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Thermodynamic modelling of the Cu-Mg-Zn ternary system
Pergamon
Q 1999 Published
Calphad Vol. 22, No. 4. pp. 527-544, 1998 by Elsevier Science Ltd. All rights reserved 0364-5916/99/$ - see front matter
PII:SO364-5916(99)00009-7
Thermodynamic
P. Liang,
H. J. Seifert,
Modelling of the Cu-Mg-Zn
H. L. Lukaz,
G. Ghosh’,
Ternary System.
G. Effenberg”,
and F. Aldinger
Max-Planck-Institut fiir Metallforschung und Universitat Stuttgart, Institut fur Nichtmetallische Anorganische Materialien, Pulvermetallurgisches Laboratorium, Heisenbergstr. 5, D-70569 Stuttgart, Germany * Department
of Materials Science and Engineering, The Technological Institute, Northwestern University, Evanston, II. 60208, USA
** MS1 (Materials Science International
Services GmbH), Nobelstr.
16, D-70569 Stuttgart,
Germany
Abstract The quasibinary
MgCuz-MgZnz system was optimized with the program BINGSS. All phase diagram data and thermodynamic values available in the literature were critically assessed before the optimization. Experimental investigations by EDX of ternary Cu-Mg-Zn alloys were specifically performed to provide missing data of the Cu solubilities of the Mg-Zn phases. The Laves-phases Cl5 (MgCuz), Cl4 (MgZnz) and C36 (r,Mg&uZns) existing in the Cu-Mg, Mg-Zn and Cu-Mg-Zn systems were described by the “Compound-Energy-Formalism” with Cu-Zn exchange, Mg(Cui_,Zn,) and a weak tendency for antistructure atom formation (Cu and Zn on the Mg sublattices, Mg on the Cu-Zn sublattices). The binary intermetallic phases MgZn, MgzZns and MgzZnir are modelled to have Cu-Zn exchange on one sublattice. The Bragg-Williams description of ordering was extended to describe the ternary range of the pCuZn phase. Estimates were made, where experimental data are not sufficient. Using the binary subsystems from the literature with small updates the Cu-Mg-Zn ternary system was calculated. In general, good agreement is obtained between calculations and experiments.
1
Introduction
The Al-Cu-Mg-Zn quaternary system is one of the key systems for designing of high strength Al alloys. Despite its technical importance this system still contains a large amount of unknown regions. Many of the published diagrams are contradictory and incorrect. In this work the Cu-Mg-Zn system was thermody namically assessed with the aim to provide a constitutional, thermodynamic database for the quaternary Al-Cu-Mg-Zn system within the COST 507 project on light metal alloys.
?%&al
version received on 29 June 1998, F&vised version on 5 January 1999 527
P.LIANG et al.
528 2 2.1
Experimental
The experimental 507 action.
Literature
Review
Information
literature
of the Cu-Mg-Zn system was critically reviewed by [94Gho] within the COST
Experimental data of this system concern mainly the quasibinary MgCuz-MgZnz section. The first phase diagram of this section was published by K&ter and Miiller [4SKoe] using metallography and thermal analysis. [52Lie] used metallography, thermal analysis and X-ray diffraction analysis in the determination of the quasibinary diagram. In this section three different Laves phases, MgCuz, MgZnz and a ternary Laves phase of the MgNiz-type (Mg&uZns) are stable [52Lie]. MgC u2 has a large solubility range and dissolves more than 60 mol% MgZnz, while MgZn2 dissolves only about 1 mol% MgCuz. The ternary MgNiz-type Laves phase is stable from approximately 73 tb 87 mol% MgZnz [52Lie]. [4SKoe] mentioned two further ternary phases on the MgCuz-MgZnz section, but without specifying their homogeneity ranges. The enthalpies of mixing of MgCu*-MgZna alloys were determined by solution calorimetry [64Kin, 72Pre, 79PreJ. [4SKoe] also determined an isopleth from r-CusZns to Mg and presented a reaction scheme and a liquidus projection. The solubility of Mg in the a-, /3- and r-Cu-Zn phases was stated to be “very small” [4SKoe]. Using thermal analysis and metallography [SOMik] investigated the isopleths: from Cu to MgZn, from Mg to CuZn, from Zn to MgCu, from Mg&u to CuZnz, from Cu to MgZnz and for constant contents of 10,20, 30, 50, 60, 70 and 90 at.% Mg and determined the whole liquidus surface. [56Gla] investigated a partial isothermal section at 673 K by metallography and X-ray analysis. The homogeneity range of the Zn-rich MgCuz solid solution was reported to be between 30 and 40 at.% Mg [56Gla], whereas [4SKoe] estimated the width of this range to be about 1 at.%. [SOWat] determined isopleths for constant contents of 5 wt.% Cu and 3 wt.% Mg in the Zn-rich region. [72Yam] investigated the vertical sections for 1.7,6 and 15 wt.% Cu as well aa for 2 and 5 wt.% Mg in the &-rich region. No experimental information is available in literature for the ternary solubilities of the binary intermetallic phases MgzCu, Mg,Zns, MgZn, MgzZns and MgzZnll. 2.2
Thermodynamic
Assessment
in Literature
A thermodynamic assessment of the Cu-Mg-Zn system was reported by Liang et al. [97Lia]. However, in this assessment the ternary phases were simplified, the C36(MgN&type) Laves phase was treated as a stoichiometric phase Cw.sMgZnr.,. The two Laves phases MgCuz and MgZnz were treated as semistoichiometric phase (Cu,Zn)lMg. The solubilities of Mg in the Cu-Zn binary phases /?, 7, c and the Cu solubilities in the Mg-Zn binary phases MgpZns, MgZn, MgzZQ and Mg,Znll were neglected.
3
Experimental
Investigations
The Cu solubilities of the Mg-‘Zn phases MgZn, MgzZns and Mg,Znll were determined Microscopy (SEM) and Energy Dispersive X-ray spectroscopy (EDX).
by Scanning Electron
Ternary alloys were prepared from high purity Mg (99.97%), Cu (99.999%) and Zn (-99.9%) in a pure, nuclear quality graphite crucible placed inside a water-cooled copper crucible and induction heated under helium atmosphere. Melting was repeated twice to ensure homogeneity of the ingot. A third inductive melting in a water cooled copper crucible was finally performed (in quasi-levitation) prior to cast the alloy in a cylindrical cooled copper crucible. Pieces from the cast alloys were sealed under argon in nuclear quality graphite crucibles, annealed at 335°C for 20 days and finally cooled to room temperature in about 10 minutes. Phase compositions were determined by EDX. The experimental results show, that the solubilities of Cu in the MgZn, Mg,Zn3 and Mg,Znll phases are at least 2, 3 and 6 at.%, respectively.
THERMODYNAMIC 4
MODELLING
529
Thermodynamic Assessment
The Gibbs energy descriptions of the pure elements were taken from Dinsdale (SlDin], except Znhcp-A3, which is dhtinguished from ZnhcrVz” a.ccording to [93Kow]. 4.1
The Binary
Systems
The descriptions of the binary systems were taken from the literature, Cu-Mg [SlCou], Cu-Zn [93Kow] and Mg-Zn [98Lial] updated from (92Aga]. The description of the Cu-Mg system needed to be updated, before it could be combined to a thermodynamic description of the ternary Cu-Mg-Zn system. For c-CuZn the descript#ion was changed to fit to the lattice stability Cu hcp-A3 of [SlDin] and approximating as near as possible *:he G’-function of [93Kow]. 4.2
The Cu-Mg
System
In the Cu-Mg description of Coughanowr et al. [SlCou] the parameters of the end members Gzzi and G,$Fz of the compound energy description of the Laves phase MgCus were adjusted. As these parameters, however, are formally unary parameters, they have to be the same in all Laves phases containing Mg or Cu, respectively. The adjustment of the Gisb$;ygy description to the experimental solubility limits can be ” done by the parameters “L&$&,r and LW,oU:oUinstead. The values of the G&T$ and G%:pz parameters are more or less arbitrary as in the stability range the Gibbs energy of the MgCus-phase essentially depends only. For the lattice stabilities of any pure on the sums G&$$ + “g$&s and Grd + oL~$& element X in the fictitious state of the Laves structure, the proposed value [93Cos, 94Coe, 95Ans, 96Dup] was accepted in this work: G?“(T)
-
3@xER(Z’) = 15006 J/mol.
Rerunning the least squares program BINGSS with the set of experimental data used by [SlCou] yielded the parameters listed in Table 2. These parameters virtually give the same phase diagram as those reported by [SlCou] with a maximal deviation of 0.02 mol% in the solubility limits of MgCus.
