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Importance of reliable phase equilibria in studying microsegregation in alloys: Al–Cu–Mg
Materials Science and Engineering A292 (2000) 96 – 103 www.elsevier.com/locate/msea
Importance of reliable phase equilibria in studying microsegregation in alloys: Al–Cu–Mg H. Liang a, T. Kraft b, Y.A. Chang a,* a
Department of Materials Science and Engineering, Uni6ersity of Wisconsin at Madison, 1509 Uni6ersity A6enue, Madison, WI 53706, USA b Fraunhofer-lnstitut fu¨r Werkstoffmechanik (IWM), Wo¨hlerstr. 11, D-79108 Freiburg, Germany Received 4 January 2000; received in revised form 12 April 2000
Abstract The solid and liquid phase equilibrium of Al-rich Al – Cu and Al – Cu – Mg alloys was investigated in order to examine the effect of small uncertainties in the solidus on model-calculated microsegregation during solidification. The phase boundaries were determined using EPMA on quenched two-phase alloys. The liquidus was obtained using a raster beam scan technique. The phase boundaries obtained for Al–Cu are in accord with experimental data available in the literature. The measured (Al) solidus in terms of Cu is found to be 0.5 at% higher than model-calculated values from a thermodynamic description reported in the literature. On the other hand, the measured (Al) liquidus in terms of Cu are in good agreement with model-calculations. Moreover, the difference between the measured and calculated solidus in ternary Al – Cu – Mg was found to be the same as that in binary Al–Cu. This difference is believed to be responsible for the deviations in the calculated microsegregation from experimental data for Al-rich Al–Cu–Mg alloys. The (Al ) phase in both the Al – Cu and Al – Cu – Mg systems was thus remodeled so that the calculated solidus using the new model description is in better agreement with experimental data. The microsegregation model-calculations show that even small differences in the phase boundaries of 0.5 at.% or less have a pronounced effect on the calculated concentration profiles of Cu in the dendrites. We thus conclude that in order to test the validity of a microsegregation model, accurate phase boundary data are needed! © 2000 Elsevier Science S.A. All rights reserved. Keywords: Phase equilibria; Microsegregation; Al–Cu–Mg alloys; Thermodynamics
1. Introduction Microsegregation in ternary alloys was calculated in the past using temperature independent partition coefficients and their values were often obtained from the constituent binary systems [1]. However, with recent advances in phase diagram calculations, numerous attempts have been made to calculate microsegregation in ternary and higher order alloys using thermodynamically calculated partition coefficients [2,3]. The readers are referred to a recent review for the literature [4]. A recent study in our group using microsegregation data measured from two directionally solidified Al-rich Al–Cu–Mg alloys suggested that model-calculated microsegregation, particularly with respect to solute redistribution in the (Al) phase, is highly sensitive to the * Corresponding author. Tel.: +1-608-2623732; fax: + 1-6082628353.
partition coefficients used [5]. In fact, sensitivity calculations considering the uncertainties in the diffusion coefficients in the (Al) phase, the gross compositions of the alloys and the solid/liquid phase boundaries indicated that the discrepancies in the calculated and experimental microsegregation were due primarily to the partition coefficients used, more specifically the solidus values in the present case. An examination of calculated isopleth Al–Cu0.5Mg0.5 [6] in comparison with experimental data [7] showed that the calculated (Al) liquidus is in agreement with experimental data while the calculated solidus in terms of Cu differ by as much as 0.5 at.% It is noteworthy to point out that another thermodynamic description of Al–Cu–Mg [8] became available subsequent to the completion of the investigation of Xie et al. [5]. However, this new description is not an improvement of that by Chen et al. [6]. The objective of the present study is to experimentally determine the Al-rich liquidus and solidus in Al–Cu and Al–Cu–Mg
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in order to verify the accuracy of the calculated phase boundaries and moreover to show the importance of accurate phase boundary data for microsegregation calculations. The binary Al – Cu alloys were selected originally to test the validity of the experimental technique used prior to applying it to Al – Cu – Mg. As to be shown later, the discrepancies in the calculated (Al) solidus from experimental data in ternary Al –Cu–Mg alloys are due to inaccuracies in the thermodynamic model-calculated (Al) solidus in the Al – Cu binary. The (Al) phases in both the Al – Cu and Al – Cu – Mg systems are thus thermodynamically remodeled and the small corrections in the solidus are shown to have a significant influence on the model-calculated concentration
Fig. 1. Microstructure of Al–15Cu annealed at 600°C for 3 h and quenched in ice-water (BSE image) (a) Mag 200; (b) Mag 4500.
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profiles in primary (Al). This study shows that accurate phase equilibrium data are crucial to microsegregation calculations. As a part of the present study, we will also report the effect of partition coefficients on microsegregation in binary Al–Cu alloys.
