Thermodynamic assessment of the La–In system

L

Journal of Alloys and Compounds 333 (2002) 118–121

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Thermodynamic assessment of the La–In system Ying Wei, Xuping Su, Fucheng Yin*, Zhi Li, Xianping Wu, Chuntao Chen Institute of Materials Research, School of Mechanical Engineering, Xiangtan University, Hunan 411105, PR China Received 9 March 2001; accepted 15 June 2001

Abstract Optimized descriptions of the phase diagram and thermodynamic properties of the La–In system are obtained from the experimental phase diagram and thermodynamic data by means of the computer program THERMO-CALC. A set of self-consistent thermodynamic model parameters is derived. The system contains seven intermetallic compounds. The standard enthalpies of formation of the seven compounds are calculated. Good agreement is obtained between the calculation and experimental results.  2002 Elsevier Science B.V. All rights reserved. Keywords: Rare earth alloys; Phase diagram; Thermodynamic modelling

1. Introduction

The coefficients a through h are taken from the work of Dinsdale [4].

The alloys of rare earths with elements of Group III have been demonstrated to be good materials for application as superconductors, catalysts and reaction promoting additives, and cathodic materials with various emission properties [1]. Interest in the phase boundaries of La-rich alloys in the La–In system arose during an investigation of the superconductive properties of La 3 In base alloys [2]. There are many reports in the literature on RE–In systems. Inconsistencies, however, can be found in the phase diagram and the thermodynamic data. By modeling the La–In system, a self-consistent description of the phase relations and thermodynamic data is presented by means of the CALPHAD technique [3].

2. Thermodynamic models

Gi 2 H

SER i

2

3

5 a 1 bT 1 cT ln T 1 dT 1 eT 1 fT 1 gT 7 1 hT 29

*Corresponding author. E-mail address: [email protected] (F. Yin).

0 F 0 F GF m 5 X La G La 1 X In G In 1 RT(X La ln X La 1 X In ln X In )

1 EG F m

(2)

0 F where 0 G F La and G In are, respectively, the molar Gibbs energies of pure lanthanum and indium with structure F in the non-magnetic state [4]. XLa and XIn denote the mole fractions of La and In. E G F m is the excess Gibbs energy, expressed as a Redlich–Kister polynomial [5]:

OL

GF m 5 X La X In

i

F La,In

(XLa 2 XIn )i

(3)

i

The Gibbs energy of pure element i, referred to the enthalpy of its stable state at 298.15 K, is described as a function of temperature by 0

The liquid, bcc and fcc phases are treated with the substitutional solution model for which the Gibbs energy expression is

E

2.1. Pure elements

0

2.2. Liquid, bcc and fcc phases

21

(1)

where i L F La,In is the binary interaction parameter evaluated in the present work. i L F La,In can be temperature dependent and two coefficients are usually sufficient, given by i

LF La,In 5 a i 1 b i T

(4)

2.3. Stoichiometric intermetallic compounds The intermetallic phases La 3 In, La 2 In, LaIn, LaIn x , La 3 In 5 , LaIn 2 and LaIn 3 in the La–In system are treated as stoichiometric compounds. La 3 In 5 , possibly having a small

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Y. Wei et al. / Journal of Alloys and Compounds 333 (2002) 118 – 121

composition range, is considered to be fixed in composition because of limited information. For the same reason, LaIn x is described to be La 43 In 57 according to its composition (atomic percent). The Gibbs energies per mole of formula unit LaA InB can be expressed as G

LaA In B La:In

0

5A G

dhcp La

0

1B G

tetragonal In

1 A 0 1 B0 T 1 C0 T ln T (5)

dhcp tetragonal where 0 G La and 0 G In are the Gibbs energies of the respective pure elements in the dhcp and tetragonal structure. The coefficients A 0 and B0 are evaluated in this work. Especially for the La 43 In 57 phase, the coefficient C0 is introduced in the assessment to fit the invariant reactions at 1346 and 1178 K.

119

Table 1 Invariant reactions in the La–In system Reaction

L→g-La(bcc)1La 3 In g-La(bcc)→b-La(fcc) 1La 3 In L1La 2 In→La 3 In L1LaIn→La 2 In L→LaIn L→LaIn1La 3 In 5 La 3 In 5 1LaIn→LaIn x LaIn x →La 3 In 5 1LaIn L→La 3 In 5 L1La 3 In 5 →LaIn 2 L→LaIn 2 1LaIn 3 L→LaIn 3 L→In(tetragonal)1LaIn 3

T (K) (X Liq. In ) Present work

Ref [6]

1019 (0.1437)

1015 (0.135)

979.3 (0.0731) 1087 (0.2045) 1211 (0.3316) 1387 1376 (0. 536) 1346 1179 1454 1424 (0.6757) 1397 (0.7158) 1409 427.4 (0.996)

975 (0.081) 1089 (0.191) 1228 (0.296) 1398 1359 (0.54) 1346 1178 1458 1426 (0.68) 1393 (0.712) 1413 428 (0.995)