<5 Optimization of the quasibinary system MgCua-MgZns The descriptions of the quasibinary MgCus-MgZns system, was optimized first with the BINGSS program [77Luk, 92Luk]. This program requires that the quasibinary system is described by Mg$(Cu-Zn). Here the three Laves phases were described bs the simplified sublattice formula Mg(Cur_,Zn,)s using as qua&nary parameters only the parameters Y&,~~~-%‘r$-2%~~ and +$$~~-%‘$-2Y$’ respectively, coming from the binary Mg-Cu and Mg-Zn descriptions. The parameters describing the Gibbs energy of the met&able quashmary compounds relative to the stable pure elements, “Glaze - Y$ - 2%$:, ‘Y$~~
- %‘ic-
2%‘&:, %$zoU - ‘Y$T - 2Y$c and cizzzn
- ‘%‘$ - 2”Gkz as well as the Redlich-Kister
parameters ‘1~g:cu,zn> so”* lL$%,~n, oL:;ou.~n and oL$%:,~n were adjusted to the available experimental data. These eight parameters were adjusted as temperature independent single coefficients. The Gibbs energy of the liquid phase was taken as the Muggianu extrapolation [75Mug] from the binary descriptions, which was transformed to a Redlich-Kister polynomial between the two species MgCus/2 and MgZns/2. It was not changed in the optimization. The experimental values in literature for the quasibinary MgCuz-MgZnz system are phase diagram data by [48Koe, 50Mik, 52Lie] and enthalpies of mixing of the quasibinary Laves phases [64Kin, 72Pre, 79Prej. In the central part of the quasibinary phase diagram, the data of [48Koe] and [52Lie] are contradictory. The liquidus temperatures by [SOMik] and [52Lie ] are 20 K and 50 K lower than those reported by [48Koe], respectively. The liquidus data in several isopleths of [ZOMik], extrapolated to the binary subsystems: contradict the binary Cu-Mg and Mg-Zn systems by values up to 40 K. The Gauss-method requires statistically random distribution of the errors. Non-random distribution of errors as in the above mentioned contradictions indicate systematic errors in at least one of contradictory
P.LIANG et al.
530
1000
MgCuz X 0 ‘z 800 3 s G
C36
3
used l [48Koe]
3 600-
/
A [52Lie] not used v [50Mik] A [52Lie]
400
MgZd I 0.4 mole fraction
I 0.2
0 MgCua Fig.
I 0.6
;
018
MgZnz
MgZm
1 The calculated MgCuz-MgZn2 quasibinary
.
-
phase diagram
MgZm/
298.15K
-2
used
+ [64Kin] m [79Pre]
-l( )-
not used 88
-1: ,_ 0
0.2
M&u2 Fig.
0.4 mole fraction
.
a 0.6 MgZnz
2 Enthalpy of mixing in the quasibinary
[72Pre]
0.8
MgCuz-MgZnz system
MgZn2
THERMODYNAMIC pairs of data sets. contradictory
MODELLING
531
In such a case the more reliable data set must be selected for the optimization
one necessarily
and the
has to be discarded.
The liquidus data of [52Lie] for the MgCur phase do not show a clear single maximum, which is expected after phase diagram rules, therefore the data of [48Koe] were preferred. The Cu rich data of [52Lie] as well as the data of [SOMik] were not used for the optimization. The enthalpies of formation of Mg(Cui_,Zn,)s reported by [72Pre] are considered to be less reliable than those reported in a later investigation of the same laboratory [79Pre] by the same authors. Therefore the old values [72Pre] were not used in the optimization. The quasibinary
parameters
derived from the optimization Table
Parameters
of the MgCus-MgZns The entities
quasibinary
are given in Table 1.
1:
system.
The values are given in SI units:
of moles are the “quasi-unary
species”:
fMgCur
Parameter
Phase
J, K and mol.
and $MgZnz Value 5000.0
MgCuz
-39412.31 12764.53 GMp2 _ Mg.Cu
MgZn2
15000.0
GMMg.Cu
-37652.74
oLLgT:,Z"
10000.0
C36-type
1000.0 -45113.13
The calculated quasibinary MgCus-MgZna phase diagram is represented in Fig. 1 and compared with all experimental values. The quasibinary enthalpy of mixing of the Laves phases, compared with the measured values is represented in Fig. 2.
6 6.1
Evaluation of the ternary parameters
The Laves phases
In addition to the parameters of antistructure The homogeneity
obtained from the quasibinary
atoms have to be considered
system, all possible combinations
in the ternary Gibbs energy descriptions
of formation
of the Laves phases.
ranges with respect to excess or deficient Mg of the three Laves phases were interpolated
between the binary end members.
Since no reliable experimental
data for the range of deviation
from the
stoichiometri’c MgXs are available in the ternary, a better determination of these parameters is not possible. This interpolation implies: for the three Laves phases the same values were taken for the parameters VLQ’ Here @ stands for the three Laves phases and the asterisk “L’p ~~,a,:. and “L:zn,~g. M.&u:*9 l:Cu.Mg? “LO (*) stands for all possible occupations
of the corresponding
sublattice.
Only those interaction
parameters
are significant, where the other sublattice is occupied by the major constituent. There it is natural, to assume the interaction parameters to be independent on the occupation of the sublattice different from the interacting one, leading to identical by the asterisk. As the atomic parameters
parameter
values for different occupation
of the sites designated
sizes of Cu and Zn are not very different, values of 15000 J/mol were chosen for the in analogy to the pure elements. - “Gi’$ - 2%::
%!&Zn - “Ggi - 2”G~~pand oG&,
532 6.2
P.LIANG et al. Mg-Zn
binary
intermetallic
phases
The experimental results (SEM and EDX) of th is work show that the Mg-Zn binary phases MgZn, MgsZns and MgsZnrr exhibit ternary solubilitics up to several at.%. As Cu-Zn substitution seems more likely than Cu-Mg substitution, these binary phases with ternary solubilities were modelled as follows: MgsZnrr: Mgz(Zn,Cu)sZns MgsZns: Mgs(Zn,Cu)s MgZn: Mgr@n,Cu)rs The major constituents are denoted in boldface. The MgsZnrr phase was modelled with three sublattices to be compatible with a model used for the quaternary solid solutions between MgsZnrr and MgsCusAls [98Lia2]. MgrZns was treated as stoichiometric phase, as there are no experimental data on its Cusolubility. This phase is stable between 614 and 598 K only, therefore a significant Cu solubility can not be expected even if the thermodynamic behavior is similar to that of the other phases. In a first attempt the Gibbs energies of the fictitious end members with Cu on the second sublattice were used as adjustable parameters to describe Cu solubilities in the MgZn, MgsZns and MgsZnrr phases. But then these end members appeared to be nearly stable in the Mg-Cu system. Therefore in a second attempt the parameters Y&c” My’_ and c$;” were set zero and the parameters oL$$z, and oL$?&z. were used to describe the Cu solubilities. good fit also in the quatemary 6.3
The liquid
For MgsZnrr both parameters, ‘G$tti, Al-Cu-Mg-Zn system [98Lia2].
and oL&$~,‘~,:z, were used to get
phase
The liquid phase was described as a substitutional solid solution with the Fledlich-Kister Muggianu formalism, which can be expressed by the formula (Cu,Mg,Zn)r. No ternary parameters were introduced. 6.4
The (Cu)
and (Zn) phases
The parameters describing the ;$~&$ies estimated by adopting “L$,zn describing metastable accepted. 6.5
~~~-~d_ ~~~~~~~~~ unary phases, “Gcu
The value of oG~p-A3 - OGz-z”
The 7-CusZns
of Mg in the binyi=&Zn cub
‘_
solid solutions, (Cu) and (Zn), were equal 22500-3.T. For the parameters OG”P-A’
Dinsdale’s
[91Din]
values
were
was adopted fror!s[93Ko$.
phase
The solubility of Mg in the binary 7-CusZr~ phase was described by a four sublattice model derived s used by [93Kow], assuming Mg to dissolve only in the from the description (Cu,Zn)s(Zn,Cu)sC&(Zn,Mg) fourth sublattice. The corresponding parameters were estimated to reproduce a small solubility of Mg in 7-CusZns. 6.6
The bee phase
(/?, /Y, 6)
In the Cu-Zn binary system a order-disorder transition of the bee phase p (A2) to p’ (B2) occurs in the temperatue range from 740 to 730 K. The p’ phase is an ordered modification of the /3 phase with the C.&l structure. A two sublattice model (Cu,Zn)r(C u ,Zn ) r with Bragg-Williams treatment was used to describe this order-disorder transformation [93Kow]. The Gibbs energy for the ordered bee phase (bee-ord) can be expressed in terms of the Bedlich-Kister parameters of the disordered bee phase (bee-dis) and an ordering contribution [88Ans]. In the disordered state, the site fractions of the same element on the two sublattices are identical (yb, = &,; yi, = &,) and the Gibbs energy description must be equivalent to that of the disordered substitutional solution (Cu,Zn)s (bee-dis). Ansara et al. [88Ans] derived constraints’between the parameters for the ordered phase, which were reformulated by Saunders [SSSau] and used by Kowalski and Spencer [93Kow] for the /3Cu-Zn phase. In the present work the BraggWilliams description of ordering was extended to the ternary range. The solubility of Mg in the bee phase was described with the model (Cu,Mg,Zn)r(Cu,Mg,Zn)r. The constraints between the parameters describing the solubility of Mg in both sublattices were derived by extending the
THERMODYNAMIC ideas of [88Ans] and [89Sau] into the ternary Cu-Mg-Zn
MODELLING system:
“c:&~d G&g
c;g oez”Mg bee-ord
OLCu,Zn:Cu bee-ord
OLCu,Zn:Zn bee-ord
‘L Cu,Zn:Cu ‘L,&:g lxx-ard %“.Zr&”
.
The correlation between the parameter Ac”,z,, and the parameter called P by [93Kow] is Ac”,z,=-2P.
