A thermodynamic description of the Al–Be system: Modeling and experiment

Computer Coupling of Phase Diagrams and Thermochemistry 28 (2004) 371–378 www.elsevier.com/locate/calphad

A thermodynamic description of the Al–Be system: Modeling and experiment Zhu Pan, Yong Du∗, B.Y. Huang, Yong Liu, R.C. Wang State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan, 410083, PR China Received 17 September 2004; received in revised form 22 November 2004; accepted 9 December 2004 Available online 4 February 2005

Abstract The Al–Be system is investigated via three steps. In the first step, all of the experimentally measured phase diagram and thermodynamic data available in the literature are critically reviewed. On the basis of the assessed phase diagram, in the second step, eight decisive samples are prepared by arc melting of Al and Be pieces and annealing at 600 ◦ C for eight days. Water-quenched samples are analyzed using differential thermal analysis (DTA), X-ray diffraction (XRD), optical microscopy, and scanning electron microscopy (SEM) techniques. In the last step, an optimal thermodynamic data set for the Al–Be system has been obtained by considering the present experimental data and the reliable literature data. The calculated phase diagram and thermodynamic properties agree well with the accurate experimental values. © 2005 Elsevier Ltd. All rights reserved. Keywords: Al–Be phase diagram; Thermodynamic calculation; X-ray diffraction; Differential thermal analysis

1. Introduction As early as in 1928, Archer and Fink [1] reported that Be has attractive properties, such as low density, high hardness, good corrosion resistance, low thermal expansion, and fairly good electrical conductivity. This could indicate that Be is worthy of consideration as an ingredient of lightweight alloys. Recently, Wang et al. [2] reported that minor addition of Be in the as-cast Al88.7 Si11 Mg0.3 alloy (wt%) causes faster precipitation of the metastable β  phase and a larger heat effect associated with its formation, and thus considerably increases the peak hardness achieved during as-cast aging. Both Yin et al. [3] and Yie et al. [4] have indicated that the addition of Be into commercial Al alloys, such as Al91.59 Si4.93 Fe1.4 Mg0.63Cu1.45 (wt%) [3] and Al87.79 Si11.1 Fe1.03 Ti0.08 (wt%) alloys [4], is beneficial for the transformation of the needle-shaped iron-rich phase into the Chinese script. It is generally believed that the needle-shaped iron-rich phase is harmful to the strength and ductility of materials. Recent experimental work by ∗ Corresponding author. Tel.: +86 731 8836213; fax: +86 731 8710855.

E-mail address: [email protected] (Y. Du). 0364-5916/$ - see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.calphad.2004.12.003

Song et al. [5,6] has shown that for Al–Mn alloys the addition of Be was found to substantially improve the thermal stability of the icosahedral quasicrystalline phase (i -phase) and to significantly reduce the critical cooling rate for the formation of the i -phase, compared to the binary Al–Mn i -phase. Song et al. [7] also indicated that the addition of Be into Al–Fe–Cu alloys modified the formation mechanism of the i -phase from the peritectic reaction to primary solidification and the volume fraction of the i -phase has been observed to increase from 45% for the ternary alloy Al62 Cu25.5 Fe12.5 (at.%) to 90% for the quaternary alloy Al55 Cu25.5 Fe12.5 Be7 (at.%). In order to prepare bulk metallic glasses with single i -phase, the primary solidification for this phase is preferable since peritectic reactions rarely proceed to completion and thus additional heat treatment is needed. In the production of commercial Al alloys and Al-based bulk metallic glasses, knowledge of phase diagrams and thermodynamic properties is a necessary prerequisite for the development of the materials. It is essential to define the processing conditions for making these materials and subsequent heat treatment to obtain optimal engineering properties. Currently, in our group, a research project for

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Table 1 Summary of the phase diagram and thermodynamic data in the Al–Be system Type of data

Reference

Experimental method

Quoted modea

Al-rich liquidus

Archer and Fink [1] Oesterheld [9] Kroll [13] Haas and Uno [14] Losana [15] Nishi [17]

DTA, metallography DTA Metallography Dilatometry, metallography DTA DTA, metallography

+ + + +
+

Solubility of Al in (αBe)

