- Email: [email protected]
Thermodynamic assessment of the Pt–Sn system
Journal of Alloys and Compounds 325 (2001) 109–112
L
www.elsevier.com / locate / jallcom
Thermodynamic assessment of the Pt–Sn system 1
Xuping Su, Fucheng Yin*, Minhwa Huang , Zhi Li, Chuntao Chen Institute of Materials Research, School of Mechanical Engineering, Xiangtan University, Hunan 411105, PR China Received 10 November 2000; accepted 23 February 2001
Abstract The phase diagram and thermodynamic data of the Pt–Sn (Platinum–Tin) system have been assessed by the CALPHAD technique. A set of self-consistent thermodynamic model parameters is presented to describe the phase equilibria of the system. The intermediate phases are modeled as stoichiometric compounds. The calculated phase diagram and thermodynamic properties using the optimized model parameters agree very well with the experimental data. 2001 Elsevier Science B.V. All rights reserved. Keywords: Transition metal alloys; Phase diagram; Thermodynamic modelling
1. Introduction
2.1. Liquid and f.c.c. phases
There are many systematic investigations on the binary alloys formed between d-block metal (transition metal) and sp-block metal [1–3]. Pt–Sn binary alloy is important for welding of Pt-wires [4]. By modeling, a self-consistent description of the phase relations and thermodynamic properties of the Pt–Sn system was derived by means of CALPHAD technique. Furthermore, the consistencies between thermodynamic data and phase diagrams have been checked. The equilibrium phase diagram of the Pt–Sn system has been previously proposed by Durussel et al. [5]. Doerinckel [6], Podkopajew [7], Ferro et al. [8] and Schaller [9] have also investigated the system. Boer et al. [10] have made semi-empirical calculations to get the excess functions of the solid and liquid phases of this binary system. More recently, Anres et al. [4] has reinvestigated the phase diagram and measured the enthalpy of formation of the system.
The liquid and fcc phases are described with the substitutional solution model for which the Gibbs energy expression is
2. Thermodynamic models
G fm 5 x Pt 0 G fPt 1 x Sn 0 G fSn 1 RTsx Pt ln x Pt 1 x Sn ln x Snd 1 E G fm
where 0 G fPt and 0 G fSn are the molar Gibbs energies of pure platinum and tin with the structure f, respectively, taken from the work of Dinsdale [11]. The x Pt and x Sn denote mole fractions of Pt and Sn, respectively. E G fm is the excess Gibbs energy, expressed as a Redlich–Kister polynomial [12]: E
*Corresponding author. E-mail address: [email protected] (F. Yin). 1 Present address: School of Materials Science & Engineering, Shanghai Jiao Tong University, Shanghai, PR China.
OL i
G fm 5 x Pt x Sn
f Pt,Sn
sx Pt 2 x Snd i
(2)
i
where i L fPt,Sn is the binary interaction parameter of degree ‘i’. i f L Pt,Sn can be temperature dependent and two terms are usually enough, i.e. i
The Gibbs energies of pure elements are referred to the enthalpies of the pure elements in their defined reference phase at 298.15 K (HSER).
(1)
L fPt,Sn 5 a i 1 b i T
(3)
2.2. Intermediate phases The intermediate phases Pt 3 Sn, PtSn, Pt 2 Sn 3 , PtSn 2 and PtSn 4 in the Pt–Sn system are treated as stoichiometric compounds. The Gibbs energies per mole of formula unit PtA SnB can be represented as
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01201-4
X. Su et al. / Journal of Alloys and Compounds 325 (2001) 109 – 112
110
fcc bct A Sn B G Pt 5 A0 G Pt 1 B 0 G Sn 1 a 1 bT m
(4)
0 bct where 0 G fcc Pt and G Sn are Gibbs energies of the respective pure elements in f.c.c. or b.c.t. structure. The parameters a and b have been evaluated in this study.
