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Thermodynamic properties of the liquid Ag–Cu–Sn lead-free solder alloys
Materials Chemistry and Physics 122 (2010) 480–484
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Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Thermodynamic properties of the liquid Ag–Cu–Sn lead-free solder alloys Marek Kopyto a , Boguslaw Onderka b , Leszek A. Zabdyr a,∗ a Institute of Metallurgy and Materials Science, Polish Academy of Sciences, Laboratory of Physical Chemistry of Materials, 25 Reymonta St., 30-059 Krakow, Poland b AGH University of Science and Technology, Faculty of Non-Ferrous Metals, Department of Physical Chemistry and Electrochemistry, 30 Mickiewicza Ave., 30-059 Krakow, Poland
a r t i c l e
i n f o
Article history: Received 20 May 2009 Received in revised form 30 July 2009 Accepted 16 March 2010 Keywords: Electrochemical techniques Thermodynamic properties Alloys Electronic materials
a b s t r a c t The electromotive force measurement method was employed to determine the thermodynamic properties of liquid Ag–Cu–Sn alloys using solid electrolyte galvanic cells as shown below: Kanthal + Re, Ag–Cu–Sn, SnO2 |Y ttria stabilized Zirconia|air, Pt, pO2 = 0.21 atm Measurements were carried out for three cross-sections with constant Ag/Cu ratio equal to: 1/3, 1 and 3 and for tin compositions ranging from 10 up to 80 at.%, every 10%, resulting in a total of 24 different alloy compositions. The temperature of the measurements varied within the range from 973 to 1325 K. A linear dependence of the e.m.f. on temperature was observed for all alloy compositions and the appropriate line equations were derived. Tin activities were calculated as function of composition and temperature. Results were presented in tables and figures. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Knowledge of the phase equilibria in Ag–Cu–Sn ternary system is of fundamental importance for the electronic packaging technologies which involve processes that require the direct contact of the solid and liquid phase near equilibrium conditions. That knowledge is important for the understanding of boundary conditions for a variety of processing steps as Ag–Sn/Cu interfacial reactions. A number of works are available regarding the phase equilibria in the Ag–Cu–Sn system. Gebhardt and Petzow [1] determined experimentally the isothermal sections of Ag–Cu–Sn ternary system at 500 and 600 ◦ C. They also suggested the invariant reaction, L + -Cu6 Sn5 = εAg3 Sn + Sn, in the Sn-rich region at 225 ◦ C. Shen [2] and Shen et al. [3] measured enthalpies of solution of Ag in Ag–Cu–Sn at 720 K and for XCu < 0.065 and XAg < 0.045 by solution calorimetry. Fedotov et al. [4,5] determined isopleths at 10 wt.% Cu, wt.% Ag/wt.% Sn = 1:1 and for wt.% Cu/wt.% Sn = 2:9. Kubaschewski [6] presented the isothermal sections at several temperatures and the liquidus projection of the Ag–Cu–Sn ternary system. Miller et al. [7] examined experimentally the phase equilibria of the Ag–Cu–Sn ternary system by microscopy, wavelength dispersive spectroscopy WDS, DTA and XRD. They discovered the invariant reaction,
∗ Corresponding author. Tel.: +48 12 2952844; fax: +48 12 2952804. E-mail address: [email protected] (L.A. Zabdyr). 0254-0584/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2010.03.030
L = + ε2 + Sn, at the Sn-rich corner, Sn–4.7 wt.% Ag–1.7 wt.% Cu, and at 216.8 ◦ C, which is inconsistent with that proposed by Gebhardt and Petzow [1]. Chada et al. [8] used EDS to study the solubility of Cu in Sn–Ag liquids containing 3.5 wt.% Ag as a function of temperature. Moon et al. [9] studied the Sn-rich corner of the Ag–Cu–Sn system (at.% Ag < 10.49 and wt.% Cu < 3.21) both by experimental determination (thermal analysis/cycling experiments) and thermodynamic calculation. Loomans and Fine [10] focused on the determination of the ternary eutectic temperature and composition through a study of the binary eutectics between Sn and Cu6 Sn5 and between Sn and Ag3 Sn based on thermal analysis. Their results are in good agreement with data of Moon et al. [9]. Lee et al. [11], Lee et al. [12] and Ohnuma et al. [13] developed thermodynamic models of the Ag–Cu–Sn ternary system to calculate the isothermal sections at various temperatures. Although not all phase relationships determined were in agreement with earlier data, they all found no ternary compounds in the Ag–Cu–Sn ternary system. Gisby and Dinsdale [14] reassessed Ag–Cu–Sn system using new phase description for sub-binaries: Ag–Sn and Cu–Sn. Moon and Boettinger [15] determined experimentally parameters of eutectic composition in Ag–Cu–Sn system. Luef et al. [16] measured calorimetrically the enthalpies of mixing of liquid alloys in Ag–Cu–Sn system. Yen and Chen [17] determined experimentally the phase equilibria in Ag–Cu–Sn system for the isothermal sections at 240 and 450 ◦ C which are of importance in soldering applications. They confirmed the absence of ternary compounds in the system and found that all the binary compounds have only limited ternary
M. Kopyto et al. / Materials Chemistry and Physics 122 (2010) 480–484
481
Fig. 1. Schematic cross-section of the galvanic cell.