Kroll [13] Losana [15] Makarov and Tarschisch [18] Myers and Smugeresky [23] Kaufman et al. [24] Hammond et al. [25] Jacobson and Hammond [26] Hindle and Slattery [27] Kleykamp [28]

Metallography Resistivity Lattice parameters Ion-beam implantation Metallography EPMA EPMA XRD EPMA









+

Solubility of Be in (Al)

Archer and Fink [1] Haas and Uno [14] Losana [15] Mikheeva [16] Nishi [17] Makarov and Tarschisch [18] Serebryakov et al. [19] Buckle [20] Buckle and Descamps [21] Ceresara [22]

Hardness Metallography Resistivity Lattice parameter Metallography Lattice parameter emf Microhardness Microhardness Electrical resistivity

+

+


+ + +

Be-rich liquidus

Archer and Fink [1] Oesterheld [9] Losana [15] Mikheeva [16] Nishi [17] Masing and Dahl [29] Nagorskaya et al. [30] This work

DTA DTA, metallography DTA DTA DTA, metallography DTA Chemical analysis DTA, XRD, metallography

+ +

+

+

Activity coefficient Activity Activity

Bienvenu et al. [32] Schaub et al. [33] Serebryakov et al. [34]

Distribution Knudsen effusion emf

  

a Indicates whether the data are used or not used in the parameter optimization: +, used; , not used but considered as reliable data for checking the modeling;
, not used.

establishing a thermodynamic database for technologically important Al-based systems by means of both modeling and experimental work is in progress. A thermodynamic description for the complicated ternary Al–Mn–Si system over the whole composition and temperature ranges has been obtained by Du et al. [8] using thermodynamic modeling and experiment. The Al–Be phase diagram has been the subject of several investigations since the early work by Oesterheld [9]. Although this system is a simple eutectic one, there is no general agreement among the published phase diagram data, especially for the Be-rich liquidus. Experimental information on the thermodynamic properties of the Al–Be system is limited. The Al–Be system has been modeled by Du et al. [10] and Piche et al. [11]. For the Be-rich liquidus, both groups of authors [10,11] trusted the experimental data published in 1916 [9]. Further experimental

work is necessary to check the reliability of these early data. The purposes of the present work are (I) to critically evaluate all the phase diagram and thermodynamic data available for the Al–Be system, (II) to provide new experimental data on the Be-rich liquidus, and (III) to provide a self-consistent set of thermodynamic parameters for the Al–Be system. 2. Evaluation of experimental data A review of the experimentally determined phase diagram and thermodynamic data available for the Al–Be system was performed by Murray and Kahan [12]. In the present assessment, the data included in that review are considered, together with the experimental data published later or not covered by them. All of the data are summarized in Table 1 and concisely categorized in the following.

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2.1. Phase diagram data 2.1.1. The Al-rich liquidus and the eutectic reaction Several groups of investigators [1,9,13–17] contributed to the measurement of the Al-rich liquidus as well as the invariant reaction among (Al), liquid and (αBe). The general agreement among them, except Nishi [17], is that this invariant reaction is a eutectic one. On the basis of thermal analysis and metallographic observations, Nishi [17] suggested a peritectic reaction L + (αBe) ↔ (Al). The peritectic reaction type is not accepted because the eutectic microstructure has been observed by the other investigators [1,9,13–16]. By means of thermal analysis and optical microscopy, Kroll [13] as well as Haas and Uno [14] reported the eutectic point to be at 640 ◦ C and 4.1 at.% Be, and at 647 ◦ C and 4.1 at.% Be, respectively. The Al-rich liquidus was measured by four groups of authors [1,9,15,16] using thermal analysis. These reported liquidus temperatures show some scatter within estimated experimental errors. In a preliminary optimization, all of the published data [1,9,15, 16] were tested. It was found that using the experimental values from Losana [15] results in a poor agreement with the other experimental data used for optimization. Consequently, the liquidus temperatures reported by Archer and Fink [1], Oesterheld [9] and Mikheeva [16] are retained in the final thermodynamic modeling. 2.1.2. Solubility of Be in (Al) The solubility of Be in (Al) was measured by many investigators [1,14–22] using different methods (Table 1). The solubility data over wide temperature ranges were given by both Archer and Fink [1] and Buckle et al. [20,21] using a hardness measurement method, by Mikheeva [16] using a lattice parameter measurement technique, and by Ceresara [22] using an ER method. In the present modeling, the data from these five groups [1,16,20–22] were used since they employed accurate methods (lattice parameter, electrical resistivity, and microhardness techniques) and the experimental results given by them agree well with each other. The solubility data resulting from metallographic observations [14,17] were excluded from the optimization since this technique is not suitable for the measurement of very low solubility. The results of Serebryakov et al. [19] (0.19 at.% Be at 645 ◦ C) agree with the selected data, but were derived from electromotive force (emf) measurements rather than directly observed. They are not used in the present modeling. Compared to those from most authors [1,16,20–22], the values published by Losana [15] as well as Makarov and Tarschisch [18] appear too high. As a consequence, the data from the above two groups of authors [15,18] were also not utilized in the optimization. 2.1.3. Solubility of Al in (αBe) In the literature, there are a few publications concerning the solubility of Al in (αBe). By the use of ion implantation