2. Experimental method The method used to determine the liquidus and solidus of the (Al)+ L two-phase equilibrium follows that of Ocansey and Fourier [9]. In brief, an alloy was first superheated 20–30°C above its liquidus, temperature according to the calculated phase diagram, then annealed at a lower temperature in the (Al)+L twophase field, and finally quenched into an ice-water mixture after equilibration. The phase compositions were determined using Electron Probe Microanalysis (EPMA) in Caineca SX-50. The composition of the primary (Al) phase, presented as coarsened particles in the quenched specimen, was measured in the center of the particles. The composition of the liquid, on the other hand, was obtained by measuring those of the quenched eutectic-like structure between the coarsened particles using a raster beam scan technique in EPMA. It is evident that the finer the microstructure of the quenched liquid, the more reliable the measured composition by EPMA. Although diffusion calculations show equilibrium in the alloys studied can be achieved within 30 min at 600–550°C, these alloys were annealed for 3–4 h at the temperatures studied. Prolonged annealing allowed the primary phase particles to coarsen and the liquid regions distributed more evenly. Under this condition, latent heat can be extracted quickly from the samples during ice-water quenching, resulting in the formation of a fine eutectic-like microstructure of the quenched liquid. To achieve a high quenching rate, each of the samples was wrapped in 1.5 mm thick graphite foil as used by Rettenmayr and Pompe [10] for Al–Cu alloys. These foils are excellent thermal conductors, far superior to quartz tubes normally used. Indeed, fine microstructures were successfully obtained using this technique. No reactions were observed between the graphite foils and the samples even after annealing for 3–4 h at the temperatures studied. Since a detailed description of the apparatus has been given elsewhere [11], a brief account is given below. Each of the samples used had a diameter of 6 mm with lengths varying from 2 to 3 cm and weighed about 3 g. It was wrapped in double layers of graphite foils, bundled with a thin nickel wire, and held in a nickel basket. A nickel wire fastened to the top of the furnace suspended the basket. The temperature of the sample was measured using a type-K thermocouple. Since melting took place in air, sample oxidation occurred imme-
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Table 1 Comparison of the solidus and liquidus, data determined experimentally with calculated values for Al–15Cu at 600, 575 and 550°C (Al), Cs(wt.%)
Al–15Cu
T (°C) 600 575 550
Al Cu Al Cu Al Cu
Liquid, CL (wt.%)
Ki =CS/CL
Exp
Calc
Exp
Calc
Exp
Calc
New
Old
New
New
Old
New
New
Old
New
96.56 3.44 95.25 4.75 94.00 6.00
97.51 2.49 96.19 3.81 94.41 5.59
97.01 2.99 95.75 4.25 94.35 5.65
78.52 21.48 72.04 27.96 67.14 32.86
79.18 20.82 72.60 27.40 67.13 32.87
78.89 21.11 72.38 27.62 67.05 32.95
1.23 0.16 1.32 0.17 1.40 0.18
1.23 0.12 1.33 0.14 1.41 0.17
1.23 0.14 1.32 0.15 1.41 0.17
diately upon heating. However, formation of an oxide layer on the surface prevented further oxidation to the inner part of the samples as confirmed by X-ray analysis. After cutting, mounting, polishing, and carbon coating the quenched samples, the longitudinal sections of the samples were analyzed using the Wavelength Dispersive Spectrometer (WDS). The probe current used was 20 mA with an accelerating voltage of 15 kV. The standards used for calibration were Al–1Cu– 0.5Mg (wt.%) for Al, pure Cu for Cu and MgO for Mg. The compositions of the alloys are always given in wt.% in the present paper unless noted otherwise. The composition of the (Al) phase was measured in the center of the coarsened solid particles while the composition of the pre-existing liquid was determined through a raster beam scan technique as noted earlier. The scanned areas, approximately 500 mm2, were randomly chosen. The results obtained from the transverse sections of several samples were the same as those of the longitudinal sections. In order to obtain statistically reliable EPMA results for the quenched liquid, 20 areas were scanned for each sample and the average of the 20 measurements was taken to be the liquid composition. In fact, the standard deviation of the measurements became stabilized beyond 10 measurements. Twenty measurements were chosen so that the standard deviations of the measurements can be kept below 1% in most cases. The exact same approach was used to measure the solid composition using areas in the center of the coarsened particles. A total of 20 measurements were also made for each composition determined for the (Al) phase.
3. Experimental results We will present the results first for binary Al–15Cu, then ternary Al– Cu – Mg alloys. Fig. 1a shows the Back-Scattered Electron (BSE) image of the microstructure of Al–15Cu quenched from 600°C. The large dark particles are the primary (Al) phase. The fine eutectic
microstructure, consisting of (Al) (dark) and u-Al2Cu (bright), represents the quenched preexisting liquid. The microstructure given in Fig. 1b in a higher resolution shows the raster beam scan area; from which the composition of the pre-existing liquid was obtained on the basis of 20 measurements. The solidus and liquidus values determined in the present study at 600, 575 and 550°C are given in Table 1 as well as the partition coefficients. Each of the data points is taken to be the average of 20 individual measurements with a standard deviation of 0.5–0.7% in most cases. The microstructures of the two solidified ternary alloys are similar to those of binary Al–15Cu as shown in Fig. 2a and b for Al–15Cu–3Mg quenched from 600°C. The measured liquidus and solidus data for Al–15Cu–3Mg and Al– 3.9Cu–0.9Mg at 600, 575 and 550°C are given in Tables 2 and 3, respectively. Fig. 3a shows a comparison of our experimental data with those reported in the literature for the liquidus [12–19] and Fig. 3b that for the solidus [17,20–23]. As shown in Fig. 3a, with the exception of the data of Stockdale [13] and Tazaki [14], which tend to be lower, all other liquidus data including those obtained in the present study are in agreement. On the other hand, as shown in Fig. 3b, with the exception of the solidus data of Matsuyama [22] which tend to be lower, all other data including those obtained by us [17,20–23] are in agreement. The lower temperatures obtained by Matsuyama are likely due to the fact that their alloys did not reach equilibrium [24]. Now let us compare the experimental data with phase boundaries calculated using thermodynamic descriptions. The best thermodynamic description currently available for the Al–Cu system is that by Saunders [25,26], which was adopted in the thermodynamic description for Al–Cu–Mg developed in our group [6,11]. Fig. 3a shows that, within the uncertainties of the experimental data, the calculated liquidus using the description by Saunders is in good agreement with the experimental data. On the other hand, this is not the case for the solidus shown in Fig. 3b; the
H. Liang et al. / Materials Science and Engineering A292 (2000) 96–103
calculated solidus based on Saunders’ description, shown as a dashed line, lies in-between the five sets of agreeing data and those of Matsuyama [22]. This suggests that the solidus calculated using this description is lower than the agreeing experimental data by 0.5 at.%. An examination of the data given in Table 1 shows that while the discrepancies between the measured and model-calculated solidus and liquidus values decrease with decreasing temperature, the discrepancies are larger for the solidus. Since the compositions of Cu in the solidus are much smaller than those in the liquidus, the percentages of the discrepancies are even larger.