solubility. The attempt to calculate a phase diagram without ternary parameters was carried out. Tin activities in the liquid Ag–Cu–Sn ternary alloys were determined in the present work using solid electrolyte galvanic cells.
Fig. 2. Scheme of cell assembly.
2. Experimental Closed-end yttria-stabilized zirconia (YSZ) tubes (5/8 mm I/OD – Yamari, Japan) were used as the electrolyte and dry air (pO2 = 0.21 atm) was used as the reference electrode. Platinum wire was used for air electrode and KanthalTM wire with rhenium tip was applied for alloy electrode as current leads; the cross-section through the cell is shown schematically in Fig. 1, and the scheme of the cell assembly is presented in Fig. 2. Experiments were performed in a vertical resistance furnace with the brass head, enabling to fix the cell within the constant temperature zone. After a constant temperature was reached, the cell was kept to stabilize electromotive force, and then the e.m.f. was recorded by data acquisition system consisted of Keithley 2000 digital voltmeter and a computer. Such a system enabled continuous recording of time-dependent e.m.f. curves, as can be seen in Fig. 3. Silver–copper–tin alloys were prepared from pure metals supplied by The Institute of Electronic Materials Technology, Warsaw, Poland (Ag and Sn 99.99%, Cu 99.999%). They were melted directly in the electrolyte tube (XSn ≥ 0.5) or pre-melted at given composition under vacuum in sealed quartz ampoules. Alloy sample was placed at the bottom of the electrolyte tube with a SnO2 (99.99%, POCH, Gliwice, Poland) pellet. An inert atmosphere was maintained inside the cell by passing 5 ml/min of argon gas of quality 5.0 (Linde, Poland) through the H-tube enabling inert gas penetration into the electrolyte tube without disturbing the local equilibrium over the sample. The reversibility of the cell was checked by passing small current from an external source for a few seconds and the e.m.f. returned to the original value within ±1 mV in about 1–10 min depending on the temperature. E.m.f. readings were taken within the range 973–1325 K on heating and cooling, producing virtually the same e.m.f. values within recorded scatter of points. The full run was completed after about 3–5 days.
Fig. 3. Time-dependent e.m.f. plot; horizontal parts represent equilibrium e.m.f. values.
3. Results E.m.f. of the cell (I): Kanthal + Re, (Ag–Cu–Sn), SnO2 |O−2 |air, Pt
(I)
was measured in the temperature range 973–1325 K and for three cross-sections with constant Ag/Cu ratio equal to: 1/3, 1 and 3 and
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for tin compositions ranging every 10%, from 10 up to 80 at.% Sn. Electrode reactions are (a) at reference electrode: O2 (g) + 4e− = 2[O−2 ]
(1)
(b) at alloy electrode: Sn(l) + 2[O−2 ] = 4e− + SnO2 (s) e− ,
(2)
[O−2 ]
where Sn(l), O2 (g) and denote: tin in a metallic liquid solution, electron, pure oxygen gas and oxygen ion, respectively. Consequently, the overall cell (I) reaction is
Table 1 The comparison of the literature data of Gibbs energy of SnO2 formation in reaction Sn(l) + O2 (g) = SnO2 (s) with present one. −1
Authors
Experimental method
Temp. range (K)
Gf0 (SnO2 , c), kJ mol
[18] [19] [20] [21] [22] [23] [24] [25] [26] [27] This work
E.m.f. E.m.f. E.m.f. E.m.f. E.m.f. E.m.f. E.m.f. E.m.f. E.m.f. E.m.f. E.m.f.
770–987 823–1023 1173–1373 940–1173 773–1380 990–1371 1023–1273 973–1273 950–1173 823–1273 973–1325
−586.5 + 0.2156 T (±1.2) −575.9 + 0.2053 T −563.6 + 0.1960 T −575.1 + 0.2070 T −576.3 + 0.2070 T (±0.4) −575.1 + 0.2074 T (±0.9) −578.8 + 0.2088 T (±0.8) −576.6 + 0.2087 T −578.5 + 0.2056 T −579.6 + 0.2070 T (±1.0) −570.4 + 0.2013 T (±0.9)
Error limits in the last column refer to G values, and not to the T term only.