Using
the above constraints Gbccord becomes equal to Gbccdis, whenever y: = yy. The parameters
0
bee-dis
1
bee-dis
2
bee-dis
Lc”,z, , L Cu,Zn 9 L Cu.~n
were taken from [93Kow]:
=
-51595.87
%$t=
=
7562.13 - 6.45432 T
=
30743.74 - 29.91503 T
=
-6170
Ac”.zn OLM,,z” bcc-dia
Acu,zn
,OLPZli u. 2Lbc”c;gi
OLb%i~ and
and
were estimated
to reproduce
+
13.06392 T
a small solubility
of Mg in PCuZn.
The ordering
parameters Aou,Ms and Aug,z, were set zero: OLbcc-dis C”.Mg
=
q,bcc-dis
-6500.0
=
-6500.0
ACU,M~
=
0
Aig,zn
=
0
Mg.,Zn
The values oit the parameters derived in the present work are collected in Table 2.
7
Ternary Calculation
Using the optimized quasibinary parameters and the estimated ternary parameters, as given above, together with the parameters of the binary subsystems, the ternary Cu-Mg-Zn system was calculated. The
P.LIANG
534 calculated
et al.
liquidus surface is represented in Fig. 3. The calculated isothermal sections at 608, 800 and
1100 K are shown in Figs. 4 to 6. Fig. 7 shows the calculated isopleth from -y-CusZns to Mg. It agrees very well with the experimental of (48Koe].
Figs. 8 to 14 represent the calculated
contents of 10, 20, 30, 50, 60 or 90 at.‘% Mg compared of the data of [SOMik] could be reproduced parameters from the literature.
data
vertical sections from MgZnz to Cu and at constant with the experimental
with the optimized
A further adjustment
quasibinary
values of [50Mik].
parameters
Most
and the binary
of the parameters to the data of [BOMik] does not
appear to be justified, because of the misfit between the extrapolated
experimental
liquidus data into the
binary boundary systems and the generally accepted liquidus data for these binaries (compare Figs. 9, 10 and 11).
8
Conclusion
The quasibinary system MgCus-MgZns could be optimized by the program BINGSS, using experimental data from the literature. The three Laves-phases MgCus, MgZnz and “MgzCuZns” (C36-type) on the MgCus-MgZns section are described by the “compound-energy-formalism” with Cu-Zn exchange, Mg(Cur-,Zn,) and slight antistructure atom formation (Cu and Zn on the Mg sublattices, Mg on the Cu-Zn sublattices).
The binary intermetallic
Cu solubilities according to experimental
phases MgZn, MgzZnz and MgsZnrr are modelled to have
results by EDX. The Bragg-Williams
treatment of ordering was
extended into the ternary system to describe the solubility of Mg in the PCuZn phase. bility data in the Cu-Zn intermediate
phases are available, the corresponding
As no Mg solu-
parameters were estimated
to reproduce Mg solubilities interpolating between the binary fcc(Cu,Mg) and hcp(Zn,Mg) solubilities. The resulting parameters allow all experimental phase diagram and thermodynamic data to be reproduced within narrow limits. Thus a reliable basis for evaluation into higher order systems containing the Cu-Mg-Zn system as a boundary, for example the quaternary Al-Cu-Mg-Zn system, has been established. Acknowledgement Financial support by the German UBundesministerium nologie”
(Contract
fiir Bildung, Wissenschaft,
03K7208 0) within the framework of the European Community
is gratefully acknowledged.
Forschung und TechProject
COST
507
The authors would also like to thank P. Ochin (CNRS, Vitry, France) for for a preparation of the alloys. One of the authors (GG) would like to thank the Max-Planck-Gesellschaft visiting fellowship.
THERMODYNAMIC
535
MODELLING
Zn
in OC
WI
0
0.2
0.1
0.3
0.4
0.5
0.7
0.6
0.8
0.9
1 .O
mole fraction Cu Fig. 3
cu
Liquidus surface of the Cu-Mg-Zn ternary system
Zn
0 Mg
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
mole fraction Cu Fig. 4 The Cu-Mg-Zn system isothermal section at 608 K
1.0 cu
P.LIANG et al.
536
of
Mg”
0’
0.1
,‘Y, 0.2
7.1:
A
0.3
Ci.k
0.4
\\w+
0.6
I\
A
A
0.7
0.8
0.9
\l/ 1.0
mole fraction Cu
cu
Fig. 5 The Cu-Mg-Zn system isothermal section at 800 K
Zn 1.0
A 0.9
0.8
0.7
- ,. Mg”
6.;
d.i
6.3
Ci.4
d.k
0.6
0.i
6.8
0.9
mole fraction Cu Fig. 6 The Cu-Mg-Zn system isothermal section at 1100 K
1.0 cu
THERMODYNAMIC I
1200
t
I
I
MODELLING I
I
I
537 I •1
I
[48Koe]
ilOOIOOO:f
900-
600
Cu,Zn,
mole fraction Zn
Mg
Fig. 7 lsopleth from Cu,Zn, to Mg
1200 y
1100
-s 1000 L $ 900 ?I !$ 800 B
700 600
400 0 M@n,
0.1
0.2
0.3
0.4
0.5
0.6
mole fraction Cu
Fig. 8 Isopieth from MgZn, to Cu
0.7
0.6
0.9
1.0 cu
P.l_\ANG
538
et al.
1300 1200 1100 y .r
1000
Lj
900
5 ‘s
800
E B
700
(Cu)+MgCu,
600 500
0:l
012
0.3
0.4
0.5
0.6
0.7
0.8
0.9
mole fraction Zn Fig. 9 lsopleth of the Cu-Mg-Zn
system at 10 at.% Mg
1200
s 800 g ES
700 600 500 400
I
0
0:1
0.2
/
1, 0.3
\\ 0.4
II, w II 5 1 0.5
0.6
0.7
0.8
mole fraction Zn Fig. 10 lsopleth of the Cu-Mg-Zn
system at 20 at.% Mg
THERMODYNAMIC
MODELLING
539
A [50Mik]
800 -
(Cu)+MgCu,
+MgZn,
700 600 -
011
012
013
014
0:5
0:s
0:7
mole fraction Zn Fig. 11 lsopleth of the Cu-Mg-Zn system at 30 at.% Mg
I
1200
I
I
I a [SOMik]
liquid
IlOO-
1000 900 800 700 600 500 400
0
0.1
0.2
0.3
0.4
0.5
mole fraction Zn Fig. 12 lsopleth of the Cu-Mg-Zn system at 50 at.% Mg
P.LIANG
540
I
0
0.05
0.10
0.15
et a/.
I
I
0.20
0.25
03
mole fraction Zn Fig. 13 lsopleth of the Cu-Mg-Zn
Y c ._
system at 60 at.% Mg
800
f 3 &
700
BE
600
400
(Mg)+Mg,Cu+MgCu,
0
0.02
0.04
0.06
0.08
0.10
mole fraction Zn Fig. 14 lsopleth of the Cu-Mg-Zn
system at 90 at.% Mg
THERMODYNAMIC
-
MODELLING
541
Table 2: Parameter set for the Cu-Mg-Zn system. Parameters are given as a + bT + cT In(T) t dT2 + e/T $ fT3 in J mol-‘. (per moles of formula units) Parameter
b
a
c
103d
-95
40.00
Liquid;
Redlich-Kister-Muggianu
oLli,a Cu.Ms
-36962.71
ILh CbM3 0Lh Cu,Zn ILh C'1.Z"
4.74394
-8182.19 -40695.54
12.65269
4402.72
-6.55425
7818.10
2LkCIl,Z”
-3.25416
0Lh M&& ILlicl MgZn
-77729.24
680.52266
3674.72
0.57139
zLlic1 - th,Zn
-1588.15 fcoA1
(Cu);
OL’“’ Cu,Mg OLfC’ CL1.Z” ILfCC Cu,,Zn 2Lf_ Cu,Zn
Redlich-Kister-Muggianu -22059.61 -42803.75 2936.39 9034.20
5.63232 10.02258 -3.05323 -5.39314
-3056.82 -3127.26
5.63801 5.65563
OLfCC W:,Zn ILfCC W:,Zn
hcp-Zn, .+w-Zn CU vhcr>-Zn Mt:
(Zn);
Redlich-Kister-Muggianu
_ CQCC CU
600.00
_
100.00
Ghcp-A3 Mg
0.20000
22500.00
-3.00000
ophg
-14432.17
-10.78140
oLh&Zn Mg.Zn
-3056.82
5.63801
ILhcF’-Zn Mg,Zn
-3127.26
5.65563
oLhcp-Zn Cu ,Mg
hcp-A3, c@w-As CU
_ ocj~c CU
oGhcp-A3 Zll
_
((Mg), e-phase);
Redlich-Kister-Muggianu 600.00
0.20000
2969.82
-1.56968
oLhcp-A3 Cu,Mg
22500.00
-3.00000
OLk”P--;
-36475.00
4.89600
24790.00
-10.13500
oLhcp-A3 Mg.,Zn
-3056.82
5.63801
ILhcp-A3 Mg.Zn
-3127.26
5.65563
%hcp-Zn Ztl
ILhc;-A3 CU,Ztl
CuMgz; .@UfkZ
Cu.Mg-“G;&
stoichiometric:
_ 2c$-A3
CuMg2
-28620.00
1.86500
P.LIANG et al.