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Analysis of the data for the ternary alloys shown in Tables 2 and 3 yield similar conclusions using the thermodynamic description of Chang and co-workers [6,11]. As noted in Section 1, the model-calculated solidus along the Al–Cu0.5Mg0.5 isopleth [6,11], shown as a dashed line in Fig. 4, is lower in Cu contents than the experimental data, i.e. the calculated partition coefficients are lower than the measured values. These data are consistent with those obtained in the present study as shown in Tables 2 and 3. We believe the model-calculated solidus with lower Cu contents in the ternary is due primarily to the thermodynamic parameters used in the binary thermodynamic description since an extrapolation approach was used in the modeling. In fact, the model-calculated solidus in the Al–Cu boundary binary becomes a constraint on the solidus surface in ternary space. It is noteworthy that discrepancies between the calculated and measured solidus in the Al-Cu0.5Mg0.5 isopleth are nearly the same as those in the Al–Cu binary. Even though these discrepancies are small, i.e. less than 0.5 at.% of Cu (or 1 wt.%), a previous study on microsegregation suggests that they could have pronounced influence on the model-calculated microsegregation [5]. Therefore, the (Al) solidus in Al–Cu as well as in Al–Cu–Mg need to be remodeled so as to ensure the accuracy of microsegregation prediction. It will be shown later that the small corrections such as less than 0.5 at.% are indeed crucial.
4. Microsegregation calculation and discussion
Fig. 2. Microstructure of Al–5Cu–3Mg annealed at 600°C for 3 h and quenched in icewater (BSE image) (a) Mag 200; (b) Mag 4500.
Considering the fact that the thermodynamic description of Al–Cu by Saunders [25,26] has been widely adopted in thermodynamic descriptions of multicomponent aluminurn alloys [11,27,28] and there is a lack of sufficient reliable thermodynamic and phase equilibrium data, particularly for the Cu-rich alloys, we resort to a more practical approach on refining only the model of the (Al) phase using Thermo–Calc [29] in terms of the data presented earlier. A set of consistent parameters is obtained giving the best description of the experimental data. Phase boundaries calculated using the new model parameters are shown in Fig. 3b as solid lines, whereas those calculated using model parameters by Saunders [25,26] shown as dashed lines. It is evident from this figure the newly calculated solidus in terms of Cu are about 0.25 at.% higher than those calculated using Saunders’ description [25,26]. Basing on the new description for (Al) in the binary, ternary interaction parameters for this phase in Al–Cu–Mg were also re-optimized using data obtained in this study in addition to those available in the literature [6,11]. The new model-calculated (Al) solidus curve along the isopleth Al–Cu0.5Mg0.5 (shown in Fig. 4 as solid lines) are about 0.25 at% higher than those calculated using the descrip-
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Table 2 Comparison of the solidus and liquidus data determined experimentally with calculated values for Al–5Cu–3Mg at 6000, 575 and 550°C Al–5Cu–3Mg
(Al), CS (wt.%)
Liquid, CL (wt.%)
Ki =CS/CL
T (°C)
Exp
Calc
Exp
Calc
Exp
Calc
New
Old
New
New
Old
New
New
Old
New
97.00 1.44 1.56 96.05 2.14 1.81 95.62 2.43 1.95
97.30 1.03 1.67 96.50 1.50 2.00 95.80 1.99 2.21
96.86 0.39 1.75 95.88 2.00 2.12 95.06 2.58 2.36
82.49 12.35 5.16 75.14 18.37 6.49 69.24 23.38 7.38
82.60 12.03 5.37 75.56 17.76 6.68 69.26 23.00 7.74
82.39 12.14 5.47 75.30 17.91 6.79 68.99 23.22 7.79
1.18 0.12 0.30 1.28 0.12 0.28 1.38 0.10 0.26
1.18 0.09 0.31 1.28 0.08 0.30 1.38 0.09 0.29
1.18 0.11 0.32 1.27 0.11 0.31 1.38 0.11 0.30
600
575
550
Al Cu Mg Al Cu Mg Al Cu Mg
Table 3 Comparison of the solidus and liquidus data determined experimentally with calculated values for Al–4Cu–1Mg at 600, 575 and 550°C Al–4Cu–1Mg
T (°C) 600
575
550
Al Cu Mg Al Cu Mg Al Cu Mg
(Al), CS (wt.%)
Liquid, CL (wt.%)
Ki = CS/CL
Exp
Calc
Exp
Calc
Exp
Calc
New
Old
New
New
Old
New
New
Old
New
96.76 2.51 0.73 95.83 3.38 0.79 95.42 3.69 0.89
97.56 1.72 0.72 96.64 2.53 0.83 95.69 3.39 0.92
97.04 2.24 0.72 96.01 3.16 0.83 95.06 3.95 0.99
79.70 17.77 2.53 72.85 24.26 2.89 67.18 29.08 3.74
80.45 17.04 2.51 73.46 23.41 3.13 67.54 28.67 3.79
80.04 17.56 2.40 73.07 23.99 2.94 67.29 28.98 3.73
1.21 0.14 0.29 1.32 0.14 0.27 1.42 0.13 0.24
1.21 0.10 0.29 1.32 0.11 0.27 1.42 0.12 0.24
1.21 0.13 0.30 1.31 0.13 0.28 1.41 0.14 0.26
tion of Chen et al. [6,11] (shown as dashed lines). Nearly the same discrepancy between the current model-calculated solidus and the experimental data for binary Al–Cu and ternary Al – Cu – Mg along the isopleth Al–Cu0.5Mg0.5 suggests that the discrepancy is due primarily to that in the binary. It is worth noting that discrepancies still exist between the newly calculated solidus and the experimental data [7] as shown in Fig. 4. However, given the absolute accuracy of the experimentally determined solidus to be within 0.25%, the calculated solidus certainly falls within that range. We will next show the effect of uncertainty in the solidus curve on the calculated microsegregation in Al-rich Al–Cu and Al – Cu – Mg alloy using the approach of Kraft et al. [30]. It is a modified Scheil model [31] incorporating back diffusion in the solids, dendrite coarsening and the effects of undercooling although the later is insignificant for the cooling rates used. Table 4 shows comparisons of the calculated microsegregation parameters for a series of Al – Cu alloys with a cooling rate I K/s using the calculated partition coefficients according to Saunders’ description [25,26]
vs. those according to ours obtained in this study. The microsegregation parameters are expressed in terms of the fraction of eutectic formed ( fE), the minimum composition of Cu in the center of the dendrite (CSmin), and dendrite arm spacing (l2). The amount of eutectic formed during solidification is a measure of the degree of deviations from equilibrium freezing and therefore, the degree of microsegregation. It can be seen from Table 4 that both the amount of eutectic formed and the minimum concentration of Cu in the center of a dendrite arm are significantly affected by the small corrections in the solidus. However, there is no effect on the calculated dendrite arm spacing as expected, since coarsening in Al alloys does not depend strongly on the solidus concentration, not in Al–Cu in any case. A similar effect of a small change in solidus was also found for ternary Al-rich Al–Cu–Mg alloys. Table 5 shows comparisons of the calculated microsegregation parameters for alloy A1–3.9Cu–0.9Mg with different cooling rates of 1, 0.78, 0.23, and 0.039 K/s with those obtained experimentally in the present study. The calculation was carried out using the partition coefficients
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Fig. 3. Comparison of the liquidus data obtained in the present study for the (Al) + liquid equilibrium in binary Al – Cu with those reported in the literature. The solid lines are calculated using the description of Saunders [25,26]. (b) Comparison of the solidus data obtained in the present study for the (Al) + liquid equilibrium in binary Al–Cu with those reported in the literature. The dashed lines are calculated using the description of Saunders [25,26] while the solid lines using the model parameters obtained in the present study.
