analysis of the powder diraction pattern, with the mass and volume of the unit cell. If all phases are identi®ed and crystalline, the weight fraction wn of phase n is given by [28]: cn Zn Mn Vn wn X cf Zf Mf Vf
3
f
2.2. Rietveld re®nement The Rietveld method [14] has been used to determine the d ' precipitated mass fraction ( fm) and the mean radius of the d ' precipitates (r ) at each stage of the aging process. In order to explain qualitatively the method, we show here the general procedure, although a full and accurate explanation of the special characteristics of its application to Al±Li alloys has been shown elsewhere [15]. This method
where cn, Zn, Mn and Vn are, respectively, the Rietveld scale factor, the number of formula units per unit cell, the mass of the formula unit and the unit-cell volume of each phase n. On the other side the full width at half maximum (Hk ) associated to each d ' peak can be related linearly to the inverse of the mean radius of the d ' precipitates [29]. Peak pro®le parameters were re®ned assuming a Lorentzian type pro®le de®ned by:
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p 2 c O 2yi ÿ 2yk " pHk
1 c 2yi ÿ 2yk 2 1 H 2k
#2
4
p where c 4 2 ÿ 1: Hk represents the full width at half maximum and yk the peak maximum position of the k re¯ection. The peak width for each re¯ection can be determined using three parameters (U, V, W ) to de®ne the half width at half maximum (Hk ) [14]: H 2k U tan 2 yk V tan yk W:
5
The re®ned parameters include scale factors, zero point and background coecients, peak width, cell parameters, pro®le parameters (Lorentzian) and preferential orientation. The knowledge of the crystallographic structure corresponding to the three present phases (a, d ', d ) leads to simulate the theoretical X-ray spectrum for each precipitate and allows to determine the angular position and the relative intensity associated to each re¯ection. Table 1 shows the theoretical peak intensity (in relative values) associated to the a, d' and d phases in function of the angular position. The associated Miller indices are also shown. It should be remarked that the two most intense d ' diraction peaks coincide with the two most intense a peaks (1,1,1) and (2,0,0). As an example to show the characteristics of the Rietveld re®nement, we have selected the spectrum associated to the 316.8 ks (88 h) at 1808C aged sample. Figure 1 shows the ®tting of the full measured spectrum. In Fig. 1(a), the full scale is shown with the standard dierences between the measured and calculated pro®les (bottom of the diagram). Only a peaks can be observed although small peaks can be appreciated. Nevertheless, in order to see the smallest peaks associated to the d ', Table 1. Angular position and relative intensity associated to the a, d ' and d phases 2y 21.9 24.17 31.20 38.48 40.00 44.70 47.30 50.31 55.51 57.85 63.62 65.09 69.59 72.65 73.93 77.85 78.20 82.40 86.30 86.60
a
d'
d
28 (1,0,0) 100 (1,1,1)
25 (1,1,0) 100 (1,1,1)
52 (2,0,0)
52 (2,0,0) 8 (2,1,0) 6 (2,1,1)
25 (2,2,0)
23 (2,2,0) 3 (2,2,1) 2 (3,1,0)
21 (3,1,1) 5 (2,2,2)
18 (3,1,1) 4 (2,2,2) 1 (3,2,0)
75 (1,1,1) 100 (2,2,0) 27 (3,1,1) 12 (4,0,0) 8 (3,3,1) 17 (4,2,2) 5 (5,1,1) 3 (4,4,0)
Fig. 1(b) shows the same spectrum but ampli®ed in the intensity scale. Application of this methodology to the spectra obtained during the precipitation process leads us to obtain the evolution of the precipitated phases with aging time at dierent temperatures. Details of the complete re®nement method are shown in Ref. [15]. 3. EXPERIMENTAL RESULTS
3.1. X-Ray diraction In order to study the d ' and d precipitation kinetics, we have followed the microstructural evolution of the samples along aging treatments at three temperatures: 160, 180 and 2008C. Figure 2 shows the sequence of spectra obtained from dierent aging times at 2008C. The intensity axis (in relative values to the maximum peak intensity which corresponds to the (1,1,1) re¯ection of the a phase) is truncated at 2% in order to see the evolution of the (1,0,0) and (1,1,0) re¯ections associated to the d ' phase (other smaller peaks appear at higher angles, but all of them show the same qualitative behaviour) and the re¯ections associated to the d phase. The direct observation of the spectra shows that the precipitation process clearly in¯uences the diraction characteristics. d' peaks heights ®rst increase and then decrease with aging time. After 4546 h at 2008C d' peaks disappear. On the other side, the full width at half maximum of the d ' peaks decrease progressively with aging time. Small peaks at 2y=24.178 and 2y=408 appear after 83 h at 2008C which correspond to the stable d phase. The increase in the d precipitated mass fraction during aging (increase in the integrated intensity associated with the d peaks) promotes the dissolution of the d ' phase. Looking at the (1,1,0) for d ' and (1,1,1) for d re¯ections located at 31.28 and at 24.178, respectively, allows to analyze qualitatively the evolution of the precipitation processes of both phases. Figure 3 shows the evolution of the d' (1,1,0) re¯ection for dierent aging times at 2008C. The full width at half maximum of the peak decreases progressively with aging time and the intensity of the peak increases up to a maximum and then disappears progressively. This indicates that the mass fraction of the d ' metastable phase increases after short aging times up to a maximum value. The average size of the d ' precipitates increases with aging. Once the maximum has been reached, the d ' mass fraction decreases progressively. The dissolution of this phase promotes the successive formation of the stable d phase at the grain boundaries for long aging times. Nevertheless, a quantitative analysis of this process requires the application of the Rietveld method described previously, and then the analysis of the full XRD pattern. The spectra obtained at 160 and 1808C
PEÂREZ-LANDAZAÂBAL et al.: PRECIPITATION KINETICS
show a similar behaviour, but the precipitation of the stable d phase can be observed at relatively shorter times (below 12 days of aging), for the treatment at 2008C. After Rietveld re®nement, the scale factor allows to know the evolution of the precipitated mass fraction of d and d ' phases by using equation (3). Figure 4 shows the precipitated mass fraction vs aging time at 160, 180 and 2008C. In the asquenched sample, it is not easy to evaluate the mass
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fraction since the re¯ections are very small and wide, and the re®nement is not very sensitive to the presence of d ' precipitates. Nevertheless, it is well known that the formation of the ®rst stages of d ' precipitation can not be avoided during quenching [24]. This process can be well studied by TEP measurement and it will be presented later. At 1608C the precipitated d ' mass fraction increases continuously with aging time. Neither the dissolution of d ' nor the precipitation of d phase is
Fig. 1. (a) Re®ned spectrum (full scale). The standard dierence between the measured and calculated pro®les is shown at the bottom of the diagram. (b) Re®ned spectrum (ampli®ed scale). The standard dierence between the measured and calculated pro®les is also shown.
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Fig. 2. Powder diraction spectra vs aging time obtained at 2008C.
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Fig. 2 (continued)
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observed in the studied time range. At 1808C the d ' precipitated mass fraction reaches a maximum value at around 2 105 s, and then the dissolution of this phase begins. In the last spectrum small d phase re¯ections appear. Finally, at 2008C the evolution shows the full precipitation sequence. First, the precipitated d' mass fraction increases continuously with aging time up to a maximum value at around 6 104 s, and then d ' precipitates dissolve, giving rise to the formation of d phase at the grain boundaries. This sequence can also be observed qualitatively in the spectra of Fig. 2. The cell parameter of the a solid solution also shows an evolution during precipitation. The evaluation of this parameter can be performed by Rietveld analysis since the a phase shows very narrow re¯ections and their shift can be very precisely analysed. Figure 5 shows this evolution at 160 and 2008C. It can be seen that the cell parameter decreases during the precipitation process tending to a ®nal value (at 2008C can be better observed) that corresponds to the cell parameter associated to the a phase with the equilibrium concentration of Li at each temperature. Nevertheless, d ' and d phases show very small and wide re¯ection peaks and the evaluation of their cell parameter evolution is dicult and does not show a clear tendency. The average of the values obtained gives a value of a = 4.0520.02 AÊ for the cell parameter associated to the d ' phase and a = 6.360 2 0.002 AÊ for the d phase.
