Thermodynamic analysis of stable and metastable equilibria in the Cu-Cr system

Calphad Vol. 19, NO. 1, pp. 93-104,

1995 Copyright Q 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0364-5916195 $9.50 + 0.00

Pergclmon

0364-5916(95)

00010-O

THERMODYNAMIC ANALYSIS OF STABLE AND METASTABLE EQUILIBRIA IN TEE Cu-Cr SYSTEM

Kejun Zeng* and Mark0 H-en Laboratory of Materials Processing and Powder Metallugy Helsinki University of Technology Vuorimiehentie 2K, SF-02150 Espoo, Finland *On leave from the Central South University of Technology Hunan 410083, P. R. China

ABSTRAC’I’: The available experimental information is not sufficient to determine the temperature dependence of

excess Gibbs energy of the liquid Cu-Cr alloys. The previously optimized excess entropy of mixing of the liquid phase is too positive. A new set of optimized thermodynamic functions of the Cu-Cr system has been obtained from thermodynamic and phase diagram data incorporating the latest data. The Tanaka-Gokcen-Morita relationship was used to constraint the excess enthalpy and entropy coefficients of the liquid phase. The opthnized thermodynamic functions can account very well for the process of precipitation in the supersaturated fee Cu-Cr alloys.

1. Introduction

The copper-chromium age-hardening alloy system has several interesting and apparently unique characteristics which have not been well understood. Among these characteristics are the origin of their excellent age-hardening properties and the nature of the Cr-rich phase precipitated in early stage of ageing. Knowledge of thermodynamic properties of the phases involved will be very useful for understanding the experimental results. In addition, the copper-chromium alloys are used in a number of engineering applications due to their high strength and good electrical and thermal conductivities. It has been found that the addition of magnesium or zirconium, alone or in combination. to the alloys can improve mechanical properties at high temperatures without impairing their good electrical and thermal conductivitier:. Knowledge of the phase relations and the thermodynamic behaviour is essential for improving the propeties of these alloys and optimizing the techniques for their production. The Cu-Cr system were analysed several times [77Kuz, 78Kau, 84Cha. 87Sau, 9OH&n]. Major discrepancies were concerned with the liquidus of the bccCr phase. Recently some new experimental results have become available. Because of ijts thermodynamic importance to the optimization and calculation of the Cu-Cr-based higher order system, the Cu-Cr system was reoptimized here. In contrast to the previous calculations, the Tanaka-Gokcen-Morita relationship for H,,,k and Sex [9oTan, 93Tan] was used in the present work for the liquid phase. 2. Experimental Information 2.1 Phase equilibrium data

The equilibrium diagram for the Cu-Cr system is of the eutectic type with a flat liquidus. The solid solution fields have restricted width. The solid solubility of Cr in (Cu) has been investigated by [3OCor, 39Ale, 48Hib, 57Doi, 67&k, 75Dri]. Their results are in agreement except [3OCor] which was omitted from the present work. [84Cha] has Original version received on 10 January 1994, Revised version on 16 December 1994 93