Sn(l) + O2 (g) = SnO2 (s)
(3)
For the reversible reaction (3) the change in Gibbs free energy can be derived as follows: 0 −4FE = Gf,SnO − RT ln aSn − RT ln(0.21)
(4)
2
If tin is in its pure, liquid state (XSn = 1) Eq. (4) takes the form: 0 Gf,SnO = −4FE 0 + RT ln(0.21)
(5)
2
The Gibbs energy of formation of the solid SnO2 , Gf0(SnO
2)
for reac-
tion Sn(l) + O2 (g) = SnO2 (s), can be determined via equation (5) from measured E0 as a function of temperature. Next, combining (4) and (5) the following expression for the activity of tin in the Ag–Cu–Sn liquid alloy can be derived: ln aSn =
4F (E − E 0 ) RT
(6)
where F is the Faraday constant, T is the absolute temperature, and R is the gas constant. The expression for the partial Gibbs free energy of tin in the alloy can be derived from measured e.m.f.’s in a form: ¯ Sn = 4F(E − E 0 ) = a + b × T
(7)
if a linear dependence of the e.m.f. on temperature is observed. Thus, having experimentally obtained E versus T plots for alloys of different composition, all partial thermodynamic functions of tin in the liquid alloy can be derived. All e.m.f. values were corrected for Pt–Kanthal thermoelectric power determined in the separate experiments. Rhenium tip was small enough to fit Kanthal–Re junction in the constant temperature zone and not generating of any thermoelectric power. The results of temperature dependence of e.m.f. E0 obtained for pure tin can be presented in the form: E 0 (V ) = 1.478 (±0.002) − 0.5553 (±0.0013) × T
(8)
Combining (5) and (8), the Gibbs free energy of formation of solid SnO2 in reaction: Sn(l) + O2 (g) = SnO2 (s)
(9)
from liquid tin and gaseous oxygen is given by the expression: G 0f ,
SnO2
, kJ/mol = − 570.4 (±0.6) + 0.2013 (±0.0046) × T (10)
0 The obtained Gf,SnO function is listed along with the existing lit2
erature data in Table 1 and compared graphically in Fig. 4; only two limiting-case literature datasets were chosen for plot clarity reason.
Fig. 4. Temperature dependence of the Gibbs energy of SnO2 formation in reaction (9) compared with the selected literature data.
Tin dioxide is the only stable phase in equilibrium with liquid tin in the experiment temperature range up to 1373 K. Above this temperature the vaporization of tin monoxide was observed according to reaction: ≥1373 K
SnO2 −→ SnO(g) +
1 O2 2
(11)
as reported by Carbo-Nover and Richardon [28] and confirmed by Dolet et al. [29]. The equations E(E0 ) = a + b × T obtained by the least square fit of e.m.f. data are listed in Tables 2–4 for cross-section XAg /XCu = 1, 1/3 Table 2 E.m.f. versus temperature line coefficients in the liquid Ag–Cu–Sn alloys for crosssection XAg /XCu = 1/3. XSn
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
E.m.f., V a
b × 103
1.396 ± 0.003 1.458 ± 0.001 1.493 ± 0.001 1.485 ± 0.002 1.478 ± 0.002 1.472 ± 0.002 1.470 ± 0.003 1.475 ± 0.003
−0.5945 ± 0.0021 −0.6011 ± 0.0008 −0.6035 ± 0.0006 −0.5847 ± 0.0019 −0.5715 ± 0.0018 −0.5611 ± 0.0020 −0.5557 ± 0.0024 −0.5564 ± 0.0026
M. Kopyto et al. / Materials Chemistry and Physics 122 (2010) 480–484
483
Table 3 E.m.f. versus temperature line coefficients in the liquid Ag–Cu–Sn alloys for crosssection XAg /XCu = 1. The result for the pure Sn is added in the first line. XSn
1.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
E0 , E, V a
b × 103
1.478 ± 0.001 1.438 ± 0.007 1.487 ± 0.005 1.479 ± 0.007 1.492 ± 0.004 1.495 ± 0.002 1.487 ± 0.003 1.492 ± 0.001 1.485 ± 0.002
−0.5553 ± 0.0013 −0.6255 ± 0.0062 −0.6259 ± 0.0042 −0.5920 ± 0.0059 −0.5911 ± 0.0035 −0.5868 ± 0.0020 −0.5749 ± 0.00254 −0.5757 ± 0.0010 −0.5653 ± 0.0019
Table 4 E.m.f. versus temperature line coefficients in the liquid Ag–Cu–Sn alloys for crosssection XAg /XCu = 3. XSn
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
E.m.f., V a
b × 103
1.403 ± 0.007 1.458 ± 0.006 1.497 ± 0.001 1.496 ± 0.003 1.496 ± 0.002 1.497 ± 0.002 1.489 ± 0.005 1.482 ± 0.006
−0.5954 ± 0.0056 −0.5976 ± 0.0050 −0.6083 ± 0.1150 −0.5947 ± 0.0026 −0.5876 ± 0.0019 −0.5829 ± 0.0021 −0.5727 ± 0.0050 −0.5628 ± 0.0054
and 3, respectively, and the example of the e.m.f. versus T plot for XAg /XCu = 1 section is shown in Fig. 5. Because of the fact that the activity curve in Fig. 6 approach the ideal behavior line, experiments for alloy composition XSn = 0.9 were not performed. Since the statistical scatter of the e.m.f. versus T plots is very small it was assumed that e.m.f. values calculated via linear equations of Tables 2–4 are equal to those measured within an experimental error, relation (6) was used to derive activity data at two arbitrary temperatures 1000 and 1300 K; they are listed
Fig. 6. Tin activity versus composition plot calculated at two temperatures for XAg /XCu = 1/3.