The full width at half maximum (Hk ) of the d ' re¯ections reveals the evolution of the mean size of the precipitates formed during aging. The d ' peaks width (Hk ) variation can be related with the d ' precipitates mean radius (R ) variation due to the inverse relation that exists between Hk and R [29]. The 1/Hk values obtained at 160, 180 and 2008C for the re¯ection (1,1,0) of the d ' phase (all re¯ections show the same behaviour) are represented in Fig. 6 vs t 1/3. All of them show a linear relationship between 1/H and t 1/3 for short times, but after a critical time, this linearity is lost (the curve corresponding to 1608C is linear in all the studied range). On the other side, for a ®xed aging time, the higher the aging temperature, the higher the value of 1/H, and then, the mean size of the d ' precipitates. Nevertheless, the change of the mean size of precipitates shown in Fig. 6 has only the meaning of a relative evolution. In order to obtain a more direct measurement of the precipitates size, a calibration by TEM should be performed. 3.2. Transmission electron microscopy TEM is the straightforward way to determine the real mean size of the precipitates through the microstructural evolution during aging. The as-quenched and 4 days room temperature (R.T.) aged sample shows a ®ne dispersion of d ' phase homogeneously distributed in the matrix and diraction spots corresponding to d ' re¯ections [Fig. 7(a)]. Consequently,
Fig. 3. Evolution of the (1,1,0) re¯ection associated to the d' phase vs time.
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all further high temperature aging treatments begin with this state. Figure 7 shows the dark ®eld photographs corresponding to dierent aging times at 2008C. The direct observation clearly shows the increase in the mean size of d ' precipitates with aging time. Nevertheless, the analysis of the precipitate mass fraction requires a more complex study. These images also show the inhomogeneous precipitation of d ' phase around b' (Al3Zr) particles, but since the Zr concentration is low the precipitated b' volume fraction is also small. The observation of these particles as black zones, in spite of having the same crystal structure, cell parameter and orientation as d' precipitates, has been extensively studied in the literature [30]. The d ' mean radius increases during aging and the analysis of the images allows to determine this variation. Figure 8 shows the linear evolution of R vs t 1/3 according to the Lifshift±Slyozov±Wagner theory [31, 32], but only in the time range where the curves of 1/H vs time (Fig. 6) are linear. This data permits a rescaling of the curves of Fig. 6 and then provides the knowledge of the quantitative evolution of the d ' mean radius at the temperatures studied. 3.3. Thermoelectric power
Fig. 4. Evolution of the mass fraction of d' (*) and d (w) phases with aging time obtained from the re®ned scale factor at 160, 180 and 2008C.
Fig. 5. Relative change of the a phase cell parameter vs aging time at 160 and 2008C.
As we commented before, TEP measurements are very sensitive to microstructural changes and allow the study of the evolution of the precipitation process and hence the characterization of its kinetics along the isothermal aging treatments. Figure 9 shows the time evolution of TEP during aging at 160, 180 and 2008C of dierent samples solid solution treated and quenched in the standard way. All measurements have similar behaviour vs time and show three consecutive stages. The asquenched TEP values show a dispersion of 0.06 mV/ K in the dierent samples used in each kinetics, linked to the small variation in the quenching rate. TEP increases during aging at 2008C from the asquenched value to a maximum value achieved after
Fig. 6. 1/Hk values obtained for the re¯ection (1,1,0) of the d ' phase vs t 1/3 at 160, 180 and 2008C.
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around 10 s during a ®rst stage. The second stage decreases continuously up to 104 s and then a transitory stage between 104 and 5 105 s begins. Finally, a third stage starts which also decreases with time. The in¯uence of the aging temperature on this gen-
eral behaviour becomes manifest in several aspects: the maximum of the curve shifts toward longer times, the end of the second stages achieves lower values and the third stage starts at longer times as far as the aging temperature decreases.
Fig. 7. Diraction pattern and dark ®eld (DF) image associated with a sample aged at room temperature during 4 days after quenching (a). DF image obtained after aging at 2008C during (b) 0.3, (c) 1.5, (d) 21, (e) 83 and (f) 146 h.
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3.4. Microhardness Figure 10 shows the R.T. Vickers' Hardness (VH) change during aging at the studied temperatures. All of them, show an as-quenched value of around 50 VH. In the early stages the VH value decreases slightly during 10 s and then increases. At 2008C the hardness achieves a maximum after aging during 4 103 s and then decreases progressively. At 1808C the curve shows a double stage before achieving the maximum after 105 s and then decreases with aging time. A similar behaviour is observed at 1608C, but now the curve achieves a local maximum before the maximum value which is not observed in the studied range. The maximum value at T = 2008C is 90 VH, at T = 1808C is 107 VH and has not been determined at T=1608C. 4. DISCUSSION
The XRD technique complemented by the Rietveld method gives accurate information of the precipitation processes. In particular, the precipitated mass fraction and the mean precipitate radius can be obtained at the same time after analysis of the diraction spectrum. This will be very important in order to optimize the control of industrial processes devoted to obtain these alloys under dierent microstructural conditions. This technique can be used as an alternative to the traditional TEM, which is a destructive technique and which also requires long periods of tedious work to prepare samples before observation. Also, observations by X-ray integrate over larger regions than TEM which is very localized. On the other side, it is not easy to use TEM in order to determine the precipitated mass fraction in Al±Li alloys [11]. Then, Xrays seem to be very promising in order to control microstructure of dierent alloys' systems and in particular in Al±Li alloys. Powder diraction methods on polycrystalline
Fig. 8. Measured d' mean radius obtained by TEM vs t 1/3 at 2008C
Fig. 9. TEP variation vs aging time at 160, 180 and 2008C.
Al±Li samples allow quantitative analysis of the evolution of d ' and d phases during precipitation, as shown in Fig. 3. Besides, the application of the Rietveld method allows the quantitative analysis of each spectrum. Figure 4 shows the evolution of the d ' and d precipitated weight fractions at 160, 180
Fig. 10. Vickers' Hardening variation vs aging time at 160, 180 and 2008C.
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and 2008C. In all of them, d ' fraction increases during aging up to a maximum value and then, the dissolution of this phase is accompanied by the d precipitation. The full sequence can only be observed during aging at 2008C, since at lower temperatures, the kinetic is very slow. When the treatment temperature increases, the maximum of the precipitated d' fraction shifts to lower times, the rate of d ' dissolution increases and the formation of d phase shifts to lower times. This behaviour is expected because the d ' phase is metastable and the evolution towards the d equilibrium phase is thermally controlled. Besides, the lower the aging temperature, the higher the maximum precipitated fraction of d ' is due to the lower concentration of Li in solid solution at lower temperatures. TEM measurements show the presence of d phase at the grain boundaries after aging the sample for 146 h at 2008C. This behaviour is in agreement with the expected process. It is very dicult to establish the lowest value of d ' mass fraction that could be accurately measured by TEM due to the simultaneous evolution of the precipitated fraction and the size of precipitates. It seems that the ®tting procedure during the application of the Rietveld method works better when the precipitates are big (sharp peaks) than when precipitates are very small (broad peaks). Obviously, the obtained result for the asquenched state, where the Li is mainly in solid solution, are meaningless and would be an artifact of the ®tting method. Even for very low aging times (below 103 s) where the peaks are small and broad, the obtained result would be probably overestimated. On the contrary, when the diraction peaks become sharpened, (e.g. at 2.5 h) the Rietveld ®tting works very well and the precipitated mass fraction is very accurately determined. A relevant parameter in the change of mechanical properties is the mean radius of the precipitated phases. The width of the diraction peaks associ-
Fig. 11. Variation of the d' mean radius at 160, 180 and 2008C obtained from X-ray data and rescaled with the data of Fig. 8.