3. Experimental information Many groups [4–9] have investigated the Pt–Sn binary system. No great difference exists in the phase diagrams proposed by [4,5,13]. The existence of five compounds, Pt 3 Sn, PtSn, Pt 2 Sn 3 , PtSn 2 and PtSn 4 , has been confirmed. Hansen et al. [13] redrew the Pt–Sn phase diagram based on thermal analysis data of Doerinckel [6] and Podkopajew [7]. Durussel et al. [5] investigated the Pt–Sn system over narrow intervals of composition (1–2 at.% Sn) by means of differential thermal analysis, X-ray diffraction and electron microprobe analysis. The phase diagram shows five stoichiometric compounds, Pt 3 Sn (face centered cubic, cP4 [14]), PtSn (hexagonal, hP4 [15]), Pt 2 Sn 3 (hexagonal, hP10 [16]), PtSn 2 (cubic, cF12 [17]) and PtSn 4 (orthorhombic, oC20 [18]). The five stoichiometric intermediate phases have higher congruent melting points than previously indicated in the literature [13] for Pt 3 Sn (167562 K) and PtSn (154962 K) and higher peritectic decomposition temperatures for Pt 2 Sn 3 (117162 K), PtSn 2 (102162 K) and PtSn 4 (81362 K). The phase PtSn has a structure similar to metastable PtSn 3 (P6 3 /mmc) and a strictly Table 1 A comparison of calculated and experimental equilibria in the Pt–Sn system Reaction
Temperature, K
Composition a
Reference
Liq.→Pt (f.c.c.)1Pt 3 Sn
1638 164362 1632 1693 167562 1677 1343 134062 1352 |1578 154962 1541 1121 117162 1171 1018 102162 1021 |795 81362 813 |501 50162 504.3
Uncertain 0.196 0.2 0.25 0.25 0.25 0.40 0.394 0.382 0.485|0.50 0.50 0.50 0.75 0.728 0.699 0.81 0.812 0.796 0.95 0.95 0.95 |0.995 |0.994 0.997
[13] [4] This study [13] [4] This study [13] [4] This study [13] [4] This study [13] [4] This study [13] [4] This study [13] [4] This study [13] [4] This study
Liq.→Pt 3 Sn
Liq.→Pt 3 Sn1PtSn
Liq.→PtSn
Liq.1PtSn→Pt 2 Sn 3 Liq.1Pt 2 Sn 3 →PtSn 2 Liq.1PtSn 2 →PtSn 4
Liq.→PtSn 4 1bSn (bct)
a
Only the liquidus points are listed (in atomic fraction of Sn).
stoichiometric composition as shown by electron microprobe and X-ray diffraction methods, which is different from the phase diagram redrawn from Hansen [13]. Anres et al. [4] obtained some data of the Pt–Sn phase diagram by calorimetric measurements, which showed a good agreement with the data presented by Durussel et al. [5] except for the low platinum concentrations. The phase PtSn 3 [19] seems to only exist at high pressure (900 K, 7 GPa). Table 1 lists the invariant reactions of the diagram together with the calculated values from this study. Enthalpies of formation of the stoichiometric compounds were measured by Ferro et al. [8] using calorimetry and Schaller [9] using emf measurements at various temperatures, respectively. Anres et al. [4] investigated the enthalpies of formation of PtSn at 1354 K and 1491 K and of Pt 3 Sn at 1659 K using a high temperature calorimeter. de Boer et al. [10] calculated the enthalpies of formation. Many determinations of the limiting partial molar enthalpy of Pt in Sn were reported [20–26]. Anres et al. [4] investigated the enthalpies of mixing from 870 K to 1660 K over the stable concentration range of the liquid phase and the partial molar enthalpies of platinum by calorimetric experiments.