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Fig. 4. Comparison of the experimental liquidus and solidus obtained in the present study along the isopleth Al–Cu0.5Mg0.5 with those calculated based on the description of Chen et al. [6] shown as solid lines (denoted as from old PD) and those obtained in the present study as dashed lines (denoted as from new PD). Table 4 Comparison of calculated amounts of the eutectic ( fE), the minimum concentration in the dendrite arm center (cSmin), and the dendrite arm spacing (l2) for binary Al–Cu alloys using distribution coefficients obtained from Saunders’s description [25,26] with those obtained in this study with a cooling rate of 1 K/s Al–Cu C0, wt.% PD source
fE vol.%
CSmin wt.%
l2 mm
2% Cu
1.2 0.6 5.2 4.5 9.6 8.8 14.4 13.4
0.5 0.6 0.9 1.1 1.2 1.5 1.6 1.9
51 52 46 47 43 43 40 40
4% Cu 6% Cu 8% Cu
Saunders This study Saunders This study Saunders This study Saunders This study
Fig. 5. Comparison of the experimental concentration profiles of Cu and Mg in alloy Al – 3.9Cu – 0.9Mg [5] with the model-calculated values using partition coefficients obtained from the description of Chen et al. [6] shown as solid lines (denoted as using original K) and those using old partition coefficients obtained from the model parameters obtain in the present study shown as solid line (denoted as using new K). This alloy was directionally solidified with a cooling rate of 0.78 K/s.
obtained from Chen et al.’s description [6]. The amount of the eutectic formed is again very sensitive to the small corrections in the solidus, but not the dendrite arm spacing. Now let us see the effect on solute distribution profile. Fig. 5 shows a comparison of the solute distribution profiles for alloy Al–3.9Cu–0.9Mg directionally solidified under a cooling rate of 0.78 K/s. The dense lines incorporating symbols are experimental data by Xie et al. [5]. As shown in Fig. 5, the calculated Cu profile using the new partition coefficients is much closer to the experimental data than that using the description of Chen et al. [6], keeping in mind that the values of the Cu solidus are changed by only 0.25 at.% or less. The calculated Mg profile using the new partition coefficient of Mg is not expected to differ appreciably since the solidus in terms of Mg remains essentially the same. As mentioned in Section 1, it was showed in a previous study in our group
Table 5 Comparison of calculated amounts of the eutectic ( fE), the minimum concentration in the dendrite arm center (cSmin), and the dendrite arm spacing (l2) for the ternary Al–3.9Cu–0.9 alloy using distribution coefficients obtained from Chen et al’s description [6] with those obtained in this study with a cooling rates of 1, 0.7, 0.23 and 0.39 K/s Cooling rate K/s
PD source
fa vol.%
fE vol.%
fter-E vol.%
l2 mm
1
Chen et al. This study Chen et al. This study Chen et al. This study Chen et al. This study
96.1 96.7 96.1 96.8 96.5 97.1 97.1 98.1
3.9 3.3 3.9 3.2 3.5 2.9 2.9 1.9
1.1 0.6 1.1 0.5 0.7 0.2 0.1 0.0
47 47 51 51 76 77 131 132
0.78 0.23 0.039
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[5] that the greatest uncertainty in the model-calculated microsegregation was due to uncertainties in the solid/ liquid phase boundaries. The present study demonstrates that obtaining accurate phase diagram data whether by experiments or a combined modeling/experimental approach is a prerequisite for reliable solidification modeling of binary and higher order alloys.
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University of Technology, Germany, and Prof. D.R. Poirier and Dr P.K. Sung at the Department of Materials Science and Engineering, University of Arizona, for helpful discussions on the experimental technique and Dr Fournell at the UW Microprobe Lab for his help in the experimental analysis. John Woodford and Peter Ladwig are gratefully acknowledged for carefully reading the manuscript.
5. Summary The liquidus and solidus of the Al-rich alloys for binary Al–Cu and ternary Al – Cu – Mg were determined experimentally. The compositions of (Al) and liquid in rapidly quenched samples from high temperatures were determined by EPMA using a raster beam scan technique. For the Al – Cu alloys, the measured (Al) solidus in terms of Cu were found to be 0.5 at.% higher than model-calculated values using the thermodynamic description of Saunders [25,26], while the measured (Al) liquidus in terms of Cu are in good agreement with model-calculations. Similar discrepancies between measured and calculated values were found in the ternary Al – Cu – Mg system. The inaccuracy in the model-calculated (Al) solidus in Al –Cu was believed to be responsible for the deviations between the model-calculated and measured microsegregation in both binary Al–Cu and ternary Al – Cu – Mg. The (Al) phase in both Al– Cu and Al – Cu – Mg were remodeled in this study. The model-calculations show that even the small discrepancies of 0.5 at.% and less in the Cu content of the (Al) solidus have a significant influence on the model-calculated concentration profile in the dendrites (as a result of microsegregation in these alloys). In order to test the validity of a microsegregation model, reliable partition coefficients (i.e. phase equilibrium data) are needed!
Acknowledgements The authors wish to acknowledge the National Science Foundation for financial support through a grant with the number NSF-DMR-94-21780 and Dr Bruce MacDonald of the Metal Program of the Materials and Processing Cluster of NSF for his interest in this work. The authors also wish to thank Dr M. Rettenmayr at the Department of Physical Metallurgy, Darmstadt
.
