A Thermodynamic Description of the Al-Mg-Zn System

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 28A, SEPTEMBER 1997—1725

A Thermodynamic Description of the Al-Mg-Zn System

H. LIANG, S.-L. CHEN, and Y.A. CHANG

A thermodynamic description of the Al-Mg-Zn system was developed based on critically evaluatedexperimental data. All binary intermetallic phases are assumed to have negligible ternary solubilityexcept for MgZn2. Three different thermodynamic models are applied to three different types ofphases in this system, i.e., disordered solution phases, stoichiometric compounds, and semistoichiom-etric phases. The model parameters are optimized based on the thermodynamic descriptions of theconstituent binaries and experimental phase equilibrium and thermodynamic data available in theliterature. The good agreement obtained between several calculated isopleths and thermodynamicvalues of the liquid phase and experimental data shows that the current description of this system isreasonable. The calculated phase equilibria in the Al-rich corner are believed to be reliable forpractical applications, while those away from the Al-rich region are subjected to large uncertainty.Additional experimental investigations are needed to firmly establish the phase equilibrium of thissystem over wide ranges of composition and temperature.

I. INTRODUCTION

BECAUSE elements Al, Cu, Mg, and Zn are basic com-ponents for many high-strength aluminum alloys such asalloy 7075, it is important to develop a thermodynamic de-scription for this quaternary system. Developing a ther-modynamic description for an alloy system meansdeveloping appropriate thermodynamic models for all thephases in the system so that we can calculate its phaseequilibria and thermodynamic properties. Such a descrip-tion is important not only for basic materials research inrelated areas, such as solidification and solid-state phasetransformation, but also for alloy and processing develop-ment and improvement. However, in order to obtain a ther-modynamic description for the quaternary, it is necessaryto develop descriptions for its constituent ternaries first. Ina previous article, we have reported a thermodynamic de-scription for the Al-Mg-Cu system.[1] In this article, we re-port a description for the second ternary system Al-Mg-Zn.Developing such a description is based on the experimentalphase equilibrium and thermodynamic data available in theliterature and the established descriptions for the three con-stituent binaries Al-Mg,[2] Al-Zn,[3] and Mg-Zn.[4] In the fol-lowing, we will first present a review of the experimentaldata, then the thermodynamic models used in this study,next optimization of the model parameters, and last a dis-cussion of the results.

II. REVIEW OF EXPERIMENTAL DATA

Ever since the first experimental investigation of theAl-Mg-Zn system by Eger[5] in 1913, many additional stud-ies have been reported in the literature.[6–60] Theexperimental results have been reviewed periodically by anumber of researchers.[9,32,34,41,49,50,53,58,60] The review by Des-pande et al.[58] is the most detailed one considering both the

H. LIANG, Graduate Student, S.-L. CHEN, Research Associate, andY.A. CHANG, Wisconsin Distinguished Professor, are with theDepartment of Materials Science and Engineering, University ofWisconsin-Madison, Madison, WI 53706-1595.

Manuscript submitted November 25, 1996.

phase equilibrium and thermodynamic data. The most re-cent review of the phase equilibrium data is given by Pe-trov.[60] Figures 1 through 3 show the assessed liquidusprojection and two isothermal sections at 25 7C and 3357C, respectively. As shown in these diagrams, there existtwo ternary phases which are the T phase with a formulaof (Al, Zn)49(Mg)32 and the f phase with a formula ofAl20.4Mg54.9Zn24.7. The T phase was determined by Bergmanet al.[33,36] and the f phase by Clark and Rhines[37] andClark.[40] Both phases exist over wide ranges of homoge-neity. Clark[40] also suggested the existence of a third ter-nary phase with an uncertain composition near the Mg-Znboundary binary, but its existence was never confirmed bylater investigators. Although all the binary phases in Fig-ures 2 and 3 show appreciable solubility for the third com-ponent, there is no sufficient experimental evidence toestablish their exact ternary solubility. To facilitate reading,the symbols used to represent the various phases in thissystem are summarized in Table I.