542
Table 2:
a
Parameter bee
(P,P',a); (Cu,Mg,Zn)l(Cu,Mg,Zn)l
- "Gg; - "G!~FC = "cbc:r YFC. C".Z" Zn.Cu- "Gi: - "GE: c@cy _ "G& _ @= = @by - "G& - "Gp; CUM3
Mg.Cu
Mg
_q; "Gbc". Mg.Zn
- "~2; = @y Zn.Mg
-
bee “Gz.
oG&
-31967.92
6.53196
-3250.00 -3250.00 -2427.44 17262.40
oLk:zn:C" = oC&",Z" lGzz":C"= 'G%IIZn OLbc; Cu.Zn:Mg = 1Lbcc Cu,Zn:Mg =
b
-9.52692 -16.57110
0Lb.x ’ Mg:Cu.Zn
-19627.94
6.53196
‘L&:c”,Zn
-1.61358
oL~z":Zn= o&%"zn
1890.53 -13770.63
1Lbcc Cu,Zn:Zn =
-13481.34
13.34394
3842.97 -92231.22 -19214.84
-3.73938 89.74512
-7685.94
7.47876 -5.60907
SE;&):*
1Lbcc ’ Zn:Cu,Zn
= S$;,
Z”
OLbc; Cu.Zn:Cu.Zn
OLbcC
=
oLi$f,Zn:Cu,Zn = OLbcc Mg.Zn:Cu,Mg
oL!$Zn:Cu,Mg
Cu.MgMg.Zn
Cu,Zn:Mg,Zn
=
OLb” Cu.Mg,Zn:Cu
=
oLk&g,Zn:Zn
oLk%u,Mg,Z”
OLbcC
OLbcs Cu:Cu,Mg = OLbcc Mg:Mg,Zn = OLbcc Cu,Mg:Zn = ILbCC
Cu,Mg:Zn =
OLbcC
Mg.Zn:Cu = 1Lbcc Mg.Zn:Cu =
=
oL&4g:Cu
=
oL~:C.,hIg
=
oL&Zn:Mg
=
OL%Mg,Z.
=
=
=
OL%Mg:Cu,Zn
oL&Mg,Zn
oLEMg:Mg
-3250.00 -4969.04 -1921.48
oL%i4g.Zn
-1187.98
1.86969 -3.48327
1921.48
-1.86969
-118719.84
-42.349
+kZns;
OGZn:Cu:Cu:Zn
_
7 e
CU
_
6 chcp-Zn ZlI hcp-Zn
5 "GE - 8 "Gz.
-
-
%n:Cu:Cu:Mg
-
wCu:Zn:Cu:Mg
-
OGZZn:Zn:Cu:Mg -
7Y$& - 6V$-A3 5 "@. _ 6 “Go-43 3 @i,
_
(j Ghcp-A3
QGM&fWl
_
2 q$;-A3
_
MgzZns Mg.Zn
Mg.Cu
-21.817
-75604.96
-47.923
-64720.63
-51.349
9857.77
-77.454
-96185.23
-30.817
-42185.23
-56.105
-73818.32
18.455
-108000.00
Mgz(Zn,W
@MBfZ"" _ 2 o@v-A3 _ 3 o&r-Z”
Mg:Cu,Zn
-68.455
-150185.23
-135000.00
Mg:Cu,Zn:Zn
)LMgzZns
Zn
6 "c'6:-5 "Gz-Z"
~LMGul
_
2 ,;~-zn 4 c@p-Zn
-44139.58
Mg@n,Cu)&e
_ 2 c@w-A3 _ 11 @z;~-Zn
~MgyZw
_
2 ,z-zn
MS
@gf”.n
Mg.Cu:Zn
_
5y$g _ 6 yy$-A3_
MgzZnll; Mg.Zn.Zn
-0.25611
(Cu,Zn)2(Cu,Zn)*Cu3(Mg,Zn)G
OCCu:zn:cu:zn - 5 "dc"u - 8 %:-'" Y&:Zn:Cu:Zn - 3 Yg - 10 "cz-z" ‘+%u:Cu:Cu:Mg
18.69690
oLi%“,Mg 1Lbcc Zn:Cu.Mg
oLk;,Zn:Zn
%Mg,Z”
yy Cu.Cu.Cu.Zn
5764.45 -3250.00
0.15456
2 4-A3
_
3 "G;;
-54406.20 0.00 -100000.00
13.602
-
THERMODYNAMIC
MODELLING
543
mble 2: continued Parameter
a stoichiometric:
Mg7Zns; “G$T;z
- 5x$-*3
- 2o”Gz+
MgZn; - 12”G$-*3
- 13”Gy”
GzF;” s
- 12YF-*3 Ms
- 13”G’d
oLMsZn Mg:Cu.Zn
- 3%$ER
losf
-335741.5
35.50000
-236980.8
59.24524
0.0
(Cu,Mg,Zn)(Cu,Mg,Zn)2
15000.00
-“G:~-z”
15000.00
- 2@;;
15000.00
OLQ du,Mg
13011.35
OLQ Cu.Mg:.
6599.45
OL@ .:Mg.Zn OLQ Mg,Zn:*
35000.00 8000.00
y-$3p: Mg.Cu _ HSER Mg _ 2HzfR
-34690.99
YFs Mg:ZlI_oG$*s
-33355.45
%ysy Cu.Mg -“($U
_ 2~~-z” -
Zn,Mg_oG!z-Z” YF36
2@$+43
_ 2%;;
OE”,Z”
364.73085
-69.276417
-0.51925
143502
-5.65953
-69.276417
-0.51925
143502
-5.65953
-69.276417
-0.51925
143502
-5.65953
8.83886
84970.96
-16.46448
63355.45
-8.83886
-90226.26
oGz;!-6&
rSER- 2HF -0 (;$-A3
_ 2”~;:-Zn
cu:hQ - “@c.C” - 2?$;-*3 @WW y$&M~~ n: g _o@~P-Z~
_ 2~;7-*3
oE% . ,
-54690.99
364.73085
-25355.45
8.83886
104970.96
-16.46448
55355.45
- 8.83886
-78824.62
lL%Z”
25529.06
‘=@? Mg.Cu - H&iR - 2H;zR
-24690.99
c+szn, _ 2~~-Zn Mg.Zn _+:-A3 Cu.Mg_ 0G&c c” - 2”Gz-*3 c#s,Znz
-35355.45
q-+&
e
Mg51Znzo
(MgCuz, MgZns, C36);
%EuTZn-“GY$; - 2oG!y”
.@$z
103d
-500000.0
Laves phases,
Y$,,
c
Mg,z(Zn,Cu)ts
“G$Z”
“c&
b
_o~~~PP-Z~
_ 21++;-*3
OLM&? *:Cu,Zn
364.73085 8.83886
74970.96
-16.46448
65355.45
- 8.83886
-75305.48
Here Cpstands for the three Laves phases and the asterisk (*) stands for ail possible occupations of one of the elements Cu, Mg and Zn on the corresponding sublattice. X denotes either Cu, Mg or Zn, but the same element in the whole formula. HZ.,ERand HcfR stand for H,$i and H&~-A3 at 298.15 K, the enthalpies of the pure elements at standard temperature,
whereas Y$G, %‘$-A3,
at the same temperature
9=~Tp-z” and exER denote the Gibbs energies of the pure elements
as the corresponding
%$...
P.LIANG et al.
544
References [48Koe]
W. Koster and F. Miiller, 2. Metallkd., 39, (1948) 352-359.
[50Mik]
V. I. Mikheeva and 0. N. Kryukova, Izv. Sekt. I%.-I&n. 76-93.
[52Lie]
K. H. Liester and H. Witte, Z. Metallkd., 43, (1952) 396-401.
[SSGla]
E. I. Gladyshevsky
and E. E. Cherkashin,
Anal., Aliad. iVauk. SSSR.,
20, (1950)
Zh. Neorg. I
J. Japan Inst. Met., 24, (1960) 672-676.
[SOWat] H. Watanabe, [64Kin]
R. C. King and 0. J. Kleppa, Acta Metall., 12, (1964) 87-97.
[72Pre]
B. Predel and H. Ruge, Mater. Sci. Eng., 9, (1972) 141-151.
[72Yam] M. Yamada and I<. Matuki, J. Japan Inst. Met., 36, (1972) 278-285.
VMugl Y.-M.
M. Gambino, and J.-P. Bros, J. Chirn. phys., 72, (19T5) 83-88.
Mug&m,
Calphad, 1, (1977) 225-236.
[77Luk]
H. L. Lukas, E.-Th. Henig, B. Zimmermann,
[79Pre]
B. Predel, H. Bencker, W. Vogelbein and M. Elmer, J. Solid State Chem., 28, (1979) 245-257.
[88Ans]
I. Ansara, B. Sundman and P. Willemin, Acta Metall., 36, (1988) 977-952.
[89Sau]
N. Saunders,
[SlCou]
C.A. Coughanowr, 574-582.
[SlDin]
A. T. Dinsdale,
WAgal R.
2. Metallkd., 80, (1989) 894-903. I. Ansara, R. Luoma, M. Hamilainen
and H.L. Lukas, Z. Metallkd., 82, (1991)
Calphad, 15, (1991) 317-425.
Agarwal, S. G. Fries, H.L. Lukas, G. Petzow, F. Sommer, T.G. Chart and G. Effenberg, 83, (1992) 216-223.