373

and ion backscattering analysis, Myers and Smugeresky [23] found that the solubility of Al in (αBe) is less than 0.007 at.% at 600 ◦ C. The extremely low solubility data were also reported by some previous investigators using different methods, metallography [13,24], electron probe microanalysis (EPMA) [25,26], and XRD [18,27]. On the basis of electrical resistivity measurements, Losana [15] reported a large solubility value of 1.7 at.% Al at 648 ◦ C. The result due to Losana [15] is not accepted since it disagrees with the other measurements [13,18,23–28]. By means of an EPMA technique, Kleykamp [28] recently reported that the solubility of Al in (αBe) is 0.01 at.% Al at 690 ◦ C. In the present modeling, the experimental data from Myers and Smugeresky [23] and Kleykamp [28] are utilized to assess the constant regular parameter for (αBe). There is no experimental information about the solubility of Al in (βBe). In view of the exceedingly low solubility of Al in (αBe), its solubility in (βBe) can probably be assumed to be negligible. 2.1.4. Be-rich liquidus from the eutectic point to pure Be Several groups of authors contributed to the measurement of the Be-rich liquidus. Employing thermal analysis techniques, both Oesterheld [9] and Losana [15] measured the liquidus over the entire composition range. Following the same method, Mikheeva [16] constructed the liquidus below 11.4 at.% Be. The liquidus temperatures in the composition ranges of 25–42 at.% Be and 40–75 at.% Be were reported by Masing and Dahl [29] and Nagorskaya et al. [30], using thermal analysis methods, respectively. Potard et al. [31] established the liquidus from 3 to 39 at.% Be through chemical analysis of liquid in equilibrium with (αBe). The liquidus temperatures for eight alloys in the composition range of 3–8 at.% Be were reported by Nishi [17], using thermal analysis. From the eutectic composition (2.5 at.% Be) to 40 at.% Be, various measurements agree within 2–3 at.% at a given temperature, except for the measurements of Mikheeva [16] and Nagorskaya et al. [30], whose results show significant deviation from the bulk of the work. As a result, the data from above two groups of researchers [16, 30] were excluded from the optimization. For the Be-rich liquidus above 40 at.% Be, thermal analysis results of Oesterheld [9] and Losana [15] disagree by 30–60 ◦ C. In the absence of further experimental data, it is difficult to judge which one is preferable, as pointed out by Murray and Kahan [12]. In the present experimental work, seven alloys with above 40 at.% Be are prepared in order to provide new experimental data on the Be-rich liquidus. With our renewed measurements, we could make a sound judgment. 2.2. Thermodynamic data Three groups of authors [32–34] measured the thermodynamic properties of the Al–Be alloys. Using the distribution method, Bienvenu et al. [32] reported the activity coefficient for Al in a dilute solution of liquid Be as 4.64 at 1600 K.

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Schaub et al. [33] measured the activities of both Al and Be in four melts (39, 66.7, 93.7, and 95.5 at.% Be) from 1653 to 1760 K, using the Knudsen effusion method. By means of an emf technique, Serebryakov et al. [34] measured the activities of Be in diluted solutions of liquid Al at 958, 999, 1039, and 1081 K. These experimental thermodynamic properties of diluted solutions [32,34] and several activity data published by Schaub et al. [33] are compared with the predicted results of the present modeling.