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Importance of reliable phase equilibria in studying microsegregation in alloys: Al–Cu–Mg H. Liang a, T. Kraft b, Y.A. Chang a,* a
Department of Materials Science and Engineering, Uni6ersity of Wisconsin at Madison, 1509 Uni6ersity A6enue, Madison, WI 53706, USA b Fraunhofer-lnstitut fu¨r Werkstoffmechanik (IWM), Wo¨hlerstr. 11, D-79108 Freiburg, Germany Received 4 January 2000; received in revised form 12 April 2000
Abstract The solid and liquid phase equilibrium of Al-rich Al – Cu and Al – Cu – Mg alloys was investigated in order to examine the effect of small uncertainties in the solidus on model-calculated microsegregation during solidification. The phase boundaries were determined using EPMA on quenched two-phase alloys. The liquidus was obtained using a raster beam scan technique. The phase boundaries obtained for Al–Cu are in accord with experimental data available in the literature. The measured (Al) solidus in terms of Cu is found to be 0.5 at% higher than model-calculated values from a thermodynamic description reported in the literature. On the other hand, the measured (Al) liquidus in terms of Cu are in good agreement with model-calculations. Moreover, the difference between the measured and calculated solidus in ternary Al – Cu – Mg was found to be the same as that in binary Al–Cu. This difference is believed to be responsible for the deviations in the calculated microsegregation from experimental data for Al-rich Al–Cu–Mg alloys. The (Al ) phase in both the Al – Cu and Al – Cu – Mg systems was thus remodeled so that the calculated solidus using the new model description is in better agreement with experimental data. The microsegregation model-calculations show that even small differences in the phase boundaries of 0.5 at.% or less have a pronounced effect on the calculated concentration profiles of Cu in the dendrites. We thus conclude that in order to test the validity of a microsegregation model, accurate phase boundary data are needed! © 2000 Elsevier Science S.A. All rights reserved. Keywords: Phase equilibria; Microsegregation; Al–Cu–Mg alloys; Thermodynamics
1. Introduction Microsegregation in ternary alloys was calculated in the past using temperature independent partition coefficients and their values were often obtained from the constituent binary systems [1]. However, with recent advances in phase diagram calculations, numerous attempts have been made to calculate microsegregation in ternary and higher order alloys using thermodynamically calculated partition coefficients [2,3]. The readers are referred to a recent review for the literature [4]. A recent study in our group using microsegregation data measured from two directionally solidified Al-rich Al–Cu–Mg alloys suggested that model-calculated microsegregation, particularly with respect to solute redistribution in the (Al) phase, is highly sensitive to the * Corresponding author. Tel.: +1-608-2623732; fax: + 1-6082628353.
partition coefficients used [5]. In fact, sensitivity calculations considering the uncertainties in the diffusion coefficients in the (Al) phase, the gross compositions of the alloys and the solid/liquid phase boundaries indicated that the discrepancies in the calculated and experimental microsegregation were due primarily to the partition coefficients used, more specifically the solidus values in the present case. An examination of calculated isopleth Al–Cu0.5Mg0.5 [6] in comparison with experimental data [7] showed that the calculated (Al) liquidus is in agreement with experimental data while the calculated solidus in terms of Cu differ by as much as 0.5 at.% It is noteworthy to point out that another thermodynamic description of Al–Cu–Mg [8] became available subsequent to the completion of the investigation of Xie et al. [5]. However, this new description is not an improvement of that by Chen et al. [6]. The objective of the present study is to experimentally determine the Al-rich liquidus and solidus in Al–Cu and Al–Cu–Mg
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in order to verify the accuracy of the calculated phase boundaries and moreover to show the importance of accurate phase boundary data for microsegregation calculations. The binary Al – Cu alloys were selected originally to test the validity of the experimental technique used prior to applying it to Al – Cu – Mg. As to be shown later, the discrepancies in the calculated (Al) solidus from experimental data in ternary Al –Cu–Mg alloys are due to inaccuracies in the thermodynamic model-calculated (Al) solidus in the Al – Cu binary. The (Al) phases in both the Al – Cu and Al – Cu – Mg systems are thus thermodynamically remodeled and the small corrections in the solidus are shown to have a significant influence on the model-calculated concentration
Fig. 1. Microstructure of Al–15Cu annealed at 600°C for 3 h and quenched in ice-water (BSE image) (a) Mag 200; (b) Mag 4500.
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profiles in primary (Al). This study shows that accurate phase equilibrium data are crucial to microsegregation calculations. As a part of the present study, we will also report the effect of partition coefficients on microsegregation in binary Al–Cu alloys.