4. Assessment procedure The above experimental information is carefully checked during the evaluation of thermodynamic model parameters. For liquid phase, the interaction parameters of i50, 1 and 2 in i L Liq. Pt,Sn are used. The optimization was carried out using the PARROT module of the computer software THERMO-CALC [27]. The phase diagram data and experimental thermodynamic information were as input to the program. All the data were first reviewed and chosen. Each selected information was offered a certain weight, which was changed by trial and error in the course of assessment, until most of them were recalculated within the expected uncertainty bounds. Generally, the weights for invariant equilibria are the highest followed by the thermodynamic data. The parameters for liquid phase were first optimized, based on experimental data of phase diagram and thermodynamic data of the liquid. Congruently melting points of compounds were fitted next. The experimental data of phase diagram were taken from Anres et al. [4] and Durussel et al. [5]. Anres et al. [4], Ferro et al. [8] and Schaller [9] determined enthalpies of formation of compounds, which were selected as input into the optimization. The data of Anres et al. is more negative than the other, especially Pt 3 Sn. During the optimization, it was found that the thermodynamic modeling parameters fitting the data of Anres et al. would result in unreasonable deviation of the calculated phase diagram from experimental data. Because
X. Su et al. / Journal of Alloys and Compounds 325 (2001) 109 – 112
111
the thermochemical data of Anres et al. [4] was not consistent with the phase diagram, they were given lower weights. The enthalpies of mixing from Anres et al. [4] were used. But the partial molar enthalpies of platinum [4] were not used on account of their deviation from the calculated values from integral enthalpies of mixing. All the parameters were eventually optimized to obtain the best consistency between phase diagram and thermodynamic data.
5. Results and discussions All evaluated thermodynamic model parameters are listed in Table 2. The calculated phase diagram is shown in Fig. 1, which is in good agreement with the experiments by Durussel [5] and Anres [4]. All invariant reactions in the Pt–Sn system are listed in Table 1, so are the recommended data by Hansen [13] and Durussel [5]. The coordinates of invariant reactions obtained in this study agree well with the experimental data. The assessed terminal solubility of tin in platinum at 1643 K is 12.7 at.% Sn, which is in accord with the result of Durussel [5]. The calculated temperature of eutectic reaction Liq.→Pt (F.c.c.)1Pt 3 Sn is slightly higher than that of Durussel [5], which may be because the Pt-rich side of the phase diagram is not accurately determined [4,5,13]. The calculated enthalpies of formation at 298 K are shown in Fig. 2, together with the data from [4,8–10]. As shown, the calculated enthalpies agreed with the experimental ones. Fig. 3 shows the calculated enthalpies of mixing of Pt and Sn, plotted with the experimental points at the range from 876 K to 1659 K from Anres [4]. The calculated values are consistent with the experimental ones.
Fig. 1. Calculated Pt–Sn phase diagram compared with the experimental measurements [4,5].
6. Conclusion The phase relations and thermodynamic properties in the Pt–Sn system were evaluated from the experimental information available in the literatures. A consistent set of thermodynamic parameters was derived. The calculated phase equilibria and thermodynamic properties agree well with the experimental data.
Table 2 The optimized parameters describing the thermodynamic properties of the Pt–Sn system a Redlich–Kister formalism Liquid
0
L Liq Pt,Sn 5 2183 917128.312T L Liq Pt,Sn 5 221 075220.297T 2 Liq L Pt,Sn 5 26766133.710T 0 fcc L Pt,Sn 5 2147 980 114.822T 1 fcc L Pt,Sn 5 2534826.091T 1
Stoichiometric phases 0 0 fcc 0 bct 3 Sn Pt 3 Sn G Pt G Sn 5 2 159 280 1 5.901T Pt:Sn 2 3 G Pt 2 0 PtSn 0 fcc 0 bct PtSn G Pt:Sn 2 G Pt 2 G Sn 5 2 114 567 1 11.512T 0 0 fcc 0 bct 2 Sn 3 Pt 2 Sn 3 G Pt Pt:Sn 2 2 G Pt 2 3 G Sn 5 2 272 719 1 47.192T 0 PtSn 2 0 fcc 0 bct PtSn 2 G Pt:Sn 2 G Pt 2 2 G Sn 5 2 147 472 1 30.0T 0 0 fcc bct 4 PtSn 4 G PtSn G Pt 2 4 0 G Sn 5 2 146 049 1 17.113T Pt:Sn 2 a All parameters are in Joules per mole. The lattice stabilities of pure elements are taken from the SGTE database.