94

KEJUN ZENG AND M. HiiMiiLlilNEN

discussed the relative accuracy of these results by reviewing the experimental procedures and the sensitivities of analysis methods. They concluded that although the data of [57Doi] do not extend to temperatures as low as those of others, the equilibrium state was more closely approached in their alloys. So in the present optimization, a greater weight was given to the data of [57Doi]. The solubiity of Cu in (Cr) is negligible below the eutectic temperature (1350 K). [77Kuz] and [86Leo] measured the solidus of (Cr) in two separate temperature ranges above the eutectic temperature, which show retrograde behaviour, but the solubility can be considered negligible and were not taken into account here. The liquidus of (Cu) has been investigated by [57Doi]. Their specimens were prepared from high purity of metals by vacuum-melting method. The liquidus and eutectic temperature were measured by thermal analysis. The determined eutectic temperature, 1349.6 K, agrees well with the results of [OIHin, 23Sie, 3OCor, 48Hib, 67Zak, 77Kuz, 86Leo]. It is of some controversy whether or not there exists a miscibility gap in the liquid state of the Cu-Cr system. In a critical review of the Cu-Cr system, [84Cha] discussed thoroughly the influence of impurities and cooling rate on the stability of the liquid miscibility gap. They supposed it was highly possible that the miscibility gap observed by [08Hin, 23Siel was stabilised by impurities, and they preferred the conclusion of [82Tim] that the miscibility gap lies below the flat portion of the experimentally determined equilibrium liquidus. [86Leo] determined the whole Cu-Cr phase diagram by using high temperature DTA, melt saturation, KRD, and metallography techniques. Their results show an invariant reaction at 2040 K which was interpreted as a monotectic reaction. The metals used are of high purity (99.98 wt.%), and the alloys were made in arc vacuum furnace under pure helium. The heating rate during DTA experiment was 1.3 K/s. It is very hard to suppose from these experimental conditions that the miscibility gap has been stabilised. In spite of this, however, the data of monotectic reaction reported by [23Sie] and [86Leo] were omitted from our work because a great difference exists between the results of [23Sie] and [86Leo], and, furthermore, the first five liquidus points measured by [86Leo] in Cr-rich region are not in agreement with the melting point of Cr, which makes the measured monotectic temperature in doubt. Of the literature on the liquidus of (Cr), [77Kuz, 82Tim, 84Ono, 86Leo] are of importance. [86Leo] determined the liquidus by two different methods, DTA and melt saturation. The authors have recommended the data by melt saturation method (25.6/1773, 34.4/1873, 39.0/1973 at.% Cr/K) to be used in thermodynamic optimization [93Boc]. Using very high purity metals (99.999 wt.% Cu and 99.998 wt.% Cr), [82Tim] determined one liquidus point: 1823 K at 42&2 at.% Cr, by a high temperature mass spectrometric technique. Based on their experimental results of the relative mass spectrometric currents of Cu and Cr, they also proposed the liquidus line of (Cr). But from Fig. 5 in [82Tim] it can be seen that as the temperature decreased, the errors of the experimental data increased and the consistency of the data became worse. The errors of the liquidus data obtained from this plot could be very large except that at 1823 K. [77Kuz] made the Cu-Cr alloys from the electrolytic copper and chromium (99.999 wt.% Cu and 99.99 wt.% Cr), and determined the liquidus in the region of 2.58-8.23 at.% Cr by measuring the weight loss of Cr crystal in the liquid alloys during its dissolution. The liquidus by [77Kuz] lies very much higher than that of [86Leo]. [84Ono] measured the liquidus at the Cr-rich concentration range by two different methods, mass spectrometry and DTA. The liquidus obtained by the two methods he very close to each other, and agree reasonably with that of [77Kuz]. But at high Cr content (4.5-9 at.% Cr) the liquidus by [84Ono] lies higher than that of [77Ktu]. 2.2 Thermodynamicdata [82Tim] determined the activities of Cu and Cr in the liquid solution by high temperature mass spectrometry between 6 and 97 at.% Cr at 1823 K. The uncertainty of the activities of Cr are very large in the region less than 30 at.% Cr. The activities of both Cu and Cr show a very large, positive deviation from ideality. With the combination of Knudsen cell and quadruple mass spectrometer, [84Ono] determined the activities of Cr at 1573 K in the copperrich liquid solution (O-4 at.% Cr). Recently, [91Ino] have studied the thermodynamic behaviour of the Cu-Cr liquid alloys at dilute concentrations. The liquid copper containing chromium was brought to equilibrium with molten CaCl&r203 slag saturated with Cr203 (s), and the equilibrium partial pressures of oxygen were measured by emf method. The activity of Cr in the liquid Cu-Cr alloys were determined from the equilibrium oxygen partial pressures. The errors for the individual

STABLE AND METASTABLE EQUILIBRIA IN THE Cu-Cr SYSTEM

95

activity data have been given. The results are generally in agreement with those of [840no] within the experimental errors. 3. Review of PreviousCalculations [77Kuz] employed the regular solution model to analyse the solution phases liquid and (Cr). The interaction parameters (see Table 1) were calculated from only a few phase equilibrium data then-available: equilibrium data of liquid/(Cr) at II150 to 1300 “C measured by themselves, and that of liquid/(Cu) by [57Doi]. The miscibility gap in the liquid state was not confmed. [78Kau] treated tire solid solutions as simple regular solutions and used an identical interaction coefficient for them. However, a complex temperature dependent formula was used for the interaction parameters of the liquid phase. A miscibility gap in the liquid phase was predicted between 1900-2000 “C.