Z.
Metallkd.,
[92Luk]
H. L. L&as, S. G.-Fries, J. Phase Equilibria, 13, (199%) 532-541.
[93Cos]
J. G. Costa Neto, S. G.-Fries, H. L. Lukas, Calphad, 17,(1993), 219-228.
[93Kow] M. KowaIski and P.J. Spencer, J. Phase Equilibria, 14, (1993) 432-438. G. C. Coelho,
[94Coe]
S. G.-Fries, H. L. L&as, P. Majewski, J. M. Zelaya Bejarano, S. Gama, C. A. Ribeiro and G. Effenberg in: Klaus Schulze Symposium on Processing and Applications of High Purity Refractory Metals and Alloys, P. Kumar, H. A. Jehn and M. Uz eds., The Minerals, Metals and Materials Society, Warrendale, Pa. 15086. USA, 1994.
[94Gho]
G. Ghosh, H. L. Lukas and G. Effenberg, report to COST 507, Coordination
[95Ans]
I. Ansara, (ed.) COST 507, Thermochemical database for light metal alloys, Action on Materials Sciences, European Commission, DG XII, Science Research and Development, L-2920 Luxembourg, 1995.
P6Dupl
N. Dupin and I. Ansara, Z. Metallkd., 7, (1996) 555-561.
[97Lia]
H. Liang and Y.A. Chang, Z. Metallkd., 88, (1997) S36-841.
[SSLial]
P. Liang, T. Tarfa, J. A. Robinson, S. Wagner, P. Ochin, M. G. Harmelin, L&as and F. Aldinger, Thermochim. Acta, 314 (199s) 87-110.
Group B, 1994.
H. J. Seifert, H. L.
[98Lia2] P. Liang, H. J. Seifert, H. L. Lukas, F. Aldinger, RI. G. Harmelin, J. Robinson, S. Wagner and T. Tarfa, Werkstoffwoche ‘98, DGM - Informationsgesellschaft.Verlag, 1998 in press
Q 1999 Published
Calphad Vol. 22, No. 4. pp. 527-544, 1998 by Elsevier Science Ltd. All rights reserved 0364-5916/99/$ - see front matter
PII:SO364-5916(99)00009-7
Thermodynamic
P. Liang,
H. J. Seifert,
Modelling of the Cu-Mg-Zn
H. L. Lukaz,
G. Ghosh’,
Ternary System.
G. Effenberg”,
and F. Aldinger
Max-Planck-Institut fiir Metallforschung und Universitat Stuttgart, Institut fur Nichtmetallische Anorganische Materialien, Pulvermetallurgisches Laboratorium, Heisenbergstr. 5, D-70569 Stuttgart, Germany * Department
of Materials Science and Engineering, The Technological Institute, Northwestern University, Evanston, II. 60208, USA
** MS1 (Materials Science International
Services GmbH), Nobelstr.
16, D-70569 Stuttgart,
Germany
Abstract The quasibinary
MgCuz-MgZnz system was optimized with the program BINGSS. All phase diagram data and thermodynamic values available in the literature were critically assessed before the optimization. Experimental investigations by EDX of ternary Cu-Mg-Zn alloys were specifically performed to provide missing data of the Cu solubilities of the Mg-Zn phases. The Laves-phases Cl5 (MgCuz), Cl4 (MgZnz) and C36 (r,Mg&uZns) existing in the Cu-Mg, Mg-Zn and Cu-Mg-Zn systems were described by the “Compound-Energy-Formalism” with Cu-Zn exchange, Mg(Cui_,Zn,) and a weak tendency for antistructure atom formation (Cu and Zn on the Mg sublattices, Mg on the Cu-Zn sublattices). The binary intermetallic phases MgZn, MgzZns and MgzZnir are modelled to have Cu-Zn exchange on one sublattice. The Bragg-Williams description of ordering was extended to describe the ternary range of the pCuZn phase. Estimates were made, where experimental data are not sufficient. Using the binary subsystems from the literature with small updates the Cu-Mg-Zn ternary system was calculated. In general, good agreement is obtained between calculations and experiments.
1
Introduction
The Al-Cu-Mg-Zn quaternary system is one of the key systems for designing of high strength Al alloys. Despite its technical importance this system still contains a large amount of unknown regions. Many of the published diagrams are contradictory and incorrect. In this work the Cu-Mg-Zn system was thermody namically assessed with the aim to provide a constitutional, thermodynamic database for the quaternary Al-Cu-Mg-Zn system within the COST 507 project on light metal alloys.
?%&al
version received on 29 June 1998, F&vised version on 5 January 1999 527
P.LIANG et al.
528 2 2.1
Experimental
The experimental 507 action.
Literature
Review
Information
literature
of the Cu-Mg-Zn system was critically reviewed by [94Gho] within the COST
Experimental data of this system concern mainly the quasibinary MgCuz-MgZnz section. The first phase diagram of this section was published by K&ter and Miiller [4SKoe] using metallography and thermal analysis. [52Lie] used metallography, thermal analysis and X-ray diffraction analysis in the determination of the quasibinary diagram. In this section three different Laves phases, MgCuz, MgZnz and a ternary Laves phase of the MgNiz-type (Mg&uZns) are stable [52Lie]. MgC u2 has a large solubility range and dissolves more than 60 mol% MgZnz, while MgZn2 dissolves only about 1 mol% MgCuz. The ternary MgNiz-type Laves phase is stable from approximately 73 tb 87 mol% MgZnz [52Lie]. [4SKoe] mentioned two further ternary phases on the MgCuz-MgZnz section, but without specifying their homogeneity ranges. The enthalpies of mixing of MgCu*-MgZna alloys were determined by solution calorimetry [64Kin, 72Pre, 79PreJ. [4SKoe] also determined an isopleth from r-CusZns to Mg and presented a reaction scheme and a liquidus projection. The solubility of Mg in the a-, /3- and r-Cu-Zn phases was stated to be “very small” [4SKoe]. Using thermal analysis and metallography [SOMik] investigated the isopleths: from Cu to MgZn, from Mg to CuZn, from Zn to MgCu, from Mg&u to CuZnz, from Cu to MgZnz and for constant contents of 10,20, 30, 50, 60, 70 and 90 at.% Mg and determined the whole liquidus surface. [56Gla] investigated a partial isothermal section at 673 K by metallography and X-ray analysis. The homogeneity range of the Zn-rich MgCuz solid solution was reported to be between 30 and 40 at.% Mg [56Gla], whereas [4SKoe] estimated the width of this range to be about 1 at.%. [SOWat] determined isopleths for constant contents of 5 wt.% Cu and 3 wt.% Mg in the Zn-rich region. [72Yam] investigated the vertical sections for 1.7,6 and 15 wt.% Cu as well aa for 2 and 5 wt.% Mg in the &-rich region. No experimental information is available in literature for the ternary solubilities of the binary intermetallic phases MgzCu, Mg,Zns, MgZn, MgzZns and MgzZnll. 2.2
Thermodynamic
Assessment
in Literature
A thermodynamic assessment of the Cu-Mg-Zn system was reported by Liang et al. [97Lia]. However, in this assessment the ternary phases were simplified, the C36(MgN&type) Laves phase was treated as a stoichiometric phase Cw.sMgZnr.,. The two Laves phases MgCuz and MgZnz were treated as semistoichiometric phase (Cu,Zn)lMg. The solubilities of Mg in the Cu-Zn binary phases /?, 7, c and the Cu solubilities in the Mg-Zn binary phases MgpZns, MgZn, MgzZQ and Mg,Znll were neglected.
3
Experimental
Investigations
The Cu solubilities of the Mg-‘Zn phases MgZn, MgzZns and Mg,Znll were determined Microscopy (SEM) and Energy Dispersive X-ray spectroscopy (EDX).
by Scanning Electron
Ternary alloys were prepared from high purity Mg (99.97%), Cu (99.999%) and Zn (-99.9%) in a pure, nuclear quality graphite crucible placed inside a water-cooled copper crucible and induction heated under helium atmosphere. Melting was repeated twice to ensure homogeneity of the ingot. A third inductive melting in a water cooled copper crucible was finally performed (in quasi-levitation) prior to cast the alloy in a cylindrical cooled copper crucible. Pieces from the cast alloys were sealed under argon in nuclear quality graphite crucibles, annealed at 335°C for 20 days and finally cooled to room temperature in about 10 minutes. Phase compositions were determined by EDX. The experimental results show, that the solubilities of Cu in the MgZn, Mg,Zn3 and Mg,Znll phases are at least 2, 3 and 6 at.%, respectively.