Fig. 2. Calculated enthalpies of formation in Pt–Sn system compared with experimental measurements [4,8–10].
112
X. Su et al. / Journal of Alloys and Compounds 325 (2001) 109 – 112
Fig. 3. Calculated enthalpies of mixing of Pt and Sn at various temperatures compared with experimental measurement [4].
References D. El Allam, Thesis, Universite´ de Provence, Marseilles, 1989. R. Haddad, Thesis, Universite´ de Provence, Marseilles, 1993. P. Anres, Thesis, Universite´ de Provence, Marseilles, 1997. P. Anres, M. Gaune-Escard, J.P. Bros, E. Hayer, J. Alloys Comp. 280 (1998) 158. [5] Ph. Durussel, R. Massara, P. Feschotte, J. Alloys Comp. 215 (1994) 175.
[1] [2] [3] [4]
[6] F. Doerinckel, Z. Anorg. Allg. Chem. 54 (1907) 349. [7] N. Podkopajew, Zh. Russ, Fiz. Khim. Obshch. 40 (1908) 249. [8] R. Ferro, R. Capelli, A. Borsese, S. Delfino, in: Rendiconti della Classe di Scienze fisiche, matematiche e naturali, Vol. LIV, 1973, p. 4, serie VIII. [9] H.J. Schaller, Z. Phys. Chem., N.F. 112 (1978) 85. [10] F.R. de Boer, R. Boom, W.C.M. Mattens, A.R. Miedema, A.K. Niessen, Cohesions in Metals, Vol. 1, North-Holland, Amsterdam, 1988. [11] A.T. Dinsdale, CALPHAD 15 (1991) 317. [12] O. Redlich, A. Kister, Ind. Eng. Chem. 40 (1948) 345. [13] H. Hansen, K. Anderko, in: T.B. Massalski, P.R. Subramanian, H. Okamoto, L. Kacprzak (Eds.), Binary Alloy Phase Diagrams, ASM International, Metals Park, OH, 1990, p. 3130. [14] I.R. Harris, M. Norman, A.W. Bryant, J. Less-Comm. Met. 16 (4) (1978) 427. [15] O. Nial, Svensk Kem. Tidskr. 59 (1947) 172. [16] K. Schubert, H. Pfisterer, Z. Metallkd. 40 (1949) 405. [17] H.J. Waldbaum, Z. Metallkd. 41 (1950) 200. ˆ [18] K. Schubert, U. Rossler, Z. Metallkd. 41 (1950) 298. [19] V.L. Larchev, S.V. Popova, Izvestiya Akademia Nauk SSSR Neorganicheskie Materialy 20 (1984) 693. [20] R.A. Walker, J.B. Darby, Acta Metall. 18 (1970) 1261. [21] G.W. Geiken, USUAEC Report, University of California, 1967, UCRL-17615. [22] R.A. Oriani, W.K. Murphy, Acta Metall. 10 (1962) 879. [23] W. Vogelbein, M. Ellner, B. Predel, Thermochim. Acta 44 (1981) 141. [24] J.N. Pratt, A.W. Bryant, D.T. Underhill, Tech. Report, US Army Control No. DAJA 37-70-C-0632, University of Birmingham, UK, 1971. [25] J.B. Darby Jr., K.M. Myles, Metall. Trans. 3 (1972) 653. [26] R. Boom, Scr. Metall. 8 (1974) 1277. [27] B. Sundman, B. Janson, J.-O. Anderson, CALPHAD 9 (2) (1985) 153.