2. Experimental method The method used to determine the liquidus and solidus of the (Al)+ L two-phase equilibrium follows that of Ocansey and Fourier [9]. In brief, an alloy was first superheated 20–30°C above its liquidus, temperature according to the calculated phase diagram, then annealed at a lower temperature in the (Al)+L twophase field, and finally quenched into an ice-water mixture after equilibration. The phase compositions were determined using Electron Probe Microanalysis (EPMA) in Caineca SX-50. The composition of the primary (Al) phase, presented as coarsened particles in the quenched specimen, was measured in the center of the particles. The composition of the liquid, on the other hand, was obtained by measuring those of the quenched eutectic-like structure between the coarsened particles using a raster beam scan technique in EPMA. It is evident that the finer the microstructure of the quenched liquid, the more reliable the measured composition by EPMA. Although diffusion calculations show equilibrium in the alloys studied can be achieved within 30 min at 600–550°C, these alloys were annealed for 3–4 h at the temperatures studied. Prolonged annealing allowed the primary phase particles to coarsen and the liquid regions distributed more evenly. Under this condition, latent heat can be extracted quickly from the samples during ice-water quenching, resulting in the formation of a fine eutectic-like microstructure of the quenched liquid. To achieve a high quenching rate, each of the samples was wrapped in 1.5 mm thick graphite foil as used by Rettenmayr and Pompe [10] for Al–Cu alloys. These foils are excellent thermal conductors, far superior to quartz tubes normally used. Indeed, fine microstructures were successfully obtained using this technique. No reactions were observed between the graphite foils and the samples even after annealing for 3–4 h at the temperatures studied. Since a detailed description of the apparatus has been given elsewhere [11], a brief account is given below. Each of the samples used had a diameter of 6 mm with lengths varying from 2 to 3 cm and weighed about 3 g. It was wrapped in double layers of graphite foils, bundled with a thin nickel wire, and held in a nickel basket. A nickel wire fastened to the top of the furnace suspended the basket. The temperature of the sample was measured using a type-K thermocouple. Since melting took place in air, sample oxidation occurred imme-
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Table 1 Comparison of the solidus and liquidus, data determined experimentally with calculated values for Al–15Cu at 600, 575 and 550°C (Al), Cs(wt.%)
Al–15Cu
T (°C) 600 575 550
Al Cu Al Cu Al Cu
Liquid, CL (wt.%)
Ki =CS/CL
Exp
Calc
Exp
Calc
Exp
Calc
New
Old
New
New
Old
New
New
Old
New
96.56 3.44 95.25 4.75 94.00 6.00
97.51 2.49 96.19 3.81 94.41 5.59
97.01 2.99 95.75 4.25 94.35 5.65
78.52 21.48 72.04 27.96 67.14 32.86
79.18 20.82 72.60 27.40 67.13 32.87
78.89 21.11 72.38 27.62 67.05 32.95
1.23 0.16 1.32 0.17 1.40 0.18
1.23 0.12 1.33 0.14 1.41 0.17
1.23 0.14 1.32 0.15 1.41 0.17
diately upon heating. However, formation of an oxide layer on the surface prevented further oxidation to the inner part of the samples as confirmed by X-ray analysis. After cutting, mounting, polishing, and carbon coating the quenched samples, the longitudinal sections of the samples were analyzed using the Wavelength Dispersive Spectrometer (WDS). The probe current used was 20 mA with an accelerating voltage of 15 kV. The standards used for calibration were Al–1Cu– 0.5Mg (wt.%) for Al, pure Cu for Cu and MgO for Mg. The compositions of the alloys are always given in wt.% in the present paper unless noted otherwise. The composition of the (Al) phase was measured in the center of the coarsened solid particles while the composition of the pre-existing liquid was determined through a raster beam scan technique as noted earlier. The scanned areas, approximately 500 mm2, were randomly chosen. The results obtained from the transverse sections of several samples were the same as those of the longitudinal sections. In order to obtain statistically reliable EPMA results for the quenched liquid, 20 areas were scanned for each sample and the average of the 20 measurements was taken to be the liquid composition. In fact, the standard deviation of the measurements became stabilized beyond 10 measurements. Twenty measurements were chosen so that the standard deviations of the measurements can be kept below 1% in most cases. The exact same approach was used to measure the solid composition using areas in the center of the coarsened particles. A total of 20 measurements were also made for each composition determined for the (Al) phase.
3. Experimental results We will present the results first for binary Al–15Cu, then ternary Al– Cu – Mg alloys. Fig. 1a shows the Back-Scattered Electron (BSE) image of the microstructure of Al–15Cu quenched from 600°C. The large dark particles are the primary (Al) phase. The fine eutectic
microstructure, consisting of (Al) (dark) and u-Al2Cu (bright), represents the quenched preexisting liquid. The microstructure given in Fig. 1b in a higher resolution shows the raster beam scan area; from which the composition of the pre-existing liquid was obtained on the basis of 20 measurements. The solidus and liquidus values determined in the present study at 600, 575 and 550°C are given in Table 1 as well as the partition coefficients. Each of the data points is taken to be the average of 20 individual measurements with a standard deviation of 0.5–0.7% in most cases. The microstructures of the two solidified ternary alloys are similar to those of binary Al–15Cu as shown in Fig. 2a and b for Al–15Cu–3Mg quenched from 600°C. The measured liquidus and solidus data for Al–15Cu–3Mg and Al– 3.9Cu–0.9Mg at 600, 575 and 550°C are given in Tables 2 and 3, respectively. Fig. 3a shows a comparison of our experimental data with those reported in the literature for the liquidus [12–19] and Fig. 3b that for the solidus [17,20–23]. As shown in Fig. 3a, with the exception of the data of Stockdale [13] and Tazaki [14], which tend to be lower, all other liquidus data including those obtained in the present study are in agreement. On the other hand, as shown in Fig. 3b, with the exception of the solidus data of Matsuyama [22] which tend to be lower, all other data including those obtained by us [17,20–23] are in agreement. The lower temperatures obtained by Matsuyama are likely due to the fact that their alloys did not reach equilibrium [24]. Now let us compare the experimental data with phase boundaries calculated using thermodynamic descriptions. The best thermodynamic description currently available for the Al–Cu system is that by Saunders [25,26], which was adopted in the thermodynamic description for Al–Cu–Mg developed in our group [6,11]. Fig. 3a shows that, within the uncertainties of the experimental data, the calculated liquidus using the description by Saunders is in good agreement with the experimental data. On the other hand, this is not the case for the solidus shown in Fig. 3b; the
H. Liang et al. / Materials Science and Engineering A292 (2000) 96–103
calculated solidus based on Saunders’ description, shown as a dashed line, lies in-between the five sets of agreeing data and those of Matsuyama [22]. This suggests that the solidus calculated using this description is lower than the agreeing experimental data by 0.5 at.%. An examination of the data given in Table 1 shows that while the discrepancies between the measured and model-calculated solidus and liquidus values decrease with decreasing temperature, the discrepancies are larger for the solidus. Since the compositions of Cu in the solidus are much smaller than those in the liquidus, the percentages of the discrepancies are even larger.