Table 5 Tin activity values calculated via relation (6) from data of Tables 2–4. XSn
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
XAg /XCu = 1/3
XAg /XCu = 1
XAg /XCu = 3
1000 K
1300 K
1000 K
1300 K
1000 K
1300 K
0.0036 0.0474 0.1982 0.3493 0.4695 0.5809 0.6740 0.8141
0.0086 0.0587 0.1821 0.3248 0.4699 0.6187 0.7346 0.8430
0.0061 0.0567 0.1909 0.3630 0.5166 0.6287 0.7472 0.8588
0.0093 0.0516 0.1887 0.3123 0.4293 0.5669 0.6423 0.7984
0.0048 0.0553 0.2061 0.3797 0.5080 0.6634 0.7418 0.8527
0.0107 0.0686 0.1681 0.3112 0.4201 0.5423 0.6590 0.8163
in Table 5. The example of tin activity versus tin content plot for XAg /XCu = 1/3 is presented in Fig. 6. 4. Conclusions As can be seen from Fig. 4 the Gibbs energy of formation of SnO2 determined in this work is in a good agreement with the available literature data. That fact can be treated as a test of accuracy of our experiments. Activity curve presented in Fig. 6 displays negative deviation from Raoult’s rule for lower tin contents, and slightly positive for higher ones at 1300 K. The results of this work are to be used along with data of [16,17] to prepare a new thermodynamic description of Ag–Cu–Sn alloy system. References [1] [2] [3] [4] [5] [6]
Fig. 5. E.m.f versus temperature plots for various tin compositions and for crosssection XAg /XCu = 1; the results for pure tin are included.
[7] [8]
E. Gebhardt, G. Petzow, Z. Metallkd. 50 (1959) 597. S.S. Shen, Ph.D. Thesis, University of Denver (1969). S.S. Shen, P.J. Spencer, M.J. Pool, Trans. AIME 245 (4) (1969) 603. V.N. Fedotov, O.E. Osinchev, E.T. Yushkina, in: N.V. Ageev, L.A. Petrova (Eds.), Fazovye Ravnovesiya Met. Splavakh, 1981, p. 42. V.N. Fedotov, O.E. Osinchev, E.T. Yushkina, in: N.V. Ageev, L.A. Petrova (Eds.), Phase Diagrams of Metallic Systems, vol. 26, 1982, p. 149. O. Kubaschewski, in: G. Petzow, G. Effenberg (Eds.), Ternary Alloys: A Comprehensive Compendium of Evaluated Constitutional Data and Phase Diagrams, in Silver–Copper–Tin, VCH Publishers, New York, 1988, p. 38. C.M. Miller, I.E. Anderson, J.K. Smith, J. Electron. Mater. 23 (1994) 595. S. Chada, W. Laub, R.A. Fournelle, D. Shangguan, J. Electron. Mater. 26 (11) (1999) 1194.