L
www.elsevier.com / locate / jallcom
Thermodynamic assessment of the Pt–Sn system 1
Xuping Su, Fucheng Yin*, Minhwa Huang , Zhi Li, Chuntao Chen Institute of Materials Research, School of Mechanical Engineering, Xiangtan University, Hunan 411105, PR China Received 10 November 2000; accepted 23 February 2001
Abstract The phase diagram and thermodynamic data of the Pt–Sn (Platinum–Tin) system have been assessed by the CALPHAD technique. A set of self-consistent thermodynamic model parameters is presented to describe the phase equilibria of the system. The intermediate phases are modeled as stoichiometric compounds. The calculated phase diagram and thermodynamic properties using the optimized model parameters agree very well with the experimental data. 2001 Elsevier Science B.V. All rights reserved. Keywords: Transition metal alloys; Phase diagram; Thermodynamic modelling
1. Introduction
2.1. Liquid and f.c.c. phases
There are many systematic investigations on the binary alloys formed between d-block metal (transition metal) and sp-block metal [1–3]. Pt–Sn binary alloy is important for welding of Pt-wires [4]. By modeling, a self-consistent description of the phase relations and thermodynamic properties of the Pt–Sn system was derived by means of CALPHAD technique. Furthermore, the consistencies between thermodynamic data and phase diagrams have been checked. The equilibrium phase diagram of the Pt–Sn system has been previously proposed by Durussel et al. [5]. Doerinckel [6], Podkopajew [7], Ferro et al. [8] and Schaller [9] have also investigated the system. Boer et al. [10] have made semi-empirical calculations to get the excess functions of the solid and liquid phases of this binary system. More recently, Anres et al. [4] has reinvestigated the phase diagram and measured the enthalpy of formation of the system.
The liquid and fcc phases are described with the substitutional solution model for which the Gibbs energy expression is
2. Thermodynamic models
G fm 5 x Pt 0 G fPt 1 x Sn 0 G fSn 1 RTsx Pt ln x Pt 1 x Sn ln x Snd 1 E G fm
where 0 G fPt and 0 G fSn are the molar Gibbs energies of pure platinum and tin with the structure f, respectively, taken from the work of Dinsdale [11]. The x Pt and x Sn denote mole fractions of Pt and Sn, respectively. E G fm is the excess Gibbs energy, expressed as a Redlich–Kister polynomial [12]: E
*Corresponding author. E-mail address: [email protected] (F. Yin). 1 Present address: School of Materials Science & Engineering, Shanghai Jiao Tong University, Shanghai, PR China.
OL i
G fm 5 x Pt x Sn
f Pt,Sn
sx Pt 2 x Snd i
(2)
i
where i L fPt,Sn is the binary interaction parameter of degree ‘i’. i f L Pt,Sn can be temperature dependent and two terms are usually enough, i.e. i
The Gibbs energies of pure elements are referred to the enthalpies of the pure elements in their defined reference phase at 298.15 K (HSER).
(1)
L fPt,Sn 5 a i 1 b i T
(3)
2.2. Intermediate phases The intermediate phases Pt 3 Sn, PtSn, Pt 2 Sn 3 , PtSn 2 and PtSn 4 in the Pt–Sn system are treated as stoichiometric compounds. The Gibbs energies per mole of formula unit PtA SnB can be represented as
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01201-4
X. Su et al. / Journal of Alloys and Compounds 325 (2001) 109 – 112
110
fcc bct A Sn B G Pt 5 A0 G Pt 1 B 0 G Sn 1 a 1 bT m
(4)
0 bct where 0 G fcc Pt and G Sn are Gibbs energies of the respective pure elements in f.c.c. or b.c.t. structure. The parameters a and b have been evaluated in this study.