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Analysis of the data for the ternary alloys shown in Tables 2 and 3 yield similar conclusions using the thermodynamic description of Chang and co-workers [6,11]. As noted in Section 1, the model-calculated solidus along the Al–Cu0.5Mg0.5 isopleth [6,11], shown as a dashed line in Fig. 4, is lower in Cu contents than the experimental data, i.e. the calculated partition coefficients are lower than the measured values. These data are consistent with those obtained in the present study as shown in Tables 2 and 3. We believe the model-calculated solidus with lower Cu contents in the ternary is due primarily to the thermodynamic parameters used in the binary thermodynamic description since an extrapolation approach was used in the modeling. In fact, the model-calculated solidus in the Al–Cu boundary binary becomes a constraint on the solidus surface in ternary space. It is noteworthy that discrepancies between the calculated and measured solidus in the Al-Cu0.5Mg0.5 isopleth are nearly the same as those in the Al–Cu binary. Even though these discrepancies are small, i.e. less than 0.5 at.% of Cu (or 1 wt.%), a previous study on microsegregation suggests that they could have pronounced influence on the model-calculated microsegregation [5]. Therefore, the (Al) solidus in Al–Cu as well as in Al–Cu–Mg need to be remodeled so as to ensure the accuracy of microsegregation prediction. It will be shown later that the small corrections such as less than 0.5 at.% are indeed crucial.
4. Microsegregation calculation and discussion
Fig. 2. Microstructure of Al–5Cu–3Mg annealed at 600°C for 3 h and quenched in icewater (BSE image) (a) Mag 200; (b) Mag 4500.
Considering the fact that the thermodynamic description of Al–Cu by Saunders [25,26] has been widely adopted in thermodynamic descriptions of multicomponent aluminurn alloys [11,27,28] and there is a lack of sufficient reliable thermodynamic and phase equilibrium data, particularly for the Cu-rich alloys, we resort to a more practical approach on refining only the model of the (Al) phase using Thermo–Calc [29] in terms of the data presented earlier. A set of consistent parameters is obtained giving the best description of the experimental data. Phase boundaries calculated using the new model parameters are shown in Fig. 3b as solid lines, whereas those calculated using model parameters by Saunders [25,26] shown as dashed lines. It is evident from this figure the newly calculated solidus in terms of Cu are about 0.25 at.% higher than those calculated using Saunders’ description [25,26]. Basing on the new description for (Al) in the binary, ternary interaction parameters for this phase in Al–Cu–Mg were also re-optimized using data obtained in this study in addition to those available in the literature [6,11]. The new model-calculated (Al) solidus curve along the isopleth Al–Cu0.5Mg0.5 (shown in Fig. 4 as solid lines) are about 0.25 at% higher than those calculated using the descrip-
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Table 2 Comparison of the solidus and liquidus data determined experimentally with calculated values for Al–5Cu–3Mg at 6000, 575 and 550°C Al–5Cu–3Mg
(Al), CS (wt.%)
Liquid, CL (wt.%)
Ki =CS/CL
T (°C)
Exp
Calc
Exp
Calc
Exp
Calc
New
Old
New
New
Old
New
New
Old
New
97.00 1.44 1.56 96.05 2.14 1.81 95.62 2.43 1.95
97.30 1.03 1.67 96.50 1.50 2.00 95.80 1.99 2.21
96.86 0.39 1.75 95.88 2.00 2.12 95.06 2.58 2.36
82.49 12.35 5.16 75.14 18.37 6.49 69.24 23.38 7.38
82.60 12.03 5.37 75.56 17.76 6.68 69.26 23.00 7.74
82.39 12.14 5.47 75.30 17.91 6.79 68.99 23.22 7.79
1.18 0.12 0.30 1.28 0.12 0.28 1.38 0.10 0.26
1.18 0.09 0.31 1.28 0.08 0.30 1.38 0.09 0.29
1.18 0.11 0.32 1.27 0.11 0.31 1.38 0.11 0.30
600
575
550
Al Cu Mg Al Cu Mg Al Cu Mg
Table 3 Comparison of the solidus and liquidus data determined experimentally with calculated values for Al–4Cu–1Mg at 600, 575 and 550°C Al–4Cu–1Mg
T (°C) 600
575
550
Al Cu Mg Al Cu Mg Al Cu Mg
(Al), CS (wt.%)
Liquid, CL (wt.%)
Ki = CS/CL
Exp
Calc
Exp
Calc
Exp
Calc
New
Old
New
New
Old
New
New
Old
New
96.76 2.51 0.73 95.83 3.38 0.79 95.42 3.69 0.89
97.56 1.72 0.72 96.64 2.53 0.83 95.69 3.39 0.92
97.04 2.24 0.72 96.01 3.16 0.83 95.06 3.95 0.99
79.70 17.77 2.53 72.85 24.26 2.89 67.18 29.08 3.74
80.45 17.04 2.51 73.46 23.41 3.13 67.54 28.67 3.79
80.04 17.56 2.40 73.07 23.99 2.94 67.29 28.98 3.73
1.21 0.14 0.29 1.32 0.14 0.27 1.42 0.13 0.24
1.21 0.10 0.29 1.32 0.11 0.27 1.42 0.12 0.24
1.21 0.13 0.30 1.31 0.13 0.28 1.41 0.14 0.26
tion of Chen et al. [6,11] (shown as dashed lines). Nearly the same discrepancy between the current model-calculated solidus and the experimental data for binary Al–Cu and ternary Al – Cu – Mg along the isopleth Al–Cu0.5Mg0.5 suggests that the discrepancy is due primarily to that in the binary. It is worth noting that discrepancies still exist between the newly calculated solidus and the experimental data [7] as shown in Fig. 4. However, given the absolute accuracy of the experimentally determined solidus to be within 0.25%, the calculated solidus certainly falls within that range. We will next show the effect of uncertainty in the solidus curve on the calculated microsegregation in Al-rich Al–Cu and Al – Cu – Mg alloy using the approach of Kraft et al. [30]. It is a modified Scheil model [31] incorporating back diffusion in the solids, dendrite coarsening and the effects of undercooling although the later is insignificant for the cooling rates used. Table 4 shows comparisons of the calculated microsegregation parameters for a series of Al – Cu alloys with a cooling rate I K/s using the calculated partition coefficients according to Saunders’ description [25,26]
vs. those according to ours obtained in this study. The microsegregation parameters are expressed in terms of the fraction of eutectic formed ( fE), the minimum composition of Cu in the center of the dendrite (CSmin), and dendrite arm spacing (l2). The amount of eutectic formed during solidification is a measure of the degree of deviations from equilibrium freezing and therefore, the degree of microsegregation. It can be seen from Table 4 that both the amount of eutectic formed and the minimum concentration of Cu in the center of a dendrite arm are significantly affected by the small corrections in the solidus. However, there is no effect on the calculated dendrite arm spacing as expected, since coarsening in Al alloys does not depend strongly on the solidus concentration, not in Al–Cu in any case. A similar effect of a small change in solidus was also found for ternary Al-rich Al–Cu–Mg alloys. Table 5 shows comparisons of the calculated microsegregation parameters for alloy A1–3.9Cu–0.9Mg with different cooling rates of 1, 0.78, 0.23, and 0.039 K/s with those obtained experimentally in the present study. The calculation was carried out using the partition coefficients
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Fig. 3. Comparison of the liquidus data obtained in the present study for the (Al) + liquid equilibrium in binary Al – Cu with those reported in the literature. The solid lines are calculated using the description of Saunders [25,26]. (b) Comparison of the solidus data obtained in the present study for the (Al) + liquid equilibrium in binary Al–Cu with those reported in the literature. The dashed lines are calculated using the description of Saunders [25,26] while the solid lines using the model parameters obtained in the present study.
