Thermodynamic assessment of the Eu–Sn system

Journal of Alloys and Compounds 379 (2004) 148–153

Thermodynamic assessment of the Eu–Sn system Lihui Liu a , Changrong Li a,∗ , Fuming Wang b , Zhenmin Du a , Weijing Zhang a b

a School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, PR China School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, PR China

Received 20 October 2003; received in revised form 3 February 2004; accepted 12 February 2004

Abstract The phase equilibria, the thermodynamic data and the phase diagram of the Eu–Sn (europium–tin) system have been critically assessed by means of CALculation of PHAse Diagram (CALPHAD) technique. The solution phases (liquid and bcc) are modeled with the Redlich–Kister equation, and the intermetallic compounds (Eu2 Sn, Eu5 Sn3 , EuSn, Eu3 Sn5 and EuSn3 ) are treated as stoichiometric compounds. The terminal bct and diamond phases are considered as phases of pure element Sn since the very small solubility of Eu in Sn. A set of self-consistent thermodynamic parameters of the Eu–Sn system was obtained. The calculations agree well with the respective experimental data. © 2004 Elsevier B.V. All rights reserved. Keywords: Eu–Sn system; Phase diagram; Thermodynamic properties

1. Introduction The Eu–Sn binary system contains five intermetallic phases: Eu2 Sn, Eu5 Sn3 , EuSn, Eu3 Sn5 and EuSn3 . They are expected to have some special properties. For example, the stoichiometric EuSn3 is of particular interest because of its magnetic properties [1–4]. Knowledge of the thermodynamic phase stabilities and of the phase diagram is important for the further application study of the Eu–Sn system. At present, comparably few data on the thermochemistry of the Eu–Sn system have been reported. Experimental difficulties may be a reason. In this case, the computer coupling appears more helpful. It can combine all available thermodynamic properties and phase diagram information and estimate the missing properties. In this work, the consistent thermodynamic analyses of the Eu–Sn binary system are presented utilizing CALculation of PHAse Diagram (CALPHAD) technique. The thermodynamic parameters for describing the Gibbs energies of all the solution phases and the intermetallic compounds are optimized.

2. Experimental information Few experimental thermodynamic data of the Eu–Sn binary system can be obtained. Only the enthalpy of the stoi∗

Corresponding author. E-mail address: [email protected] (C. Li).

0925-8388/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2004.02.012

chiometric EuSn3 , the partial enthalpy and the logarithm of the activity coefficient of Eu in dilute solutions of Eu–Sn are available. The French researchers, Bacha et al. [5] reported the enthalpy of formation of the EuSn3 and the partial enthalpy of Eu in dilute solution. The former Soviet researchers, Kober et al. [6] provided the activity coefficient of Eu as a function of temperature in dilute liquid solutions. The phase diagram has been investigated by Palenzona et al. [7] using differential thermal analysis, metallographic analysis, X-ray analysis and electron microscopy method. The whole composition range of the Eu–Sn binary was covered. The Eu–Sn binary system is mainly composed of the liquid solution phase (liquid), the terminal solid solution (bcc), the pure component phases (bct and diamond), and the stoichiometric compounds (Eu2 Sn, Eu5 Sn3 , EuSn, Eu3 Sn5 and EuSn3 ). The experimental data are summarized in Table 1. The related crystal structures are listed in Table 2. Among all the five intermetallic phases, Eu3 Sn5 (Pu3 Pd5 -type), Eu5 Sn3 (W5 Si3 -type) and Eu2 Sn (Co2 Si-type) were prepared and characterized by Palenzona et al. [7] for the very first time. The other two intermetallic compounds, EuSn3 (AuCu3 -type) and EuSn (CrB-type), were reported by Harris and Raynor [8] and Merlo and Fornasini [9], respectively. Two peritectic reactions exist in the Eu–Sn system at temperatures of 1173 and 1398 K, respectively. And four eutectic points occur at: 5 at.% Sn, 1063 K; 44 at.% Sn, 1348 K; 74 at.% Sn, 1058 K; and less than 1 at.% Eu, 503 K.