The liquidus projection shown in Figure 1 is mainlybased on the work of Eger,[5] Koster and co-workers,[14,15,16]

and Clark,[40] following the nomenclature of Rhines[61] andthe format of presentation used by Chang et al.[62] The 3357C isotherm shown in Figure 2 is that proposed by Wil-ley,[50] mainly based on the work of Koster and co-work-ers,[14,15,16] Fink et al.,[18] Little et al.,[22,23] and Clark.[40] The25 7C isotherm shown in Figure 3 incorporates the exis-tence of the f phase with the other features reported byDrits[54] based on the study of Mikheeva.[29] The stability ofthe f phase has not been determined with certainty. How-ever, because it was found to be stable at 335 7C and 2047C by Clark,[40] it seems reasonable to assume that its sta-bility extends down to room temperature.

In general, phase equilibria of the Al-Mg-Zn system arenot well established over the entire composition region.However, the liquidus, solidus, and solvus in the Al-richcorner, which are the major interest regions of the presentstudy, are well established. They have been reported in aseries of studies.[14–16,18,22,23,26,55] Near the Al-Zn side, the twoinvariant reactions I1 and II1, as shown in Figure 1, weredetermined by Stiller et al.,[55] updating the work by Kosterand co-workers.[14,15,16] The phase equilibria in the Mg-rich

1726—VOLUME 28A, SEPTEMBER 1997 METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 1—Assessed experimental liquidus projection.

Fig. 2—Assessed experimental isotherm at 298 K (25 7C).

Fig. 3—Assessed experimental isotherm at 608 K (335 7C).

Table I. Phase Nomenclature in the Al-Mg-Zn System

Symbols Phases

LFccHcpbgrnsTf

Mg7Zn3

Mg2Zn3

MgZnMg2Zn11

liquid(Al)

(Mg), (Zn)Al8Mg5

Al12Mg17

Al56Mg44

Al105Mg95

(Al,Zn)2Mg(Al,Zn)49Mg32

Al2Mg5Zn2

Mg7Zn3

Mg2Zn3

MgZnMg2Zn11

corner are less established, especially for those involvingthe f phase.[40] The invariant reactions near the Mg-Zn sideproposed by Clark[40] were suggested to be taken with largeuncertainty. The phase equilibria near the Al-Mg boundarybinary are likewise not well established due to lack of ex-perimental data.

The assessed invariant reactions including the four saddlepoints are summarized in Table II; they have been acceptedby most reviewers except for some modifications of the in-variant equilibria in the Mg-Zn side, such as II3, II6, and I4.The modifications are made in the present study in view ofthe currently accepted boundary binary phase equilibria andthe need for self-consistency between all ternary reactions.

In comparison to phase equilibrium data, very few ther-modynamic data are available in the literature. The vaporpressures of Zn in liquid alloys at 660 7C and above were

measured by Kozuka et al.[39] and at 800 7C by Lukashenkoand Pogodayev[48] using a gas-carrier method. The activitydata for Al and Mg in liquid state were calculated usingthe Darken equations.[39,48] Pogodayev and Lukashenko[51]

also reported the activity data of Mg in liquid state at 6607C and 800 7C using an EMF method.

III. THERMODYNAMIC MODELS

In the present study, three types of models are employedto describe three different types of phases in the Al-Mg-Znsystem: disordered solution for the liquid, fcc, and hcpphases; stoichiometric compound for the f phaseAl2Mg5Zn2; and semistoichiometric compound for the sphase (Al, Zn)2Mg and the T phase (Al, Zn)49Mg32. All thebinary intermetallic phases are assumed to have negligibleternary solubility except for MgZn2. The MgZn2 in ternaryis modeled as (Al, Zn)2Mg in order to be consistent withthe model used for its isomorphous phase in the Al-Mg-Cuand Cu-Mg-Zn systems. The model for the T phase is also


Table II. Assessed Experimental Invariant Equilibria

Reaction Class T(K)

Liquid

X(Al) X(Mg) X(Zn) Reference

L 1 T→(Al) 1 sL→(Al) 1 T 1 b

L 1 s→(Al) 1 Mg2Zn11

L→(Al) 1 (Zn) 1 Mg2Zn11

L→(Mg) 1 T 1 MgZnL 1 s→T 1 Mg2Zn3

L 1 Mg2Zn3→T 1 MgZnL 1 f→(Mg) 1 T

L 1 T→f 1 gL→f 1 g 1 (Mg)