ated with the d ' phase allows the evolution of precipitate means radius to be determined (Fig. 6). As expected, the precipitate mean radius increases during aging in the temperature-time range studied. Figures 6 and 8 show that the evolution of 1/H vs t1/3 is linear in the time range, where the precipitated d ' mass fraction increases. As far as the dissolution of d ' begins, 1/H vs t 1/3 separates from linearity. The direct analysis by TEM of the evolution of precipitate means radius during aging at 2008C (Fig. 8) reveals the proportionality factor that relates 1/H and R, and then allows the data of Fig. 6 to be rescaled. It is assumed that this factor is the same for the three kinetics studied which seems to be reasonable since all samples are similar and were measured in the same conditions. The rescaled data are shown in Fig. 11. The linear behaviour of R vs t 1/3 in the range of increasing d ' phase can be analysed using the LSW theory [31, 32]. Previous experimental and theoretical works on this topic assume that the d ' precipitated mass fraction is constant during the coarsening process [33, 34]. Then they assume that the full precipitated fraction is obtained after quenching. This is not true, although eectively an important fraction of d ' phase forms during quenching [20]. Then, the increase in the precipitated mass fraction of d ' phase is simultaneous with the coarsening process and this evolution can be approximated by the LSW theory. When the aging time is long enough, the linear behaviour is lost since d ' precipitates dissolves, and this dissolution reduces the mean size of the d ' precipitates causing their evolution to be far from a linear tendency. Nevertheless, a more precise analysis shows that the linear behaviour is not true even before dissolution of the d ' phase. The 1608C aging curve (Fig. 11) shows the lowest dispersion in the data and the d ' mass fraction increases continuously in the studied range. This curve is concave relative to the ordinate axis, showing a deviation from the LSW theory. At the beginning, the slope of this curve is higher than that at the end of the curve. This can be explained since at the beginning, the radius increase is due to a growing process and to an increase in the precipitated mass fraction. This aspect has not been taken into account in previous work [33, 34] due to the lack of precision in the measured curves. The contribution of the increase in the precipitated mass fraction reduces to zero when the maximum value of precipitated mass fraction is achieved. Then, only the coarsening process contributes to the increase in the mean radius and the slope reduces slightly as shown in Fig. 11. This analysis shows again the usefulness of the proposed methodology. On the other side, the X-ray diraction technique and the Rietveld method give information on the evolution of parameters that are not so important from the point of view of industrial application, but
PEÂREZ-LANDAZAÂBAL et al.: PRECIPITATION KINETICS
can be important for a fundamental study. In particular, the change of the cell parameter can be easily followed by this technique. The a phase cell parameter decreases when aging time increases. Then the lower the Li concentration in solid solution, the lower the cell parameter of the a phase, showing that Li expands the aluminium lattice (Fig. 5). Our results are in opposition to those where the in¯uence of Li in the aluminium lattice has been studied [17], and propose that Li in aluminium reduces the cell parameter of the aluminium matrix. Nevertheless, the ionic and atomic radius of Li (ri=0.6 AÊ, ra=1.55 AÊ) are larger than those of aluminium (ri=0.5 AÊ, ra=1.43 AÊ), and then, it is expected that lithium expands the aluminium lattice. Consequently, during the precipitation process, the concentration of Li in solid solution decreases and a decrease of the cell parameter of the aluminium matrix should be expected in agreement with our results in Fig. 5. This previous analysis allows the microstructural changes to be determine systematically by X-ray diraction which is a non-destructive technique. Nevertheless, TEP technique can give accurate and quick information of the precipitation kinetics. As an example, the usefulness of this technique can be demonstrated for looking at the evolution of the early stages obtained after quenching (aging during 10 s at 2008C). This evolution is very fast and Xray diraction requires long periods of time to study the changes produced in the sample at every aging step. Furthermore the analysis by X-ray diffraction is dicult since the precipitates formed during quenching are very small and produce wide diraction peaks that can not be accurately re®ned by the Rietveld method. Then changes in this stage can be followed in a quantitative way very easily by TEP. But in order to apply the TEP technique in a systematic way, it is necessary to identify the dierent stages associated with the TEP measurement. This has been done comparing with the X-ray results. After quenching from solid solution temperature, the TEP reduces at room temperature as shown elsewhere [24]. Nevertheless, during aging at high temperatures the TEP increases in the ®rst 10 s and then, reduces progressively (Fig. 9). This increasing stage (1st stage) is linked to the dissolution of small nonstable precipitates formed during quenching or during aging at room temperature [35] and consequently to a transitory increase of the Li concentration in solid solution. As mentioned before, asquenched TEP values show a dispersion of 0.06 mV/ K. Nevertheless, if these samples (with dierent as quenched TEP values) are subjected to a thermal treatment at 2008C during 10 s, all of them reach the same TEP value. This allows to conclude that the dierences in as-quenched TEP value can be associated with dierences in the microstructure of
1295
the as-quenched alloys (early stages), and are not due to experimental errors. In order to know the in¯uence of the phase evolution on the TEP value for longer aging times, Fig. 12 shows comparatively the TEP evolution at 2008C and the corresponding mass fraction fm (d ' and d ) obtained by XRD. As shown, the precipitation of the d ' phase promotes the decreasing of the TEP between 101 s and 104 s (second stage). The lower the aging temperature (higher precipitated mass fraction), the lower the minimum TEP value associated to the second stage, showing that d ' reduces the TEP value. A transitory stage between 104 and 105 s can be linked to the coarsening of d ' precipitates. This interpretation is in agreement with the fact that the increase of the precipitated mass fraction of d ' is accompanied by a much slower decrease of TEP evolution, indicating that the Li solid solution remains almost constant. Besides, the end of this stage corresponds with the begining of the dissolution of d ' precipitates (Fig. 11). Finally the third stage is linked to the precipitation of d phase at the grain boundaries, which occurs at the expense of the d ' dissolution. This last stages shifts to higher times as long as the temperature decreases. Finally, microhardness curves show also a behaviour dependent on the microstructural stage. Nevertheless, this correlation is not so simple. Associated with the increase of TEP during the early stages of aging, the VH curves show a small decrease which can be explained by the dissolution of small precipitates formed during quenching or room temperature aging. For longer aging times, the VH curves show dierent stages linked to dierent microstructural states. At 2008C, a maximum can be observed before the maximum of precipitated mass fraction is achieved. This means that the hardening evolution, although traditionally used to characterize the precipitation kinetics, is not representative of the precipitated mass fraction evolution. We should then distinguish between the
Fig. 12. TEP (r) and precipitated mass fraction fm [d' (*)and d (w)] at 2008C vs aging time.
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PEÂREZ-LANDAZAÂBAL et al.: PRECIPITATION KINETICS
precipitation kinetics and the hardening kinetics. Indeed, the hardening kinetics behaviour is strongly dependent on the complexity of the dislocation±precipitate interaction. Nevertheless, the knowledge of the mean radius of precipitates and the d' precipitated mass fraction are the main microstructural parameters to be determined in order to analyse the hardening mechanism. These parameters change simultaneously during aging and then the dislocation±precipitate interaction need a detailed study which will be performed in a further work. 5. CONCLUSIONS
The precipitation kinetics at high temperatures (160, 180 and 2008C) have been determined by XRD, TEP and microhardness measurements. The Rietveld method has been applied to the Xray spectra in order to study the precipitated mass fraction of d ' and d phases in Al±Li alloys. The method allows us to obtain quantitatively the d ' and d precipitated mass fraction and their evolution with aging time. Furthermore, this method gives directly the cell parameter evolution of the matrix phase, and indirectly the mean radius of d ' precipitates through an appropriate calibration curve. Experimentally, this calibration has been determined studying the evolution of the mean radius of d ' by TEM. TEP has been shown to be a powerful technique to study the microstructural evolution of Al±Li alloys, since it is sensitive to the dierent stages of precipitation associated to the d ' and d phases. The comparison of the dierent experimental results allow us to establish a clear dierence between the precipitation kinetics and the hardening kinetics. Finally, we are now ready to evaluate the in¯uence of the microstructure on the hardening of the sample, since we know the time evolution of the mean radius and mass fraction of d ' precipitates. AcknowledgementsÐThis work has been carried out with the ®nancial support of the Spanish ``ComisioÂn Interministerial de Ciencia y TecnologõÂ a'' (CICyT) in the framework of the ``Plan Nacional de Materiales'' (Project No. MAT 97-1059-C02-02). The authors thank Rafael Garcia-Roja, from the University of Cadiz, the facilities oered for the TEM observations. The authors also wish to thank the Pechiney Company for supplying the alloy. REFERENCES 1. Hatch, J. E. (ed.), Aluminium: Properties and Physical Metallurgy. ASM, Metals Park, OH, 1984. 2. Peel, C. J., New Light Alloys, Lecture Serie No. 174, 2-1 AGARD, NATO, 1990.