Refs. 77Kuz

78Kau

TABLE 1 Summary of Thermodynamic Parameters of the Cu-Cr System Phase Parameters in Regular Solution Model liquid Lo = 88533 - 35.56 T Lo = 99998 -34.10 T (Cr) liquid (Cu) (Cr)

b=549965-815.168T+0.41978T2-7.0819x10-ST3 Lt = 482185 -798.432 T + 0.41978 T2 -7.0819x10-5 T3 b = 104600 Le = 104600

84Cha

liquid

r, = 83400 - 27.9 T L1 = -2200

87Sau

liquid

Lg=83954-34T Lt=lOOO &)=77252-25T b=95330-10T

(Cu) (Cr) 9OHam

this work

liquid (Cu) (Cr)

Lo = 62797.75 - 18.95186 T L, = 1184 Lo=53196-3.31182T r, = 77 107.5

liquid

b = 35495.91288 - 2.95799274 T 2 = -1001.17645 5704.64789 4, = 88112-30.38315 T

Based on the ,activity data for the liquid by [82Timl and the liquidus and solidus data of (0) by [77Kuz], [84Cha] derived an optimized expression for the interaction parameters of the liquid. Both the temperature dependence and composition dependence were taken into account. The calculated phase equilibrium of liquid/bee-Cr demonstrates that the liquid Idevelops a miscibility gap that lies just below the liquidus. But the calculated liquidus is shitted upward from the experimental data of [77Kuz] and very close to those of [84Ono]. [87Sau] incorporated all the experimental results available at that time except for [840no] and [86Leo]. His calculated liquidus of (0) agrees very well with the data of [77Kuz] and is consistent with those of [23Sie, 82Tim]. The calculated solvus of (Cu) is in excellent agreement with the observed one above 850” C.

96

KEJUN ZENG AND M. HAMALiilNEN

[9OHiim] derived another set of thermodynamic parameters for the Cu-Cr system. The calculated liquidus of (Cr) agrees well with the data of [77Kuz, 84Ono]. The liquidus and solvus of (Cu) are supported by experimental results. From Table 1 it can be seen that there is a common point among the previous calculations that the excess entropy of mixing of the liquid phase has a very positive value. This means that the contribution of the excess entropy of mixing in lowering the excess Gibbs energy becomes very large at high temperatures. In fact, however, it is rare in metallic systems for the excess entropy of mixing of the liquid phase to be outside the range of -10 - +5 J/m01 [91Oka]. In the Cu-Cr system the reason for the large positive coefficient of the excess entropy of mixing is that experimental data am not sufficient to determine it reliably. 4. Thermodynamic

ModelUng

4.1 Models The Gibbs energies of the pure elements (phase stabilities) vs. temperature “G(T) = G(T) represented by: “G(T)=~+~T+cTI~(T)+~T~+~T~~+~T~+~T~+~T~~

Hsm (298.15 K) were

(1)

HSER is the enthalpy of the “Stable Element Reference”, the pure element in its stable state at 298.15 K and 105 Pa, viz. fee Cu and bee Cr. The temperature may be divided into several ranges, where the coefftcients a, b, c, d, e, f, j, and k have different values. The values of these coefficients were taken from [91Dm] and are listed in Table 2.

TABLE 2 Phase Stabilities of the Elements Cu and Cr (in J/mole-atom) “G(T)=a+bT+cTln(T)+dT2+eT-1+fT3+jT7+kTm9 Phase

dx103

ex104

fx10’

cu (fee)

298 - 1358

-7770.458

a

130.485403

-24.112392

-2.65684

5.2478

1.29223

cu @cc)

> 1358 298 - 1358

-13542.33 -3753.46

183.804197 1.29230403

-31.38 -24.112392

-2.65684

5.2478

1.29223

> 1358 Cu (liquid) 298 - 1358 > 1358

-9525.33 5194.382 -46.93

182.549197 120.975160 173.883734

-31.38 -24.112392 -3 1.38

-2.65684

5.2478

1.29223

-58.3932

Cr(liquid)