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Fig. 4. Comparison of the experimental liquidus and solidus obtained in the present study along the isopleth Al–Cu0.5Mg0.5 with those calculated based on the description of Chen et al. [6] shown as solid lines (denoted as from old PD) and those obtained in the present study as dashed lines (denoted as from new PD). Table 4 Comparison of calculated amounts of the eutectic ( fE), the minimum concentration in the dendrite arm center (cSmin), and the dendrite arm spacing (l2) for binary Al–Cu alloys using distribution coefficients obtained from Saunders’s description [25,26] with those obtained in this study with a cooling rate of 1 K/s Al–Cu C0, wt.% PD source
fE vol.%
CSmin wt.%
l2 mm
2% Cu
1.2 0.6 5.2 4.5 9.6 8.8 14.4 13.4
0.5 0.6 0.9 1.1 1.2 1.5 1.6 1.9
51 52 46 47 43 43 40 40
4% Cu 6% Cu 8% Cu
Saunders This study Saunders This study Saunders This study Saunders This study
Fig. 5. Comparison of the experimental concentration profiles of Cu and Mg in alloy Al – 3.9Cu – 0.9Mg [5] with the model-calculated values using partition coefficients obtained from the description of Chen et al. [6] shown as solid lines (denoted as using original K) and those using old partition coefficients obtained from the model parameters obtain in the present study shown as solid line (denoted as using new K). This alloy was directionally solidified with a cooling rate of 0.78 K/s.
obtained from Chen et al.’s description [6]. The amount of the eutectic formed is again very sensitive to the small corrections in the solidus, but not the dendrite arm spacing. Now let us see the effect on solute distribution profile. Fig. 5 shows a comparison of the solute distribution profiles for alloy Al–3.9Cu–0.9Mg directionally solidified under a cooling rate of 0.78 K/s. The dense lines incorporating symbols are experimental data by Xie et al. [5]. As shown in Fig. 5, the calculated Cu profile using the new partition coefficients is much closer to the experimental data than that using the description of Chen et al. [6], keeping in mind that the values of the Cu solidus are changed by only 0.25 at.% or less. The calculated Mg profile using the new partition coefficient of Mg is not expected to differ appreciably since the solidus in terms of Mg remains essentially the same. As mentioned in Section 1, it was showed in a previous study in our group
Table 5 Comparison of calculated amounts of the eutectic ( fE), the minimum concentration in the dendrite arm center (cSmin), and the dendrite arm spacing (l2) for the ternary Al–3.9Cu–0.9 alloy using distribution coefficients obtained from Chen et al’s description [6] with those obtained in this study with a cooling rates of 1, 0.7, 0.23 and 0.39 K/s Cooling rate K/s
PD source
fa vol.%
fE vol.%
fter-E vol.%
l2 mm
1
Chen et al. This study Chen et al. This study Chen et al. This study Chen et al. This study
96.1 96.7 96.1 96.8 96.5 97.1 97.1 98.1
3.9 3.3 3.9 3.2 3.5 2.9 2.9 1.9
1.1 0.6 1.1 0.5 0.7 0.2 0.1 0.0
47 47 51 51 76 77 131 132
0.78 0.23 0.039
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[5] that the greatest uncertainty in the model-calculated microsegregation was due to uncertainties in the solid/ liquid phase boundaries. The present study demonstrates that obtaining accurate phase diagram data whether by experiments or a combined modeling/experimental approach is a prerequisite for reliable solidification modeling of binary and higher order alloys.
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University of Technology, Germany, and Prof. D.R. Poirier and Dr P.K. Sung at the Department of Materials Science and Engineering, University of Arizona, for helpful discussions on the experimental technique and Dr Fournell at the UW Microprobe Lab for his help in the experimental analysis. John Woodford and Peter Ladwig are gratefully acknowledged for carefully reading the manuscript.
5. Summary The liquidus and solidus of the Al-rich alloys for binary Al–Cu and ternary Al – Cu – Mg were determined experimentally. The compositions of (Al) and liquid in rapidly quenched samples from high temperatures were determined by EPMA using a raster beam scan technique. For the Al – Cu alloys, the measured (Al) solidus in terms of Cu were found to be 0.5 at.% higher than model-calculated values using the thermodynamic description of Saunders [25,26], while the measured (Al) liquidus in terms of Cu are in good agreement with model-calculations. Similar discrepancies between measured and calculated values were found in the ternary Al – Cu – Mg system. The inaccuracy in the model-calculated (Al) solidus in Al –Cu was believed to be responsible for the deviations between the model-calculated and measured microsegregation in both binary Al–Cu and ternary Al – Cu – Mg. The (Al) phase in both Al– Cu and Al – Cu – Mg were remodeled in this study. The model-calculations show that even the small discrepancies of 0.5 at.% and less in the Cu content of the (Al) solidus have a significant influence on the model-calculated concentration profile in the dendrites (as a result of microsegregation in these alloys). In order to test the validity of a microsegregation model, reliable partition coefficients (i.e. phase equilibrium data) are needed!
Acknowledgements The authors wish to acknowledge the National Science Foundation for financial support through a grant with the number NSF-DMR-94-21780 and Dr Bruce MacDonald of the Metal Program of the Materials and Processing Cluster of NSF for his interest in this work. The authors also wish to thank Dr M. Rettenmayr at the Department of Physical Metallurgy, Darmstadt
.
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