Table 2 Summary of the phases and phase transition temperatures for the samples in the Al–Be system annealed at 600 ◦ C for eight days ◦

No

at.% Be

Phasea

Transition temperature ( C)b

1 2 3 4 5 6 7 8

0 45 50 70 80 85 95 100

(Al) (Al) + (αBe) (Al) + (αBe) (Al) + (αBe) (Al) + (αBe) (Al) + (αBe) (Al) + (αBe) (αBe)

659 644, 1122 643, 1135 644, 1156 643, 1174 644, 1181 643, 1235 1251, 1285

a Identified with XRD, metallography and SEM/EDX methods. b Obtained from DTA measurement with a heating rate of 5 ◦ C/min.

3. Experiment As indicated in the preceding section, further experimental work is of interest for the refinement of the Al–Be phase diagram above 40 at.% Be. The phase diagram assessed by Murray and Kahan [12] was used to select the alloy compositions. 3.1. Sample preparation The starting materials were rods of Al (99.999% purity, Johnson-Matthey Company, MA 01835, USA) and pieces of Be (99.8% purity, Northwest Institute for Non-ferrous Metal Research, Xi’an, China). The Be pieces were burnished in order to remove the oxide from the surface. In addition to pure Al and Be, six binary alloys with a weight of about 1 g were prepared by arc melting Al and Be pieces in a purified Ar atmosphere. The as-cast alloys were encapsulated in evacuated silica capsules under a vacuum of 10−3 bar, annealed at 600 ◦ C for eight days, and then water quenched. Table 2 lists the alloy compositions. Weight losses during arc melting were generally less than 1 mass %. Chemical analysis for the selected alloys was conducted in order to determine the deviation from the nominal composition. The elemental concentrations were measured with an inductively coupled plasma mass spectrometer (ICP-MS) instrument (IRIS Advantage 1000, Thermo Elemental, USA). The measured compositions closely match the nominal ones within 1 at.% Be.

3.2. Sample characterization The XRD technique (Rigaku D/max2550VB, Japan) was used to identify the phases and determine their lattice parameters with Ge as an internal standard. Lattice parameters were calculated by means of the JADE program [35]. DTA (STA 409 PC, NETZSCH, Germany) was used to measure phase transition temperatures. The measurements were performed between room temperature and 1450 ◦ C with heating and cooling rates of 5 ◦ C/min in an argon atmosphere. A Pt–Pt/Rh thermocouple was used. It was calibrated to the melting points of Al (660.32 ◦ C), Au (1064.18 ◦ C), and Si (1413.85 ◦ C). In the temperature range examined, the accuracy of the temperature measurement was estimated to be ±2 ◦ C. The eutectic reaction temperature was determined from the onset of the first thermal effect during the heating step, and the peak temperature of the second thermal effect on heating was taken for the liquidus. In order to confirm the results from XRD and DTA measurements, most of the alloys in both as-cast and annealed states were ground, polished, and then analyzed by optical microscopy (Leica DMLP, Wetzlar, Germany). Some typical alloys were subjected to scanning electron microscopy with energy dispersive X-ray (SEM/EDX) analysis (JSM-5600LV, JEOL, Japan) to verify the optical microscopy observation. 3.3. Experimental results Table 2 summarizes the phases identified by XRD, optical microscopy and SEM/EDX methods along with the phase transition temperatures resulting from DTA measurement. XRD examinations of the samples in both ascast and annealed states show the existence of two phases, (Al) and (αBe). Since the lattice parameters of (Al) and (αBe) calculated from the binary alloys agree well with those for the pure elements [36], the mutual solubility of Al and Be is presumably negligible. This confirms the previous findings [1,13,16,20–28]. The backscattered electron micrograph for the as-cast alloy containing 45 at.% Be is presented in Fig. 1, showing the existence of a eutectic structure and primary (αBe) phase. Using a point counting technique, the volumes of the primary (αBe) and the eutectic in the as-cast Al55 Be45 alloy were calculated to be 35% and 65%, respectively. The currently obtained phase transition temperatures in the composition range of 45 at.% Be to pure Be are shown in Fig. 2. As indicated in this figure, there is a reasonable agreement between the present measurement and that by Oesterheld [9]. Compared to the experimental results from the present work and Oesterheld [9], the liquidus temperatures published by Losana [15] appear too high. Consequently, the currently obtained liquidus temperatures plus the data of Oesterheld [9] are utilized in the thermodynamic optimization.