15483.01 -16459.98

146.0598 335.6163

-26.908 -50.0

1.89435

13.925

-0.147721

23.7615

Temp. range (K)

298-2180 > 2180

b

c

jxl@*

kxlo-32

.00364643 .00364643

Cc (fee)

298-2180

-1567.93

157.643

-26.908

1.89435

13.925

-0.147721

Cr(bcc)

> 2180 298-2180

-27580.0 -8851.93

344.343 157.48

-50.0 -26.908

1.89435

13.925

-0.147721

>2180

-34864.0

344.18

-50.0

-2.88526 -2.88526

For the concentration dependence of G for the liquid phase and the solid solution phase (Cu). the Redlich-Kister formula [48Red] was used: G-HsER=

ixi”Gi+RT i=l

iXiln(Xi)

+Ge*

(2)

i=l

m c”“=

x,x2

C(x, n=O

- x*Y

L”

(3)

L, = a, + b,T

where L, are the interaction parameters, a, correspond to the enthalpy and b, to the negative of the excess entropy of mixing. The solubility of Cu in (Cr) was neglected, i.e. the bee phase was treated as a stoichiometric phase.

STABLE AND METASTABLE EQUILIBRIA IN THE Cu-Cr SYSTEM

97

4.2 Sektion of the adjustable coefficients Because every parameter to be optimized in the thermodynamic model of a phase has its own physicochemical meaning, the quality of optimization of thermodynamic parameters and calculation of phase diagram depends strongly on the selection of adjustable parameters. One should consider what thermodynamic quantities are connected with the measured values and how these quantities are connected with the parameters. From these considerations one can get the best ideas as to how many and which of the parameters can be optimized. Only those parameters are optimized which are connected with the reliable experimental values. Too many parameters may reduce the optimization to an arbitrary mathematical smoothing. Since only phase diagram data and activities of the elements are available but no enthalpy data, only the Gibbs energies of the phases can be adjusted. On the other hand, as mentioned in section 3, the previously optimized excess entropy of mixing of the liquid phase are too positive and the values of this coefficient obtained by different authors are very different. For instance, [87Sau] and [9OH&nJ used the same models and similar experimental information, but the optimized excess entropy of mixing of the liquid phase by [87Sau] is nearly twice as large as that by [9OH&n] (Table 1). So it can be concluded that the available experimental information is not sufficient to determine the temperature dependence of the excess Gibbs energy of the liquid Cu-Cr alloys. In this situation some constraints should be introduced between the enthalpy and entropy terms if the entropy term is necessary to reproduce the phase diagram data. This problem has been discussed in [88Luk]. [79Kub] has shown that a linear relationship exists between the maximum enthalpy of mixing Al&k and excess entropy of mixing ASex for a number of binary liquid and solid solutions, or AH,,&W~ = 3000 K. Recently, a thermodynamic solution model for liquid binary alloys has been derived to evaluate the excess entropy of mixing from the enthalpy of mixing based on the free volume theory [9OTan, 93Tan]. On the basis of this model it was shown that the relationship between AiY,h and ASe* in liquid A-B binary alloys depends on the melting points of comoonent elements: 14 AH,i, = Asex ~/T~.A+~/T~.LI I

where T,,, is the melting point of pure element. This expression applied to the Cu-Cr system gives a value of 11715 K for the ratio of mmir to ASeX.In the present work, 12000 K was used to constraint the enthalpy and entropy coefficients of the liquid phase. Because the activities of Cu and Cr in the liquid alloys showed a large positive deviation from the Raoult’s law, the excess Gibbs energy of the liquid phase is strongly dependent on the alloy compositions. After several attempts using different numbers of coefficients, m = 2 in Eq.(3) was chosen and the entropy term b, in Eq.(4) was used for Lo. For the solid smolution(Cu) only one parameter b is needed because the maximum solubility of Cr in it is very small (-0.8 at.%). The pre-optimization showed that the parameter for entropy was necessary to fit the experimental data. As the solubilities of Cr in (Cu) have been measured in a big temperature range and the entropy parameter for (Cu) can be optimized independently of the enthalpy one, no constraint was used between them. 5. Results and Discussions