L 1 Mg7Zn3→MgZn 1 (Mg)L→(Al) 1 T

L 1 s→TL→g 1 TL→T 1 b

II1

I1

II2

I2

I3

II3

II4

II5

II6

I4

II7

S1

S2

S3

S4

748720638616611618615616666635612762808723722

0.4240.6030.0970.0870.0400.041*0.023*0.113*0.308*0.205*0.027*0.4840.306*0.384*0.611*

0.1970.3460.0840.0730.6880.671*0.678*0.659*0.572*0.627*0.696*0.2660.354*0.526*0.341*

0.3790.0510.8190.8400.2720.288*0.299*0.228*0.130*0.168*0.277*0.2500.340*0.090*0.048*

555553534040404040404014141616

*The original value was estimated.

(a)(b)

Fig. 4—(a) Comparison of calculated liquidus curves in the Al-rich corner with the experimental data of Stiller and Hoffmeister[55] from 500 7C to 6007C. The corresponding solidus curves are also shown. (b) Comparison of calculated solidus curves in the Al-rich corner with the experimental data ofStiller and Hoffmeister[55] from 500 7C to 600 7C.

consistent with that for its isomorphous phase in the Al-Cu-Mg system. Both the s and T phases are modeled withcompositions close to their actual homogeneity ranges.These treatments are obviously only approximations, but itdoes not affect our goal in developing a thermodynamicdescription to calculate phase equilibria in the Al-rich re-gion in agreement with experimental data. In Sections Athrough C, the analytical expressions of the models used inthis study are presented.

A. Disordered Solution Phases

The following expression is used to represent the Gibbsenergy of a ternary disordered solution phase:

G 5 x 7G 1 x 7G 1 x 7G 1 RT(x ln x 1 x ln x 1 x ln x )A A B B C C A A B B C C

i i i i1 x x (Σ L (x 2 x ) ) 1 x x (Σ L (x 2 x ) )A B AB A B A C AC A C [1]i i1x x (Σ L (x 2 x ) )B C BC B C

0 1 21 x x x ( L x 1 L x 1 L x )A B C ABC A ABC B ABC C

where iLAB, iLAC, and iLBC (i 5 0, 1, 2, . . .) are the inter-action parameters in the binaries A-B, A-C, and B-C, re-spectively. The summation of the first three terms on theright-hand side of Eq. [1] represents the reference part of theGibbs energy of the phase. The next term is the ideal mixingterm, and the next three summations represent the contri-butions to the excess Gibbs energy of the phase from thethree boundary binaries using the Muggianu extrapolation.[63]

The last term represents the ternary interaction. The Redlich–


(a) (b)

(c)

Fig. 5—(a) Comparison of calculated isopleth at the section Al-MgZn2 with the experimental data of Fink and Willey.[18] (b) Comparison of calculatedisopleth at the section Al-MgZn with the experimental data of Fink and Willey.[18] (c) Comparison of calculated isopleth at the section Al-Mg2Zn with theexperimental data of Fink and Willey.[18]

Kister polynomial[64] is used to describe the excess Gibbsenergies of the constituent binaries. Values of the ternaryinteraction parameters iLABC (i 5 0, 1, 2, . . .) are obtainedby optimization using available experimental data.

B. Stoichiometric Compounds

The Gibbs energy for a ternary stoichiometric compoundApBqCr is described by the following equation:

G 5 x 7G 1 x 7G 1 x 7G 1 DG [2]A B C A A B B C C fp q r

where xA, xB, and xC are the mole fractions of componentsA, B, and C, respectively; 7GA, 7GB, and 7GC are the Gibbs

energies of the components in their standard states; and DGf

is the Gibbs energy of formation in per mole atoms of thecompound.

C. Semistoichiometric Phases

The Gibbs energy of a semistoichiometric phase (A,C)pBq, formed by mixing two binary stoichiometric com-pounds ApBq and CpBq, is

pG 5 y G 1 y G 1 RT(y ln y 1 y ln y )A A:B C C:B A C Cp 1 q [3]

i i1 y y (Σ G (y 2 y ) )A C A,C:B A C


(a) (b)

(c)(d)