3. Graham, R. H., Rioja, R. J. and Newman, J. M., Al± Li alloys. DGM Informationgesellschaft mbh, 15 Oberrursell, 1992. 4. Fridlyander, I. N., Bratukhin, A. G. and Davidov, V. G., Al±Li alloys. DGM Informationgesellschaft mbh, 35 Oberrursell, 1992. 5. Fielding, P. S. and Wolf, G. J., Adv. Mater. Proc., 1996, 150(4), 21. 6. Malone, J., Adv. Mater. Proc., 1998, 153(4), 7. 7. Starke, E. A. Jr and Quist, W. E., New Light Alloys, Lecture Serie No. 174, AGARD, NATO, 1990. 8. PeÂrez-LandazaÂbal, J. I., Ph. D. thesis, Univ. PaõÂ s Vasco, Bilbao, Spain, 1995. 9. Lavernia, E. J. and Grant, N. J., J. Metals Sci., 1987, 22, 1521. 10. Huang, J. C. and Ardell, A. J., Mater. Sci. Engng, 1988, A104, 149. 11. Furukawa, M., Miura, Y. and Nemoto, M., Trans. Japan Inst. Metals, 1985, 26(4), 230. 12. Rietveld, H. M., J. appl. Crystallogr., 1967, 22, 151. 13. Rietveld, H. M., J. appl. Crystallogr., 1969, 2, 65. 14. Young, R. A., The Rietveld Method. International Union of Crystallography, Oxford Science Publications, 1993. 15. PeÂrez-LandazaÂbal, J. I., No, M. L., Madariaga, G. and San Juan, J., J. appl. Crystallogr., 1997, 30, 107. 16. Davis, J. R., Aluminium and Aluminium Alloys. ASM International, Materials Park, OH, 1993. 17. Levine, E. D. and Rapperport, E. J., Trans. A.I.M.E., 1963, 227, 1204. 18. Williams, D. B. and Edington, J. W., Metal Sci., 1975, 9, 529. 19. Vecchio, H. S. and Williams, D. B., Acta metall., 1987, 35, 2959. 20. Kuriyama, K. and Masaki, N., Acta crystallogr., 1975, B31, 1793. 21. Jha, S. C., Sanders Jr, T. H. and Dayananda, M. A., Acta metall., 1987, 35, 473. 22. Reppich, B., Plastic Deformation and Fracture of Materials. Mughrabi VCH, Weinhein, 1993. 23. Nembach, E., Particle Strengthening of Metals and Alloys. Wiley, New York, 1997. 24. PeÂrez-LandazaÂbal, J. I., No, M. L. and San Juan, J., Scripta metall. mater., 1995, 32, 1307. 25. Pelletier, J. M. and Borrelly, R., Mater. Sci. Engng, 1982, 55, 191. 26. Pelletier, J. M., Vigier, G., Mai, C. and Borrelly, R., Acta metall. mater., 1983, 31(10), 1491. 27. Wiles, D. B. and Young, R. A., J. appl. Crystallogr., 1981, 14, 149. 28. Bish, D. L. and Howard, S. A., J. appl. Crystallogr., 1988, 21, 86. 29. AzaÂro, L. V., Elements of X-Ray Crystallography. McGraw-Hill, New York, 1968. 30. Gu, B. P., Liedl, G. L., Sanders Jr, T. H. and Welpmann, K., Mater. Sci. Engng, 1985, 76, 147. 31. Lifshith, I. M. and Slyozov, V. V., J. Phys. Chem. Solids, 1961, 19, 489. 32. Wagner, C. Z., Electrochem., 1961, 65, 581. 33. Mahalingam, K., Gu, B. P., Liedl, G. L. and Sanders Jr, T. H., Acta metall., 1987, 35, 483. 34. Gu, B. P., Liedl, G. L., Kulwicki, J. H. and Sanders Jr, T. H., Mater. Sci. Engng, 1985, 76, 217. 35. Lambri, O. A., PeÂrez-LandazaÂbal, J. I., No, M. L. and San Juan, J., Scripta mater., 1997, 37, 851.
QUANTITATIVE ANALYSIS OF d' PRECIPITATION KINETICS IN Al±Li ALLOYS J. I. PEÂREZ-LANDAZAÂBAL{ 1, M. L. NOÂ 2, G. MADARIAGA 1, V. RECARTE 1 and J. SAN JUAN 1{ 1 Departamento FõÂ sica Materia Condensada, Facultad de Ciencias, Universidad del PaõÂ s Vasco, Apdo. 644, 48080, Bilbao, Spain and 2Departamento FõÂ sica Aplicada II, Facultad de Ciencias, Universidad del PaõÂ s Vasco, Apdo. 644, 48080, Bilbao, Spain
(Received 30 April 1999; received in revised form 7 November 1999; accepted 7 November 1999) AbstractÐThe Rietveld method has been applied to X-ray spectra in order to study the precipitated mass fraction of d' and d in Al±Li alloys. The method allows us to obtain quantitatively the d' and d precipitate mass fractions, and their evolution with aging time. Furthermore, this method also gives directly the cell parameter evolution of the matrix phase and indirectly the mean half radius of d ' precipitates through an appropriate calibration curve. Experimentally, this calibration has been approached by previously studying the evolution of the mean half radius of d ' by transmission electron microscopy (TEM). Thermoelectric power has also been shown to be a powerful technique to study the microstructural evolution of Al±Li alloys, being sensitive to the dierent stages of precipitation associated to the d' and d phases. The comparison of the dierent experimental results allow us to stablish a clear dierence between the precipitation kinetics and the hardening kinetics. 7 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Transmision electron microscopy (TEM); X-ray diraction (XRD); Aluminum±lithium; Phase transformations; Kinetics
1. INTRODUCTION
Aluminium±lithium alloys show special characteristics and performances compared with classical aluminium alloys due to the presence of lithium. Lithium is one of the eight elements with a solubility above 1 at.% in the aluminium matrix, and among them lithium produces the highest modulus and strength increases, and the strongest density decreases [1]. Although binary Al±Li alloys show poor mechanical properties, these other advantages promoted the development of several ternary Al± Li±Cu (2090), quaternary Al±Li±Cu±Mg (2090, 8090, 8091) and more complex Al±Li alloys such as the Al±Li±Cu±Mg±Ag (W-049). See Refs [2]±[6] as overviews of technological developments. Due to their high strength and modulus and low density, Al±Li alloys have become very attractive for the aerospace industries and more and more applications are being developed using them (e.g. the
{ Present address: Departamento FõÁ sica, UPNA, 31006 Pamplona, Spain. { To whom all correspondence should be addressed. Fax: +34-94-464-8500. E-mail address: [email protected] (J. San Juan).
recently built fuel tanks for the space shuttle [5, 6]). Nevertheless, in order to ful®ll the requirements of such high responsibility applications, the microstructure of the Al±Li alloys must be carefully controlled. From a microstructural point of view, Al±Li alloys are treatable and show a complex microstructure under dierent thermo-mechanical treatments with the presence of a broad family of precipitates (d', d, b', T1, S', T2, . . .). See Refs [7] and [8] for overviews of the microstructure. However, comparing with traditional aluminium alloys, the Al±Li alloys show precipitation of the metastable d' phase as a major strengthening precipitate. d ' phase precipitates homogeneously in all this family of alloys, and remains coherent even after extensive aging [9]. Due to their strong in¯uence on the mechanical properties [10], the knowledge of the d ' phase evolution during thermomechanical treatments is a critical point to control the progress of the microstructure and to establish a theoretical relation between microstructure and mechanical properties. In particular, the evolution of the d ' precipitated mass fraction ( fm) and the mean size of the precipitates (r ) should be precisely evaluated in order to determine the micro-
1359-6454/00/$20.00 7 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 5 4 ( 9 9 ) 0 0 4 2 1 - 8
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mechanisms responsible for the hardening associated to the d ' precipitates, since these parameters determine the characteristics of the d '±dislocation interaction. Nevertheless, the evaluation of the d ' mass fraction in a microstructural state can not be well determined by TEM [11] which is, on the other hand, the technique most widely used for this kind of microstructural characterization in such alloys. Although the measurement of the mean size of the precipitates, can be carried out by TEM, it represents a hard task that takes too much time to be used as a systematic method of microstructural control. As an alternative technique, we have considered the use of X-ray powder diraction together with spectra re®nement by the Rietveld method [12±15] to determine quantitatively the mass fraction and the mean size evolution of the precipitates. The Rietveld method is being applied increasingly for structure re®nement of crystal structures. However, it has been scarcely used in other scienti®c areas such as physical metallurgy, although X-ray powder diraction techniques are frequently utilized. To exploit the capabilities of the X-ray powder diraction coupled with the Rietveld method, we have applied this methodology to a pseudobinary Al±Li alloy (with Zr as grain re®ner). In Al±Li binary alloys three phases are consecutively formed during thermal treatments [16]. The a phase, which appears after quenching from high temperature solid solution treatment, is a disordered substitutional solid solution of lithium in aluminium (space group Fm3 m). The cell parameter of aluminium (aa=4.0496 AÊ) is only slightly dependent on lithium concentration [17]. Subsequently, during aging treatment, the metastable d ' (Al3Li) phase develops inside the a phase in the form of perfectly coherent spherical precipitates. The d ' phase has a Cu3Au type structure (space group Pm3 m) with practically the same cell parameter as the a phase (ad '=4.03 AÊ) [18]. The b' (Al3Zr) phase has the same structure as that of d ' phase and is obtained by the addition of Zr as grain re®ner, but in such small quantities that it can be neglected [19]. Finally for long aging times, the stable d phase forms at the grain boundaries by dissolution of d ' precipitates. The d phase is a NaTl type structure (space group Fd3 m) with a cell parameter ad=6.3685 AÊ [20]. The appearance of the d phase at the grain boundaries produces d ' precipitate-free zones that promote intergranular failures [21]. Therefore, the detection of the d phase is an important point in order to control the mechanical behaviour of this alloy. The aim of this work is to determine quantitatively the d ' mass fraction in a binary mixture of d ' (minor) and a phases for short aging times, and also the d mass fraction for longer aging times using X-ray powder diraction and the Rietveld method. In addition, we will also test the ability of this methodology to obtain the mean size of the d '