The optimization and calculation were performed using Parrot [84Jan]. Each set of the selected data was assigned an uncertainty value based on the experimental method or on authors’ statements in their paper. During the optimization, a certain value of weight factor was also given to each set of experimental data by trial and error method in order to get a satisfactory fit to most of the selected data. The new thermodynamic description of the Cu-Cr system thus obtained is given in Table 1. The phase diagram calculated with this description is compared with the used experimental data in Fig. 1 to 3. It can be seen that the calculated liquidus of bee-Cr agrees well with the experimental results of [77Kuz, 82Tim, 84Ono]. The liquidus of (Cu) by [57Doi] has been reproduced. The predicted maximum sohtbiity of Cr in (Cu), 0.82 at.%, is strongly supported by experimental results. The calculated solvus of (Cu) is in very good agreement with the measured one above 1100 K. Below this temperature, the solubilities of Cr in (Cu) is smaller than the observed data. This is consistent with the conclusion of [84Cha] that the equilibrium has not been achieved at lower temperatures. The ratio

98

KEJUN ZENG AND M. HiiMiiLiilNEN

of the optimized parameter for enthalpy of mixing to that for excess entropy of mixing is very close to the Kubaschewski’s relationship [79Kub], which means that the experimental data are sufficient to separate the enthalpy and entropy terms. Fig. 4 compares the liquidus of bee-Cr proposed by different authors and all the experimental liquidus data available. The stable miscibility gap of the liquid alloys has not been predicted. The calculated liquidus by the present authors locates higher than those calculated by [77Kuz] and estimated by [82Tim], but is very close to that by [84Cha] on the Cu-rich side. The predicted activities of Cr in liquid alloys agree very well with the experimental data of [840no] and [91Ino], especially at the lower temperatures (Fig. 5). The calculated chromium activities at 1823 K lie within the experimental error limit of [82Tim], but those of copper are a little bit higher than the observed ones (Fig. 6). By checking the Gibbs energy curve of the (Cu) phase (Fig. 7), a metastable miscibility gap of the fee phase can be expected. Fig. 8 shows this gap together with the corresponding spinodal region calculated using the present thermodynamic description. It can be predicted from Fig. 8 that if the supersaturated fee alloy lies in the gap, the process of precipitation will proceed in two stages. In early stage of ageing metastable feeCr particles precipitate and grow coherently with the fee (Cu) matrix, and the strength of alloy will reach the maximum value at the end of this stage. In later stage the previously formed coherent fee-Cr phase are transformed into the equilibrium noncoherent bee-Cr phase and the strength of alloy will decrease with the ageing time increased. The latter stage has been generally contirmed by experimental work, while the former is still in controversy. Up till now no clear evidence has been obtained on the structure of precipitates at the first stage. [6OWil] studied the precipitation process of chromium from the supersaturated Cu-Cr alloys containing 0.19-1.33 wt.% Cr at 400 and 500 “C using X-ray techniques. Weak diffuse streaking in cl 1l> directions was observed at the first stage. It was suggested that the precipitates are tbin platelets of metastable fee or hcp chromium coherent on the matrix closed packed planes. [73Kni] observed no electron diffraction from small precipitates in the Cu-0.15 wt.% Cr alloys aged in the temperature range 300 to 550 “C for 2-4 hours. Based on this result, they concluded that the small precipitates must have the same structure of the matrix. At early stage of ageing of Cu-0.55 wt.% Cr alloy (10 minutes at 475 “C), [79Wea] has also observed very weak diffuse stmakings in the diffraction patterns, but the streakings are too weak to infer anything about the structure of the precipitates. As all the reported experimental alloys are in the metastable miscibility gap of the fee phase, however, it might be safe to conclude from Fig. 8 that the early precipitates in the above-mentioned experimental work are feeCr. The reason why a strong streaking in diffraction has not been detected at early stages of ageing is that the volume fraction of the precipitates has not reached the critical value for determining their crystal structure before the second stage of decomposition occurs. Gn the decomposition mode at the first stage of ageing, preferential precipitations on grain boundaries and twin boundaries were observed in Cu-1.15 at.% Cr alloy at 500°C by [87Sto]. Although [79Wea] have observed periodic structures in Cu-0.67 at. % Cr alloy at 475°C they have not got direct evidence for spinodal decomposition. Because the experimental alloys are even outside the chemical spinodal region shown in Fig. 7, a conclusion can be made that the decomposition of the fee Cu-Cr alloy at the first stage of ageing proceeds by a process of nucleation and growth. Acknowledgement The authors are grateful to Professor K. Lilius for providing excellent working conditions at the laboratory. Discussions with Dr. N. Bochvar of Baikov Institute of Metallurgy, Russia, are greatly appreciated. One of the authors (K. J. Z.) wishes to express his special gratitude to Professors Huang Peiyun and Jin Zhanpeng for their constant support, and to thank the Finnish Centre for International Mobility (CIMO) for scholarship. References [OIHin]