THERMODYNAMIC 4
MODELLING
529
Thermodynamic Assessment
The Gibbs energy descriptions of the pure elements were taken from Dinsdale (SlDin], except Znhcp-A3, which is dhtinguished from ZnhcrVz” a.ccording to [93Kow]. 4.1
The Binary
Systems
The descriptions of the binary systems were taken from the literature, Cu-Mg [SlCou], Cu-Zn [93Kow] and Mg-Zn [98Lial] updated from (92Aga]. The description of the Cu-Mg system needed to be updated, before it could be combined to a thermodynamic description of the ternary Cu-Mg-Zn system. For c-CuZn the descript#ion was changed to fit to the lattice stability Cu hcp-A3 of [SlDin] and approximating as near as possible *:he G’-function of [93Kow]. 4.2
The Cu-Mg
System
In the Cu-Mg description of Coughanowr et al. [SlCou] the parameters of the end members Gzzi and G,$Fz of the compound energy description of the Laves phase MgCus were adjusted. As these parameters, however, are formally unary parameters, they have to be the same in all Laves phases containing Mg or Cu, respectively. The adjustment of the Gisb$;ygy description to the experimental solubility limits can be ” done by the parameters “L&$&,r and LW,oU:oUinstead. The values of the G&T$ and G%:pz parameters are more or less arbitrary as in the stability range the Gibbs energy of the MgCus-phase essentially depends only. For the lattice stabilities of any pure on the sums G&$$ + “g$&s and Grd + oL~$& element X in the fictitious state of the Laves structure, the proposed value [93Cos, 94Coe, 95Ans, 96Dup] was accepted in this work: G?“(T)
-
3@xER(Z’) = 15006 J/mol.
Rerunning the least squares program BINGSS with the set of experimental data used by [SlCou] yielded the parameters listed in Table 2. These parameters virtually give the same phase diagram as those reported by [SlCou] with a maximal deviation of 0.02 mol% in the solubility limits of MgCus.
<5 Optimization of the quasibinary system MgCua-MgZns The descriptions of the quasibinary MgCus-MgZns system, was optimized first with the BINGSS program [77Luk, 92Luk]. This program requires that the quasibinary system is described by Mg$(Cu-Zn). Here the three Laves phases were described bs the simplified sublattice formula Mg(Cur_,Zn,)s using as qua&nary parameters only the parameters Y&,~~~-%‘r$-2%~~ and +$$~~-%‘$-2Y$’ respectively, coming from the binary Mg-Cu and Mg-Zn descriptions. The parameters describing the Gibbs energy of the met&able quashmary compounds relative to the stable pure elements, “Glaze - Y$ - 2%$:, ‘Y$~~
- %‘ic-
2%‘&:, %$zoU - ‘Y$T - 2Y$c and cizzzn
- ‘%‘$ - 2”Gkz as well as the Redlich-Kister
parameters ‘1~g:cu,zn> so”* lL$%,~n, oL:;ou.~n and oL$%:,~n were adjusted to the available experimental data. These eight parameters were adjusted as temperature independent single coefficients. The Gibbs energy of the liquid phase was taken as the Muggianu extrapolation [75Mug] from the binary descriptions, which was transformed to a Redlich-Kister polynomial between the two species MgCus/2 and MgZns/2. It was not changed in the optimization. The experimental values in literature for the quasibinary MgCuz-MgZnz system are phase diagram data by [48Koe, 50Mik, 52Lie] and enthalpies of mixing of the quasibinary Laves phases [64Kin, 72Pre, 79Prej. In the central part of the quasibinary phase diagram, the data of [48Koe] and [52Lie] are contradictory. The liquidus temperatures by [SOMik] and [52Lie ] are 20 K and 50 K lower than those reported by [48Koe], respectively. The liquidus data in several isopleths of [ZOMik], extrapolated to the binary subsystems: contradict the binary Cu-Mg and Mg-Zn systems by values up to 40 K. The Gauss-method requires statistically random distribution of the errors. Non-random distribution of errors as in the above mentioned contradictions indicate systematic errors in at least one of contradictory
P.LIANG et al.
530
1000
MgCuz X 0 ‘z 800 3 s G
C36
3
used l [48Koe]
3 600-
/
A [52Lie] not used v [50Mik] A [52Lie]
400
MgZd I 0.4 mole fraction
I 0.2
0 MgCua Fig.
I 0.6
;
018
MgZnz
MgZm
1 The calculated MgCuz-MgZn2 quasibinary
.
-
phase diagram
MgZm/
298.15K
-2
used
+ [64Kin] m [79Pre]
-l( )-
not used 88
-1: ,_ 0
0.2
M&u2 Fig.
0.4 mole fraction
.
a 0.6 MgZnz
2 Enthalpy of mixing in the quasibinary
[72Pre]
0.8
MgCuz-MgZnz system
MgZn2
THERMODYNAMIC pairs of data sets. contradictory
MODELLING
531
In such a case the more reliable data set must be selected for the optimization
one necessarily
and the
has to be discarded.
The liquidus data of [52Lie] for the MgCur phase do not show a clear single maximum, which is expected after phase diagram rules, therefore the data of [48Koe] were preferred. The Cu rich data of [52Lie] as well as the data of [SOMik] were not used for the optimization. The enthalpies of formation of Mg(Cui_,Zn,)s reported by [72Pre] are considered to be less reliable than those reported in a later investigation of the same laboratory [79Pre] by the same authors. Therefore the old values [72Pre] were not used in the optimization. The quasibinary
parameters
derived from the optimization Table
Parameters
of the MgCus-MgZns The entities
quasibinary
are given in Table 1.
1:
system.
The values are given in SI units:
of moles are the “quasi-unary
species”:
fMgCur
Parameter
Phase
J, K and mol.
and $MgZnz Value 5000.0
MgCuz
-39412.31 12764.53 GMp2 _ Mg.Cu
MgZn2
15000.0
GMMg.Cu
-37652.74
oLLgT:,Z"
10000.0
C36-type
1000.0 -45113.13
The calculated quasibinary MgCus-MgZna phase diagram is represented in Fig. 1 and compared with all experimental values. The quasibinary enthalpy of mixing of the Laves phases, compared with the measured values is represented in Fig. 2.
6 6.1
Evaluation of the ternary parameters
The Laves phases
In addition to the parameters of antistructure The homogeneity
obtained from the quasibinary
atoms have to be considered
system, all possible combinations
in the ternary Gibbs energy descriptions
of formation
of the Laves phases.
ranges with respect to excess or deficient Mg of the three Laves phases were interpolated
between the binary end members.
Since no reliable experimental
data for the range of deviation
from the
stoichiometri’c MgXs are available in the ternary, a better determination of these parameters is not possible. This interpolation implies: for the three Laves phases the same values were taken for the parameters VLQ’ Here @ stands for the three Laves phases and the asterisk “L’p ~~,a,:. and “L:zn,~g. M.&u:*9 l:Cu.Mg? “LO (*) stands for all possible occupations
of the corresponding
sublattice.
Only those interaction
parameters
are significant, where the other sublattice is occupied by the major constituent. There it is natural, to assume the interaction parameters to be independent on the occupation of the sublattice different from the interacting one, leading to identical by the asterisk. As the atomic parameters
parameter
values for different occupation
of the sites designated
sizes of Cu and Zn are not very different, values of 15000 J/mol were chosen for the in analogy to the pure elements. - “Gi’$ - 2%::
%!&Zn - “Ggi - 2”G~~pand oG&,
532 6.2
P.LIANG et al. Mg-Zn
binary
intermetallic
phases
The experimental results (SEM and EDX) of th is work show that the Mg-Zn binary phases MgZn, MgsZns and MgsZnrr exhibit ternary solubilitics up to several at.%. As Cu-Zn substitution seems more likely than Cu-Mg substitution, these binary phases with ternary solubilities were modelled as follows: MgsZnrr: Mgz(Zn,Cu)sZns MgsZns: Mgs(Zn,Cu)s MgZn: Mgr@n,Cu)rs The major constituents are denoted in boldface. The MgsZnrr phase was modelled with three sublattices to be compatible with a model used for the quaternary solid solutions between MgsZnrr and MgsCusAls [98Lia2]. MgrZns was treated as stoichiometric phase, as there are no experimental data on its Cusolubility. This phase is stable between 614 and 598 K only, therefore a significant Cu solubility can not be expected even if the thermodynamic behavior is similar to that of the other phases. In a first attempt the Gibbs energies of the fictitious end members with Cu on the second sublattice were used as adjustable parameters to describe Cu solubilities in the MgZn, MgsZns and MgsZnrr phases. But then these end members appeared to be nearly stable in the Mg-Cu system. Therefore in a second attempt the parameters Y&c” My’_ and c$;” were set zero and the parameters oL$$z, and oL$?&z. were used to describe the Cu solubilities. good fit also in the quatemary 6.3
The liquid
For MgsZnrr both parameters, ‘G$tti, Al-Cu-Mg-Zn system [98Lia2].
and oL&$~,‘~,:z, were used to get
phase
The liquid phase was described as a substitutional solid solution with the Fledlich-Kister Muggianu formalism, which can be expressed by the formula (Cu,Mg,Zn)r. No ternary parameters were introduced. 6.4
The (Cu)
and (Zn) phases
The parameters describing the ;$~&$ies estimated by adopting “L$,zn describing metastable accepted. 6.5
~~~-~d_ ~~~~~~~~~ unary phases, “Gcu
The value of oG~p-A3 - OGz-z”
The 7-CusZns
of Mg in the binyi=&Zn cub
‘_
solid solutions, (Cu) and (Zn), were equal 22500-3.T. For the parameters OG”P-A’
Dinsdale’s
[91Din]
values
were
was adopted fror!s[93Ko$.