precipitates. Nevertheless, the evaluation of the d ' mean radius requires a calibration of the full width at half maximum (Hk ) of the X-ray peaks which, in our case, has been accomplished by TEM. Our purpose is to know the d ' mass fraction along the thermal treatments in a sample cut directly from a plate obtained by extrusion, which is one of the most usual treatments for industrially-produced alloys. Nevertheless, the precipitation hardening is strongly dependent on the microscopic precipitate± dislocation interaction, and becomes very complex when both precipitated fraction and precipitate size evolve simultaneously (see e.g. Refs [22] and [23] as overviews). Consequently, in this work we have also studied the microstructural evolution of Al±Li alloys at 160, 180 and 2008C through thermoelectric power (TEP) and Vickers hardness (VH) measurements. Both techniques are sensitive to microstructural changes in metallic alloys. In particular, TEP measurements have proved to be a very good tool to follow the microstructural evolution of metallic materials [24±26]. The comparison of the microstructural evolution of the precipitates (by XRD) and the precipitation kinetics (by TEP) with the hardening kinetics (by VH), during the dierent stages of the precipitation process, should give an important and useful knowledge to optimize the mechanical properties through the microstructural control. 2. EXPERIMENTAL PROCEDURES
2.1. Experimental techniques The material employed in this work is an Al±2.25 wt% Li±0.1 wt% Zr (Al±8.1 at.% Li±0.03 at.% Zr) alloy supplied by Pechiney as an extruded plate. The samples were treated at 5308C for 30 min in a salt bath and quenched into iced water to obtain the a solid solution. In order to produce the evolution of the d ' and d phases mass fractions present in the alloy, the samples were further aged in salt baths at 160, 180 and 2008C along dierent times. For X-ray measurements, plane samples (10 mm 10 mm 1 mm) were cut with their normal parallel to the extrusion direction. They were electropolished to reduce the thickness below 0.3 mm in a solution of 10 vol.% perchloric acid in ethanol using a platinum electrode. It is important to point out that the powder diraction patterns were obtained with only one sample for every temperature. It means that after quenching, the dierent aging treatments were performed on the same sample, adding the aging time for each dierent heat treatments. This procedure avoids problems related with possible dierences in grain structure (texture), deformations, and in reproducibility of thermal treatments in dierent samples. Measurements were carried out on a STOE powder diractometer with Ge monochromated Cu Ka1
PEÂREZ-LANDAZAÂBAL et al.: PRECIPITATION KINETICS
radiation (l=1.54056 AÊ). Transmission X-ray powder diraction data were collected from 108 to 908 in 2y. Samples are spinning around the normal of the sample plane. In order to support the X-ray analysis, TEM at room temperature was employed to know the microstructure of the binary Al±Li alloys at dierent aging stages. After quenching from the high solid solution temperature, samples for TEM were prepared following a three step process. First, speci®c thermal treatments were performed on samples with thickness between 0.8 and 1 mm. Then, they were electropolished using a mixture of 20% perchloric acid in ethanol to reduce their thickness down to 0.2±0.3 mm. Finally, these samples were prepared for TEM observations by a Tenupol-3 (Struers) equipment (I = 0.2 A, V = 15 V at ÿ308C) using as electrolyte a mixture of 25% nitric acid in methanol. Measurements were carried out on a JEOL 1200±EX at 120 kV, working in selected area diraction pattern (SADP) and image modes. Although X-ray diraction and TEM allow analysis of the microstructural evolution of the sample, it is necessary to devote long periods of preparation and measurement. Then, in order to have a quick method of analysis, TEP measurements were also performed. The TEP samples were strips of 60 mm length and a maximum section of 2 mm2 in order to avoid temperature gradients. The TEP unit is equipped with pure aluminium blocks. The TEP values measured refer to the absolute value of the aluminium reference (ÿ1.4 mV/K). The low temperature block was set at T = 15 2 0.18C and the dierence between the low and high temperature blocks at DT = 10 20.18C. The resolution of the equipment is 20.002 mV/K. To measure the TEP along the aging time, the sample after heat treatment was quenched in water at room temperature and measured in the TEP unit. Then, the sample was introduced again into the salt bath to follow the aging treatment. Finally, to compare the hardening and precipitation kinetics, Vickers' Hardness measurements were performed using Zeiss MHP equipment. The values considered are the average of 20 dierent measurements performed in dierent points of the sample with an error of 23 Vickers' units.
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provides accurate phase analysis without the need of standards or laborious experimental calibration procedures. Quantitative phase analysis has been carried out with the program DBWS [27]. A Rietveld re®nement involves the ®tting of the full experimental diraction pattern with calculated pro®les and background. The model utilized to describe completely the intensity corresponding to the ith step (Yi ) can be written as: Yi
X X cf Lfk j F j2fk f
ÿ2Mf
e
k
1
Pfk Ak O 2yi ÿ 2yfk bi
where f and k are the phase and re¯ection labels, respectively, cf is the scale factor, Lfk contains the Lorentz, polarization and multiplicity factors, Ffk are the structure factors, Mf B sin 2 yf =l2 is the global temperature factor being B the Debye± Waller factor, Pfk is the preferred orientation function, Ak represents the absorption correction function and O is the re¯ection pro®le function which approximates the eects of both the instrumental and specimen features. Finally, bi represents the background intensity at the ith step. All these parameters are changed in a recurrent process in order to minimize the weighted squared dierence between the experimental data (Yi ) and the theoretically predicted value (Yicalc) at each angular position: X wi Yi ÿ Yicalc 2
2
i
where i varies from 1 to the number of observation, and wi=1/Yi is the reciprocal of the variance associated to the i observation. The weight of a phase in a mixture is proportional to the product of the scale factor, as derived in the multicomponent Rietveld analysis of the powder diraction pattern, with the mass and volume of the unit cell. If all phases are identi®ed and crystalline, the weight fraction wn of phase n is given by [28]: cn Zn Mn Vn wn X cf Zf Mf Vf
3
f
2.2. Rietveld re®nement The Rietveld method [14] has been used to determine the d ' precipitated mass fraction ( fm) and the mean radius of the d ' precipitates (r ) at each stage of the aging process. In order to explain qualitatively the method, we show here the general procedure, although a full and accurate explanation of the special characteristics of its application to Al±Li alloys has been shown elsewhere [15]. This method
where cn, Zn, Mn and Vn are, respectively, the Rietveld scale factor, the number of formula units per unit cell, the mass of the formula unit and the unit-cell volume of each phase n. On the other side the full width at half maximum (Hk ) associated to each d ' peak can be related linearly to the inverse of the mean radius of the d ' precipitates [29]. Peak pro®le parameters were re®ned assuming a Lorentzian type pro®le de®ned by:
PEÂREZ-LANDAZAÂBAL et al.: PRECIPITATION KINETICS
1286
p 2 c O 2yi ÿ 2yk " pHk
1 c 2yi ÿ 2yk 2 1 H 2k
#2
4
p where c 4 2 ÿ 1: Hk represents the full width at half maximum and yk the peak maximum position of the k re¯ection. The peak width for each re¯ection can be determined using three parameters (U, V, W ) to de®ne the half width at half maximum (Hk ) [14]: H 2k U tan 2 yk V tan yk W:
5
The re®ned parameters include scale factors, zero point and background coecients, peak width, cell parameters, pro®le parameters (Lorentzian) and preferential orientation. The knowledge of the crystallographic structure corresponding to the three present phases (a, d ', d ) leads to simulate the theoretical X-ray spectrum for each precipitate and allows to determine the angular position and the relative intensity associated to each re¯ection. Table 1 shows the theoretical peak intensity (in relative values) associated to the a, d' and d phases in function of the angular position. The associated Miller indices are also shown. It should be remarked that the two most intense d ' diraction peaks coincide with the two most intense a peaks (1,1,1) and (2,0,0). As an example to show the characteristics of the Rietveld re®nement, we have selected the spectrum associated to the 316.8 ks (88 h) at 1808C aged sample. Figure 1 shows the ®tting of the full measured spectrum. In Fig. 1(a), the full scale is shown with the standard dierences between the measured and calculated pro®les (bottom of the diagram). Only a peaks can be observed although small peaks can be appreciated. Nevertheless, in order to see the smallest peaks associated to the d ', Table 1. Angular position and relative intensity associated to the a, d ' and d phases 2y 21.9 24.17 31.20 38.48 40.00 44.70 47.30 50.31 55.51 57.85 63.62 65.09 69.59 72.65 73.93 77.85 78.20 82.40 86.30 86.60
a
d'
d
28 (1,0,0) 100 (1,1,1)
25 (1,1,0) 100 (1,1,1)
52 (2,0,0)
52 (2,0,0) 8 (2,1,0) 6 (2,1,1)
25 (2,2,0)
23 (2,2,0) 3 (2,2,1) 2 (3,1,0)
21 (3,1,1) 5 (2,2,2)