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[9] K.W. Moon, W.J. Boettinger, U.R. Kattner, F.S. Biancaniello, C.A. Handwerker, J. Electron. Mater. 29 (2000) 1122. [10] M.E. Loomans, M.E. Fine, Metall. Mater. Trans. A 31A (2000) 1155. [11] B.J. Lee, N.M. Hwang, H.M. Lee, Acta Mater. 45 (1997) 1867. [12] H.M. Lee, S.W. Yoon, B.J. Lee, J. Electron. Mater. 27 (1998) 1161. [13] I. Ohnuma, M. Miyashita, K. Anzai, X.J. Liu, H. Ohtani, R. Kainuma, K. Ishida, J. Electron. Mater. 29 (2000) 1137. [14] J.A. Gisby, A.T. Dinsdale, COST Action 531 – Atlas of Phase Diagrams for Lead-free Soldering, vol. 1, p. 175. [15] K.-W. Moon, W.J. Boettinger, J. Metals 56 (4) (2004) 22. [16] C. Luef, H. Flandorfer, H. Ipser, Z. Metallkd. 95 (3) (2004) 151. [17] Y. Yen, S. Chen, J. Mater. Res. 19 (8) (2004) 2298. [18] T.N. Belford, C.B. Alcock, Trans. Faraday. Soc. 61 (1965) 443.
[19] T. Palamutcu, Ph.D. Thesis, Imperial College of Science and Technology, London (1970). [20] T. Oishi, T. Hiruma, J. Moriyama, Nippon Kinzoku Gakkaaishi 36 (1972) 481. [21] T.A. Ramanarayanan, R.A. Rapp, Met. Trans. 3 (1972) 3239. [22] G. Petot-Ervas, R. Farhi, C. Petot, J. Chem. Thermodyn. 7 (1975) 1131. [23] S. Seetharaman, L.-I. Staffansson, Scan. J. Metall. 6 (1977) 143. [24] M. Iwase, M. Yasuda, S. Miki, T. Mori, Trans. JIM 19 (1978) 654. [25] R. Kammel, J. Osterwald, T. Oishi, Metall (Berl.) 2 (1983) 141. [26] Z. Panek, K. Fitzner, Thermochem. Acta 78 (1984) 261. [27] R. Kurchania, G.M. Kale, J. Mater. Res. 15 (7) (2000) 1576. [28] J. Carbo-Nover, F.D. Richardson, Trans. Inst. Min. Met. C81 (1972) 443. [29] N. Dolet, J.M. Heintz, M. Onillon, J.P. Bonet, J. Eur. Ceram. Soc. 9 (1992) 19.
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Thermodynamic properties of the liquid Ag–Cu–Sn lead-free solder alloys Marek Kopyto a , Boguslaw Onderka b , Leszek A. Zabdyr a,∗ a Institute of Metallurgy and Materials Science, Polish Academy of Sciences, Laboratory of Physical Chemistry of Materials, 25 Reymonta St., 30-059 Krakow, Poland b AGH University of Science and Technology, Faculty of Non-Ferrous Metals, Department of Physical Chemistry and Electrochemistry, 30 Mickiewicza Ave., 30-059 Krakow, Poland
a r t i c l e
i n f o
Article history: Received 20 May 2009 Received in revised form 30 July 2009 Accepted 16 March 2010 Keywords: Electrochemical techniques Thermodynamic properties Alloys Electronic materials
a b s t r a c t The electromotive force measurement method was employed to determine the thermodynamic properties of liquid Ag–Cu–Sn alloys using solid electrolyte galvanic cells as shown below: Kanthal + Re, Ag–Cu–Sn, SnO2 |Y ttria stabilized Zirconia|air, Pt, pO2 = 0.21 atm Measurements were carried out for three cross-sections with constant Ag/Cu ratio equal to: 1/3, 1 and 3 and for tin compositions ranging from 10 up to 80 at.%, every 10%, resulting in a total of 24 different alloy compositions. The temperature of the measurements varied within the range from 973 to 1325 K. A linear dependence of the e.m.f. on temperature was observed for all alloy compositions and the appropriate line equations were derived. Tin activities were calculated as function of composition and temperature. Results were presented in tables and figures. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Knowledge of the phase equilibria in Ag–Cu–Sn ternary system is of fundamental importance for the electronic packaging technologies which involve processes that require the direct contact of the solid and liquid phase near equilibrium conditions. That knowledge is important for the understanding of boundary conditions for a variety of processing steps as Ag–Sn/Cu interfacial reactions. A number of works are available regarding the phase equilibria in the Ag–Cu–Sn system. Gebhardt and Petzow [1] determined experimentally the isothermal sections of Ag–Cu–Sn ternary system at 500 and 600 ◦ C. They also suggested the invariant reaction, L + -Cu6 Sn5 = εAg3 Sn + Sn, in the Sn-rich region at 225 ◦ C. Shen [2] and Shen et al. [3] measured enthalpies of solution of Ag in Ag–Cu–Sn at 720 K and for XCu < 0.065 and XAg < 0.045 by solution calorimetry. Fedotov et al. [4,5] determined isopleths at 10 wt.% Cu, wt.% Ag/wt.% Sn = 1:1 and for wt.% Cu/wt.% Sn = 2:9. Kubaschewski [6] presented the isothermal sections at several temperatures and the liquidus projection of the Ag–Cu–Sn ternary system. Miller et al. [7] examined experimentally the phase equilibria of the Ag–Cu–Sn ternary system by microscopy, wavelength dispersive spectroscopy WDS, DTA and XRD. They discovered the invariant reaction,