3. Experimental information Many groups [4–9] have investigated the Pt–Sn binary system. No great difference exists in the phase diagrams proposed by [4,5,13]. The existence of five compounds, Pt 3 Sn, PtSn, Pt 2 Sn 3 , PtSn 2 and PtSn 4 , has been confirmed. Hansen et al. [13] redrew the Pt–Sn phase diagram based on thermal analysis data of Doerinckel [6] and Podkopajew [7]. Durussel et al. [5] investigated the Pt–Sn system over narrow intervals of composition (1–2 at.% Sn) by means of differential thermal analysis, X-ray diffraction and electron microprobe analysis. The phase diagram shows five stoichiometric compounds, Pt 3 Sn (face centered cubic, cP4 [14]), PtSn (hexagonal, hP4 [15]), Pt 2 Sn 3 (hexagonal, hP10 [16]), PtSn 2 (cubic, cF12 [17]) and PtSn 4 (orthorhombic, oC20 [18]). The five stoichiometric intermediate phases have higher congruent melting points than previously indicated in the literature [13] for Pt 3 Sn (167562 K) and PtSn (154962 K) and higher peritectic decomposition temperatures for Pt 2 Sn 3 (117162 K), PtSn 2 (102162 K) and PtSn 4 (81362 K). The phase PtSn has a structure similar to metastable PtSn 3 (P6 3 /mmc) and a strictly Table 1 A comparison of calculated and experimental equilibria in the Pt–Sn system Reaction
Temperature, K
Composition a
Reference
Liq.→Pt (f.c.c.)1Pt 3 Sn
1638 164362 1632 1693 167562 1677 1343 134062 1352 |1578 154962 1541 1121 117162 1171 1018 102162 1021 |795 81362 813 |501 50162 504.3
Uncertain 0.196 0.2 0.25 0.25 0.25 0.40 0.394 0.382 0.485|0.50 0.50 0.50 0.75 0.728 0.699 0.81 0.812 0.796 0.95 0.95 0.95 |0.995 |0.994 0.997
[13] [4] This study [13] [4] This study [13] [4] This study [13] [4] This study [13] [4] This study [13] [4] This study [13] [4] This study [13] [4] This study
Liq.→Pt 3 Sn
Liq.→Pt 3 Sn1PtSn
Liq.→PtSn
Liq.1PtSn→Pt 2 Sn 3 Liq.1Pt 2 Sn 3 →PtSn 2 Liq.1PtSn 2 →PtSn 4
Liq.→PtSn 4 1bSn (bct)
a
Only the liquidus points are listed (in atomic fraction of Sn).
stoichiometric composition as shown by electron microprobe and X-ray diffraction methods, which is different from the phase diagram redrawn from Hansen [13]. Anres et al. [4] obtained some data of the Pt–Sn phase diagram by calorimetric measurements, which showed a good agreement with the data presented by Durussel et al. [5] except for the low platinum concentrations. The phase PtSn 3 [19] seems to only exist at high pressure (900 K, 7 GPa). Table 1 lists the invariant reactions of the diagram together with the calculated values from this study. Enthalpies of formation of the stoichiometric compounds were measured by Ferro et al. [8] using calorimetry and Schaller [9] using emf measurements at various temperatures, respectively. Anres et al. [4] investigated the enthalpies of formation of PtSn at 1354 K and 1491 K and of Pt 3 Sn at 1659 K using a high temperature calorimeter. de Boer et al. [10] calculated the enthalpies of formation. Many determinations of the limiting partial molar enthalpy of Pt in Sn were reported [20–26]. Anres et al. [4] investigated the enthalpies of mixing from 870 K to 1660 K over the stable concentration range of the liquid phase and the partial molar enthalpies of platinum by calorimetric experiments.