18 (3,1,1) 4 (2,2,2) 1 (3,2,0)
75 (1,1,1) 100 (2,2,0) 27 (3,1,1) 12 (4,0,0) 8 (3,3,1) 17 (4,2,2) 5 (5,1,1) 3 (4,4,0)
Fig. 1(b) shows the same spectrum but ampli®ed in the intensity scale. Application of this methodology to the spectra obtained during the precipitation process leads us to obtain the evolution of the precipitated phases with aging time at dierent temperatures. Details of the complete re®nement method are shown in Ref. [15]. 3. EXPERIMENTAL RESULTS
3.1. X-Ray diraction In order to study the d ' and d precipitation kinetics, we have followed the microstructural evolution of the samples along aging treatments at three temperatures: 160, 180 and 2008C. Figure 2 shows the sequence of spectra obtained from dierent aging times at 2008C. The intensity axis (in relative values to the maximum peak intensity which corresponds to the (1,1,1) re¯ection of the a phase) is truncated at 2% in order to see the evolution of the (1,0,0) and (1,1,0) re¯ections associated to the d ' phase (other smaller peaks appear at higher angles, but all of them show the same qualitative behaviour) and the re¯ections associated to the d phase. The direct observation of the spectra shows that the precipitation process clearly in¯uences the diraction characteristics. d' peaks heights ®rst increase and then decrease with aging time. After 4546 h at 2008C d' peaks disappear. On the other side, the full width at half maximum of the d ' peaks decrease progressively with aging time. Small peaks at 2y=24.178 and 2y=408 appear after 83 h at 2008C which correspond to the stable d phase. The increase in the d precipitated mass fraction during aging (increase in the integrated intensity associated with the d peaks) promotes the dissolution of the d ' phase. Looking at the (1,1,0) for d ' and (1,1,1) for d re¯ections located at 31.28 and at 24.178, respectively, allows to analyze qualitatively the evolution of the precipitation processes of both phases. Figure 3 shows the evolution of the d' (1,1,0) re¯ection for dierent aging times at 2008C. The full width at half maximum of the peak decreases progressively with aging time and the intensity of the peak increases up to a maximum and then disappears progressively. This indicates that the mass fraction of the d ' metastable phase increases after short aging times up to a maximum value. The average size of the d ' precipitates increases with aging. Once the maximum has been reached, the d ' mass fraction decreases progressively. The dissolution of this phase promotes the successive formation of the stable d phase at the grain boundaries for long aging times. Nevertheless, a quantitative analysis of this process requires the application of the Rietveld method described previously, and then the analysis of the full XRD pattern. The spectra obtained at 160 and 1808C
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show a similar behaviour, but the precipitation of the stable d phase can be observed at relatively shorter times (below 12 days of aging), for the treatment at 2008C. After Rietveld re®nement, the scale factor allows to know the evolution of the precipitated mass fraction of d and d ' phases by using equation (3). Figure 4 shows the precipitated mass fraction vs aging time at 160, 180 and 2008C. In the asquenched sample, it is not easy to evaluate the mass
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fraction since the re¯ections are very small and wide, and the re®nement is not very sensitive to the presence of d ' precipitates. Nevertheless, it is well known that the formation of the ®rst stages of d ' precipitation can not be avoided during quenching [24]. This process can be well studied by TEP measurement and it will be presented later. At 1608C the precipitated d ' mass fraction increases continuously with aging time. Neither the dissolution of d ' nor the precipitation of d phase is
Fig. 1. (a) Re®ned spectrum (full scale). The standard dierence between the measured and calculated pro®les is shown at the bottom of the diagram. (b) Re®ned spectrum (ampli®ed scale). The standard dierence between the measured and calculated pro®les is also shown.
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Fig. 2. Powder diraction spectra vs aging time obtained at 2008C.
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Fig. 2 (continued)
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observed in the studied time range. At 1808C the d ' precipitated mass fraction reaches a maximum value at around 2 105 s, and then the dissolution of this phase begins. In the last spectrum small d phase re¯ections appear. Finally, at 2008C the evolution shows the full precipitation sequence. First, the precipitated d' mass fraction increases continuously with aging time up to a maximum value at around 6 104 s, and then d ' precipitates dissolve, giving rise to the formation of d phase at the grain boundaries. This sequence can also be observed qualitatively in the spectra of Fig. 2. The cell parameter of the a solid solution also shows an evolution during precipitation. The evaluation of this parameter can be performed by Rietveld analysis since the a phase shows very narrow re¯ections and their shift can be very precisely analysed. Figure 5 shows this evolution at 160 and 2008C. It can be seen that the cell parameter decreases during the precipitation process tending to a ®nal value (at 2008C can be better observed) that corresponds to the cell parameter associated to the a phase with the equilibrium concentration of Li at each temperature. Nevertheless, d ' and d phases show very small and wide re¯ection peaks and the evaluation of their cell parameter evolution is dicult and does not show a clear tendency. The average of the values obtained gives a value of a = 4.0520.02 AÊ for the cell parameter associated to the d ' phase and a = 6.360 2 0.002 AÊ for the d phase.
The full width at half maximum (Hk ) of the d ' re¯ections reveals the evolution of the mean size of the precipitates formed during aging. The d ' peaks width (Hk ) variation can be related with the d ' precipitates mean radius (R ) variation due to the inverse relation that exists between Hk and R [29]. The 1/Hk values obtained at 160, 180 and 2008C for the re¯ection (1,1,0) of the d ' phase (all re¯ections show the same behaviour) are represented in Fig. 6 vs t 1/3. All of them show a linear relationship between 1/H and t 1/3 for short times, but after a critical time, this linearity is lost (the curve corresponding to 1608C is linear in all the studied range). On the other side, for a ®xed aging time, the higher the aging temperature, the higher the value of 1/H, and then, the mean size of the d ' precipitates. Nevertheless, the change of the mean size of precipitates shown in Fig. 6 has only the meaning of a relative evolution. In order to obtain a more direct measurement of the precipitates size, a calibration by TEM should be performed. 3.2. Transmission electron microscopy TEM is the straightforward way to determine the real mean size of the precipitates through the microstructural evolution during aging. The as-quenched and 4 days room temperature (R.T.) aged sample shows a ®ne dispersion of d ' phase homogeneously distributed in the matrix and diraction spots corresponding to d ' re¯ections [Fig. 7(a)]. Consequently,
Fig. 3. Evolution of the (1,1,0) re¯ection associated to the d' phase vs time.
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all further high temperature aging treatments begin with this state. Figure 7 shows the dark ®eld photographs corresponding to dierent aging times at 2008C. The direct observation clearly shows the increase in the mean size of d ' precipitates with aging time. Nevertheless, the analysis of the precipitate mass fraction requires a more complex study. These images also show the inhomogeneous precipitation of d ' phase around b' (Al3Zr) particles, but since the Zr concentration is low the precipitated b' volume fraction is also small. The observation of these particles as black zones, in spite of having the same crystal structure, cell parameter and orientation as d' precipitates, has been extensively studied in the literature [30]. The d ' mean radius increases during aging and the analysis of the images allows to determine this variation. Figure 8 shows the linear evolution of R vs t 1/3 according to the Lifshift±Slyozov±Wagner theory [31, 32], but only in the time range where the curves of 1/H vs time (Fig. 6) are linear. This data permits a rescaling of the curves of Fig. 6 and then provides the knowledge of the quantitative evolution of the d ' mean radius at the temperatures studied. 3.3. Thermoelectric power
Fig. 4. Evolution of the mass fraction of d' (*) and d (w) phases with aging time obtained from the re®ned scale factor at 160, 180 and 2008C.
Fig. 5. Relative change of the a phase cell parameter vs aging time at 160 and 2008C.
As we commented before, TEP measurements are very sensitive to microstructural changes and allow the study of the evolution of the precipitation process and hence the characterization of its kinetics along the isothermal aging treatments. Figure 9 shows the time evolution of TEP during aging at 160, 180 and 2008C of dierent samples solid solution treated and quenched in the standard way. All measurements have similar behaviour vs time and show three consecutive stages. The asquenched TEP values show a dispersion of 0.06 mV/ K in the dierent samples used in each kinetics, linked to the small variation in the quenching rate. TEP increases during aging at 2008C from the asquenched value to a maximum value achieved after
Fig. 6. 1/Hk values obtained for the re¯ection (1,1,0) of the d ' phase vs t 1/3 at 160, 180 and 2008C.