G. Hindrichs, 2. Anorg. Chem., 59,420 (1908).

[23Sie]

E. Siedschlag, 2. Anorg. Chem., 131, 173 (1923).

[3OCor]

M. G. Corson, Rev. Met., 27, 83 (1930).

[39Ale]

W. 0. Alexander, J. Inst. Met., 64,93 (1939).

STABLE AND METASTABLE EQUILIBRIA IN THE Cu-Cr SYSTEM

[48Hib]

W. R. Hibbard, Jr., F. D. Rosi, H. T. Clark, Jr., R. I. O’Herron, Trans. AZME, 175,283 (1948).

[48Red]

0. Redlich and A. T. Kister, Ind. Engng. Chem., 40,345 (1948).

[57Doi]

T. Doi, J. Jpn. Inst. Met., 21,337 (1957).

[6OWil]

R. 0. Williams, Trans. ASM, 52,530 (1960).

[67Zakl

M:. V. Zakharov and 0. E. Osintsev, Zzv. Vyssh. Ucheb. Zaved., Tsvtn. Met., 5, 152-155 (1967)

[73Kni]

R W. Knights and P. Wilkes, Metull. Trans., 4,2389 (1973).

[75Dri]

M. E. Drits, L. L. Rokhlin, N. R. Bochvar, E. V. Lysova, V. M. Rozenberg, A. K. Nikolaev, N. B. Shparo, Sov. Non-Ferrous Met. Res., 2,74 (1975).

[77Kuz]

G. M. Kuznetsov, V. N. Fedorov, A. L. Rodnyanskaya, Izv. VUZ Tsvetn, Metall., 3,84 (1977).

[78Kau]

L. Kaufman, CAEPHAD, 2, 117 (1978).

[79Kub]

0. Kubaschewski and C. B. Alcock, Metallurgical Thermochemistry, 5th edition, Pergamon Press, New York, p.55 (1979).

[79Wea]

G. C. Weatherly, P. Humble, and D. Borland, Acta Metall., 27, 1815 (1979).

[82Tim]

L. Timberg and J. M. Toguri, J. C&m. Thermodyn., 14, 193 (1982).

[84Cha]

D. J. Chakrabarti and D. E. Laughlin, Bull. Alloy Phase Diagrams, 5,59 (1984).

[84Jan]

B. Jansson, PhD Thesis, Royal Institute of Technology, Stockholm, Sweden (1984).

[840no]

K. Ono, S. Nishi, and T. Oishi, Trans. JIM, 25,810 (1984).

[86Leo]

M. Leonov, N. Bochvar, and V. Ivanchenko, Dokl. Akad. Nauk SSSR, 290,888 (1986).

[87Sau]

N. Saunders, Mater, Sci. Technol., 3,671 (1987).

[87Sto]

J. Stobrawa and Z. Rdzawski, Ser. Metall., 21, 1269 (1987).

[88Luk]

H. L. Lukas, J. Weiss, U. Kattner, and E.-Th. Henig, Manual of the Computer Programs BINGSS, TEIRGSS, QUAGSS, BINFKT, TERFKT, QUAFKT and PMLFKT, Version 11, Max Planck Institut fur Metallforschung (1988).