4. Assessment procedure The above experimental information is carefully checked during the evaluation of thermodynamic model parameters. For liquid phase, the interaction parameters of i50, 1 and 2 in i L Liq. Pt,Sn are used. The optimization was carried out using the PARROT module of the computer software THERMO-CALC [27]. The phase diagram data and experimental thermodynamic information were as input to the program. All the data were first reviewed and chosen. Each selected information was offered a certain weight, which was changed by trial and error in the course of assessment, until most of them were recalculated within the expected uncertainty bounds. Generally, the weights for invariant equilibria are the highest followed by the thermodynamic data. The parameters for liquid phase were first optimized, based on experimental data of phase diagram and thermodynamic data of the liquid. Congruently melting points of compounds were fitted next. The experimental data of phase diagram were taken from Anres et al. [4] and Durussel et al. [5]. Anres et al. [4], Ferro et al. [8] and Schaller [9] determined enthalpies of formation of compounds, which were selected as input into the optimization. The data of Anres et al. is more negative than the other, especially Pt 3 Sn. During the optimization, it was found that the thermodynamic modeling parameters fitting the data of Anres et al. would result in unreasonable deviation of the calculated phase diagram from experimental data. Because
X. Su et al. / Journal of Alloys and Compounds 325 (2001) 109 – 112
111
the thermochemical data of Anres et al. [4] was not consistent with the phase diagram, they were given lower weights. The enthalpies of mixing from Anres et al. [4] were used. But the partial molar enthalpies of platinum [4] were not used on account of their deviation from the calculated values from integral enthalpies of mixing. All the parameters were eventually optimized to obtain the best consistency between phase diagram and thermodynamic data.
5. Results and discussions All evaluated thermodynamic model parameters are listed in Table 2. The calculated phase diagram is shown in Fig. 1, which is in good agreement with the experiments by Durussel [5] and Anres [4]. All invariant reactions in the Pt–Sn system are listed in Table 1, so are the recommended data by Hansen [13] and Durussel [5]. The coordinates of invariant reactions obtained in this study agree well with the experimental data. The assessed terminal solubility of tin in platinum at 1643 K is 12.7 at.% Sn, which is in accord with the result of Durussel [5]. The calculated temperature of eutectic reaction Liq.→Pt (F.c.c.)1Pt 3 Sn is slightly higher than that of Durussel [5], which may be because the Pt-rich side of the phase diagram is not accurately determined [4,5,13]. The calculated enthalpies of formation at 298 K are shown in Fig. 2, together with the data from [4,8–10]. As shown, the calculated enthalpies agreed with the experimental ones. Fig. 3 shows the calculated enthalpies of mixing of Pt and Sn, plotted with the experimental points at the range from 876 K to 1659 K from Anres [4]. The calculated values are consistent with the experimental ones.
Fig. 1. Calculated Pt–Sn phase diagram compared with the experimental measurements [4,5].
6. Conclusion The phase relations and thermodynamic properties in the Pt–Sn system were evaluated from the experimental information available in the literatures. A consistent set of thermodynamic parameters was derived. The calculated phase equilibria and thermodynamic properties agree well with the experimental data.
Table 2 The optimized parameters describing the thermodynamic properties of the Pt–Sn system a Redlich–Kister formalism Liquid
0
L Liq Pt,Sn 5 2183 917128.312T L Liq Pt,Sn 5 221 075220.297T 2 Liq L Pt,Sn 5 26766133.710T 0 fcc L Pt,Sn 5 2147 980 114.822T 1 fcc L Pt,Sn 5 2534826.091T 1
Stoichiometric phases 0 0 fcc 0 bct 3 Sn Pt 3 Sn G Pt G Sn 5 2 159 280 1 5.901T Pt:Sn 2 3 G Pt 2 0 PtSn 0 fcc 0 bct PtSn G Pt:Sn 2 G Pt 2 G Sn 5 2 114 567 1 11.512T 0 0 fcc 0 bct 2 Sn 3 Pt 2 Sn 3 G Pt Pt:Sn 2 2 G Pt 2 3 G Sn 5 2 272 719 1 47.192T 0 PtSn 2 0 fcc 0 bct PtSn 2 G Pt:Sn 2 G Pt 2 2 G Sn 5 2 147 472 1 30.0T 0 0 fcc bct 4 PtSn 4 G PtSn G Pt 2 4 0 G Sn 5 2 146 049 1 17.113T Pt:Sn 2 a All parameters are in Joules per mole. The lattice stabilities of pure elements are taken from the SGTE database.