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around 10 s during a ®rst stage. The second stage decreases continuously up to 104 s and then a transitory stage between 104 and 5 105 s begins. Finally, a third stage starts which also decreases with time. The in¯uence of the aging temperature on this gen-
eral behaviour becomes manifest in several aspects: the maximum of the curve shifts toward longer times, the end of the second stages achieves lower values and the third stage starts at longer times as far as the aging temperature decreases.
Fig. 7. Diraction pattern and dark ®eld (DF) image associated with a sample aged at room temperature during 4 days after quenching (a). DF image obtained after aging at 2008C during (b) 0.3, (c) 1.5, (d) 21, (e) 83 and (f) 146 h.
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3.4. Microhardness Figure 10 shows the R.T. Vickers' Hardness (VH) change during aging at the studied temperatures. All of them, show an as-quenched value of around 50 VH. In the early stages the VH value decreases slightly during 10 s and then increases. At 2008C the hardness achieves a maximum after aging during 4 103 s and then decreases progressively. At 1808C the curve shows a double stage before achieving the maximum after 105 s and then decreases with aging time. A similar behaviour is observed at 1608C, but now the curve achieves a local maximum before the maximum value which is not observed in the studied range. The maximum value at T = 2008C is 90 VH, at T = 1808C is 107 VH and has not been determined at T=1608C. 4. DISCUSSION
The XRD technique complemented by the Rietveld method gives accurate information of the precipitation processes. In particular, the precipitated mass fraction and the mean precipitate radius can be obtained at the same time after analysis of the diraction spectrum. This will be very important in order to optimize the control of industrial processes devoted to obtain these alloys under dierent microstructural conditions. This technique can be used as an alternative to the traditional TEM, which is a destructive technique and which also requires long periods of tedious work to prepare samples before observation. Also, observations by X-ray integrate over larger regions than TEM which is very localized. On the other side, it is not easy to use TEM in order to determine the precipitated mass fraction in Al±Li alloys [11]. Then, Xrays seem to be very promising in order to control microstructure of dierent alloys' systems and in particular in Al±Li alloys. Powder diraction methods on polycrystalline
Fig. 8. Measured d' mean radius obtained by TEM vs t 1/3 at 2008C
Fig. 9. TEP variation vs aging time at 160, 180 and 2008C.
Al±Li samples allow quantitative analysis of the evolution of d ' and d phases during precipitation, as shown in Fig. 3. Besides, the application of the Rietveld method allows the quantitative analysis of each spectrum. Figure 4 shows the evolution of the d ' and d precipitated weight fractions at 160, 180
Fig. 10. Vickers' Hardening variation vs aging time at 160, 180 and 2008C.
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and 2008C. In all of them, d ' fraction increases during aging up to a maximum value and then, the dissolution of this phase is accompanied by the d precipitation. The full sequence can only be observed during aging at 2008C, since at lower temperatures, the kinetic is very slow. When the treatment temperature increases, the maximum of the precipitated d' fraction shifts to lower times, the rate of d ' dissolution increases and the formation of d phase shifts to lower times. This behaviour is expected because the d ' phase is metastable and the evolution towards the d equilibrium phase is thermally controlled. Besides, the lower the aging temperature, the higher the maximum precipitated fraction of d ' is due to the lower concentration of Li in solid solution at lower temperatures. TEM measurements show the presence of d phase at the grain boundaries after aging the sample for 146 h at 2008C. This behaviour is in agreement with the expected process. It is very dicult to establish the lowest value of d ' mass fraction that could be accurately measured by TEM due to the simultaneous evolution of the precipitated fraction and the size of precipitates. It seems that the ®tting procedure during the application of the Rietveld method works better when the precipitates are big (sharp peaks) than when precipitates are very small (broad peaks). Obviously, the obtained result for the asquenched state, where the Li is mainly in solid solution, are meaningless and would be an artifact of the ®tting method. Even for very low aging times (below 103 s) where the peaks are small and broad, the obtained result would be probably overestimated. On the contrary, when the diraction peaks become sharpened, (e.g. at 2.5 h) the Rietveld ®tting works very well and the precipitated mass fraction is very accurately determined. A relevant parameter in the change of mechanical properties is the mean radius of the precipitated phases. The width of the diraction peaks associ-
Fig. 11. Variation of the d' mean radius at 160, 180 and 2008C obtained from X-ray data and rescaled with the data of Fig. 8.
ated with the d ' phase allows the evolution of precipitate means radius to be determined (Fig. 6). As expected, the precipitate mean radius increases during aging in the temperature-time range studied. Figures 6 and 8 show that the evolution of 1/H vs t1/3 is linear in the time range, where the precipitated d ' mass fraction increases. As far as the dissolution of d ' begins, 1/H vs t 1/3 separates from linearity. The direct analysis by TEM of the evolution of precipitate means radius during aging at 2008C (Fig. 8) reveals the proportionality factor that relates 1/H and R, and then allows the data of Fig. 6 to be rescaled. It is assumed that this factor is the same for the three kinetics studied which seems to be reasonable since all samples are similar and were measured in the same conditions. The rescaled data are shown in Fig. 11. The linear behaviour of R vs t 1/3 in the range of increasing d ' phase can be analysed using the LSW theory [31, 32]. Previous experimental and theoretical works on this topic assume that the d ' precipitated mass fraction is constant during the coarsening process [33, 34]. Then they assume that the full precipitated fraction is obtained after quenching. This is not true, although eectively an important fraction of d ' phase forms during quenching [20]. Then, the increase in the precipitated mass fraction of d ' phase is simultaneous with the coarsening process and this evolution can be approximated by the LSW theory. When the aging time is long enough, the linear behaviour is lost since d ' precipitates dissolves, and this dissolution reduces the mean size of the d ' precipitates causing their evolution to be far from a linear tendency. Nevertheless, a more precise analysis shows that the linear behaviour is not true even before dissolution of the d ' phase. The 1608C aging curve (Fig. 11) shows the lowest dispersion in the data and the d ' mass fraction increases continuously in the studied range. This curve is concave relative to the ordinate axis, showing a deviation from the LSW theory. At the beginning, the slope of this curve is higher than that at the end of the curve. This can be explained since at the beginning, the radius increase is due to a growing process and to an increase in the precipitated mass fraction. This aspect has not been taken into account in previous work [33, 34] due to the lack of precision in the measured curves. The contribution of the increase in the precipitated mass fraction reduces to zero when the maximum value of precipitated mass fraction is achieved. Then, only the coarsening process contributes to the increase in the mean radius and the slope reduces slightly as shown in Fig. 11. This analysis shows again the usefulness of the proposed methodology. On the other side, the X-ray diraction technique and the Rietveld method give information on the evolution of parameters that are not so important from the point of view of industrial application, but
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can be important for a fundamental study. In particular, the change of the cell parameter can be easily followed by this technique. The a phase cell parameter decreases when aging time increases. Then the lower the Li concentration in solid solution, the lower the cell parameter of the a phase, showing that Li expands the aluminium lattice (Fig. 5). Our results are in opposition to those where the in¯uence of Li in the aluminium lattice has been studied [17], and propose that Li in aluminium reduces the cell parameter of the aluminium matrix. Nevertheless, the ionic and atomic radius of Li (ri=0.6 AÊ, ra=1.55 AÊ) are larger than those of aluminium (ri=0.5 AÊ, ra=1.43 AÊ), and then, it is expected that lithium expands the aluminium lattice. Consequently, during the precipitation process, the concentration of Li in solid solution decreases and a decrease of the cell parameter of the aluminium matrix should be expected in agreement with our results in Fig. 5. This previous analysis allows the microstructural changes to be determine systematically by X-ray diraction which is a non-destructive technique. Nevertheless, TEP technique can give accurate and quick information of the precipitation kinetics. As an example, the usefulness of this technique can be demonstrated for looking at the evolution of the early stages obtained after quenching (aging during 10 s at 2008C). This evolution is very fast and Xray diraction requires long periods of time to study the changes produced in the sample at every aging step. Furthermore the analysis by X-ray diffraction is dicult since the precipitates formed during quenching are very small and produce wide diraction peaks that can not be accurately re®ned by the Rietveld method. Then changes in this stage can be followed in a quantitative way very easily by TEP. But in order to apply the TEP technique in a systematic way, it is necessary to identify the dierent stages associated with the TEP measurement. This has been done comparing with the X-ray results. After quenching from solid solution temperature, the TEP reduces at room temperature as shown elsewhere [24]. Nevertheless, during aging at high temperatures the TEP increases in the ®rst 10 s and then, reduces progressively (Fig. 9). This increasing stage (1st stage) is linked to the dissolution of small nonstable precipitates formed during quenching or during aging at room temperature [35] and consequently to a transitory increase of the Li concentration in solid solution. As mentioned before, asquenched TEP values show a dispersion of 0.06 mV/ K. Nevertheless, if these samples (with dierent as quenched TEP values) are subjected to a thermal treatment at 2008C during 10 s, all of them reach the same TEP value. This allows to conclude that the dierences in as-quenched TEP value can be associated with dierences in the microstructure of
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the as-quenched alloys (early stages), and are not due to experimental errors. In order to know the in¯uence of the phase evolution on the TEP value for longer aging times, Fig. 12 shows comparatively the TEP evolution at 2008C and the corresponding mass fraction fm (d ' and d ) obtained by XRD. As shown, the precipitation of the d ' phase promotes the decreasing of the TEP between 101 s and 104 s (second stage). The lower the aging temperature (higher precipitated mass fraction), the lower the minimum TEP value associated to the second stage, showing that d ' reduces the TEP value. A transitory stage between 104 and 105 s can be linked to the coarsening of d ' precipitates. This interpretation is in agreement with the fact that the increase of the precipitated mass fraction of d ' is accompanied by a much slower decrease of TEP evolution, indicating that the Li solid solution remains almost constant. Besides, the end of this stage corresponds with the begining of the dissolution of d ' precipitates (Fig. 11). Finally the third stage is linked to the precipitation of d phase at the grain boundaries, which occurs at the expense of the d ' dissolution. This last stages shifts to higher times as long as the temperature decreases. Finally, microhardness curves show also a behaviour dependent on the microstructural stage. Nevertheless, this correlation is not so simple. Associated with the increase of TEP during the early stages of aging, the VH curves show a small decrease which can be explained by the dissolution of small precipitates formed during quenching or room temperature aging. For longer aging times, the VH curves show dierent stages linked to dierent microstructural states. At 2008C, a maximum can be observed before the maximum of precipitated mass fraction is achieved. This means that the hardening evolution, although traditionally used to characterize the precipitation kinetics, is not representative of the precipitated mass fraction evolution. We should then distinguish between the
Fig. 12. TEP (r) and precipitated mass fraction fm [d' (*)and d (w)] at 2008C vs aging time.