3. Experimental The phase diagram of the La–In system was established by McMasters et al. [6]. Two liquidus data points on the In-rich side were reported by Degtyar et al. [7]. McMasters et al. [6] confirmed the existence of six intermetallic compounds, namely La 3 In, La 2 In, LaIn, La 3 In 5 , LaIn 2 and LaIn 3 . He believed that LaIn x existed in the temperature range 1178–1346 K between 50 and 60 at.% In, although further information about this compound was uncertain. He suggested that only La 3 In 5 was not a line compound, but did not give the composition range. Novozhenov et al. [8] found that LaIn 3 melts at 1498 K and the La 2 In 3 phase melts congruently at 1458 K. Palenzona et al. [9] suggested that La 2 In 3 is actually La 3 In 5 . Kober et al. [10] indicated the absence of La 3 In 5 , which was suggested to be La 5 In 3 by Palenzona et al. [9]. Delfino et al. [11] believed that La 5 In 3 did not exist. He confirmed that there are six intermetallic compounds in the La–In system as reported by McMasters et al. [6]. La 3 In, La 2 In and LaIn 2 are peritectic compounds. LaIn, La 3 In 5 and LaIn 3 melt congruently. There are four eutectic reactions: L→g-La(bcc)1La 3 In, L→LaIn1La 3 In 5 , L→LaIn 2 1LaIn 3 , L→In(tetragonal)1LaIn 3 . Two eutectoid reactions occur: g-La(bcc)→b-La(fcc)1La 3 In, LaIn x →La 3 In 5 1LaIn, and one peritectoid reaction: La 3 In 5 1LaIn→LaIn x . There are two terminal solutions g-La and b-La in the La–In system. The maximum experimental terminal solubilities of indium in g-La and b-La are 10.2 and 3.5 at.% In, respectively [6]. Data for the phase diagram used in the assessment are summarized in Table 1. Many groups [7,8,10,12,13] have measured the enthalpies of formation of LaIn 3 at various temperatures by different methods. Among these reports, Borsese et al. [13] investigated the heats of formation of La–In alloys at 300 K systematically by isoperibol calorimetry. The corresponding thermodynamic properties were obtained over the

large composition range from 15.060.25 to 75.860.25 at.% La. Since from 35.160.25 to 75.860.25 at.% La, equilibria were not attained in the calorimeter, he suggested that the data could be considered only as partial values of D f H.

4. Assessment procedure Most of the experimental data given above were considered during the evaluation of the thermodynamic model parameters. The phase diagram data of McMasters et al. [6] were adopted. The existence of seven compounds, La 3 In, La 2 In, LaIn, LaIn x , La 3 In 5 , LaIn 2 and LaIn 3 , was accepted in the present work. La 3 In 5 was treated as a stochiometric compound. For the enthalpies of formation of La–In alloys, only the values of La–In compounds were chosen as input. Optimization was carried out using the software package THERMO-CALC [14]. Experimental phase diagram data and thermodynamic information were used as input to the program. All the data was first reviewed and selected as above. Each piece of selected information was given a certain weight, which was changed by trial and error in the course of the assessment until most of the calculated results were recalculated within the expected uncertainty limits. On the basis of experimental data for the phase diagram and thermodynamic properties, the parameters of the liquid phase were first optimized, next those of the congruent intermediate phases, and other compounds, then LaInx and, finally, terminal solutions. Generally, the weights for invariant equilibria are the highest followed by the thermodynamic data. All the parameters were finally optimized to obtain the best consistency between the phase diagram and thermodynamic data.

Y. Wei et al. / Journal of Alloys and Compounds 333 (2002) 118 – 121

120

Table 2 Optimized parameters describing the thermodynamic properties of the La–In system Liquid

0

L Liq. La,In 5 2 166 490.2 1 45.5134T L Liq. La,In 5 2 44 871.7 1 1.5873T 0 bcc L La,In 5 2 152 646.8 1 27.9591T 1 bcc L La,In 5 2 52 648.1 0 fcc L La,In 5 2 127 980.5 1 9.5541T 1 fcc L La,In 5 2 68 324.3 1 13.4417T 0 0 dhcp tetragonal 3 In G La 2 0 G In 5 2 112 347.5 1 14.2968T La:In 2 3 G La 0 0 dhcp 0 tetragonal 2 In G La 2 2 G 2 G 5 2 113 074.8 1 17.5289T La:In La In 0 0 dhcp tetragonal G LaIn 2 0 G In 5 2 115 213.94 1 27.0353T La:In 2 G La 0 tetragonal 43 In 57 G La 2 43 0 G dhcp 2 57 0 G In 5 2 5 710 452.4 1 La:In La 1229.9886T 1 0.21016T ln T 0 La 3 In 5 dhcp tetragonal G La:In 2 3 0 G La 2 5 0 G In 5 2 453 715.8 1 90.9890T 0 LaIn 2 0 dhcp 0 tetragonal G La:In 2 G La 2 2 G In 5 2 170 278.1 1 36.5438T 0 LaIn 3 G La:In 2 0 G dhcp 2 3 0 G tetragonal 5 2 228 367.6 1 59.5022T La In 1

bcc fcc La 3 In La 2 In LaIn LaIn x La 3 In 5 LaIn 2 LaIn 3

The values are given in SI units per mole formula unit.