Fig. 2. Calculated enthalpies of formation in Pt–Sn system compared with experimental measurements [4,8–10].
112
X. Su et al. / Journal of Alloys and Compounds 325 (2001) 109 – 112
Fig. 3. Calculated enthalpies of mixing of Pt and Sn at various temperatures compared with experimental measurement [4].
References D. El Allam, Thesis, Universite´ de Provence, Marseilles, 1989. R. Haddad, Thesis, Universite´ de Provence, Marseilles, 1993. P. Anres, Thesis, Universite´ de Provence, Marseilles, 1997. P. Anres, M. Gaune-Escard, J.P. Bros, E. Hayer, J. Alloys Comp. 280 (1998) 158. [5] Ph. Durussel, R. Massara, P. Feschotte, J. Alloys Comp. 215 (1994) 175.
[1] [2] [3] [4]
[6] F. Doerinckel, Z. Anorg. Allg. Chem. 54 (1907) 349. [7] N. Podkopajew, Zh. Russ, Fiz. Khim. Obshch. 40 (1908) 249. [8] R. Ferro, R. Capelli, A. Borsese, S. Delfino, in: Rendiconti della Classe di Scienze fisiche, matematiche e naturali, Vol. LIV, 1973, p. 4, serie VIII. [9] H.J. Schaller, Z. Phys. Chem., N.F. 112 (1978) 85. [10] F.R. de Boer, R. Boom, W.C.M. Mattens, A.R. Miedema, A.K. Niessen, Cohesions in Metals, Vol. 1, North-Holland, Amsterdam, 1988. [11] A.T. Dinsdale, CALPHAD 15 (1991) 317. [12] O. Redlich, A. Kister, Ind. Eng. Chem. 40 (1948) 345. [13] H. Hansen, K. Anderko, in: T.B. Massalski, P.R. Subramanian, H. Okamoto, L. Kacprzak (Eds.), Binary Alloy Phase Diagrams, ASM International, Metals Park, OH, 1990, p. 3130. [14] I.R. Harris, M. Norman, A.W. Bryant, J. Less-Comm. Met. 16 (4) (1978) 427. [15] O. Nial, Svensk Kem. Tidskr. 59 (1947) 172. [16] K. Schubert, H. Pfisterer, Z. Metallkd. 40 (1949) 405. [17] H.J. Waldbaum, Z. Metallkd. 41 (1950) 200. ˆ [18] K. Schubert, U. Rossler, Z. Metallkd. 41 (1950) 298. [19] V.L. Larchev, S.V. Popova, Izvestiya Akademia Nauk SSSR Neorganicheskie Materialy 20 (1984) 693. [20] R.A. Walker, J.B. Darby, Acta Metall. 18 (1970) 1261. [21] G.W. Geiken, USUAEC Report, University of California, 1967, UCRL-17615. [22] R.A. Oriani, W.K. Murphy, Acta Metall. 10 (1962) 879. [23] W. Vogelbein, M. Ellner, B. Predel, Thermochim. Acta 44 (1981) 141. [24] J.N. Pratt, A.W. Bryant, D.T. Underhill, Tech. Report, US Army Control No. DAJA 37-70-C-0632, University of Birmingham, UK, 1971. [25] J.B. Darby Jr., K.M. Myles, Metall. Trans. 3 (1972) 653. [26] R. Boom, Scr. Metall. 8 (1974) 1277. [27] B. Sundman, B. Janson, J.-O. Anderson, CALPHAD 9 (2) (1985) 153.