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precipitation kinetics and the hardening kinetics. Indeed, the hardening kinetics behaviour is strongly dependent on the complexity of the dislocation±precipitate interaction. Nevertheless, the knowledge of the mean radius of precipitates and the d' precipitated mass fraction are the main microstructural parameters to be determined in order to analyse the hardening mechanism. These parameters change simultaneously during aging and then the dislocation±precipitate interaction need a detailed study which will be performed in a further work. 5. CONCLUSIONS
The precipitation kinetics at high temperatures (160, 180 and 2008C) have been determined by XRD, TEP and microhardness measurements. The Rietveld method has been applied to the Xray spectra in order to study the precipitated mass fraction of d ' and d phases in Al±Li alloys. The method allows us to obtain quantitatively the d ' and d precipitated mass fraction and their evolution with aging time. Furthermore, this method gives directly the cell parameter evolution of the matrix phase, and indirectly the mean radius of d ' precipitates through an appropriate calibration curve. Experimentally, this calibration has been determined studying the evolution of the mean radius of d ' by TEM. TEP has been shown to be a powerful technique to study the microstructural evolution of Al±Li alloys, since it is sensitive to the dierent stages of precipitation associated to the d ' and d phases. The comparison of the dierent experimental results allow us to establish a clear dierence between the precipitation kinetics and the hardening kinetics. Finally, we are now ready to evaluate the in¯uence of the microstructure on the hardening of the sample, since we know the time evolution of the mean radius and mass fraction of d ' precipitates. AcknowledgementsÐThis work has been carried out with the ®nancial support of the Spanish ``ComisioÂn Interministerial de Ciencia y TecnologõÂ a'' (CICyT) in the framework of the ``Plan Nacional de Materiales'' (Project No. MAT 97-1059-C02-02). The authors thank Rafael Garcia-Roja, from the University of Cadiz, the facilities oered for the TEM observations. The authors also wish to thank the Pechiney Company for supplying the alloy. REFERENCES 1. Hatch, J. E. (ed.), Aluminium: Properties and Physical Metallurgy. ASM, Metals Park, OH, 1984. 2. Peel, C. J., New Light Alloys, Lecture Serie No. 174, 2-1 AGARD, NATO, 1990.
3. Graham, R. H., Rioja, R. J. and Newman, J. M., Al± Li alloys. DGM Informationgesellschaft mbh, 15 Oberrursell, 1992. 4. Fridlyander, I. N., Bratukhin, A. G. and Davidov, V. G., Al±Li alloys. DGM Informationgesellschaft mbh, 35 Oberrursell, 1992. 5. Fielding, P. S. and Wolf, G. J., Adv. Mater. Proc., 1996, 150(4), 21. 6. Malone, J., Adv. Mater. Proc., 1998, 153(4), 7. 7. Starke, E. A. Jr and Quist, W. E., New Light Alloys, Lecture Serie No. 174, AGARD, NATO, 1990. 8. PeÂrez-LandazaÂbal, J. I., Ph. D. thesis, Univ. PaõÂ s Vasco, Bilbao, Spain, 1995. 9. Lavernia, E. J. and Grant, N. J., J. Metals Sci., 1987, 22, 1521. 10. Huang, J. C. and Ardell, A. J., Mater. Sci. Engng, 1988, A104, 149. 11. Furukawa, M., Miura, Y. and Nemoto, M., Trans. Japan Inst. Metals, 1985, 26(4), 230. 12. Rietveld, H. M., J. appl. Crystallogr., 1967, 22, 151. 13. Rietveld, H. M., J. appl. Crystallogr., 1969, 2, 65. 14. Young, R. A., The Rietveld Method. International Union of Crystallography, Oxford Science Publications, 1993. 15. PeÂrez-LandazaÂbal, J. I., No, M. L., Madariaga, G. and San Juan, J., J. appl. Crystallogr., 1997, 30, 107. 16. Davis, J. R., Aluminium and Aluminium Alloys. ASM International, Materials Park, OH, 1993. 17. Levine, E. D. and Rapperport, E. J., Trans. A.I.M.E., 1963, 227, 1204. 18. Williams, D. B. and Edington, J. W., Metal Sci., 1975, 9, 529. 19. Vecchio, H. S. and Williams, D. B., Acta metall., 1987, 35, 2959. 20. Kuriyama, K. and Masaki, N., Acta crystallogr., 1975, B31, 1793. 21. Jha, S. C., Sanders Jr, T. H. and Dayananda, M. A., Acta metall., 1987, 35, 473. 22. Reppich, B., Plastic Deformation and Fracture of Materials. Mughrabi VCH, Weinhein, 1993. 23. Nembach, E., Particle Strengthening of Metals and Alloys. Wiley, New York, 1997. 24. PeÂrez-LandazaÂbal, J. I., No, M. L. and San Juan, J., Scripta metall. mater., 1995, 32, 1307. 25. Pelletier, J. M. and Borrelly, R., Mater. Sci. Engng, 1982, 55, 191. 26. Pelletier, J. M., Vigier, G., Mai, C. and Borrelly, R., Acta metall. mater., 1983, 31(10), 1491. 27. Wiles, D. B. and Young, R. A., J. appl. Crystallogr., 1981, 14, 149. 28. Bish, D. L. and Howard, S. A., J. appl. Crystallogr., 1988, 21, 86. 29. AzaÂro, L. V., Elements of X-Ray Crystallography. McGraw-Hill, New York, 1968. 30. Gu, B. P., Liedl, G. L., Sanders Jr, T. H. and Welpmann, K., Mater. Sci. Engng, 1985, 76, 147. 31. Lifshith, I. M. and Slyozov, V. V., J. Phys. Chem. Solids, 1961, 19, 489. 32. Wagner, C. Z., Electrochem., 1961, 65, 581. 33. Mahalingam, K., Gu, B. P., Liedl, G. L. and Sanders Jr, T. H., Acta metall., 1987, 35, 483. 34. Gu, B. P., Liedl, G. L., Kulwicki, J. H. and Sanders Jr, T. H., Mater. Sci. Engng, 1985, 76, 217. 35. Lambri, O. A., PeÂrez-LandazaÂbal, J. I., No, M. L. and San Juan, J., Scripta mater., 1997, 37, 851.