5. Results and discussion All evaluated parameters are listed in Table 2. Fig. 1 shows the calculated phase diagram, together with the experimental data from McMasters et al. [6] and Degtyar et al. [7]. The calculated phase diagram is in excellent agreement with the measured diagram. The temperatures and compositions of the assessed invariant reactions in the La–In system are listed in Table 1 and compared with experimental data [6]. The invariant reactions obtained in this work agree well with the experimental information, with a discrepancy within 4 K; there are only three exceptions, which are discussed below. Clearly, there are deviations in the liquidus line of the calculated phase diagram on the In-rich side, compared with the two experimental data points from Degtyar et al.

Fig. 2. Calculated enthalpies of formation of La–In intermediate phases compared with experimental measurements [13].

[7]. In addition, there is a discrepancy of more than 10 K from the experimental data in three reactions: L→LaIn1 La 3 In 5 (eutectic), L1LaIn→La 2 In (peritectic) and L→LaIn (congruently melting). In the range 29.6 to 54 at.% In of the diagram [6], the liquidus line is visually asymmetrical, which is improbable thermodynamically [15]. As can be seen from the experimental phase diagram, the region of liquidus line in the range 50 to 54 at.% In is steeper than that in the range 29.6 to 50 at.% In. Considering the symmetry of the liquidus line, the deviation between the calculated phase diagram and the experimental diagram is reasonable. Further experimental work on this system may be needed to clarify the result. Fig. 2 shows the assessed enthalpies of formation and also data from Refs. [7,8,10,12,13]. The level of agreement of the calculated enthalpies of formation with the experimental information is also good except for that reported by Novozhenov et al. [8], which is too negative compared with the others. There are also deviations with respect to the experimental values [13] obtained under conditions of incomplete reaction.

6. Conclusion

Fig. 1. Calculated La–In phase diagram compared with experimental measurements [6,7].

The phase relations and thermodynamic properties of the La–In system were evaluated from experimental information available in the literature. A set of self-consistent thermodynamic parameters was derived for describing the Gibbs energies in this system. The calculated phase equilibria agree well with most of the literature data. More experimental work may be necessary to clarify this result. The calculated standard enthalpies of formation of La 3 In,

Y. Wei et al. / Journal of Alloys and Compounds 333 (2002) 118 – 121

La 2 In, LaIn, La 3 In 5 , LaIn 2 and LaIn 3 are 228.087, 237.692, 257.607, 256.714, 256.759 and 257.092 kJ / mol, respectively.

Acknowledgements This investigation was supported by the Youth Science Foundation of the Hunan Educational Committee, China.

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[5] O. Redlich, A. Kister, Ind. Eng. Chem. 40 (1948) 345. [6] O.D. McMasters, K.A. Gschneidner Jr., J. Less-Common Met. 38 (1974) 137. [7] V.A. Degtyar, A.P. Bayonov, L.A. Vnuchkova, V.V. Serebrennikov, Izv. Akad. Nauk SSSR, Metally 4 (1971) 149, Engl. Transl., Russ. Metall. 4 (1971)103. [8] V.A. Novozhenov, T.M. Skhol’nikova, V.V. Serebrennikov, Zh. Fiz. Khim. 49 (1975) 3012. [9] A. Palenzona, S. Cirafici, in: C.E.T. White, H. Okamoto (Eds.), Phase Diagrams of Indium Alloys and Their Engineering Applications, ASM International, Materials Park, OH, 1992, p. 145. [10] V.I. Kober, V.A. Dubinin, A.I. Kochkin, I.F. Nichkov, S.P. Raspopin, Izv. V.U.Z. Tsvetn. Metall. 6 (1983) 113, in Russian; V.I. Kober, V.A. Dubinin, A.I. Kochkin, I.F. Nichkov, S.P. Raspopin, Sov. Non-Ferrous Met. Res. 11 (1983) 449. [11] S. Delfino, A. Saccone, R. Ferro, J. Less-Common Met. 102 (1984) 289. [12] A. Palenzona, S. Cirafici, Thermochim. Acta 9 (1974) 419. [13] A. Borsese, A. Calabretta, S. Delfino, R. Ferro, J. Less-Common Met. 51 (1977) 45. [14] B. Sundman, B. Janson, J.-O. Anderson, The THERMO-CALC databank system, CALPHAD 9 (2) (1985) 153. [15] H. Okamoto, T.B. Massalski, J. Phase Equil. 12 (2) (1991) 148.