∗ Corresponding author. Tel.: +48 12 2952844; fax: +48 12 2952804. E-mail address: [email protected] (L.A. Zabdyr). 0254-0584/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2010.03.030
L = + ε2 + Sn, at the Sn-rich corner, Sn–4.7 wt.% Ag–1.7 wt.% Cu, and at 216.8 ◦ C, which is inconsistent with that proposed by Gebhardt and Petzow [1]. Chada et al. [8] used EDS to study the solubility of Cu in Sn–Ag liquids containing 3.5 wt.% Ag as a function of temperature. Moon et al. [9] studied the Sn-rich corner of the Ag–Cu–Sn system (at.% Ag < 10.49 and wt.% Cu < 3.21) both by experimental determination (thermal analysis/cycling experiments) and thermodynamic calculation. Loomans and Fine [10] focused on the determination of the ternary eutectic temperature and composition through a study of the binary eutectics between Sn and Cu6 Sn5 and between Sn and Ag3 Sn based on thermal analysis. Their results are in good agreement with data of Moon et al. [9]. Lee et al. [11], Lee et al. [12] and Ohnuma et al. [13] developed thermodynamic models of the Ag–Cu–Sn ternary system to calculate the isothermal sections at various temperatures. Although not all phase relationships determined were in agreement with earlier data, they all found no ternary compounds in the Ag–Cu–Sn ternary system. Gisby and Dinsdale [14] reassessed Ag–Cu–Sn system using new phase description for sub-binaries: Ag–Sn and Cu–Sn. Moon and Boettinger [15] determined experimentally parameters of eutectic composition in Ag–Cu–Sn system. Luef et al. [16] measured calorimetrically the enthalpies of mixing of liquid alloys in Ag–Cu–Sn system. Yen and Chen [17] determined experimentally the phase equilibria in Ag–Cu–Sn system for the isothermal sections at 240 and 450 ◦ C which are of importance in soldering applications. They confirmed the absence of ternary compounds in the system and found that all the binary compounds have only limited ternary
M. Kopyto et al. / Materials Chemistry and Physics 122 (2010) 480–484
481
Fig. 1. Schematic cross-section of the galvanic cell.
solubility. The attempt to calculate a phase diagram without ternary parameters was carried out. Tin activities in the liquid Ag–Cu–Sn ternary alloys were determined in the present work using solid electrolyte galvanic cells.
Fig. 2. Scheme of cell assembly.
2. Experimental Closed-end yttria-stabilized zirconia (YSZ) tubes (5/8 mm I/OD – Yamari, Japan) were used as the electrolyte and dry air (pO2 = 0.21 atm) was used as the reference electrode. Platinum wire was used for air electrode and KanthalTM wire with rhenium tip was applied for alloy electrode as current leads; the cross-section through the cell is shown schematically in Fig. 1, and the scheme of the cell assembly is presented in Fig. 2. Experiments were performed in a vertical resistance furnace with the brass head, enabling to fix the cell within the constant temperature zone. After a constant temperature was reached, the cell was kept to stabilize electromotive force, and then the e.m.f. was recorded by data acquisition system consisted of Keithley 2000 digital voltmeter and a computer. Such a system enabled continuous recording of time-dependent e.m.f. curves, as can be seen in Fig. 3. Silver–copper–tin alloys were prepared from pure metals supplied by The Institute of Electronic Materials Technology, Warsaw, Poland (Ag and Sn 99.99%, Cu 99.999%). They were melted directly in the electrolyte tube (XSn ≥ 0.5) or pre-melted at given composition under vacuum in sealed quartz ampoules. Alloy sample was placed at the bottom of the electrolyte tube with a SnO2 (99.99%, POCH, Gliwice, Poland) pellet. An inert atmosphere was maintained inside the cell by passing 5 ml/min of argon gas of quality 5.0 (Linde, Poland) through the H-tube enabling inert gas penetration into the electrolyte tube without disturbing the local equilibrium over the sample. The reversibility of the cell was checked by passing small current from an external source for a few seconds and the e.m.f. returned to the original value within ±1 mV in about 1–10 min depending on the temperature. E.m.f. readings were taken within the range 973–1325 K on heating and cooling, producing virtually the same e.m.f. values within recorded scatter of points. The full run was completed after about 3–5 days.
Fig. 3. Time-dependent e.m.f. plot; horizontal parts represent equilibrium e.m.f. values.