Fig. 6—(a) Comparison of calculated isopleth at 4 wt pct Mg with the experimental data of Koster et al.[16] (b) Comparison of calculated isopleth at 1.69at. pct Zn with the experimental data of Kuznetsov et al.[59] (c) Comparison of calculated isopleth at 5.33 at. pct Zn with the experimental data of Kuznetsovet al.[59] (d) Comparison of calculated isopleth at Al-10 wt pct Mg with the experimental data of Watanabe.[38]

with

x xA Cy 5 and y 5A Cx 1 x x 1 xA C A C

where yA and yC are the site fractions of components A andC in sublattice 1; GA:B and GC:B are the Gibbs energies ofthe compounds ApBq and CpBq in per mole of atoms, re-spectively; and iGA,C:B (i 5 0, 1, 2, . . .) represents theparameters to be obtained by optimization for describingthe interactions between atoms A and C in sublattice 1.

IV. OPTIMIZATION OF MODEL PARAMETERS

The Al-Mg-Zn ternary was first modeled by Chen[65] 2years ago using the methodology presented by Chen and

co-workers[66,67,68] but employing the PMLFKT pro-gram[69,70] for calculating phase equilibria. However, themodels used for the s and T phases were found to be in-consistent with those for their isomorphous phases in theAl-Mg-Cu system.[1] Moreover, the optimized results couldbe improved. Accordingly, we decided to remodel the ther-modynamics of this ternary, adopting the thermodynamicdescriptions of the Al-Mg from Zuo and Chang,[2] the Al-Zn from Chen and Chang,[3] and the Mg-Zn from Agarwalet al.[4] The Al-Mg system has also been modeled by Saun-ders,[71] but the description by Zuo and Chang[2] yields re-sults in better agreement with experimental data. The sameis true for the description of the Al-Zn by Chen andChang[3] vs those of Mey and Effenberg[12] and Mey.[13]

Using Thermo-Calc,[74] the model parameters are opti-


(a)(b)

(c)(d)

Fig. 7—Comparison between calculated chemical potential of Zn in liquid state at 1073 K for the section with a ratio of Al/Mg 5 1 and experimentaldata of Lukashenco et al.[48] using Zn (,) as reference state. (b) Comparison between calculated chemical potential of Zn in liquid state at 1073 K for thesection with a ratio of Al/Mg 5 1/2 and experimental data of Lukashenco et al.[48] using Zn (,) as reference state. (c) Comparison between calculatedchemical potential of Mg in liquid state at 933 K for the section with a ratio of Al/Zn 5 1 and experimental data of Pogodayev et al.[51] using Mg (,) asreference state. (d) Comparison between calculated chemical potential of Mg in liquid state at 933 K for the section with a ratio of Al/Zn 5 1/3 andexperimental data of Pogodayev et al.[51] using Mg (,) as reference state.

mized based on the phase equilibrium and thermodynamicdata available in the literature. The lattice stability data forpure elements are from the SGTE database.[75] As stated inSection II, the experimental liquidus, solidus, and solvus inthe Al-rich corner are believed to be reliable, but values forthe published invariant equilibria especially for those nearthe Mg-Zn and Al-Mg boundaries are subjected to large un-certainty. Accordingly, more weight is given to the reliabledata in the Al-rich corner when optimizing the model param-

eters for all the phases in this system. However, as far as theinvariant equilibrium data are concerned, more weight wasgiven to the more established values near the Al-Zn side thanthe less established ones near the other two boundary binaries.The optimized model parameters are presented in Table III.Comparisons of the model-calculated phase diagrams andthermodynamic properties with experimental results are pre-sented in Figures 4 through 9. The calculated results and thediscussion of the results are given in next section.


(a) (b)

(c)

Fig. 8—(a) Calculated isothermal section at 298 K (25 7C). (b) Calculated isothermal section at 608 K (335 7C). (c) Calculated isothermal section at 673K (400 7C).