L. Liu et al. / Journal of Alloys and Compounds 379 (2004) 148–153

149

Table 1 Experimental data of the Eu–Sn binary system Type of data

Methoda

Value

Reference

Eutectic reaction Liquid → EuSn3 + (bct)Sn Liquid → Eu3 Sn5 + EuSn3 Liquid → Eu5 Sn3 + EuSn Liquid → Eu2 Sn + (bcc)Eu

DTA, DTA, DTA, DTA,

≥99 at.%Sn, 503 K 74 at.%Sn, 1058 K 44 at.%Sn, 1348 K 5 at.%Sn, 1063 K

[10] [7] [7] [7]

Peritectic reactions Liquid + EuSn → Eu3 Sn5 Liquid + Eu2 Sn → Eu5 Sn3

DTA, MGA DTA, MGA

62 at.%Sn, 1173 K 37.5 at.%Sn, 1398 K

[7] [7]

MGA MGA MGA MGA

Pure elements Eu Sn

1095 K (melting point) 505 K (melting point)

[11] [12]

Congruent melting points Eu2 Sn EuSn EuSn3

DTA, MGA DTA, MGA DTA, MGA

1628 K 1398 K 1068 K

[7] [7] [7]

Enthalpy of EuSn3 Logarithm of the activity coefficient Partial enthalpy of Eu in dilute Sn

EMF EMF EMF

−211.006 ± 7.733 KJ mol−1

[5] [6] [5]

a

DTA: Differential thermal analysis; MGA: metallographic analysis; EMF: electromotive force.

Table 2 Eu–Sn crystal structure data Phase

Composition (at.%Sn)

Pearson symbol

Space group

Strukturbericht designation

Prototype

Reference

Eu Eu2 Sn Eu5 Sn3 EuSn Eu3 Sn5 EuSn3 ␤Sn ␣Sn

0 33.3 37.5 50 62.5 75 100 100

cI2 oP12 tI32 oC8 oC32 cP4 tI4 cF8

¯ Im3m Pnma I4/mcm Cmcm Cmcm ¯ Pm3m I41 /amd ¯ Fd3m

A2 C23 D8m Bf – LI2 A5 A4

w Co2 Si W5 Si3 CrB Pd5 Pu3 AuCu3 ␤Sn C diamond)

[13] [7] [7] [9] [7] [8] [13] [13]

All the experimental data mentioned in Table 1 were adopted in this assessment.

3.1. Pure elements

3.2. Solution phases 0 Gφ (T) i

φ Gi (T) − HiSER ,

The Gibbs energy function, = of the pure element i (i: Eu or Sn) in the phase φ (φ: liquid, bcc, bct or diamond) is described by the following equation: φ

φ

Gi (T) = Gi (T) − HiSER = a + bT + cT ln(T) + dT 2 +eT + fT 3

(3)

In the present work, the Gibbs energy functions for pure elements are taken from the SGTE (Scientific Group Thermodata Europe) compilation compiled by Dinsdale [14].

3. Thermodynamic models

0

bct SER GHSERSn = 0 Gbct Sn (T) = GSn (T) − HSn

−1

+ gT + hT 7

−9

φ

(1)

HiSER

refers to the molar enthalpy of the element i at where 298.15 K in its standard element reference (SER) state, i.e. bcc for the pure element Eu and bct for the pure element Sn. The Gibbs energy of the element i in its SER state is denoted by GHSERi : bcc SER GHSEREu = 0 Gbcc Eu (T) = GEu (T) − HEu

In the Eu–Sn system, there are two solution phases: liquid and bcc. The Gibbs energies are described by the following expression:

(2)

φ

SER SER Gφm − xEu HEu − xSn HSn = xEu 0 GEu (T) + xSn 0 GSn (T)

+RT(xEu ln xEu + xSn ln xSn ) + E Gφm

(4)

φ

where E Gm is the excess Gibbs energy expressed by the Redlich–Kister polynomials: E

Gφm = xEu xSn




i φ

L (xEu − xSn )i

i

(i = 0, 1, 2 in this work)

(5)