3. Results E.m.f. of the cell (I): Kanthal + Re, (Ag–Cu–Sn), SnO2 |O−2 |air, Pt
(I)
was measured in the temperature range 973–1325 K and for three cross-sections with constant Ag/Cu ratio equal to: 1/3, 1 and 3 and
482
M. Kopyto et al. / Materials Chemistry and Physics 122 (2010) 480–484
for tin compositions ranging every 10%, from 10 up to 80 at.% Sn. Electrode reactions are (a) at reference electrode: O2 (g) + 4e− = 2[O−2 ]
(1)
(b) at alloy electrode: Sn(l) + 2[O−2 ] = 4e− + SnO2 (s) e− ,
(2)
[O−2 ]
where Sn(l), O2 (g) and denote: tin in a metallic liquid solution, electron, pure oxygen gas and oxygen ion, respectively. Consequently, the overall cell (I) reaction is
Table 1 The comparison of the literature data of Gibbs energy of SnO2 formation in reaction Sn(l) + O2 (g) = SnO2 (s) with present one. −1
Authors
Experimental method
Temp. range (K)
Gf0 (SnO2 , c), kJ mol
[18] [19] [20] [21] [22] [23] [24] [25] [26] [27] This work
E.m.f. E.m.f. E.m.f. E.m.f. E.m.f. E.m.f. E.m.f. E.m.f. E.m.f. E.m.f. E.m.f.
770–987 823–1023 1173–1373 940–1173 773–1380 990–1371 1023–1273 973–1273 950–1173 823–1273 973–1325
−586.5 + 0.2156 T (±1.2) −575.9 + 0.2053 T −563.6 + 0.1960 T −575.1 + 0.2070 T −576.3 + 0.2070 T (±0.4) −575.1 + 0.2074 T (±0.9) −578.8 + 0.2088 T (±0.8) −576.6 + 0.2087 T −578.5 + 0.2056 T −579.6 + 0.2070 T (±1.0) −570.4 + 0.2013 T (±0.9)
Error limits in the last column refer to G values, and not to the T term only.
Sn(l) + O2 (g) = SnO2 (s)
(3)
For the reversible reaction (3) the change in Gibbs free energy can be derived as follows: 0 −4FE = Gf,SnO − RT ln aSn − RT ln(0.21)
(4)
2
If tin is in its pure, liquid state (XSn = 1) Eq. (4) takes the form: 0 Gf,SnO = −4FE 0 + RT ln(0.21)
(5)
2
The Gibbs energy of formation of the solid SnO2 , Gf0(SnO
2)
for reac-
tion Sn(l) + O2 (g) = SnO2 (s), can be determined via equation (5) from measured E0 as a function of temperature. Next, combining (4) and (5) the following expression for the activity of tin in the Ag–Cu–Sn liquid alloy can be derived: ln aSn =
4F (E − E 0 ) RT
(6)
where F is the Faraday constant, T is the absolute temperature, and R is the gas constant. The expression for the partial Gibbs free energy of tin in the alloy can be derived from measured e.m.f.’s in a form: ¯ Sn = 4F(E − E 0 ) = a + b × T
(7)
if a linear dependence of the e.m.f. on temperature is observed. Thus, having experimentally obtained E versus T plots for alloys of different composition, all partial thermodynamic functions of tin in the liquid alloy can be derived. All e.m.f. values were corrected for Pt–Kanthal thermoelectric power determined in the separate experiments. Rhenium tip was small enough to fit Kanthal–Re junction in the constant temperature zone and not generating of any thermoelectric power. The results of temperature dependence of e.m.f. E0 obtained for pure tin can be presented in the form: E 0 (V ) = 1.478 (±0.002) − 0.5553 (±0.0013) × T
(8)
Combining (5) and (8), the Gibbs free energy of formation of solid SnO2 in reaction: Sn(l) + O2 (g) = SnO2 (s)
(9)
from liquid tin and gaseous oxygen is given by the expression: G 0f ,
SnO2
, kJ/mol = − 570.4 (±0.6) + 0.2013 (±0.0046) × T (10)
0 The obtained Gf,SnO function is listed along with the existing lit2
erature data in Table 1 and compared graphically in Fig. 4; only two limiting-case literature datasets were chosen for plot clarity reason.
Fig. 4. Temperature dependence of the Gibbs energy of SnO2 formation in reaction (9) compared with the selected literature data.