V. RESULTS AND DISCUSSION

The model-calculated liquidus and solidus curves in theAl-rich corner are compared with the experimental data ofStiller and Hoffmeister,[55] as given in Figures 4(a) and (b).As shown in Figure 4(a), the calculated liquidus curves arein reasonable agreement with the experimental data at 5007C, 525 7C, 550 7C, 575 7C, and 600 7C, respectively. Thecalculated solidus curves shown in Figure 4(a) are enlargedand presented in Figure 4(b). Agreement between the cal-culation and experimentation is again as good as that forthe liquidus curves shown in Figure 4(a). Figures 5(a)through (c) show comparisons between the calculated (Al)solvus with experimental data from Fink and Willey[18] forthree isoplethal sections: Al-MgZn2, Al-MgZn, and Al-Mg2Zn. As shown in these figures, good agreement is ob-tained. Figures 6(a) through (d) show another four

calculated isopleths: one with a constant Mg content of 4wt pct, two with constant Zn contents of 1.69 and 5.33 at.pct, and the last one for the section from Al to 10 wt pctMg. For these four isopleths, the calculated phase bound-aries are in good agreement with the available experimentaldata by Koster and Dullenkopf[16] in the first case, by Kuz-netsov et al.[59] in the second and third cases, and by Wa-tanabe[38] in the last case. Figures 7(a) and (b) showcomparisons of the calculated chemical potentials of Zn inliquid state with the experimental values of Lukashenko etal.[48] at 1073 K for two sections with ratios of Al/Mg at 1and 0.5, respectively; Figures 7(c) and (d) show compari-sons of the calculated chemical potential of Mg in liquidstate with the experimental data of Pogodayev and Lukash-enco[51] at 933 K for the sections with ratios of Al/Zn at 1and 0.333, respectively. In all of the preceding cases, there


Fig. 9—Calculated liquidus projection.

Table III. The Model Parameters for All Phases in theAl-Mg-Zn System (in J/mol)

Binary phasesbAlMg : Al0.615Mg0.385

b fcc hcpG 20.615 7G 20.385 7G 5 21451.1 2 1.907TAl:Mg Al Mg

rAlMg : Al0.56Mg0.44r fcc hcpG 2 0.56 7G 2 0.44 7G 5 2768.6 2 3.119TAl:Mg Al Mg

gAlMg : (Mg)0.4483(Al,Mg)0.1379(Al,Mg)0.4138g fcc hcpG 2 0.5517 7G 2 0.4483 7G 5 21270 2 1.75TMg:Al:Al Al Mgg fcc hcpG 2 0.1379 7G 2 0.8621 7G 5 1279.6 1 1.1606TMg:Al:Mg Al Mgg fcc hcpG 2 0.4138 7G 2 0.5862 7G 5 22441.4 1 0.219TMg:Mg:Al Al Mgg hcpG 5 7G 1 5000Mg:Mg:Mg Mg

nAlMg : Al0.525Mg0.475n fcc fccG 2 0.525 7G 2 0.475 7G 5 2837.8 2 3.163TAl:Mg Al Mg

Mg7Zn3 : Mg0.71831Zn0.28169Mg Zn hcp hcp7 3G 2 0.71831 7G 2 0.28169 7G 5 24814.11 1 1.0TMg:Zn Mg Zn

MgZn : Mg0.48Zn0.52MgZn hcp hcpG 2 0.48 7G 2 0.52 7G 5 29590.44 1 3.19681TMg:Zn Mg Zn

Mg2Zn3 : Mg0.4Zn0.6Mg2Zn hcp hcp3G 2 0.4 7G 2 0.6 7G 5 211,014.5 1 3.67151TMg:Zn Mg Zn

Mg2Zn11 : Mg0.153846Zn0.846154Mg Zn hcp hcp2 11G 2 0.153846 7G 2 0.846154 7G 5 25823.05 1Mg:Zn Mg Zn

1.94323T

Ternary phasesLIQUID: Disordered solution

0 <L 5 110,288 2 3.035TAl,Zn1 <L 5 2810 1 0.471TAl,Zn0 <L 5 211,200 1 9.578TAl,Mg0 <L 5 281,439.68 1 518.25T 2 64.7144T ln TMg,Zn1 <L 5 12627.54 1 2.93061TMg,Zn2 <L 5 21673.28Mg,Zn0 <L 5 24094.48Al,Mg,Zn1 <L 5 239,973.74Al,Mg,Zn2 <L 5 211,337.52Al,Mg,Zn

Fcc: Disordered solution0 fccL 5 16656 1 1.615TAl,Zn1 fccL 5 16793 2 4.982TAl,Zn2 fccL 5 25352 1 7.261TAl,Zn0 fccL 5 14945.7 2 1.318TAl,Mg1 fccL 5 11594.4 2 0.973TAl,Mg0 fccL 5 118,000Mg,Zn0 fccL 5 220,000Al,Mg,Zn