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modeling, the Gibbs energies for the pure elements are taken from the compilation of Dinsdale [37]. 4.2. The liquid phase The liquid phase is described with a substitutional solution model: L L + x o G L + RT (x ln x + x ln x ) = x Al o G Al Gm Be Al Al Be Be Be

+

ex G L m

(2)

where x i (i = Al, Be) is the mole fraction of element i and o G L the Gibbs energy of element i in the liquid form. The i third term in Eq. (2) is the ideal entropy of mixing and the last term is the excess Gibbs energy. The excess Gibbs energy is described by the Redlich– Kister polynomial [38]: Fig. 1. Backscattered electron micrograph of as-cast Al55 Be45 (at.%) alloy.

ex G L m

= x Al x Be ( L a oAl,Be + L boAl,BeT ) + (x Al − x Be ) × ( L a 1Al,Be + L b1Al,BeT ) + · · ·

in which the coefficients

Lao Al,Be,

L bo La1 Al,Be, Al,Be

(3) and

L b1 Al,Be

are the parameters to be optimized. The Gibbs energies of the other phases are described by equations similar to Eqs. (2) and (3). 5. Results and discussion

Fig. 2. Calculated Al–Be phase diagram, compared with the experimental data from the present work and the literature [1,9,15–17,29–31].

4. Thermodynamic model 4.1. The unary phases ϕ

The Gibbs energy function oG ϕi (T ) = G i (T ) − HiSER for element i (i = Al, Be) in the phase ϕ (ϕ = (Al), (αBe), (βBe), or liquid) is described by an equation of the form o G ϕ (T ) i

= a + b · T + c · T · ln(T ) + d · T 2 + e · T −1 + f · T 3 + g · T 7 + h · T −9

(1)

in which HiSER is the molar enthalpy of the element i at 298.15 K and 1 bar in its standard element reference (SER) state, and T is the absolute temperature. In the present

The evaluation of the model parameters is conducted by recurrent runs of the PARROT program [39], which works by minimizing the square sum of the differences between measured and computed values. In the assessment procedure, each set of experimental information is given a certain weight. The weights were changed systematically during the assessment until most of the experimental data were accounted for within the claimed uncertainty limits. The optimization begins with (αBe). Using the selected experimental solubility data for Al in (αBe), the constant regular parameter oa (αBe) Al,Be was assessed and then fixed during the subsequent optimization steps. Assuming the negligible solubility for Al in (βBe), the regular parameter oa (βBe) was taken to be equal that of (αBe). Secondly, Al,Be the (Al) phase was included in the optimization. For this phase, a suggested relationship between the partial enthalpy o fcc and excess entropy of the solute [40] ( oa fcc Al,Be/ b Al,Be = −3400 K) is applied in order to reduce the description of this phase to only one independent coefficient. The solid solubility data of Be in (Al) as well as the Al-rich liquidus selected in the preceding section are utilized to obtain the approximate parameter for the (Al) phase. Thirdly, the thermodynamic parameters for the liquid phase were optimized. In the literature, there are plentiful experimental data on the liquidus from pure Al to 40 at.% Be. The Berich liquidus above 45 at.% Be has been measured accurately in the present work. The literature data and the present measurement imply that at least L a oAl,Be, L boAl,Be, and

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La1 Al,Be

could be introduced for the description of the liquid phase. Finally, all the phases were optimized simultaneously by taking into account all of the selected phase diagram data. The thermodynamic parameters finally obtained in the present work are listed in Table 3. Using two-term lattice stability for the elements, Murray and Kahan [12] obtained a set of parameters describing the Al–Be system. In view of the SGTE data for the pure elements [37], the twoterm lattice stability are now out of date. Both the present authors and Piche [11] employed a sub-regular model to describe the liquid phase. In the present optimization, a suggested relationship between the partial enthalpy and o fcc excess entropy of the solute ( oa fcc Al,Be/ b Al,Be = −3400 K) is applied for the (Al) phase in order to minimize the number of coefficients needed to describe this phase. Piche [11] uses two parameters to describe the (Al) phase, although accurate experimental data associated with the (Al) phase are available only in a narrow temperature range between 600 ◦ C and 660 ◦ C, which warrants only one parameter. Fig. 3. Calculated Al-rich part of the Al–Be phase diagram along with the experimental data [1,9,13–18,20–22,30,31]. Table 3 Summary of the thermodynamic parameter for the Al–Be systema Liquid: (Al, Be) o L L = 56 939 − 28T Al,Be 1 L L = −9856 Al,Be