150

L. Liu et al. / Journal of Alloys and Compounds 379 (2004) 148–153

where i Lφ is the ith interaction parameter between elements Eu and Sn in the phase φ, and its general form is the function of temperature: i φ

L = ai + bi T + ci T lnT + di T 2 + ei T 3 + fi T −1

(6)

where ai , bi , ci , di , ei and fi are the coefficients to be optimized. Based on all the phase equilibria and the thermodynamic data, the most terms we use in the present work are up to the first two, i.e. i φ

L = ai + bi T

(7)

3.3. Intermetallic compounds All intermetallic compounds, Eu2 Sn, Eu5 Sn3 , EuSn, Eu3 Sn5 and EuSn3 , are treated as stoichiometric compounds Eum Snn . The Gibbs energy for per mole of formula unit Eum Snn is expressed as follows: Eum Snn SER − mHSER Gm Eu − nHSn = mGHSEREu + nGHSERSn m Snn +GEu f

(8)

m Snn is the Gibbs energy of formation for per where GEu f mole of formula unit Eum Snn . Owing to lack of experimental measurements, it is assumed that: Cp = 0. Thus, m Snn GEu can be given by the following expression: f n Snn GEu = a + bT f

(9)

where the parameters a and b were assessed in the present work.

4. Thermodynamic assessment procedure The assessment mainly includes the selection of the thermodynamic data and the optimization of the thermodynamic model parameters. The optimization of thermodynamic parameters has been carried out with the help of the PARROT module of Thermo-Calc software developed by Sundman et al. [15]. The working strategy is the minimization of the square sum of the difference between the experimental data and the computed values. The key to the successful optimization by using the PARROT program strongly depends on three points [16]: Firstly, the models selected for the phases. Secondly, how many and which of the model parameters can be assessed with the experimental data available. Then comes the third, the start values for most of the model parameters. The operations in details will be discussed as follows. Based on the thermodynamic model selected for each phase, a set of model parameters of about seventeen for the Eu–Sn binary was prepared to be optimized. The experimental phase equilibria and the thermodynamic data were used as input. The model parameters are optimized in proper order. The process started with the pre-adjustment of the model parameters of the liquid solution phase, which is the phase of connection with many other phases. Since the enthalpy of the stoichiometric compound, EuSn3 , has been reported, the model parameters of the EuSn3 phase were optimized secondly. Whereafter, the parameters of the congruent intermetallic phases and the other incongruent compounds were optimized from left to right in turn. During the period of the

Table 3 Thermodynamic parameters of Eu–Sn systema Phase

Parameters

Liquid

0 Lliquid

= −166740.093 + 9.35648626T = 50387.7145 − 7.89834928T 2 Lliquid = 20426.2867 + 6.30622781T 0 Gliquid =b Eu 298.15 < T < 400.00 − 1482.46 + 128.661522T − 32.8418896T × ln(T) + 0.00931735T2 − 4.006564 × 10−6 T3 + 102717/T 400.00 < T < 1095.00 10972.726 − 103.688201T + 4.3501554T × ln(T) − 0.036811218T2 + 5.452934 × 10−6 T3 − 646908/T 1095.00 < T < 1900.00 − 6890.641+175.517247T−38.11624T × ln(T) 1900.00 < T < 6000.00 − 150.3617078T + 65530.22 1 Lliquid

bcc

0 Lbcc

= −63584.1875 =b 298.15 < T < 1095.00 − 9864.965 + 135.836737T−32.8418896T × ln(T) + 0.00931735T2 −4.006564 × 10−6 T3 + 102717/T 1095.00 < T < 1900.00 − 287423.476 + 2174.73304T −309.357101T × ln(T) + 0.114530917T2 − 8.809866 × 10−6 T3 + 48455305/T 1900.00
Eu2 Sn Eu5 Sn3 EuSn Eu3 Sn5 EuSn3 a

0 bct GEu2 Sn − 20 Gbcc Eu − GSn = −111028.8 − 17.5995254T bcc Eu 0 Sn 3 5 G − 5 GEu − 30 Gbct Sn = −333142.041 − 34.0773552T 0 bct GEuSn − 0 Gbcc Eu − GSn = −111088.341 + 2.52913384T 0 bct GEu3 Sn5 − 30 Gbcc Eu − 5 GSn = −444204.072 + 31.2926257T 0 Gbct = −219508.836 + 45.082154T GEuSn3 − 0 Gbcc − 3 Eu Sn