Hcp: Disordered solution0 hcpL 5 14063.4 2 3.243TAl,Mg1 hcpL 5 21642.1Al,Mg0 hcpL 5 114,620Al,Zn0 hcpL 5 21600.77 1 7.62441TMg,Zn1 hcpL 5 23823.03 1 8.02575TMg,Zn

f phase: Al2Mg5Zn2f < < <G 2 2 7G 2 5 7G 2 2 7G 5 2169,985.46 1Al:Mg:Zn Al Mg Zn

136.8TT phase: (Al,Zn)0.605(Mg)0.395

T < <G 2 0.605 7G 2 0.395 7G 5 210,910.836 1 8.71TAl:Mg Al MgT < <G 2 0.605 7G 2 0.395 7G 5 215,733.501 1Zn:Mg Zn Mg

12.6746T0 TL 5 225,696.19 1 25TAl,Zn:Mg1 TL 5 19153.84Al,Zn:Mg

s phase: (Al,Zn)0.66667(Mg)0.33333s < <G 2 0.66667 7G 2 0.33333 7G 5 20,133.73 1Al,Mg Al Mg

6.3946Ts < <G 2 0.66667 7G 2 0.33333 7G 5 219,389.65 1Zn,Mg Zn Mg

13.644T0 sL 5 223,927.13Al,Zn:Mg1 sL 5 19335.47Al,Zn:Mg

is good agreement between the calculated values and ex-perimental data. The agreement between calculated liqui-dus, solidus, and solvus in the Al-rich corner, isopleths, andthermodynamic values and experimental data, as shown inFigures 4 through 7, suggest that the model parameters ob-tained in the present study are reasonable.

A comparison of the calculated isotherms at 25 7C and335 7C given in Figures 8(a) and (b) with the assesseddiagrams given in Figures 2 and 3 shows agreement forequilibria involving the (Al) phase. It is understood that thecalculated phase boundaries of the T and f phases wouldbe different in view of the assumptions made in describingthe T phase to be a semistoichiometric phase and the fphase to be a line compound. Other differences betweenthe calculated and assessed equilibria are due to the as-sumptions made that none of the binary phases dissolvesthe third component in the calculation except for the s andT phases. Figure 8(c) shows a calculated isotherm at 4007C; at this temperature, an appreciable amount of liquidforms in two regions of the diagram, i.e., the Zn corner andthe valley extending from the Mg-rich eutectic of the Mg-Zn binary to ternary region.

We shall next discuss the calculated liquidus projectionshown in Figure 9 with the assessed one in Figure 1. Inaddition to these two diagrams, the calculated temperaturesand liquid compositions for all the invariant reactions, aswell as the assessed values, are summarized in Table IV.Although the general features of the calculated liquidus pro-jection are in accord with those of the assessed one, quan-titative or semiquantitative agreement is obtained only forthe invariant reaction II, and the saddle points S1 and S2.The calculated equilibrium compositions of the liquid forII1 are about the same as the assessed values, while thecalculated temperature is 7 7C lower than the assessed one.For the two saddle points S1 and S2, although the calculatedtemperatures are in accord with the assessed ones, the cal-culated compositions of the liquid differ appreciably withthe assessed values. For all the other invariant reactions,appreciable discrepancies exist. Additional experimental in-vestigations are needed before the phase diagram for this


Table IV. Calculated Temperatures and Compositions of the Liquid at the Invariant Equilibria (Compared with ExperimentalData Available in Parentheses)

Reaction Class T(K)

Liquid

X(Al) X(Mg) X(Zn)

L1T→(Al)1s

L→(Al)1T1b

L1s→(Al)1Mg2Zn11

L→(Al)1(Zn)1Mg2Zn11

L→(Mg)1T1MgZn

L1s→T1Mg2Zn3

L1Mg2Zn3→T1MgZn

L1f→(Mg)1T

L1T→f1g

L→f1g1(Mg)

L1Mg7Zn3→MgZn1(Mg)