fcc-(Al): (Al, Be) o fcc L = 61 880 − 18.2T Al,Be

hcp-(αBe): (Al, Be) o (αBe) L = 60 000 Al,Be

bcc-(βBe): (Al, Be) o (βBe) L = 60 000 Al,Be a In J/(mole of atoms); temperature (T ) in K. The Gibbs energies for the pure elements are taken from the compilation of Dinsdale [37].

Fig. 2 shows the calculated Al–Be phase diagram along with the experimental data from the present work and the literature. The invariant reaction among liquid, (αBe), and (βBe) is of degenerate features because of the extremely small solubilities of Al in (αBe) and (βBe). As can be seen in this figure, the present experimental data and the reliable literature data are well reproduced by the modeling. The experimental values due to Losana [15] and Mikheeva [16] show a noticeable discrepancy from the calculated results. A comparison of the computed Al-rich region of the Al–Be phase diagram with the corresponding experimental data is made in Fig. 3, showing a reasonable agreement with the critically selected literature data [1,9,16,17,20–22,31]. In this paragraph, we compare the thermodynamic quantities predicted by using the thermodynamic parameters with three sets of experimental data, which are not used in the evaluation of the model parameters. Fig. 4 compares the predicted activities of Al and Be in the liquid at 1600 K with the corresponding experimental values [33]. In Fig. 5,

Fig. 4. Model-predicted activities of Al and Be (αBe and βBe) in the liquid phase at 1600 K, compared with the experimental data [33]. The reference states for both Al and Be are liquid.

the predicted activity of Be in the liquid at 1000 K is compared with the corresponding experimental values [34]. These experimental data [33,34] can be well accounted for by the present modeling although they are not used in the evaluation of thermodynamic parameters. In accordance with the parameters obtained in the present work, the calculated activity coefficient for Al in a dilute solution of liquid Be at 1600 K is 5.2, which agrees with the measured value of 4.64 [32]. The currently obtained Al–Be phase diagram is shown in Fig. 6 for easy perception without the data points and on the

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phase diagram in the composition range of 45–100 at.% Be has been investigated by using XRD and DTA methods, supplemented with optical microscopy, SEM/EDX, and ICP analysis. • An optimal thermodynamic data set for the Al–Be system was obtained by considering the present experimental results as well as critically evaluated literature data. The comparison demonstrates that the computed phase diagram is in good agreement with the reliable experimental information. It is also found that the model can describe the experimentally measured thermodynamic properties, which are not employed in the thermodynamic optimization.

Acknowledgements

Fig. 5. Model-predicted activity of Be in the liquid phase at 1000 K, compared with the experimental data [34]. The reference state for Be is (αBe).

This research work was supported by the National Advanced Materials Committee of China through grant No. 2003AA302520. The Thermo-Calc program developed by Thermo-Calc software AB Company of Sweden is gratefully acknowledged. Y. Du gratefully acknowledges the Furong Chair Professorship program released by Hunan Province of P.R. China for financial support. The donation of a Leica DMLP microscope from the Alexander von Humboldt foundation is greatly appreciated. Thanks are also due to Professor J.C. Schuster (University of Vienna, Austria) for the revision of the manuscript. References

Fig. 6. Revised Al–Be phase diagram in accordance with the present work. The mutual solid solubilities were found to be below the XRD detection limit in agreement with the reported 0.2 at.% Be in (Al) at the eutectic reaction temperature [20,22] and 0.01 at.% Al in (αBe) at 690 ◦ C [28].

practical Celsius scale. This phase diagram is expected to substitute for the currently accepted version [41]. The thermodynamic parameters of the Al–Be system obtained in the present work have been used to calculate the phase relationships in the Al–Be–Si system successfully [42]. 6. Summary • All the experimental phase diagram data available for the Al–Be system have been critically evaluated. The Al–Be

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