phase
The solubility of Mg in the binary 7-CusZr~ phase was described by a four sublattice model derived s used by [93Kow], assuming Mg to dissolve only in the from the description (Cu,Zn)s(Zn,Cu)sC&(Zn,Mg) fourth sublattice. The corresponding parameters were estimated to reproduce a small solubility of Mg in 7-CusZns. 6.6
The bee phase
(/?, /Y, 6)
In the Cu-Zn binary system a order-disorder transition of the bee phase p (A2) to p’ (B2) occurs in the temperatue range from 740 to 730 K. The p’ phase is an ordered modification of the /3 phase with the C.&l structure. A two sublattice model (Cu,Zn)r(C u ,Zn ) r with Bragg-Williams treatment was used to describe this order-disorder transformation [93Kow]. The Gibbs energy for the ordered bee phase (bee-ord) can be expressed in terms of the Bedlich-Kister parameters of the disordered bee phase (bee-dis) and an ordering contribution [88Ans]. In the disordered state, the site fractions of the same element on the two sublattices are identical (yb, = &,; yi, = &,) and the Gibbs energy description must be equivalent to that of the disordered substitutional solution (Cu,Zn)s (bee-dis). Ansara et al. [88Ans] derived constraints’between the parameters for the ordered phase, which were reformulated by Saunders [SSSau] and used by Kowalski and Spencer [93Kow] for the /3Cu-Zn phase. In the present work the BraggWilliams description of ordering was extended to the ternary range. The solubility of Mg in the bee phase was described with the model (Cu,Mg,Zn)r(Cu,Mg,Zn)r. The constraints between the parameters describing the solubility of Mg in both sublattices were derived by extending the
THERMODYNAMIC ideas of [88Ans] and [89Sau] into the ternary Cu-Mg-Zn
MODELLING system:
“c:&~d G&g
c;g oez”Mg bee-ord
OLCu,Zn:Cu bee-ord
OLCu,Zn:Zn bee-ord
‘L Cu,Zn:Cu ‘L,&:g lxx-ard %“.Zr&”
.
The correlation between the parameter Ac”,z,, and the parameter called P by [93Kow] is Ac”,z,=-2P.
Using
the above constraints Gbccord becomes equal to Gbccdis, whenever y: = yy. The parameters
0
bee-dis
1
bee-dis
2
bee-dis
Lc”,z, , L Cu,Zn 9 L Cu.~n
were taken from [93Kow]:
=
-51595.87
%$t=
=
7562.13 - 6.45432 T
=
30743.74 - 29.91503 T
=
-6170
Ac”.zn OLM,,z” bcc-dia
Acu,zn
,OLPZli u. 2Lbc”c;gi
OLb%i~ and
and
were estimated
to reproduce
+
13.06392 T
a small solubility
of Mg in PCuZn.
The ordering
parameters Aou,Ms and Aug,z, were set zero: OLbcc-dis C”.Mg
=
q,bcc-dis
-6500.0
=
-6500.0
ACU,M~
=
0
Aig,zn
=
0
Mg.,Zn
The values oit the parameters derived in the present work are collected in Table 2.
7
Ternary Calculation
Using the optimized quasibinary parameters and the estimated ternary parameters, as given above, together with the parameters of the binary subsystems, the ternary Cu-Mg-Zn system was calculated. The
P.LIANG
534 calculated
et al.
liquidus surface is represented in Fig. 3. The calculated isothermal sections at 608, 800 and
1100 K are shown in Figs. 4 to 6. Fig. 7 shows the calculated isopleth from -y-CusZns to Mg. It agrees very well with the experimental of (48Koe].
Figs. 8 to 14 represent the calculated
contents of 10, 20, 30, 50, 60 or 90 at.‘% Mg compared of the data of [SOMik] could be reproduced parameters from the literature.
data
vertical sections from MgZnz to Cu and at constant with the experimental
with the optimized
A further adjustment
quasibinary
values of [50Mik].
parameters
Most
and the binary
of the parameters to the data of [BOMik] does not
appear to be justified, because of the misfit between the extrapolated
experimental
liquidus data into the
binary boundary systems and the generally accepted liquidus data for these binaries (compare Figs. 9, 10 and 11).
8
Conclusion
The quasibinary system MgCus-MgZns could be optimized by the program BINGSS, using experimental data from the literature. The three Laves-phases MgCus, MgZnz and “MgzCuZns” (C36-type) on the MgCus-MgZns section are described by the “compound-energy-formalism” with Cu-Zn exchange, Mg(Cur-,Zn,) and slight antistructure atom formation (Cu and Zn on the Mg sublattices, Mg on the Cu-Zn sublattices).
The binary intermetallic
Cu solubilities according to experimental
phases MgZn, MgzZnz and MgsZnrr are modelled to have
results by EDX. The Bragg-Williams
treatment of ordering was
extended into the ternary system to describe the solubility of Mg in the PCuZn phase. bility data in the Cu-Zn intermediate
phases are available, the corresponding
As no Mg solu-
parameters were estimated
to reproduce Mg solubilities interpolating between the binary fcc(Cu,Mg) and hcp(Zn,Mg) solubilities. The resulting parameters allow all experimental phase diagram and thermodynamic data to be reproduced within narrow limits. Thus a reliable basis for evaluation into higher order systems containing the Cu-Mg-Zn system as a boundary, for example the quaternary Al-Cu-Mg-Zn system, has been established. Acknowledgement Financial support by the German UBundesministerium nologie”
(Contract
fiir Bildung, Wissenschaft,
03K7208 0) within the framework of the European Community
is gratefully acknowledged.
Forschung und TechProject
COST
507
The authors would also like to thank P. Ochin (CNRS, Vitry, France) for for a preparation of the alloys. One of the authors (GG) would like to thank the Max-Planck-Gesellschaft visiting fellowship.
THERMODYNAMIC
535
MODELLING
Zn
in OC
WI
0
0.2
0.1
0.3
0.4
0.5
0.7
0.6
0.8
0.9
1 .O
mole fraction Cu Fig. 3
cu
Liquidus surface of the Cu-Mg-Zn ternary system
Zn
0 Mg
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
mole fraction Cu Fig. 4 The Cu-Mg-Zn system isothermal section at 608 K
1.0 cu
P.LIANG et al.
536
of
Mg”
0’
0.1
,‘Y, 0.2
7.1:
A
0.3
Ci.k
0.4
\\w+
0.6
I\
A
A
0.7
0.8
0.9
\l/ 1.0
mole fraction Cu
cu
Fig. 5 The Cu-Mg-Zn system isothermal section at 800 K
Zn 1.0
A 0.9
0.8
0.7
- ,. Mg”
6.;
d.i
6.3
Ci.4
d.k
0.6
0.i
6.8
0.9
mole fraction Cu Fig. 6 The Cu-Mg-Zn system isothermal section at 1100 K
1.0 cu
THERMODYNAMIC I
1200
t
I
I
MODELLING I
I
I
537 I •1
I
[48Koe]
ilOOIOOO:f
900-
600
Cu,Zn,
mole fraction Zn
Mg
Fig. 7 lsopleth from Cu,Zn, to Mg
1200 y
1100
-s 1000 L $ 900 ?I !$ 800 B
700 600
400 0 M@n,
0.1
0.2
0.3
0.4
0.5
0.6
mole fraction Cu
Fig. 8 Isopieth from MgZn, to Cu
0.7
0.6
0.9
1.0 cu
P.l_\ANG
538
et al.
1300 1200 1100 y .r
1000
Lj
900
5 ‘s
800
E B
700
(Cu)+MgCu,
600 500
0:l
012
0.3
0.4
0.5
0.6
0.7
0.8
0.9
mole fraction Zn Fig. 9 lsopleth of the Cu-Mg-Zn
system at 10 at.% Mg
1200
s 800 g ES
700 600 500 400
I
0
0:1
0.2
/
1, 0.3
\\ 0.4
II, w II 5 1 0.5
0.6
0.7
0.8
mole fraction Zn Fig. 10 lsopleth of the Cu-Mg-Zn
system at 20 at.% Mg
THERMODYNAMIC
MODELLING
539
A [50Mik]
800 -
(Cu)+MgCu,
+MgZn,
700 600 -
011
012
013
014
0:5
0:s
0:7
mole fraction Zn Fig. 11 lsopleth of the Cu-Mg-Zn system at 30 at.% Mg
I
1200
I
I
I a [SOMik]
liquid
IlOO-
1000 900 800 700 600 500 400
0
0.1
0.2
0.3
0.4
0.5
mole fraction Zn Fig. 12 lsopleth of the Cu-Mg-Zn system at 50 at.% Mg
P.LIANG
540
I
0
0.05
0.10
0.15
et a/.