In J/mole of formula unit. The Gibbs energy functions for pure Eu from 298.15 to 1900 K are taken from [14] and those from 1900 to 6000 K were obtained by extrapolation for the purpose of inspecting the optimized thermodynamic parameters. b

L. Liu et al. / Journal of Alloys and Compounds 379 (2004) 148–153 1800

1240 Palenzona et al. (1998) [7]

1628K

1600

1220

1400

EuSn+liquid

liquid

1395K

Temperature,K

1356K 1171K

1200 1095K

1069K

1063K

1000

600

EuSn3

b.c.c.

EuSn

800

Eu3Sn5

1060K

501.6K

400

liquid

1200 1180

1171 K

1160

Eu3Sn5

1396K

Eu 2Sn Eu 5Sn 3

Temperature, k

151

1140

504.9682K

b.c.t. 286K

1120

diamond

200 0

0.2

0.4 0.6 Mole Fraction Sn

0.8

1.0

EuSn+Eu3 Sn5

1100 0.55

Fig. 1. The calculated Eu–Sn phase diagram and the comparison with the experimental data [7].

Eu3 Sn5 +liquid

0.60 0.65 Mole Fraction Sn

0.70

Fig. 2. The enlarged section of the phase diagram calculated by present thermodynamic description.

optimization, each item of the selected information was offered a certain weight by judgement, which was changed by trial and error. The weights play an important role throughout the course of the optimization. The phase equilibria needed to be guaranteed and emphasized and the thermodynamic data with perfect precision should be given a relatively large weight. In the Eu–Sn binary, the weights for the invariant equilibria and the congruently melting points are the first largest and those for the thermodynamic data the second. The final data set was obtained after the integrative consideration of all the experimental data with different scales of balance weights.

Fig. 1 and Table 4, the satisfactory agreement is obtained between the calculations and experiments. The largest difference is about 8 K in the invariant temperature of the reaction: liquid → Eu5 Sn3 + EuSn. Though the difference seems a little bit large, it is necessary to ensure that the next invariant equilibrium, liquid+EuSn → Eu3 Sn5 , is still peritectic as reported in [7]. This can be seen clearly in Fig. 2 which is the enlarged section of Fig. 1. Further optimizing the relevant parameters of the above equilibria to lessen the difference of the former invariant temperature will cause the change of the reaction type of the latter invariant equilibrium from peritectic to eutectic. And the difference will be less than 2 K. However, there has been no such kind of report by far. New experimental evidences are needed to confirm this reaction type. In view of the estimated experimental errors (about 1–2 at.%), the experimental compositions of all invariant reactions are well reproduced. Fig. 3 shows the standard enthalpies of formation of intermetallic compounds calculated using the present optimized thermodynamic parameters together with the experimental data from [5].

5. Results and discussions The thermodynamic description and the optimized parameters of the Eu–Sn binary obtained in the present assessment are listed in Table 3. The Eu–Sn phase diagram calculated using the present thermodynamic parameters is given in Fig. 1 together with the experimental data from Ref. [7]. The invariant equilibria in the Eu–Sn system are listed in Table 4. As shown in Table 4 Invariant reactions in the Eu–Sn system Reaction

Experimental data [7] liquid XSn

Liquid → Eu2 Sn + Eu(bcc) Liquid → Eu2 Sn Liquid + Eu2 Sn → Eu5 Sn3 Liquid → Eu5 Sn3 + EuSn Liquid → EuSn Liquid + EuSn → Eu3 Sn5 Liquid → Eu3 Sn5 + EuSn3 Liquid → EuSn3 Liquid → EuSn3 + Sn(bct) a

(mole fraction)

0.05 0.3333 0.419a 0.44 0.5 0.62a 0.73 0.75 0.998

The value is metered from the phase diagram given by [7].