Tin dioxide is the only stable phase in equilibrium with liquid tin in the experiment temperature range up to 1373 K. Above this temperature the vaporization of tin monoxide was observed according to reaction: ≥1373 K
SnO2 −→ SnO(g) +
1 O2 2
(11)
as reported by Carbo-Nover and Richardon [28] and confirmed by Dolet et al. [29]. The equations E(E0 ) = a + b × T obtained by the least square fit of e.m.f. data are listed in Tables 2–4 for cross-section XAg /XCu = 1, 1/3 Table 2 E.m.f. versus temperature line coefficients in the liquid Ag–Cu–Sn alloys for crosssection XAg /XCu = 1/3. XSn
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
E.m.f., V a
b × 103
1.396 ± 0.003 1.458 ± 0.001 1.493 ± 0.001 1.485 ± 0.002 1.478 ± 0.002 1.472 ± 0.002 1.470 ± 0.003 1.475 ± 0.003
−0.5945 ± 0.0021 −0.6011 ± 0.0008 −0.6035 ± 0.0006 −0.5847 ± 0.0019 −0.5715 ± 0.0018 −0.5611 ± 0.0020 −0.5557 ± 0.0024 −0.5564 ± 0.0026
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483
Table 3 E.m.f. versus temperature line coefficients in the liquid Ag–Cu–Sn alloys for crosssection XAg /XCu = 1. The result for the pure Sn is added in the first line. XSn
1.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
E0 , E, V a
b × 103
1.478 ± 0.001 1.438 ± 0.007 1.487 ± 0.005 1.479 ± 0.007 1.492 ± 0.004 1.495 ± 0.002 1.487 ± 0.003 1.492 ± 0.001 1.485 ± 0.002
−0.5553 ± 0.0013 −0.6255 ± 0.0062 −0.6259 ± 0.0042 −0.5920 ± 0.0059 −0.5911 ± 0.0035 −0.5868 ± 0.0020 −0.5749 ± 0.00254 −0.5757 ± 0.0010 −0.5653 ± 0.0019
Table 4 E.m.f. versus temperature line coefficients in the liquid Ag–Cu–Sn alloys for crosssection XAg /XCu = 3. XSn
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
E.m.f., V a
b × 103
1.403 ± 0.007 1.458 ± 0.006 1.497 ± 0.001 1.496 ± 0.003 1.496 ± 0.002 1.497 ± 0.002 1.489 ± 0.005 1.482 ± 0.006
−0.5954 ± 0.0056 −0.5976 ± 0.0050 −0.6083 ± 0.1150 −0.5947 ± 0.0026 −0.5876 ± 0.0019 −0.5829 ± 0.0021 −0.5727 ± 0.0050 −0.5628 ± 0.0054
and 3, respectively, and the example of the e.m.f. versus T plot for XAg /XCu = 1 section is shown in Fig. 5. Because of the fact that the activity curve in Fig. 6 approach the ideal behavior line, experiments for alloy composition XSn = 0.9 were not performed. Since the statistical scatter of the e.m.f. versus T plots is very small it was assumed that e.m.f. values calculated via linear equations of Tables 2–4 are equal to those measured within an experimental error, relation (6) was used to derive activity data at two arbitrary temperatures 1000 and 1300 K; they are listed
Fig. 6. Tin activity versus composition plot calculated at two temperatures for XAg /XCu = 1/3.
Table 5 Tin activity values calculated via relation (6) from data of Tables 2–4. XSn
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
XAg /XCu = 1/3
XAg /XCu = 1
XAg /XCu = 3
1000 K
1300 K
1000 K
1300 K
1000 K
1300 K
0.0036 0.0474 0.1982 0.3493 0.4695 0.5809 0.6740 0.8141
0.0086 0.0587 0.1821 0.3248 0.4699 0.6187 0.7346 0.8430
0.0061 0.0567 0.1909 0.3630 0.5166 0.6287 0.7472 0.8588
0.0093 0.0516 0.1887 0.3123 0.4293 0.5669 0.6423 0.7984
0.0048 0.0553 0.2061 0.3797 0.5080 0.6634 0.7418 0.8527
0.0107 0.0686 0.1681 0.3112 0.4201 0.5423 0.6590 0.8163
in Table 5. The example of tin activity versus tin content plot for XAg /XCu = 1/3 is presented in Fig. 6. 4. Conclusions As can be seen from Fig. 4 the Gibbs energy of formation of SnO2 determined in this work is in a good agreement with the available literature data. That fact can be treated as a test of accuracy of our experiments. Activity curve presented in Fig. 6 displays negative deviation from Raoult’s rule for lower tin contents, and slightly positive for higher ones at 1300 K. The results of this work are to be used along with data of [16,17] to prepare a new thermodynamic description of Ag–Cu–Sn alloy system. References [1] [2] [3] [4] [5] [6]
Fig. 5. E.m.f versus temperature plots for various tin compositions and for crosssection XAg /XCu = 1; the results for pure tin are included.
[7] [8]
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