[9OHiim]

M Hginllainen, K. J%skelainen, R. Luoma, P. Taskinen, 0. Teppo, and M. Vanninen, CALPHAD, 14,

[9OTan]

T. Tanaka, N. A. Gokcen, and Z. Morita, Z. Metal&de., 81,49 (1990).

[91Din]

A. T. Dinsdale, CALPHAD, 15,317 (1991).

[91Ino]

T. K. Inouye, H. Fujiwara, and M. Iwase, Metall. Trans., 22B, 475 (1991).

[910ka]

H. Okamoto, J. Phase Equilibria, 12,623 (1991).

[93Boc]

N. Bochvar, private communication (1993).

[93Tan]

T. Tanaka, N. A. Gokcen, Z. Morita, and T. Iida, Z. Metal&de., 84, 192 (1993).

125 (1990).

KEJUN ZENG AND M. HiiMiiLiilNEN

100

2400 2200 z 5 ijj Y Ill’

2000

5 % E

1600

s r

1400

1800

1200

MOLE-FRACTION

CR

FIG. 1 The Cu-Cr phase diagram calculated using the present themmdynamic description, compared with the experimental liquidus data of bee-Cr used in optimization.

0.5

1.0

1.5

2.0

MOLE-PERCENT

2.5

3.0

CR

FIG. 2 Comparison between the calculated liquidus of fee-(Cu) using the present thermodynamic description and the measured values.

STABLE AND METASTABLE EQUILIBRIA IN THE Cu-Cr SYSTEM

liquid

cI39Ale e 75Dri A 57Doi *67Zak + 46Hib o 67Kaw

700 -m 800 0

E-3

I 5

I 10

I 25

I 20

I 15

MOLE-FRACTION

30

CR

FIG. 3 Comparison between the calculated solvus of (Cu) using the present thermodynamic description and the experimental data from various sows.

2200

t 77Kuz A 62Tim 0 640no + 66Leo 0 23Sie

_

2000 -

0

0.2

0.4

0.8

0.6

MOLE-FRACTION

1.0

CR

FIG. 4 Comparison between the liquidus of bee-Cr proposed by different authors and all the experimental liquidus data available.

101

KEJUN ZENG AND M. HiiMliLiilNEN

‘102

0.501

’

’

’

’

’

’

1’

‘1’

i

61423K 91lno * 1523 K 91lno

I

I

I

I

I

I

I

I

I

12 14 16 18 20 MOLE-FRACTION

CR

1.0 0.9 0.8 0.7 g

i= 2

0.6

040.3 0.2 0.1

0 1473 K

91lno A1573K 91lno q 1573 K 940no

0 MOLE-FRACTION

CR

FIG. 5 The activities of Cr in the Cu-Cr liquid phase: comparison between the calculated and the experimental values at 1423,1473,1523, and 1573K.

STABLE AND METASTABLE

EQUILIBRIA

IN THE Cu-Cr SYSTEM

CIacu 1823

K 02Ttm * E+~ 1823 K 82Tim

I

0

0.2

I

I

I

0.4

0.6

0.8

MOLE-FRACTION

CR

FW. 6 The activities of Cu and Cr in the Cu-Cr liquid phase.: c~arison calculated and the experimental values at 1823 K.

I

9

I

1.0

I

I

I

I 0.4

I 0.6

I 0.8

between the

8-

6E g

6-

$

4-

g

3-

;

2lO_:” 0

I 0.2

MOLE-FRACTION

1.0

CR

FIG. 7 The calculated Gibbs energy of the fee-(Cu) phase at 1350 K (reference states: feeCu and bee-Cr at 1350 K).

103

104

KEJUN ZENG AND M. HliMiiliilNEN

z >I

2000

i5

1800

5

1000

miscibilitygap =-

k- spinodal

’ I

0.2

0

0.4

0.6

0.8

MOLE-FRACTION

1.O

CR

FIG. 8 (a) The rnetastable miscibility gap and spinodaI region of the fee-(Cu) phase imposed on the stable Cu-Cr phase diagram.

Liquid

Z 5

1600 -

iii

liquid + bee-Cr

.

,

,

.

.

.+’

,

/ : k

0 ~tpinodal

/

800 600 400 0

E-3

/ I I 25

/

/

0) + b&r / / / I 50

I 75

I 100

I 125

MOLE_FRACTlON CR

FIG. 8 (b) An enlarged part of (a) on the Cu-rich side.

150