Present work liquid

Temperature (K)

XSn

1063 1628 1398 1348 1398 1173 1058 1068 503

0.054 0.3333 0.4296 0.4452 0.5 0.6255 0.7194 0.75 0.9915

(mole fraction)

Temperature (K) 1063 1628 1396 1356 1395 1171 1060 1069 501.6

152

L. Liu et al. / Journal of Alloys and Compounds 379 (2004) 148–153 0

25

Bacha et al.[5]

15 10

-20

a --- XEu = 0.3

Kober et al.[6]

b --- XEu = 0.2 c --- XEu = 0.1 d --- XEu = 0.001

5

log γ

Enthalpy of Formation,kJ/mol

20

-10

-30

0 a b c d

-5

-40

-10 -15

-50

-20

-60

-25 1.00

0

0.2

0.4 0.6 0.8 Mole Fraction Sn

1.05

1.10

1.0

1.15

1.20

1.25

1.30

1.35

1000/T

Fig. 3. The calculated and the experimental enthalpy of formation in the Eu–Sn system.

Fig. 4 compares the calculated results and the experimental data of the logarithm of the activity coefficient of Eu in dilute solutions of Eu–Sn. Fig. 5 gives the calculated partial enthalpy of Eu in dilute liquid Sn with the comparison of the experimental data.

6. Parameters inspection In order to inspect the rationality of the optimized parameters, the thermodynamic equilibrium calculation is extended to relatively high temperature. To do this, the Gibbs energy functions of pure elements are checked firstly. Using the data from [14], the Gibbs energies of the liquid and the bcc phases of the pure element Eu are given in Fig. 6a. It is shown that the Gibbs energy of the bcc phase is lower than that of the liquid phase at both the lower and

Fig. 4. The calculated and the experimental activity coefficient of Eu in dilute solutions.

the higher temperature ranges. Based on [14], the effective temperature range for both of the liquid and the bcc Eu is from 298.15 to 1900 K. The lower Gibbs energy of bcc Eu above about 3900 K is abnormal. For the higher temperature range above 1900 K, a linear extrapolation—continuous in slope and value at 1900 K, is adopted by the present author to avoid the stable bcc Eu. The Gibbs energy expressions after extrapolation are listed in Table 3 and are plotted in Fig. 6b. Considering the extrapolated Gibbs energy functions for pure element Eu, the Gibbs energies of all the phases of the Eu–Sn binary at 5000 K were drawn in Fig. 7. The catenary type of the Gibbs energy curves of the liquid and the bcc phases guarantees that the miscibility gap will not appear at very high temperature. The relative magnitudes of the Gibbs energies illustrate that it is the liquid phase but the solid phases is the most stable phase when no vapor phase is considered in the system.

HEu , kJ/mol

955.5 K 958.5 K

955.5 K

958.5 K

Mole Fraction Eu Fig. 5. The calculated and the experimental partial enthalpy of Eu in dilute solutions.

L. Liu et al. / Journal of Alloys and Compounds 379 (2004) 148–153

153

Fig. 6. Gibbs energy for pure element Eu before (a) and after (b) extrapolation.

Acknowledgements -540

bc c

-580 -600

uid

Eu3Sn5

-620

liq

Gibbs energy, kJ/mole

-560

The authors would like to express their appreciation to the Royal Institute of Technology Sweden for supplying the Thermo-Calc software. This work was supported by the National Natural Science Foundation of China (No. 5-0174005).

EuSn3

-640

References

EuSn

-660 Eu5Sn3

-680

Eu2Sn

-700 -720 0

0.2

0.4

0.6

0.8

1.0

Mole Fraction Sn Fig. 7. The calculated Gibbs energies at 5000 K.

7. Conclusions All of the experimental phase equilibria and thermodynamic data of the Eu–Sn system from the available literature have been critically evaluated. Within the regime of CALPHAD technique, the thermodynamic models for all the solution phases and the intermetallic compounds are selected and the Gibbs energy functions are optimized. A set of consistent thermodynamic parameters for the Eu–Sn binary system was obtained. The calculated phase equilibria and thermodynamic properties agree well with the experimental data.

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