I
I
0.20
0.25
03
mole fraction Zn Fig. 13 lsopleth of the Cu-Mg-Zn
Y c ._
system at 60 at.% Mg
800
f 3 &
700
BE
600
400
(Mg)+Mg,Cu+MgCu,
0
0.02
0.04
0.06
0.08
0.10
mole fraction Zn Fig. 14 lsopleth of the Cu-Mg-Zn
system at 90 at.% Mg
THERMODYNAMIC
-
MODELLING
541
Table 2: Parameter set for the Cu-Mg-Zn system. Parameters are given as a + bT + cT In(T) t dT2 + e/T $ fT3 in J mol-‘. (per moles of formula units) Parameter
b
a
c
103d
-95
40.00
Liquid;
Redlich-Kister-Muggianu
oLli,a Cu.Ms
-36962.71
ILh CbM3 0Lh Cu,Zn ILh C'1.Z"
4.74394
-8182.19 -40695.54
12.65269
4402.72
-6.55425
7818.10
2LkCIl,Z”
-3.25416
0Lh M&& ILlicl MgZn
-77729.24
680.52266
3674.72
0.57139
zLlic1 - th,Zn
-1588.15 fcoA1
(Cu);
OL’“’ Cu,Mg OLfC’ CL1.Z” ILfCC Cu,,Zn 2Lf_ Cu,Zn
Redlich-Kister-Muggianu -22059.61 -42803.75 2936.39 9034.20
5.63232 10.02258 -3.05323 -5.39314
-3056.82 -3127.26
5.63801 5.65563
OLfCC W:,Zn ILfCC W:,Zn
hcp-Zn, .+w-Zn CU vhcr>-Zn Mt:
(Zn);
Redlich-Kister-Muggianu
_ CQCC CU
600.00
_
100.00
Ghcp-A3 Mg
0.20000
22500.00
-3.00000
ophg
-14432.17
-10.78140
oLh&Zn Mg.Zn
-3056.82
5.63801
ILhcF’-Zn Mg,Zn
-3127.26
5.65563
oLhcp-Zn Cu ,Mg
hcp-A3, c@w-As CU
_ ocj~c CU
oGhcp-A3 Zll
_
((Mg), e-phase);
Redlich-Kister-Muggianu 600.00
0.20000
2969.82
-1.56968
oLhcp-A3 Cu,Mg
22500.00
-3.00000
OLk”P--;
-36475.00
4.89600
24790.00
-10.13500
oLhcp-A3 Mg.,Zn
-3056.82
5.63801
ILhcp-A3 Mg.Zn
-3127.26
5.65563
%hcp-Zn Ztl
ILhc;-A3 CU,Ztl
CuMgz; .@UfkZ
Cu.Mg-“G;&
stoichiometric:
_ 2c$-A3
CuMg2
-28620.00
1.86500
P.LIANG et al.
542
Table 2:
a
Parameter bee
(P,P',a); (Cu,Mg,Zn)l(Cu,Mg,Zn)l
- "Gg; - "G!~FC = "cbc:r YFC. C".Z" Zn.Cu- "Gi: - "GE: c@cy _ "G& _ @= = @by - "G& - "Gp; CUM3
Mg.Cu
Mg
_q; "Gbc". Mg.Zn
- "~2; = @y Zn.Mg
-
bee “Gz.
oG&
-31967.92
6.53196
-3250.00 -3250.00 -2427.44 17262.40
oLk:zn:C" = oC&",Z" lGzz":C"= 'G%IIZn OLbc; Cu.Zn:Mg = 1Lbcc Cu,Zn:Mg =
b
-9.52692 -16.57110
0Lb.x ’ Mg:Cu.Zn
-19627.94
6.53196
‘L&:c”,Zn
-1.61358
oL~z":Zn= o&%"zn
1890.53 -13770.63
1Lbcc Cu,Zn:Zn =
-13481.34
13.34394
3842.97 -92231.22 -19214.84
-3.73938 89.74512
-7685.94
7.47876 -5.60907
SE;&):*
1Lbcc ’ Zn:Cu,Zn
= S$;,
Z”
OLbc; Cu.Zn:Cu.Zn
OLbcC
=
oLi$f,Zn:Cu,Zn = OLbcc Mg.Zn:Cu,Mg
oL!$Zn:Cu,Mg
Cu.MgMg.Zn
Cu,Zn:Mg,Zn
=
OLb” Cu.Mg,Zn:Cu
=
oLk&g,Zn:Zn
oLk%u,Mg,Z”
OLbcC
OLbcs Cu:Cu,Mg = OLbcc Mg:Mg,Zn = OLbcc Cu,Mg:Zn = ILbCC
Cu,Mg:Zn =
OLbcC
Mg.Zn:Cu = 1Lbcc Mg.Zn:Cu =
=
oL&4g:Cu
=
oL~:C.,hIg
=
oL&Zn:Mg
=
OL%Mg,Z.
=
=
=
OL%Mg:Cu,Zn
oL&Mg,Zn
oLEMg:Mg
-3250.00 -4969.04 -1921.48
oL%i4g.Zn
-1187.98
1.86969 -3.48327
1921.48
-1.86969
-118719.84
-42.349
+kZns;
OGZn:Cu:Cu:Zn
_
7 e
CU
_
6 chcp-Zn ZlI hcp-Zn
5 "GE - 8 "Gz.
-
-
%n:Cu:Cu:Mg
-
wCu:Zn:Cu:Mg
-
OGZZn:Zn:Cu:Mg -
7Y$& - 6V$-A3 5 "@. _ 6 “Go-43 3 @i,
_
(j Ghcp-A3
QGM&fWl
_
2 q$;-A3
_
MgzZns Mg.Zn
Mg.Cu
-21.817
-75604.96
-47.923
-64720.63
-51.349
9857.77
-77.454
-96185.23
-30.817
-42185.23
-56.105
-73818.32
18.455
-108000.00
Mgz(Zn,W
@MBfZ"" _ 2 o@v-A3 _ 3 o&r-Z”
Mg:Cu,Zn
-68.455
-150185.23
-135000.00
Mg:Cu,Zn:Zn
)LMgzZns
Zn
6 "c'6:-5 "Gz-Z"
~LMGul
_
2 ,;~-zn 4 c@p-Zn
-44139.58
Mg@n,Cu)&e
_ 2 c@w-A3 _ 11 @z;~-Zn
~MgyZw
_
2 ,z-zn
MS
@gf”.n
Mg.Cu:Zn
_
5y$g _ 6 yy$-A3_
MgzZnll; Mg.Zn.Zn
-0.25611
(Cu,Zn)2(Cu,Zn)*Cu3(Mg,Zn)G
OCCu:zn:cu:zn - 5 "dc"u - 8 %:-'" Y&:Zn:Cu:Zn - 3 Yg - 10 "cz-z" ‘+%u:Cu:Cu:Mg
18.69690
oLi%“,Mg 1Lbcc Zn:Cu.Mg
oLk;,Zn:Zn
%Mg,Z”
yy Cu.Cu.Cu.Zn
5764.45 -3250.00
0.15456
2 4-A3
_
3 "G;;
-54406.20 0.00 -100000.00
13.602
-
THERMODYNAMIC
MODELLING
543
mble 2: continued Parameter
a stoichiometric:
Mg7Zns; “G$T;z
- 5x$-*3
- 2o”Gz+
MgZn; - 12”G$-*3
- 13”Gy”
GzF;” s
- 12YF-*3 Ms
- 13”G’d
oLMsZn Mg:Cu.Zn
- 3%$ER
losf
-335741.5
35.50000
-236980.8
59.24524
0.0
(Cu,Mg,Zn)(Cu,Mg,Zn)2
15000.00
-“G:~-z”
15000.00
- 2@;;
15000.00
OLQ du,Mg
13011.35
OLQ Cu.Mg:.
6599.45
OL@ .:Mg.Zn OLQ Mg,Zn:*
35000.00 8000.00
y-$3p: Mg.Cu _ HSER Mg _ 2HzfR
-34690.99
YFs Mg:ZlI_oG$*s
-33355.45
%ysy Cu.Mg -“($U
_ 2~~-z” -
Zn,Mg_oG!z-Z” YF36
2@$+43
_ 2%;;
OE”,Z”
364.73085
-69.276417
-0.51925
143502
-5.65953
-69.276417
-0.51925
143502
-5.65953
-69.276417
-0.51925
143502
-5.65953
8.83886
84970.96
-16.46448
63355.45
-8.83886
-90226.26
oGz;!-6&
rSER- 2HF -0 (;$-A3
_ 2”~;:-Zn
cu:hQ - “@c.C” - 2?$;-*3 @WW y$&M~~ n: g _o@~P-Z~
_ 2~;7-*3
oE% . ,
-54690.99
364.73085
-25355.45
8.83886
104970.96
-16.46448
55355.45
- 8.83886
-78824.62
lL%Z”
25529.06
‘=@? Mg.Cu - H&iR - 2H;zR
-24690.99
c+szn, _ 2~~-Zn Mg.Zn _+:-A3 Cu.Mg_ 0G&c c” - 2”Gz-*3 c#s,Znz
-35355.45
q-+&
e
Mg51Znzo
(MgCuz, MgZns, C36);
%EuTZn-“GY$; - 2oG!y”
.@$z
103d
-500000.0
Laves phases,
Y$,,
c
Mg,z(Zn,Cu)ts
“G$Z”
“c&
b
_o~~~PP-Z~
_ 21++;-*3
OLM&? *:Cu,Zn
364.73085 8.83886
74970.96
-16.46448
65355.45
- 8.83886
-75305.48
Here Cpstands for the three Laves phases and the asterisk (*) stands for ail possible occupations of one of the elements Cu, Mg and Zn on the corresponding sublattice. X denotes either Cu, Mg or Zn, but the same element in the whole formula. HZ.,ERand HcfR stand for H,$i and H&~-A3 at 298.15 K, the enthalpies of the pure elements at standard temperature,
whereas Y$G, %‘$-A3,
at the same temperature
9=~Tp-z” and exER denote the Gibbs energies of the pure elements
as the corresponding
%$...
P.LIANG et al.
544
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[52Lie]
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N. Dupin and I. Ansara, Z. Metallkd., 7, (1996) 555-561.
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