L1b→r1TL1r→n1TL1n→g1TL→(Al)1T

L1s→T

L→g1T

L→T1b

L→T1fL→(Mg)1f

II1

I1

II2

I2

I3

II3

II4

II5

II6

I4

II7

II8

II9

II10

S1

S2

S3

S4

S5

S6

741.4(748)701.5(720)609.3(638)607.9(616)603.7(611)619.1(618)609.8(615)654.9(616)655.2(666)648.9(635)608.2(612)696.1695.9695.6765.3(762)808.5(808)695.2(723)702.2(722)671.3660.5

0.422(0.424)

0.561(0.603)

0.086(0.097)

0.083(0.087)

0.015(0.040)

0.017(0.041)*

0.016(0.023)*

0.110(0.113)*

0.251(0.308)*

0.233(0.205)*

0.008(0.027)*

0.4950.4930.4790.545

(0.484)0.210

(0.306)*0.440

(0.384)*0.545

(0.611)*0.1630.143

0.199(0.197)

0.392(0.346)

0.076(0.084)

0.073(0.073)

0.696(0.688)

0.685(0.671)*

0.691(0.678)*

0.711(0.659)*

0.657(0.572)*

0.679(0.627)*

0.699(0.696)*

0.4530.4560.4670.250

(0.266)0.385

(0.354)*0.495

(0.526)*0.400

(0.341)*0.6850.705

0.379(0.379)

0.047(0.051)

0.838(0.819)

0.844(0.840)

0.289(0.272)

0.298(0.288)*

0.293(0.299)*

0.179(0.228)*

0.092(0.130)*

0.088(0.168)*

0.293(0.277)*

0.0520.0510.0540.205

(0.250)0.405

(0.340)*0.065

(0.090)*0.055

(0.048)*0.1520.152

*Original value was estimated.

system is well established over wide ranges of compositionand temperature. However, it is of interest to note that forthe Al-rich alloys with low Mg contents, the calculatedphase equilibria involving the (Al) and liquid are in rea-sonable accord with the assessed data. Moreover, as pointedout earlier, there is good agreement between the calculatedisopleths and thermodynamic properties and experimentaldata, as shown in Figures 5 through 7. On the basis of thisevidence, we conclude that the calculated liquidus projec-tion given in Figure 9, as well as the calculated invariantreactions given in Table IV, should be used instead of theassessed data given in Figure 1 and Table II for engineeringapplications and related materials research. Until more ex-perimental data become available, they should be used withcaution.

VI. CONCLUSIONS

A thermodynamic description of the Al-Mg-Zn systemhas been developed based on the descriptions of its threeconstituent binaries and experimental phase equilibrium andthermodynamic data available in the literature. The ther-modynamic models used in this study are for disordered

solutions such as the liquid, fcc, and hcp phases; line com-pound f-Al2Mg5Zn2; and semistoichiometric phases T-(Al,Zn)49Mg32 and s-(Al,Zn)2Mg. All binary intermetallicphases are assumed to have negligible ternary solubility ex-cept for MgZn2. The model parameters are optimized basedon both experimental phase equilibrium and thermody-namic data. Several calculated isopleths and chemical po-tentials of Mg and Zn in liquid state are in good agreementwith experimental data. Moreover, the calculated liquidus,solidus, and solvus of the (Al) phase are also in accord withavailable experimental data.

However, discrepancies do exist between the calculatedinvariant equilibria and assessed values which were ob-tained based on limited experimental data. It is clear thatadditional experimental investigations are needed before wewill have definitive information on the phase equilibria forthis system over a wide range of composition and temper-ature. However, in the absence of additional experimentaldata, we believe the calculated phase equilibria in compo-sitions away from the Al corner should be used cautiouslyfor practical applications, instead of the assessed data. Thisconclusion is reached on the basis of agreement obtainedbetween the calculation and experimentation for the liqui-


dus, solidus, and solvus of the (Al) phase and thermody-namic properties of the liquid phase.

ACKNOWLEDGMENTS

The authors wish to acknowledge the National ScienceFoundation for financial support through Grant No. NSF-DMR-94-21780 and Dr. Bruce MacDonald of the MetalProgram, Materials and Processing Cluster, NSF, for hisinterest in this work. The authors would also like to thankDrs. H.L. Lukas and U. Kattner for supplying us thePMLKT software and Dr. Bo Sundman for the Thermo-Calc software to carry out the optimization and calculation,Dr. Weiming Huang for her help in using Thermo-Calc,and Doug Ingerly for carefully reading the manuscript.

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